Research Article Effect of Population Structures on...

Research ArticleEffect of Population Structures on Quantum-InspiredEvolutionary Algorithm

Nija Mani1 Gursaran Srivastava1 A K Sinha1 and Ashish Mani2

1Department of Mathematics Dayalbagh Educational Institute Dayalbagh Agra 282005 India2USIC Dayalbagh Educational Institute Dayalbagh Agra 282005 India

Correspondence should be addressed to Ashish Mani maniashishgmailcom

Received 4 August 2014 Revised 21 November 2014 Accepted 22 November 2014 Published 24 December 2014

Academic Editor Zhang Yi

Copyright copy 2014 Nija Mani et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Quantum-inspired evolutionary algorithm (QEA) has been designed by integrating some quantum mechanical principles in theframework of evolutionary algorithms They have been successfully employed as a computational technique in solving difficultoptimization problems It is well known that QEAs provide better balance between exploration and exploitation as comparedto the conventional evolutionary algorithms The population in QEA is evolved by variation operators which move the Q-bittowards an attractor A modification for improving the performance of QEA was proposed by changing the selection of attractorsnamely versatile QEA The improvement attained by versatile QEA over QEA indicates the impact of population structure onthe performance of QEA and motivates further investigation into employing fine-grained model The QEA with fine-grainedpopulation model (FQEA) is similar to QEA with the exception that every individual is located in a unique position on a two-dimensional toroidal grid and has four neighbors amongst which it selects its attractor Further FQEA does not use migrationswhich is employed by QEAs This paper empirically investigates the effect of the three different population structures on theperformance of QEA by solving well-known discrete benchmark optimization problems

1 Introduction

Evolutionary algorithms (EAs) represent a class of compu-tational techniques which draw inspiration from nature [1]and are loosely based on the Darwinian principle of ldquosurvivalof the fittestrdquo [2ndash4] EAs have been successfully applied insolving wide variety of real life difficult optimization prob-lems (ie problems which do not have efficient deterministicalgorithms for solving them yet known) and where nearoptimal solutions are acceptable (as EAs do not guaranteefinding optimal solutions) Moreover EAs are not limited bythe requirements of domain specific information as in thecase of traditional calculus based optimization techniques [5]EAs typically maintain a population of candidate solutionswhich compete for survival from one generation to the nextand with the generation of new solutions by employing thevariation operators like crossover mutation rotation gateand so forth the population gradually evolves to containthe optimal or near optimal solutions EAs are popular dueto their simplicity and ease of implementation However

EAs suffer from convergence issues like stagnation slowconvergence and premature convergence [6]

Efforts have been made by researchers to overcome theconvergence issues by establishing a better balance betweenexploitation and exploration Quantum-inspired evolution-ary algorithm (QEA) [7 8] provides a better balance betweenexploration and exploitation during the evolutionary searchprocess by using probabilistic Q-bit QEAs have performedbetter than classical EAs on many complex problems [9ndash17]

Some investigations have also been made in using struc-tured populations to improve the performance of EAs [18]The structure of a population is classified as follows pan-mixia coarse-grained and fine-grained models The QEAdescribed in [7 19] has employed a population structuredas coarse-grained model The performance of this algorithmhas been improved by changing the global update strategyin [8] and has been named versatile QEA (vQEA) Themodification to convertQEA into vQEAcan be also viewed asequivalent to changing the population structure from coarse-grained model in QEA to panmictic in vQEA The improve-ment attained by vQEA over QEA indicates the impact of

Hindawi Publishing CorporationApplied Computational Intelligence and So ComputingVolume 2014 Article ID 976202 22 pageshttpdxdoiorg1011552014976202

2 Applied Computational Intelligence and Soft Computing

Panmictic

(a) Unstructured

Coarse grained Fine grained

(b) Structured

Figure 1 Population structures

population structure on the performance of QEA This alsomotivates investigation for employing fine-grained modelin the population structure of QEA This paper empiricallyevaluates the effect of population structures in QEA bysolving some instances of well-known benchmark problemslike COUNTSAT 119875-PEAKS and 0-1 knapsack problemsThe paper is further organized as follows Section 2 brieflydiscusses population structures QEA vQEA and FQEA arepresented and their population structure is established inSection 3 Results and analysis are presented in Section 4Section 5 draws conclusions and shows some directions forfurther work

2 Population Structures

The population structures in EAs can be divided into twobroad categories namely unstructured and structured [20]and are shown in Figure 1 The unstructured populationmodel has beenwidely used in EAs where a single populationof individuals is evolved by employing variation operatorsThe advantage of unstructured population is its conceptualand implementation simplicity The dissemination of infor-mation regarding the best individual is quickest as all theindividuals are connected with all the other individuals Itworks fine for EAs in which diversity can be maintainedby suitably designed variation operators for a given prob-lem However if the search space is highly deceptive andmultimodal the panmictic population may not be the mosteffective model Structured population models are viablealternatives to the unstructured model They have beenprimarily developed during efforts to parallelize EAs forrunning on multiprocessors hardware [2] However theyhave also been used with simple EAs (run on monoprocessorhardware) in place of panmictic population and have beenfound to provide better sampling of search space along withconsequent improvement in empirical performance [21]

The structured models can be divided into two maingroups namely coarse-grained and fine-grainedmodelsThecoarse-grainedmodel is also known as distributedmodel andisland model It has multiple panmictic populations whichevolve in parallel and communicate with each other period-ically often exchanging or updating individuals dependingon the specific strategyThe advantage of island model is thatit encourages niching and also allows slow dissemination of

information across the structured subpopulation evolving inparallel Thus it maintains diversity in overall population toavoid premature convergence However it is known to berelatively slow in converging to optimal solution

Fine-grained model is also known as cellular model anddiffusion model A unique coordinate is assigned to everyindividual of the single population in some space which istypically a grid of some dimensionality with fixed or cyclicboundary Individuals can only interact within a neighbor-hood defined by neighborhood topology through variationoperatorsThe advantage of cellularmodel is slow diffusion ofinformation through overlapped small neighborhoods whichhelps in exploring the search space by maintaining betterdiversity than panmicticmodelThis in turn helps in avoidingpremature convergence [22] Moreover it is slower than acorresponding panmictic model in a given EA but is fasterthan a coarse-grained model It has less communicationoverhead than a coarse-grainedmodel as it maintains a singlestructured population rather than multiple subpopulationsevolving in parallel Further it has been shown that a cellularmodel is more effective in complex optimization tasks ascompared to the other models [23 24]

3 Quantum-Inspired Evolutionary Algorithms

Quantum-inspired proposals are subset of a much largerattempt to apply quantum models in information process-ing which is also referred to as quantum interaction [25]The potential advantages of parallelism offered by quantumcomputing [26] through superposition of basis states in qubitregisters and simultaneous evaluation of all possible repre-sented states have led to the development of approaches thatsuggest ways to integrate aspects of quantum computing withevolutionary computation [25] Most types of hybridizationhave focused on designing algorithms that would run onconventional computers and not on quantum computersand are most appropriately classified as ldquoquantum-inspiredrdquoThe first attempt was made by Narayanan and Moore [27]to use quantum interpretation for designing a quantum-inspired genetic algorithm A number of other types ofhybridization have also been proposed of which the mostpopular is the proposal made by Han and Kim [7] whichuses a Q-bit as the smallest unit of information and a Q-bitindividual as a string ofQ-bits rather than binary numeric or

Applied Computational Intelligence and Soft Computing 3

symbolic representations Results of experiments show thatQEA performs well even with a small population withoutpremature convergence as compared to the conventionalgenetic algorithms Experimental studies have also beenreported by Han and Kim to identify suitable parametersettings for the algorithm [19] Platel et al [8] have shownthe weaknesses of QEA and proposed a new algorithm calledversatile quantum-inspired evolutionary algorithm (vQEA)They claim that vQEA is better than the QEA [7] as it guidesthe search towards the best solution found in the last iterationwhich facilitates smoother and more efficient explorationThis claim is supported by experimental evaluations

A qubit is the smallest information element in a quantumcomputer and is quantum analog of classical bitThe classicalbit can be either in state ldquozerordquo or in state ldquoonerdquo whereasa quantum bit can be in a superposition of basis states inthe quantum system It is represented by a vector in Hilbertspace with |0⟩ and |1⟩ being the basis states The qubit can berepresented by vector |120595⟩ which is given by

1003816100381610038161003816120595⟩ = 120572 |0⟩ + 120573 |1⟩ (1)

where |120572|2 and |120573|2 are the probability amplitudes of qubitto be in state |0⟩ and |1⟩ respectively and should satisfy thefollowing condition

|120572|2+10038161003816100381610038161205731003816100381610038161003816

2

= 1 (2)

The QEA proposed in [7 19] primarily hybridizes the super-position and measurement principles of quantum mechan-ics in evolutionary computing framework by implementingqubit as Q-bit which is essentially a probabilistic bit andstores 120572 and 120573 values A Q-bit string acts as the genotype ofan individual and the binary bit string formed by collapsingthe Q-bit forms the phenotype of the individual A Q-bitis modified by using quantum gates or operators whichare also unitary in nature as restricted by the postulatesof linear quantum mechanics [26] The quantum gates areimplemented in QEA as unitary matrix [7] A quantum gateknown as rotation gate has been employed in [19] and itupdates a Q-bit in the following manner

[

120572119905+1

119894

120573119905+1

119894

] = [

cos (Δ120579119894) minus sin (Δ120579

119894)

sin (Δ120579119894) cos (Δ120579

119894)] [

120572119905

119894

120573119905

119894

] (3)

where 120572119905+1119894

and 120573119905+1119894

denote probabilities of 119894th Q-bit in (119905 +1)th iteration Δ120579

119894is the angle of rotation It acts as the main

variation operator that rotates Q-bit strings to obtain goodcandidate solutions for the next generation It also requiresan attractor [8] towards which the Q-bit will be rotated Itfurther takes into account the relative current fitness levelof the individual and the attractor and also their binarybit values for determining the magnitude and direction ofrotation The selection of an attractor is determined by thepopulation model employed in a QEA A close scrutiny ofthe architecture of QEAs designed in [7 8 19] reveal thatattractors are the only mechanism available for interactionbetween the individuals

The QEA in [7 19] divides the population into localgroups and implements two types ofmigrations namely local

and global In local migration the best solution within thegroup is used as the attractor whereas in case of globalmigration the global best solution is used as the attractorThe migration periods and size of local group are designparameters and have to be chosen appropriately for theproblem being solved

The quantum-inspired evolutionary algorithm is shownin Algorithm 1 [7 8]

In step (a) Q(t) containing Q-bit strings for all theindividuals are initialized randomly In step (b) the binarysolutions in 119875(0) are constructed by measuring the statesof 119876(0) The process of measuring or collapsing Q-bit isperformed by generating a random number between 0 and1 and comparing it with |120572|2 If the random number is lessthan |120572|2 then the Q-bit collapses to 0 or else to 1 and thisvalue is assigned to the corresponding binary bit In step(c) each binary solution is evaluated to give a measure ofits fitness In step (d) the initial solutions are then storedfor each individual into 119861(0) In step (e) the initial bestsolution for each group 119866

119895 is then selected and stored into

respective 119866119861119895(0) In step (f) the initial global best solution

119887 is then selected amongst 119866119861119895(0) In step (g) the attractors

are selected for each individual according to the strategydecided by migration criteria In case of local migration thegroup best 119866119861

119895(119905) is used as the attractor whereas in case

of global migration global best 119887 is used In step (h) Q-bitindividuals in119876(119905) are updated by applying Q-gates by takinginto account 119860119877(119905) and 119875(119905) The quantum rotation gate hasbeen used as the variation operator In steps (i) and (j) thebinary solutions in 119875(119905) are formed by observing the states of119876(119905 minus 1) as in step (c) and each binary solution is evaluatedfor the fitness value In step (k) the best solutions among119861(119905 minus 1) and 119875(119905) are selected and stored into 119861(119905) In step (l)the best solution for each group 119866

119895 is then selected amongst

119866119861119895(119905 minus 1) and 119861(119905) and stored into respective 119866119861

119895(119905) In

step (m) the global best solution 119887 is then selected amongst119866119861119895(119905)It is suggested that QEA designed in [7] should have

population divided equally in 5 groups where attractors ineach group are individuals with best fitness There is a fixedglobal migration cycle at the end of which the attractors areselected as the individual with the best fitness in the entirepopulation Thus upon comparing the population structureof QEA in [7 19] with coarse-grained model the groupsare islands of subpopulation which interact with each otherduring global migration that occurs after fixed number ofgenerations The vQEA [8] does away with the local groupsby making global migration in every generation thus thepopulation model is now panmictic and the interaction istaking place between every individual in every generationThus the QEA with panmictic population model is referredto as PQEA and the QEA with coarse-grained populationstructure is referred to as CQEA

The QEA with fine-grained population model FQEAhas all the operators and strategies similar to those used inCQEA and PQEA except for the population structure and theneighborhood topology The fine-grained population modeldoes not have local groups Every individual is located ina unique position on a two-dimensional toroidal grid as


119878POP Size of the population that is number of individuals119878GRP Size of the Group that is population is divided in groups119878PB Size of the Problem being solved that is number of variables119905 Generation Counter119902119896 119896th 119876-bit that stores the value of their 120572 and 120573

119876119894 119894th Quantum Individual comprising of their 119902

119896 where 119896 = 1 119878PB

119876(119905) Quantum Register that comprises of all the Quantum individuals 119876119894 where 119894 = 1 119878POP

119901119896 119896th binary bit that stores the value of 0 or 1 formed by collapsing corresponding 119902

119896

119875119894 119894th Binary Individual comprising of their 119901

119896 where 119896 = 1 119878PB

119875(119905) Binary Register that comprises of all the Binary individuals 119875119894 where 119894 = 1 119878POP

119861(119905) stores the best solution of all the Binary individuals 119875119894 where 119894 = 1 119878POP

119866119861119895(119905) stores the Best solution of Group 119866

119895 in the current (119905th) generation

AR(119905) Attractor Register that stores the attractor individual for every 119876119894 where 119894 = 1 119878POP

119887 current Global Best Solutionbegin

t = 0 assign SPOP SGRP SPB

(a) initialize Q(t)

(b) make P(t) by observing the states of Q(t)

(c) evaluate P(t)

(d) store the best solutions among P(t) into B(t)

(e) stores the best solution in each Group Gj into respective GBj(t) j = 1 SPOPSGRP

(f) store the best solution b amongst GBj(t)

while (termination condition is not met) dobegint = t + 1

(g) select AR(t) according to migration condition

(h) update Q(tminus1) according to P(tminus1) and AR(t) using Q-gates

(i) make P(t) by observing the states of Q(t)

(j) evaluate P(t)

(k) store the best solutions among P(t) and B(tminus1) into B(t)

(l) store the best solution in each Group Gj and GBj(tminus1) into GBj(t) respectively

j = 1 SPOPSGRP

(m) store the best solution b amongst GBj(t)

endend

Algorithm 1

(a) Von-Neumann topology (b) Von-Neumann topology on two-dimensional grid

Figure 2 Details of fine-grained population structure

shown in Figure 2 which is the most common topologyin fine-grained model The size of the grid is ldquo119860 cross 119861rdquowhere ldquo119860rdquo is the number of rows and ldquo119861rdquo is the number ofcolumns The neighborhood on the grid is defined by Von-Neumann topology which has five individuals that is the

current individual and its immediate north east west andsouth neighbors Thus it is also called NEWS or linear 5 (L5)neighborhood topology The neighborhood is kept static inthe current work so it is computed only once during a singlerun


119878POP Size of the population that is number of individuals119878PB Size of the Problem being solved that is number of variables119860 Number of Rows119861 Number of Columns119905 Generation Counter119902119896 119896th 119876-bit that stores the value of their 120572 and 120573


119896 where 119896 = 1 119878PB



119896


119896 where 119896 = 1 119878PB




119887 current Global Best SolutionNL List of neighbors of all the individuals 119876

119894 where 119894 = 1 119878POP

Begint = 0 assign SPOP SPB A B

(a) initialize Q(t)


(c) evaluate P(t)


(e) compute NL

(f) store the best solution b amongst B(t)


(g) select AR(t)



(j) evaluate P(t)


(l) stores the best solution b amongst B(t)

endend

Algorithm 2

The steps in FQEA are shown in Algorithm 2 [7 8]The steps (a) to (d) are the same as those for the QEA

described earlier In step (e) the neighborhood list NL iscomputed for each individual in the population In step (f)the initial global best solution 119887 is then selected amongst119861(0) In step (g) the attractors are selected for each individualby selecting the fittest neighbor from the four neighbors listedin the neighborhood list NL of each individualThe steps (h)to (k) are the same as those for the QEA described earlier Instep (l) the global best solution 119887 is then selected amongst119861(119905) Further there are no local or global migrations as wellas local isolated groups in FQEA

The computation of neighborhood list NL is an addi-tional component in FQEA as compared to the QEAs Theneighborhood list NL is computed only once during a singlerun of FQEA so the overhead involved in computation of theneighborhood is dependent on the population size 119878POP andthe number of neighbors of each individual in the populationand is independent of the size of the optimization problembeing solved and the number of generations executed in a runof FQEA

The implementation of selection of attractors for all theindividuals is different for the three QEAs It is the simplest

and cheapest for PQEA as the global best solution 119887 is theattractor for all the individuals The selection of attractorsis dependent on the local group size and the populationsize in CQEA whereas in FQEA it is dependent on theneighborhood size and the population size so if the localgroup size and the neighborhood size are equal along withthe population size in CQEA and FQEA then the selectionof attractors is equally expensive in both CQEA and FQEAThe rest of the functions has the same implementation in allthe QEAs and is equally expensive

4 Testing Results and Analysis

The testing has been performed to evaluate the effect of allthe three populationmodels onQEA namely coarse-grainedQEA (CQEA) panmictic QEA (PQEA) and fine-grainedQEA (FQEA) on discrete optimization problemsThe testingis performed with equivalent parameter setting for all thethree algorithms so that a fair comparison of the impact ofthree population structures on the performance of QEA canbe made statistically An important point to note here is thatthe parameters suggested in [7 8 17] especially 120579

1to 1205798have

been mostly used as they all use the same variation operator


Table 1 Parameter setting for PQEA CQEA and FQEA

Parameters PQEA CQEA FQEAPopulation size 50 50 501205791to 1205798

0 0 001120587 0 minus001120587 0 0 0 respectivelyNumber of observations 1 1 1Local group size NA 5 NALocal migration period (generations) NA 1 NAGlobal migration period (generations) 1 100 NAToroidal grid size NA NA 5 cross 10Neighborhood topology NA NA Von-NeumannNeighborhood size NA NA 5Stopping criterion (generations) Problem specific

and our main motive has been to determine the effect ofdifferent population structures keeping all the other factorssimple and similar

The testing is performed on thirty-eight instances ofwell-known diverse problems namely COUNTSAT (nineinstances) 119875-PEAKS (five instances) and 0-1 knapsackproblems (eight instances each for three different profit andweight distributions) COUNTSAT and 119875-PEAKS probleminstances have been selected as their optimal values areknown thus it becomes easier to empirically evaluate theperformance of algorithms 0-1 knapsack problems havebeen selected as they have several practical applications Theproblem instances used in testing of the QEAs are generallylarge and difficult and are explained in detail in respectiveSections 41 to 43

The parameters used for all the three algorithms in all theproblems are given in Table 1 A population size of fifty andnumber of observations per Q-bit as one in each generationhave been used in all the three algorithms The value of 120579

1to

1205798is the same for all the three QEAs The local group size is

five local migration period is one iteration and the globalmigration period is 100 generations for CQEA The globalmigration period is one in PQEAThe toroidal grid size of ldquo5cross 10rdquo with Von-Neumann topology having neighborhoodsize of five individuals is used in FQEAThe toroidal grid sizeof ldquo5 cross 10rdquo has been used as the population size is fiveThestopping criterion is the maximum number of permissiblegenerations which is problem specific

41 COUNSATProblem [18] It is an instance of theMAXSATproblem In COUNTSAT the value of a given solution isthe number of satisfied clauses (among all the possible Hornclauses of three variables) by an input composed of 119899 Booleanvariables It is easy to check that the optimum is obtainedwhen the value of all the variables is 1 that is 119904 = 119899 In thisstudy nine different instances have been considered with 119899 =20 50 100 150 200 400 600 800 and 1000 variables andthus the value of the optimal solution varies from 6860 to997003000 as given by

119891COUNTSAT (119904) = 119904 + 119899 sdot (119899 minus 1) sdot (119899 minus 2) minus 2 sdot (119899 minus 2)

sdot (119904

2) + 6 sdot (

119904

3)

56

58

60

62

64

66

68

70

0 5 10 15 20 25

Fitn

ess v

alue

Number of variables with value 1 (s)

times102

Figure 3 COUNTSAT function with 119899 being 20

For (119899 = 20) = 119904 + 6840 minus 18 sdot 119904 sdot (119904 minus 1) + 119904 sdot (119904 minus 1)

sdot (119904 minus 2)

For (119899 = 1000) = 119904 + 997002000 minus 998 sdot 119904 sdot (119904 minus 1) + 119904

sdot (119904 minus 1) sdot (119904 minus 2)

(4)

The COUNTSAT function is extracted from MAXSATwith the objective of being very difficult to be solved byevolutionary algorithms [28] The variables are randomlyassigned values following a uniform distribution and sowill have approximately 1198992 ones Then the local changesdecreasing the number of oneswill lead to better results whilelocal changes increasing the number of ones decrease thefitness as shown in Figures 3 and 4 Hence it is expected thatEAs would quickly converge to all-zero and have difficultiesin reaching the all-one string

The results of testing of all the three algorithms onnine COUNTSAT problem instances have been presented inTable 2 A total of thirty independent runs of each algorithmwere executed and the Best Worst Average Median success runs that is number of runs in which an optimumsolution was reached and standard deviation (Std) of thefitness alongwith the average number of function evaluations(NFE) were recorded The maximum number of generations


Table 2 Comparative study between PQEA CQEA and FQEA using statistical results on COUNTSAT problem instances

Problem size(119899) Statistic Best Worst Average Median success

runs Std Average NFE

20PQEA 6860 6841 6857 6860 833 72 90917CQEA 6860 6860 6860 6860 1000 00 11517FQEA 6860 6860 6860 6860 1000 00 11383

50PQEA 117650 117601 117639 117650 767 211 142567CQEA 117650 117650 117650 117650 1000 00 49067FQEA 117650 117650 117650 117650 1000 00 44883

100PQEA 970300 970201 9702703 970300 700 461 202683CQEA 970300 970300 970300 970300 1000 00 104617FQEA 970300 970201 9702967 970300 967 181 106500

150PQEA 3307950 3307801 33078904 3307950 600 742 273033CQEA 3307950 3307801 33079252 3307950 833 565 208633FQEA 3307950 3307950 3307950 3307950 1000 00 133450

200PQEA 7880600 7880401 78805204 7880600 600 992 297233CQEA 7880600 7880401 78805801 7880600 900 607 223000FQEA 7880600 7880600 7880600 7880600 1000 00 166050

400PQEA 63521200 62847292 63425153 63521200 767 1899322 411483CQEA 63521200 63258981 63512459 63521200 967 478744 344833FQEA 63521200 63521200 63521200 63521200 1000 00 279683

600PQEA 214921800 209608152 212033464 211953199 100 14073464 499633CQEA 214921800 209881401 213598979 214385692 367 15243880 487317FQEA 214921800 214921800 214921800 214921800 1000 00 372017

800PQEA 499089026 488046846 493854763 494709763 00 28503156 500500CQEA 508810386 498371881 504276211 504764499 00 25028902 500500FQEA 510082400 510082400 510082400 510082400 1000 00 451867

1000PQEA 964320421 937999876 951762456 953408640 00 56144299 500500CQEA 979662826 948748605 969462614 972362722 00 87505108 500500FQEA 997003000 994023961 995543257 996005997 67 7703622 500100

84

86

88

90

92

94

96

98

100

102

0 200 400 600 800 1000 1200

Fitn

ess v

alue


times107


was one thousand All the three algorithms were able to reachthe global maxima till problem size 119899 being 600 however inproblem sizes 119899 being 800 and 1000 only FQEA could reach

the global optima The performance of PQEA is inferior tothe other two algorithms on all the statistical parametersTheperformance of CQEA is as good as FQEA for problem sizes20 and 50 on all the statistical parameters except for averageNFE which indicates that FQEA is faster than CQEA CQEAhas better success rate than FQEA in the problem size 119899being 100 but FQEA has performed better than CQEA onthe remaining six problem instances as it has better successrate

Figures 5 6 7 8 9 10 11 12 and 13 show relativeconvergence rate of the QEAs on the COUNTSAT probleminstancesThe convergence graphs have been plotted betweenthe number of generations and the objective function valuesof the three QEAs The rate of convergence of PQEA isfastest during the early part of the search in all the probleminstances In fact for small size problem instances PQEAis the fastest QEA However as the problem size increasesthe performance of PQEA deteriorates and FQEA whichwas slowest on the small size problem instances emergesas the fastest amongst all the QEAs CQEA has beenfaster than FQEA on small size problem instances and hasalso outperformed PQEAs on large size problem instances


596061626364656667686970

1 11 21 31 41 51 61 71 81 91

Obj

fun

c va

lue

Generation number

PQEACQEAFQEA

PQEACQEAFQEA

times102

Figure 5 Convergence graph of PQEA CQEA and FQEA onCOUNTSAT problem size 119899 being 20

PQEACQEAFQEA

90

95

100

105

110

115

120

1 21 41 61 81 101 121 141

Obj

fun

c va

lue

Generation numberPQEACQEAFQEA

times103


The reason for poor performance of FQEA initially onsmall size problem instances is the slowest dispersion ofinformation as compared to PQEA and CQEA which infact enables FQEA to explore the solution space morecomprehensively before converging to the global optimumIn fact slow dispersion of information helps FQEA to reachthe global optimum in large size problem instances as itdoes not get trapped in the local optimum The dispersionof information is quickest in the case of PQEA which helpsit to outperform both CQEA and FQEA but also causes itto get trapped in the local optimum especially in large sizeproblem instances The dispersion of information is slowerin CQEA as compared to PQEA so it has found globaloptimum in more numbers of problem instances OverallFQEA has performed better than PQEA and CQEA on allthe instances of COUNSAT problems Therefore the slowrate of dispersion of information in the fine-grained model

75

80

85

90

95

100

1 31 61 91 121 151 181 211 241

Obj

fun

c va

lue

times104

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


26

27

28

29

30

31

32

33

34

1 51 101 151 201 251 301 351 401 451

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


had helped FQEA to perform better than the QEAs with theother two population models in the COUNTSAT probleminstances

42 119875-PEAKS Problem [18 29] It is a multimodal problemgenerator which can easily create problem instances whichhave tunable degree of difficulty The advantage of using aproblem generator is that it removes the opportunity to hand-tune algorithms to a particular problem thus allowing alarge fairness while comparing the performance of differentalgorithms or different instances of the same algorithm Ithelps in evaluating the algorithms on a large number ofrandom problem instances so that the predictive power ofthe results for the problem class as a whole is very high [29]

The idea of 119875-PEAKS is to generate ldquo119875rdquo random N-bitstrings that represent the location of 119875 peaks in the search


62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


spaceThe fitness value of a string is the hamming distancebetween and the closest peak Peak

119894 divided by 119873 (as

shown in (5)) Using a higher (or lower) number of peaks weobtain a problemwithmore (or less) degree ofmultimodalityThe maximum fitness value for the problem instances is 10Consider

119891119875-PEAKS( 119909) =

1

119873max1le119894le119901

119873 minus Hamming 119863(Peak119894) (5)

The results of testing of all three algorithms on 119875-PEAKSproblem instances with 119873 being 1000 and number of peaks119875 being 20 50 100 500 and 1000 have been presented inTable 3 A total of thirty independent runs of each algorithmwere executed and the Best Worst Average and Median success runs that is number of runs in which an optimum

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solution was reached and standard deviation (Std) of thefitness along with average number of function evaluations(NFE) were recorded The maximum number of generationswas three thousand PQEA was quickest in the beginningof the search process but could not reach a global optimumeven in a single run of any problem instance CQEAwas slowin the beginning but performed better than PQEA FQEAoutperformed all the other QEAs as it was able to reach aglobal optimum in all the runs of all the problem instances

Figures 14 15 16 17 and 18 show relative convergencerate of the QEAs for 119875-PEAKS problem instances Theconvergence graphs have been plotted between the numberof generations and the objective function values of the threeQEAs The rate of convergence of PQEA is fastest duringthe early part of the search in all the five problem instances


Table 3 Comparative study between PQEA CQEA and FQEA using statistical results on 119875-PEAKS problem instances with size119873 as 1000

Number ofpeaks (119875) Algo Best Worst Average Median success


20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

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PQEACQEAFQEA

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however PQEA could not reach a global optimum even ina single run of any instance CQEA has been the slowest ofthe three QEAs but has performed better than PQEA FQEAis faster than CQEA and has also outperformed PQEA andCQEA on all the five problem instances The reason for poorperformance of FQEA initially is due to the slow dispersionof information as compared to PQEA which enables itto explore the solution space more comprehensively beforeconverging to a global optimum In fact slow dispersion ofinformation helps FQEA to reach a global optimum in largesize problem instances as it does not get trapped in a localoptimum The dispersion of information is the quickest incase of PQEAwhich helps it to outperformCQEAand FQEA

0

02

04

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fun

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PQEACQEAFQEA

PQEACQEAFQEA

Generation number

Figure 14 Convergence graph of PQEA CQEA and FQEA on 119875-PEAKS problem of size 119873 being 1000 and number of peaks 119875being 20

in the initial part of search process but also causes it to gettrapped in a local optimum The dispersion of informationis slower in CQEA as compared to PQEA so it has found aglobal optimum in some runs of a problem instance OverallFQEA has performed better than PQEA and CQEA on all theinstances of 119875-PEAKS problems Therefore the slow rate ofdispersion of information in fine-grained model had helpedFQEA to perform better than the other population models in119875-PEAKS problem instances

43 0-1 Knapsack Problem [30] The 0-1 knapsack problem isa profit maximization problem in which there are 119872 itemsof different profit and weight available for selection [30]The selection is made to maximize the profit while keeping


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PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

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PQEACQEAFQEA

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the weight of the selected items below the capacity of theknapsack It is formulated as follows

Given a set of119872 items and a knapsack of capacity119862 selecta subset of the items to maximize the profit 119891(119909)

119891 (119909) = sum pt119894lowast 119909119894

(6)

subject to the condition

sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt

119894is the profit of 119894th item

and wt119894is the weight of 119894th item If the 119894th item is selected for

the knapsack 119909119894= 1 else 119909

119894= 0 and 119894 = 1 119872

Three groups of randomly generated instances of difficultknapsack problems (KP) have been constructed to test theQEAs In all instances the weights are uniformly distributedin a given interval The profits are expressed as a function

0

02

04

06

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1

12

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Obj

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c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


of the weights yielding the specific properties of each groupEight different problem instances for each group of KP havebeen constructed Four different capacities of the knapsackhave been considered namely 10 5 2 and 1 of thetotal weight of all the items taken together The number ofitems available for selection in this study is 200 and 5000items

431 Multiple Strongly Correlated Instances 119898119904119905119903(1198961 1198962 119889)

They are constructed as a combination of two sets of stronglycorrelated instances which have profits pt

119895= wt119895+119896119898where

119896119898119898 = 1 2 is different for the two setsThemultiple strongly

correlated instances mstr(1198961 1198962 119889) have been generated in

this work as follows the weights of the119872 items are randomlydistributed in [1 1000] If the weight wt

119895is divisible by 119889 = 6

then we set the profit pt119895= wt

119895+ 1198961 otherwise set it to

pt119895= wt

119895+ 1198962 The weights wt

119895in the first group (ie

where pt119895= wt119895+ 1198961) will all be multiples of 119889 so that using


Table 4 Comparative study between PQEA CQEA and FQEA using statistical results on 0-1 knapsack problem with multiple stronglycorrelated data instances

of totalweight Number of items (119872) Algo Best Worst Average Median Std Average NFE

10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153

only these weights can at most use 119889[119862119889] of the capacitytherefore in order to obtain a completely filled knapsacksome of the items from the second distribution will also beincluded Computational experiments have shown that verydifficult instances could be obtainedwith the parametersmstr(300 200 and 6) [30]

The results of testing of all the three algorithms on 0-1 knapsack problem with multiple strongly correlated datainstances have been presented in Table 4 A total of thirtyindependent runs of each algorithm were executed and theBest Worst Average and Median and standard deviation(Std) of the fitness along with average number of functionevaluations (NFE) were recorded The maximum numberof generations was ten thousand FQEA has outperformedPQEA and CQEA on all the problem instances as indicatedby the statistical results CQEA has performed better thanPQEA on problems with smaller number of items but PQEAhas performed better than CQEA on problems with largernumber of items

Figures 19 20 21 22 23 24 25 and 26 show relativeconvergence rate of the QEAs for 0-1 knapsack problem withmultiple strongly correlated data instances The convergencegraphs have been plotted between the number of generationsand the objective function values of the three QEAs Therate of convergence of PQEA is fastest during the early part

of the search in most of the problem instances howeverFQEA was able to overtake both the QEAs in later part ofthe search process CQEA has been the slowest of the threeQEAs inmost of the instances except when the capacity of theknapsack is small that is it has performed better than PQEAin such problem instances PQEA has performed better thanCQEA on all other problem instances FQEA has been slowinitially but has performed better than PQEA and CQEA onall the problem instances The reason for poor performanceof FQEA during the initial part of the search process is dueto slow dispersion of information in FQEA as compared tothe other QEAs which enables FQEA to explore the solutionspace more comprehensively before reaching near a globaloptimum In fact slow dispersion of information helps it toreach near the global optimum as it avoids getting trapped ina local optimumThe dispersion of information is quickest incase of PQEAwhich helps it to outperformCQEAand FQEAduring the initial part of search process but also causes it toget trapped in a local optimumThedispersion of informationis slower in CQEA as compared to PQEA but CQEA has beenable to reach near best solution found by PQEA in the laterpart of the search and in some cases CQEA has outperformedPQEA Overall FQEA has performed better than PQEAand CQEA on all the instances of 0-1 knapsack problemwithmultiple strongly correlated data distributionTherefore


157167177187197207217227237247257

1 301 601 901 1201

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fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102

Figure 19 Convergence graph of PQEA CQEA and FQEA on 0-1knapsack problem with multiple strongly correlated data instanceswith number of items119872 being 200 and capacity 119862 being 10 oftotal weight

36213721382139214021412142214321442145214621

1 301 601 901 1201

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c va

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times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


the slow rate of dispersion of information in the fine-grainedmodel had helped FQEA to perform better than QEAs withthe other population models in 0-1 knapsack problem withmultiple strongly correlated data instances

432 Profit Ceiling Instances 119901119888119890119894119897(119886) These instances haveprofits of all items as multiples of a given parameter 119886 Theweights of the119872 items are randomly distributed in [1 1000]and their profits are set to pt

119895= 119886[wt

119895119886] The parameter 119886

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1 301 601 901 1201

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fun

c va

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times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

Figure 21 Convergence graph of PQEA CQEA and FQEA on 0-1knapsack problem with multiple strongly correlated data instanceswith number of items 119872 being 200 and capacity 119862 being 5 oftotal weight

181

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261

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301

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fun

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times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


has been experimentally chosen as 119886 = 3 as this resulted insufficiently difficult instances [30]

The results of testing of all the three algorithms on 0-1knapsack problem with profit ceiling distribution instanceshave been presented in Table 5 A total of thirty indepen-dent runs of each algorithm were executed and the BestWorst Average and Median and standard deviation (Std)of the fitness along with the average number of functionevaluations (NFE) were recorded The maximum number ofgenerations was ten thousand FQEA has outperformed both


Table 5 Comparative study between PQEA CQEA and FQEA using statistical results on 0-1 knapsack problem with profit ceiling datainstances


1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

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c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

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fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

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lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


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1 501 1001 1501 2001 2501 3001 3501 4001

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times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


the other QEAs on all the problem instances as indicatedby the statistical results CQEA has performed better thanPQEA on problems with smaller number of items but PQEAhas performed better than CQEA on problems with largernumber of items

Figures 27 28 29 30 31 32 33 and 34 show relativeconvergence rate of the QEAs for 0-1 knapsack problem withprofit ceiling data instances The convergence graphs havebeen plotted between the number of generations and theobjective function values of the three QEAs The rate ofconvergence of PQEA is fastest during the early part of the

10055

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10135

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c va

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PQEACQEAFQEA

PQEACQEAFQEA

Generation number

Figure 27 Convergence graph of PQEA CQEA and FQEA on 0-1knapsack problem with profit ceiling data instances with number ofitems119872 being 200 and capacity 119862 being 10 of total weight

249180

249280

249380

249480

249580

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1 301 601 901 1201

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c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


search process in most of the problem instances howeverFQEA was able to overtake both the QEAs during later partof the search process CQEA has been the slowest of thethree QEAs in most of the instances except when capacityof knapsack is small that is CQEA has performed betterthan PQEA in such problem instances PQEA has performedbetter than CQEA on the other problem instances FQEAhas been slow initially but has performed better than bothPQEA and CQEA on all the problem instances The reasonfor poor performance of FQEA initially is due to the slowdispersion of information as compared to the other QEAswhich enables FQEA to explore the solution space morecomprehensively before reaching near a global optimum Infact slow dispersion of information helps FQEA to reach


5015

5025

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5045

5055

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1 301 601 901 1201

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PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

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1249

1250

1 301 601 901 1201 1501 1801

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PQEACQEAFQEA

times102

Generation number

Figure 30 Convergence graph of PQEA CQEA and FQEA on 0-1 knapsack problem profit ceiling data instances with number ofitems119872 being 5000 and capacity 119862 being 5 of total weight

near a global optimum as it avoids getting trapped in a localoptimum The dispersion of information is quickest in thecase of PQEAwhich helps it to outperformCQEAand FQEAin the initial part of the search process but also causes it to gettrapped in a local optimumThe dispersion of information isslower in CQEA as compared to PQEA but CQEA has beenable to reachnear the best solution foundbyPQEA in the laterpart of the search process in some cases Overall FQEA hasperformed better than PQEA and CQEA on all the instancesof 0-1 knapsack problem with profit ceiling data distributionTherefore the slow rate of dispersion of information in thefine-grained model had helped FQEA to perform better thanthe QEAs with other population models in 0-1 knapsackproblems with profit ceiling data distribution

2009

2014

2019

2024

2029

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2039

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c va

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PQEACQEAFQEA

Generation number


49830

49880

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50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

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PQEACQEAFQEA

Generation number


433 Circle Instances 119888119894119903119888119897119890(119889119888) These instances have the

profit of their items as function of the weights forming an arcof a circle (actually an ellipsis)Theweights are uniformly dis-tributed in [1 1000] and for each weight wt

119894the correspond-

ing profit is chosen to be pt119894= 119889119888radic2000

2minus (wt119894minus 2000)

2Experimental results have shown in [30] that difficultinstances appeared by choosing 119889

119888= 23 which was chosen

for testing in this workThe results of testing of all the three algorithms on 0-

1 knapsack problem with circle data instances have beenpresented in Table 6 A total of thirty independent runs ofeach algorithm were executed and the Best Worst Averageand Median and standard deviation (Std) of the fitness alongwith average number of function evaluations (NFE) were


Table 6 Comparative study between PQEA CQEA and FQEA using statistical results on 0-1 knapsack problem with circle data instances


1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


recorded The maximum number of generations was tenthousand FQEA has outperformed both PQEA and CQEAon all the problem instances as indicated by the statisticalresults CQEA has performed better than PQEA on problems

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1 301 601 901 1201

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PQEACQEAFQEA

Generation number


with smaller number of items but PQEAhas performed betterthan CQEA on problems with larger number of items


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1 301 601 901 1201 1501

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times103

Generation number

Figure 35 Convergence graph of PQEA CQEA and FQEA on 0-1knapsack problem with circle data instances with number of items119872 being 200 and capacity 119862 being 10 of total weight

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times103

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Figures 35 36 37 38 39 40 41 and 42 show relativeconvergence rate of the QEAs for 0-1 knapsack problem withcircle data distribution instances The convergence graphshave been plotted between the number of generations andthe objective function values of the three QEAs The rateof convergence of PQEA is fastest during the early partof the search process in some problem instances howeverFQEA was able to overtake both the QEAs during laterpart of the search process CQEA has been the slowest ofthe three QEAs in most of the problem instances CQEAhas performed better than PQEA on most of the probleminstances FQEA has been slow initially but has performedbetter than both PQEA and CQEA on all the problem

92

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Generation number

Figure 38 Convergence graph of PQEA CQEA and FQEA on 0-1 knapsack problem circle data instances with number of items119872being 5000 and capacity 119862 being 5 of total weight

instancesThe reason for poor performance of FQEA initiallyis due to the slow dispersion of information as comparedto the other QEAs which enables it to explore the solutionspace more comprehensively before reaching near a globaloptimum In fact slow dispersion of information helps it toreach near the global optimum as it avoids getting trapped ina local optimumThe dispersion of information is quickest incase of PQEAwhich helps it to outperformCQEAand FQEAin initial part of the search process but also causes it to gettrapped in a local optimumThe dispersion of information isslower in CQEA as compared to PQEA but it has been able toreach near the best solution found by PQEA in the later partof the search in some cases CQEA has also outperformed


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PQEA in some cases Overall FQEA has performed betterthan PQEA and CQEA on all the instances of 0-1 knapsackproblemwith circle data distributionTherefore the slow rateof dispersion of information in the fine-grained model hadhelped FQEA to perform better than the QEAs with otherpopulation models in 0-1 knapsack problem with circle datadistribution

44 Comparative Study A comparative study has been per-formed between FQEA and recently proposed ldquostate-of-the-artrdquo algorithm known as ldquohybrid cuckoo search algorithmwith improved shuffled frog leaping algorithmrdquo (CSISFLA)[31] It was shown in [31] that CSISFLA has performed betterthan genetic algorithm [3] Differential Evolution Algorithm

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Figure 41 Convergence graph of PQEA CQEA and FQEA on 0-1knapsack problem circle data instances with number of items 119872being 200 and capacity 119862 being 1 of total weight

44

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Generation number


[32 33] and Cuckoo Search [34] on some 0-1 knapsackproblem instances The size of the knapsack is very large asit is 75 of the total weight of all the items taken togetherTable 7 empirically compares the performance of FQEA andCSISFLA on KP-1 KP-2 KP-3 and KP-7 which are 0-1knapsack problem instances with uncorrelated weight andprofit instances given in [31] The duration of execution ofFQEA (compiled with Visual Studio 6) was five secondsfor KP-1 KP-2 and KP-3 and eight seconds on a computerwith AMD Athlon 7750 Dual-Core 271 GHz 175GB RAMrunning under Windows XP which was a similar machine tothat used for running CSISFLA in [31] The target capacity


Table 7 Comparative study between CSISFLA and FQEA on 0-1knapsack problem with uncorrelated distribution

Instance Algorithm Best Worst Mean Median Std

KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769

total capacity and total value of the items in each problemare the same as those given in [31]

Results in Table 7 show that FQEA outperforms CSISFLAon KP-1 KP-2 and KP-3 but CSISFLA performs better thanFQEA on KP-7 This shows that FQEA is performing betteron small dimension problems compared to CSISFLA butCSISFLA is performing better than FQEAon large dimensionproblems In order to find the reason for poor performanceof FQEA on large dimension problems an investigationwas made on the conditions of comparative study It wasfound that KP-1 has 150 items KP-2 has 200 items KP-3has 300 items and KP-7 has 1200 items Thus by keepingtotal running time of five seconds for KP-1 to KP-3 showsthat it is either more for KP-1 or less for KP-3 becausethe problem size in KP-3 is double that of KP-1 So let usassume that if 5 seconds of run time was adequate for KP-3 then it is considerably more for KP-1 However even whenCSISFLA has evolved for more time in case of KP-1 it hasproduced inferior result as compared to FQEA showing thatCSISFLA has a tendency of getting trapped in suboptimalregion The search process of FQEA is slow initially as itexplores the search space in a more comprehensive waydue to slow dissemination information in its populationstructure as compared to other algorithms In case of KP-7the problem size is eight times that of KP-1 Thus if FQEA isevolved for forty seconds instead of eight seconds it shouldproduce better results than CSISFLA It can be argued thatCSISFLA may produce better result if it evolved for fortyseconds but as we have seen in KP-1 evolving for moreduration is not necessarily helping CSISFLA Table 8 showsthe results of FQEA with forty seconds of execution time onKP-7 KP-14 KP-19 KP-24 KP-29 and KP-34 along with theresults of CSISFLA given in [31] Table 8 shows that FQEAis able to produce better results when evolved for longerduration However CSISFLA produces better result in largedimension problem instances than FQEA when evolved foreight seconds only

5 Conclusions

Quantum-inspired evolutionary algorithm are a type ofevolutionary algorithms which have been designed byintegrating probabilistic bit representation superpositionand measurement principles in evolutionary framework for

Table 8 Comparative study between CSISFLA and FQEA on 0-1knapsack problems with the number of items being 1200


KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257

computationally solving difficult optimization problemsTheQEA in [7] has been developed on coarse-grained populationmodel which has been subsequentlymodified into panmicticmodel vQEA and is shown to be better than QEA in solvingsome problems [8] This motivated further investigationsof the effect of fine-grained population structure on theperformance of QEA [35] The experimental testing hasshown that fine-grained model improves the performance ofQEA in comparison to the other models on COUNTSATproblem instances 119875-PEAKS problem instances and threedifficult knapsack problem instances Thus the contributionof this work is twofold namely the first is the criticalexamination of the population structures employed in QEAand the implementation of QEA on the two-dimensionaltoroidal grid for fair comparison of the effect of all the threepopulation models on QEA A comparative study was alsoperformed with the ldquostate-of-the-artrdquo hybrid cuckoo searchalgorithm [31] which showed that FQEA is slow but producesbetter solutions Future endeavors will be made to furtherimprove the speed of convergence in FQEA for solvingbenchmark as well as real world search and optimizationproblems

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are thankful to anonymous reviewers for givinginsightful comments which helped in improving the paperNija Mani is thankful to her department and UGC for sup-porting her PhD through Meritorious Studentrsquos Fellowship

References

[1] X-S Yang S Koziel and L Leifsson ldquoComputational optimiza-tion modelling and simulation recent trends and challengesrdquoin Proceedings of the 13th Annual International Conference on


Computational Science (ICCS rsquo13) vol 18 pp 855ndash860 June2013

[2] E Alba and M Tomassini ldquoParallelism and evolutionaryalgorithmsrdquo IEEE Transactions on Evolutionary Computationvol 6 no 5 pp 443ndash462 2002

[3] Z Michalewicz Genetic Algorithms + Data Structures = Evolu-tion Programs Springer London UK 3rd edition 1996

[4] Z Michalewicz and D B Fogel How To Solve It ModernHeuristics Springer Berlin Germany 2nd edition 2004

[5] D Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1989

[6] A Mani and C Patvardhan ldquoAnalysis of photoluminescencemeasurement data from interdiffused quantum wells by realcoded quantum inspired evolutionary algorithmrdquo in Proceed-ings of the 13th International Workshop on Advanced Computingand Analysis Techniques in Physics Research Proceedings ofScience Jaipur India February 2010

[7] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002

[8] M D Platel S Sehliebs and N Kasabov ldquoA versatile quantum-inspired evolutionary algorithmrdquo in Proceedings of the IEEECongress on Evolutionary Computation (CEC rsquo07) pp 423ndash430Singapore September 2007

[9] L Kliemann O Kliemann C Patvardhan V Sauerlandand A Srivastav ldquoA new QEA computing near-optimal low-discrepancy colorings in the hypergraph of arithmetic pro-gressionsrdquo in Proceedings of 12th International SymposiumExperimental Algorithms vol 7933 of Lecture Notes in ComputerScience pp 67ndash78 June 2013

[10] D H Kim Y H Yoo S J Ryu W Y Go and J H Kim ldquoAuto-matic color detection for MiroSOT using quantum-inspiredevolutionary algorithmrdquo in Intelligent Robotics Systems Inspir-ing the NEXT Communications in Computer and InformationScience vol 376 pp 11ndash20 2013

[11] A C Kumari K Srinivas and M P Gupta ldquoSoftware require-ments selection using quantum-inspired elitist multi-objectiveevolutionary algorithmrdquo in Proceedings of the 1st InternationalConference on Advances in Engineering Science and Manage-ment (ICAESM rsquo12) pp 782ndash787 March 2012

[12] H Lei and K Qin ldquoQuantum-inspired evolutionary algorithmfor analog test point selectionrdquo Analog Integrated Circuits andSignal Processing vol 75 no 3 pp 491ndash498 2013

[13] Y Li S Feng X Zhang and L Jiao ldquoSAR image segmentationbased on quantum-inspired multiobjective evolutionary clus-tering algorithmrdquo Information Processing Letters vol 114 no 6pp 287ndash293 2014

[14] A Mani and C Patvardhan ldquoA hybrid quantum evolution-ary algorithm for solving engineering optimization problemsrdquoInternational Journal of Hybrid Intelligent System vol 7 no 3pp 225ndash235 2010

[15] A Mani and C Patvardhan ldquoAn improved model of ceramicgrinding process and its optimization by adaptive Quantuminspired evolutionary algorithmrdquo International Journal of Simu-lations Systems Science and Technology vol 11 no 3 pp 76ndash852012

[16] C PatvardhanANarain andA Srivastav ldquoEnhanced quantumevolutionary algorithms for difficult knapsack problemsrdquo inProceedings of International Conference on Pattern RecognitionandMachine Intelligence vol 4815 of Lecture Notes in ComputerScience Springer Berlin Germany 2007

[17] G Zhang ldquoQuantum-inspired evolutionary algorithms a sur-vey and empirical studyrdquo Journal of Heuristics vol 17 pp 303ndash351 2011

[18] E Alba and B Dorronsoro ldquoThe explorationexploitationtradeoff in dynamic cellular genetic algorithmsrdquo IEEE Transac-tions on Evolutionary Computation vol 9 no 2 pp 126ndash1422005

[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithms with a new termination criterion H120576 gate and two-phase schemerdquo IEEE Transactions on Evolutionary Computa-tion vol 8 no 2 pp 156ndash169 2004

[20] J Kennedy and R Mendes ldquoPopulation structure and particleswarmperformancerdquo inProceeding of theCongress onEvolution-ary Computation (CEC rsquo02) vol 2 pp 1671ndash1676 May 2002

[21] E Alba and J M Troya ldquoImproving flexibility and efficiencyby adding parallelism to genetic algorithmsrdquo Statistics andComputing vol 12 no 2 pp 91ndash114 2002

[22] P Spiessens and B Manderick ldquoA massively parallel geneticalgorithmrdquo in Proceeding of 4th International Conference onGenetic Algorithms R Bclew and L Booker Eds pp 279ndash2861991

[23] K W C Ku M W Mak and W C Siu ldquoAdding learningto cellular genetic algorithms for training recurrent neuralnetworksrdquo IEEE Transactions on Neural Networks vol 10 no2 pp 239ndash252 1999

[24] G Folino C Pizzuti and G Spezzano ldquoParallel hybrid methodfor SAT that couples genetic algorithms and local searchrdquo IEEETransactions on Evolutionary Computation vol 5 no 4 pp323ndash334 2001

[25] D A Sofge ldquoProspective algorithms for quantum evolutionarycomputationrdquo in Proceedings of the 2nd Quantum InteractionSymposium (QI rsquo08) College Publications Oxford UK 2008httparxivorgftparxivpapers080408041133pdf

[26] M A Nielsen and I L Chuang Quantum Computationand Quantum Information Cambridge University Press Cam-bridge UK 2006

[27] A Narayanan and M Moore ldquoQuantum-inspired genetic algo-rithmsrdquo in Proceedings of the IEEE International Conference onEvolutionary Computation (ICEC rsquo96) pp 61ndash66 May 1996

[28] S Droste T Jansen and I Wegener ldquoA natural and simplefunction which is hard for all evolutionary algorithmsrdquo in Pro-ceedings of the 26th Annual Conference of the IEEE ElectronicsSociety (IECON rsquo00) pp 2704ndash2709 Nagoya Japan October2000

[29] K de JongM Potter andW Spears ldquoUsing problem generatorsto explore the effects of epistasisrdquo in Proceedings of the 7thInternational Conference onGenetic Algorithms T Back Ed pp338ndash345 1997

[30] D Pisinger ldquoWhere are the hard knapsack problemsrdquoComput-ers amp Operations Research vol 32 no 9 pp 2271ndash2284 2005

[31] Y Feng G-G Wang Q Feng and X-J Zhao ldquoAn effectivehybrid cuckoo search algorithm with improved shuffled frogleaping algorithm for 0-1 Knapsack problemsrdquo ComputationalIntelligence and Neuroscience vol 2014 Article ID 857254 17pages 2014

[32] S Das and P N Suganthan ldquoDifferential evolution a surveyof the state-of-the-artrdquo IEEE Transactions on EvolutionaryComputation vol 15 no 1 pp 4ndash31 2011

[33] R Mallipeddi P N Suganthan Q K Pan andM F TasgetirenldquoDifferential evolution algorithm with ensemble of parametersand mutation strategiesrdquo Applied Soft Computing Journal vol11 no 2 pp 1679ndash1696 2011


[34] A Gherboudj A Layeb and S Chikhi ldquoSolving 0-1 knapsackproblems by a discrete binary version of cuckoo search algo-rithmrdquo International Journal of Bio-Inspired Computation vol4 no 4 pp 229ndash236 2012

[35] NMani G Srivastava A K Sinha andAMani ldquoAn evaluationof cellular population model for improving quantum-inspiredevolutionary algorithmrdquo in Proceedings of the 14th InternationalConference on Genetic and Evolutionary Computation (GECCOrsquo12) pp 1437ndash1438 Philadelphia Pa USA July 2012

Submit your manuscripts athttpwwwhindawicom

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Distributed Sensor Networks


Advances in

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



Panmictic

(a) Unstructured

Coarse grained Fine grained

(b) Structured

Figure 1 Population structures

population structure on the performance of QEA This alsomotivates investigation for employing fine-grained modelin the population structure of QEA This paper empiricallyevaluates the effect of population structures in QEA bysolving some instances of well-known benchmark problemslike COUNTSAT 119875-PEAKS and 0-1 knapsack problemsThe paper is further organized as follows Section 2 brieflydiscusses population structures QEA vQEA and FQEA arepresented and their population structure is established inSection 3 Results and analysis are presented in Section 4Section 5 draws conclusions and shows some directions forfurther work

2 Population Structures

The population structures in EAs can be divided into twobroad categories namely unstructured and structured [20]and are shown in Figure 1 The unstructured populationmodel has beenwidely used in EAs where a single populationof individuals is evolved by employing variation operatorsThe advantage of unstructured population is its conceptualand implementation simplicity The dissemination of infor-mation regarding the best individual is quickest as all theindividuals are connected with all the other individuals Itworks fine for EAs in which diversity can be maintainedby suitably designed variation operators for a given prob-lem However if the search space is highly deceptive andmultimodal the panmictic population may not be the mosteffective model Structured population models are viablealternatives to the unstructured model They have beenprimarily developed during efforts to parallelize EAs forrunning on multiprocessors hardware [2] However theyhave also been used with simple EAs (run on monoprocessorhardware) in place of panmictic population and have beenfound to provide better sampling of search space along withconsequent improvement in empirical performance [21]

The structured models can be divided into two maingroups namely coarse-grained and fine-grainedmodelsThecoarse-grainedmodel is also known as distributedmodel andisland model It has multiple panmictic populations whichevolve in parallel and communicate with each other period-ically often exchanging or updating individuals dependingon the specific strategyThe advantage of island model is thatit encourages niching and also allows slow dissemination of

information across the structured subpopulation evolving inparallel Thus it maintains diversity in overall population toavoid premature convergence However it is known to berelatively slow in converging to optimal solution

Fine-grained model is also known as cellular model anddiffusion model A unique coordinate is assigned to everyindividual of the single population in some space which istypically a grid of some dimensionality with fixed or cyclicboundary Individuals can only interact within a neighbor-hood defined by neighborhood topology through variationoperatorsThe advantage of cellularmodel is slow diffusion ofinformation through overlapped small neighborhoods whichhelps in exploring the search space by maintaining betterdiversity than panmicticmodelThis in turn helps in avoidingpremature convergence [22] Moreover it is slower than acorresponding panmictic model in a given EA but is fasterthan a coarse-grained model It has less communicationoverhead than a coarse-grainedmodel as it maintains a singlestructured population rather than multiple subpopulationsevolving in parallel Further it has been shown that a cellularmodel is more effective in complex optimization tasks ascompared to the other models [23 24]

3 Quantum-Inspired Evolutionary Algorithms

Quantum-inspired proposals are subset of a much largerattempt to apply quantum models in information process-ing which is also referred to as quantum interaction [25]The potential advantages of parallelism offered by quantumcomputing [26] through superposition of basis states in qubitregisters and simultaneous evaluation of all possible repre-sented states have led to the development of approaches thatsuggest ways to integrate aspects of quantum computing withevolutionary computation [25] Most types of hybridizationhave focused on designing algorithms that would run onconventional computers and not on quantum computersand are most appropriately classified as ldquoquantum-inspiredrdquoThe first attempt was made by Narayanan and Moore [27]to use quantum interpretation for designing a quantum-inspired genetic algorithm A number of other types ofhybridization have also been proposed of which the mostpopular is the proposal made by Han and Kim [7] whichuses a Q-bit as the smallest unit of information and a Q-bitindividual as a string ofQ-bits rather than binary numeric or




1003816100381610038161003816120595⟩ = 120572 |0⟩ + 120573 |1⟩ (1)


|120572|2+10038161003816100381610038161205731003816100381610038161003816

2

= 1 (2)


[

120572119905+1

119894

120573119905+1

119894

] = [

cos (Δ120579119894) minus sin (Δ120579

119894)

sin (Δ120579119894) cos (Δ120579

119894)] [

120572119905

119894

120573119905

119894

] (3)

where 120572119905+1119894

and 120573119905+1119894
















119895(119905) In







119896 where 119896 = 1 119878PB



119896


119896 where 119896 = 1 119878PB








(a) initialize Q(t)


(c) evaluate P(t)








(j) evaluate P(t)



j = 1 SPOPSGRP


endend

Algorithm 1








119896 where 119896 = 1 119878PB



119896


119896 where 119896 = 1 119878PB





119894 where 119894 = 1 119878POP


(a) initialize Q(t)


(c) evaluate P(t)


(e) compute NL



(g) select AR(t)



(j) evaluate P(t)



endend

Algorithm 2








1to 1205798have









1to





sdot (119904

2) + 6 sdot (

119904

3)

56

58

60

62

64

66

68

70

0 5 10 15 20 25

Fitn

ess v

alue


times102






(4)







20PQEA 6860 6841 6857 6860 833 72 90917CQEA 6860 6860 6860 6860 1000 00 11517FQEA 6860 6860 6860 6860 1000 00 11383

50PQEA 117650 117601 117639 117650 767 211 142567CQEA 117650 117650 117650 117650 1000 00 49067FQEA 117650 117650 117650 117650 1000 00 44883

100PQEA 970300 970201 9702703 970300 700 461 202683CQEA 970300 970300 970300 970300 1000 00 104617FQEA 970300 970201 9702967 970300 967 181 106500

150PQEA 3307950 3307801 33078904 3307950 600 742 273033CQEA 3307950 3307801 33079252 3307950 833 565 208633FQEA 3307950 3307950 3307950 3307950 1000 00 133450

200PQEA 7880600 7880401 78805204 7880600 600 992 297233CQEA 7880600 7880401 78805801 7880600 900 607 223000FQEA 7880600 7880600 7880600 7880600 1000 00 166050

400PQEA 63521200 62847292 63425153 63521200 767 1899322 411483CQEA 63521200 63258981 63512459 63521200 967 478744 344833FQEA 63521200 63521200 63521200 63521200 1000 00 279683

600PQEA 214921800 209608152 212033464 211953199 100 14073464 499633CQEA 214921800 209881401 213598979 214385692 367 15243880 487317FQEA 214921800 214921800 214921800 214921800 1000 00 372017

800PQEA 499089026 488046846 493854763 494709763 00 28503156 500500CQEA 508810386 498371881 504276211 504764499 00 25028902 500500FQEA 510082400 510082400 510082400 510082400 1000 00 451867

1000PQEA 964320421 937999876 951762456 953408640 00 56144299 500500CQEA 979662826 948748605 969462614 972362722 00 87505108 500500FQEA 997003000 994023961 995543257 996005997 67 7703622 500100

84

86

88

90

92

94

96

98

100

102

0 200 400 600 800 1000 1200

Fitn

ess v

alue


times107






596061626364656667686970

1 11 21 31 41 51 61 71 81 91

Obj

fun

c va

lue

Generation number

PQEACQEAFQEA

PQEACQEAFQEA

times102


PQEACQEAFQEA

90

95

100

105

110

115

120

1 21 41 61 81 101 121 141

Obj

fun

c va

lue


times103



75

80

85

90

95

100

1 31 61 91 121 151 181 211 241

Obj

fun

c va

lue

times104

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


26

27

28

29

30

31

32

33

34

1 51 101 151 201 251 301 351 401 451

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number






62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



119894 divided by 119873 (as


119891119875-PEAKS( 119909) =

1

119873max1le119894le119901



165170175180185190195200205210215220

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


38

40

42

44

46

48

50

52

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number








20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






1003816100381610038161003816120595⟩ = 120572 |0⟩ + 120573 |1⟩ (1)


|120572|2+10038161003816100381610038161205731003816100381610038161003816

2

= 1 (2)


[

120572119905+1

119894

120573119905+1

119894

] = [

cos (Δ120579119894) minus sin (Δ120579

119894)

sin (Δ120579119894) cos (Δ120579

119894)] [

120572119905

119894

120573119905

119894

] (3)

where 120572119905+1119894

and 120573119905+1119894
















119895(119905) In







119896 where 119896 = 1 119878PB



119896


119896 where 119896 = 1 119878PB








(a) initialize Q(t)


(c) evaluate P(t)








(j) evaluate P(t)



j = 1 SPOPSGRP


endend

Algorithm 1








119896 where 119896 = 1 119878PB



119896


119896 where 119896 = 1 119878PB





119894 where 119894 = 1 119878POP


(a) initialize Q(t)


(c) evaluate P(t)


(e) compute NL



(g) select AR(t)



(j) evaluate P(t)



endend

Algorithm 2








1to 1205798have









1to





sdot (119904

2) + 6 sdot (

119904

3)

56

58

60

62

64

66

68

70

0 5 10 15 20 25

Fitn

ess v

alue


times102






(4)







20PQEA 6860 6841 6857 6860 833 72 90917CQEA 6860 6860 6860 6860 1000 00 11517FQEA 6860 6860 6860 6860 1000 00 11383

50PQEA 117650 117601 117639 117650 767 211 142567CQEA 117650 117650 117650 117650 1000 00 49067FQEA 117650 117650 117650 117650 1000 00 44883

100PQEA 970300 970201 9702703 970300 700 461 202683CQEA 970300 970300 970300 970300 1000 00 104617FQEA 970300 970201 9702967 970300 967 181 106500

150PQEA 3307950 3307801 33078904 3307950 600 742 273033CQEA 3307950 3307801 33079252 3307950 833 565 208633FQEA 3307950 3307950 3307950 3307950 1000 00 133450

200PQEA 7880600 7880401 78805204 7880600 600 992 297233CQEA 7880600 7880401 78805801 7880600 900 607 223000FQEA 7880600 7880600 7880600 7880600 1000 00 166050

400PQEA 63521200 62847292 63425153 63521200 767 1899322 411483CQEA 63521200 63258981 63512459 63521200 967 478744 344833FQEA 63521200 63521200 63521200 63521200 1000 00 279683

600PQEA 214921800 209608152 212033464 211953199 100 14073464 499633CQEA 214921800 209881401 213598979 214385692 367 15243880 487317FQEA 214921800 214921800 214921800 214921800 1000 00 372017

800PQEA 499089026 488046846 493854763 494709763 00 28503156 500500CQEA 508810386 498371881 504276211 504764499 00 25028902 500500FQEA 510082400 510082400 510082400 510082400 1000 00 451867

1000PQEA 964320421 937999876 951762456 953408640 00 56144299 500500CQEA 979662826 948748605 969462614 972362722 00 87505108 500500FQEA 997003000 994023961 995543257 996005997 67 7703622 500100

84

86

88

90

92

94

96

98

100

102

0 200 400 600 800 1000 1200

Fitn

ess v

alue


times107






596061626364656667686970

1 11 21 31 41 51 61 71 81 91

Obj

fun

c va

lue

Generation number

PQEACQEAFQEA

PQEACQEAFQEA

times102


PQEACQEAFQEA

90

95

100

105

110

115

120

1 21 41 61 81 101 121 141

Obj

fun

c va

lue


times103



75

80

85

90

95

100

1 31 61 91 121 151 181 211 241

Obj

fun

c va

lue

times104

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


26

27

28

29

30

31

32

33

34

1 51 101 151 201 251 301 351 401 451

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number






62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



119894 divided by 119873 (as


119891119875-PEAKS( 119909) =

1

119873max1le119894le119901



165170175180185190195200205210215220

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


38

40

42

44

46

48

50

52

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number








20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119896 where 119896 = 1 119878PB



119896


119896 where 119896 = 1 119878PB








(a) initialize Q(t)


(c) evaluate P(t)








(j) evaluate P(t)



j = 1 SPOPSGRP


endend

Algorithm 1








119896 where 119896 = 1 119878PB



119896


119896 where 119896 = 1 119878PB





119894 where 119894 = 1 119878POP


(a) initialize Q(t)


(c) evaluate P(t)


(e) compute NL



(g) select AR(t)



(j) evaluate P(t)



endend

Algorithm 2








1to 1205798have









1to





sdot (119904

2) + 6 sdot (

119904

3)

56

58

60

62

64

66

68

70

0 5 10 15 20 25

Fitn

ess v

alue


times102






(4)







20PQEA 6860 6841 6857 6860 833 72 90917CQEA 6860 6860 6860 6860 1000 00 11517FQEA 6860 6860 6860 6860 1000 00 11383

50PQEA 117650 117601 117639 117650 767 211 142567CQEA 117650 117650 117650 117650 1000 00 49067FQEA 117650 117650 117650 117650 1000 00 44883

100PQEA 970300 970201 9702703 970300 700 461 202683CQEA 970300 970300 970300 970300 1000 00 104617FQEA 970300 970201 9702967 970300 967 181 106500

150PQEA 3307950 3307801 33078904 3307950 600 742 273033CQEA 3307950 3307801 33079252 3307950 833 565 208633FQEA 3307950 3307950 3307950 3307950 1000 00 133450

200PQEA 7880600 7880401 78805204 7880600 600 992 297233CQEA 7880600 7880401 78805801 7880600 900 607 223000FQEA 7880600 7880600 7880600 7880600 1000 00 166050

400PQEA 63521200 62847292 63425153 63521200 767 1899322 411483CQEA 63521200 63258981 63512459 63521200 967 478744 344833FQEA 63521200 63521200 63521200 63521200 1000 00 279683

600PQEA 214921800 209608152 212033464 211953199 100 14073464 499633CQEA 214921800 209881401 213598979 214385692 367 15243880 487317FQEA 214921800 214921800 214921800 214921800 1000 00 372017

800PQEA 499089026 488046846 493854763 494709763 00 28503156 500500CQEA 508810386 498371881 504276211 504764499 00 25028902 500500FQEA 510082400 510082400 510082400 510082400 1000 00 451867

1000PQEA 964320421 937999876 951762456 953408640 00 56144299 500500CQEA 979662826 948748605 969462614 972362722 00 87505108 500500FQEA 997003000 994023961 995543257 996005997 67 7703622 500100

84

86

88

90

92

94

96

98

100

102

0 200 400 600 800 1000 1200

Fitn

ess v

alue


times107






596061626364656667686970

1 11 21 31 41 51 61 71 81 91

Obj

fun

c va

lue

Generation number

PQEACQEAFQEA

PQEACQEAFQEA

times102


PQEACQEAFQEA

90

95

100

105

110

115

120

1 21 41 61 81 101 121 141

Obj

fun

c va

lue


times103



75

80

85

90

95

100

1 31 61 91 121 151 181 211 241

Obj

fun

c va

lue

times104

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


26

27

28

29

30

31

32

33

34

1 51 101 151 201 251 301 351 401 451

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number






62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



119894 divided by 119873 (as


119891119875-PEAKS( 119909) =

1

119873max1le119894le119901



165170175180185190195200205210215220

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


38

40

42

44

46

48

50

52

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number








20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






119896 where 119896 = 1 119878PB



119896


119896 where 119896 = 1 119878PB





119894 where 119894 = 1 119878POP


(a) initialize Q(t)


(c) evaluate P(t)


(e) compute NL



(g) select AR(t)



(j) evaluate P(t)



endend

Algorithm 2








1to 1205798have









1to





sdot (119904

2) + 6 sdot (

119904

3)

56

58

60

62

64

66

68

70

0 5 10 15 20 25

Fitn

ess v

alue


times102






(4)







20PQEA 6860 6841 6857 6860 833 72 90917CQEA 6860 6860 6860 6860 1000 00 11517FQEA 6860 6860 6860 6860 1000 00 11383

50PQEA 117650 117601 117639 117650 767 211 142567CQEA 117650 117650 117650 117650 1000 00 49067FQEA 117650 117650 117650 117650 1000 00 44883

100PQEA 970300 970201 9702703 970300 700 461 202683CQEA 970300 970300 970300 970300 1000 00 104617FQEA 970300 970201 9702967 970300 967 181 106500

150PQEA 3307950 3307801 33078904 3307950 600 742 273033CQEA 3307950 3307801 33079252 3307950 833 565 208633FQEA 3307950 3307950 3307950 3307950 1000 00 133450

200PQEA 7880600 7880401 78805204 7880600 600 992 297233CQEA 7880600 7880401 78805801 7880600 900 607 223000FQEA 7880600 7880600 7880600 7880600 1000 00 166050

400PQEA 63521200 62847292 63425153 63521200 767 1899322 411483CQEA 63521200 63258981 63512459 63521200 967 478744 344833FQEA 63521200 63521200 63521200 63521200 1000 00 279683

600PQEA 214921800 209608152 212033464 211953199 100 14073464 499633CQEA 214921800 209881401 213598979 214385692 367 15243880 487317FQEA 214921800 214921800 214921800 214921800 1000 00 372017

800PQEA 499089026 488046846 493854763 494709763 00 28503156 500500CQEA 508810386 498371881 504276211 504764499 00 25028902 500500FQEA 510082400 510082400 510082400 510082400 1000 00 451867

1000PQEA 964320421 937999876 951762456 953408640 00 56144299 500500CQEA 979662826 948748605 969462614 972362722 00 87505108 500500FQEA 997003000 994023961 995543257 996005997 67 7703622 500100

84

86

88

90

92

94

96

98

100

102

0 200 400 600 800 1000 1200

Fitn

ess v

alue


times107






596061626364656667686970

1 11 21 31 41 51 61 71 81 91

Obj

fun

c va

lue

Generation number

PQEACQEAFQEA

PQEACQEAFQEA

times102


PQEACQEAFQEA

90

95

100

105

110

115

120

1 21 41 61 81 101 121 141

Obj

fun

c va

lue


times103



75

80

85

90

95

100

1 31 61 91 121 151 181 211 241

Obj

fun

c va

lue

times104

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


26

27

28

29

30

31

32

33

34

1 51 101 151 201 251 301 351 401 451

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number






62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



119894 divided by 119873 (as


119891119875-PEAKS( 119909) =

1

119873max1le119894le119901



165170175180185190195200205210215220

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


38

40

42

44

46

48

50

52

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number








20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










1to





sdot (119904

2) + 6 sdot (

119904

3)

56

58

60

62

64

66

68

70

0 5 10 15 20 25

Fitn

ess v

alue


times102






(4)







20PQEA 6860 6841 6857 6860 833 72 90917CQEA 6860 6860 6860 6860 1000 00 11517FQEA 6860 6860 6860 6860 1000 00 11383

50PQEA 117650 117601 117639 117650 767 211 142567CQEA 117650 117650 117650 117650 1000 00 49067FQEA 117650 117650 117650 117650 1000 00 44883

100PQEA 970300 970201 9702703 970300 700 461 202683CQEA 970300 970300 970300 970300 1000 00 104617FQEA 970300 970201 9702967 970300 967 181 106500

150PQEA 3307950 3307801 33078904 3307950 600 742 273033CQEA 3307950 3307801 33079252 3307950 833 565 208633FQEA 3307950 3307950 3307950 3307950 1000 00 133450

200PQEA 7880600 7880401 78805204 7880600 600 992 297233CQEA 7880600 7880401 78805801 7880600 900 607 223000FQEA 7880600 7880600 7880600 7880600 1000 00 166050

400PQEA 63521200 62847292 63425153 63521200 767 1899322 411483CQEA 63521200 63258981 63512459 63521200 967 478744 344833FQEA 63521200 63521200 63521200 63521200 1000 00 279683

600PQEA 214921800 209608152 212033464 211953199 100 14073464 499633CQEA 214921800 209881401 213598979 214385692 367 15243880 487317FQEA 214921800 214921800 214921800 214921800 1000 00 372017

800PQEA 499089026 488046846 493854763 494709763 00 28503156 500500CQEA 508810386 498371881 504276211 504764499 00 25028902 500500FQEA 510082400 510082400 510082400 510082400 1000 00 451867

1000PQEA 964320421 937999876 951762456 953408640 00 56144299 500500CQEA 979662826 948748605 969462614 972362722 00 87505108 500500FQEA 997003000 994023961 995543257 996005997 67 7703622 500100

84

86

88

90

92

94

96

98

100

102

0 200 400 600 800 1000 1200

Fitn

ess v

alue


times107






596061626364656667686970

1 11 21 31 41 51 61 71 81 91

Obj

fun

c va

lue

Generation number

PQEACQEAFQEA

PQEACQEAFQEA

times102


PQEACQEAFQEA

90

95

100

105

110

115

120

1 21 41 61 81 101 121 141

Obj

fun

c va

lue


times103



75

80

85

90

95

100

1 31 61 91 121 151 181 211 241

Obj

fun

c va

lue

times104

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


26

27

28

29

30

31

32

33

34

1 51 101 151 201 251 301 351 401 451

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number






62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



119894 divided by 119873 (as


119891119875-PEAKS( 119909) =

1

119873max1le119894le119901



165170175180185190195200205210215220

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


38

40

42

44

46

48

50

52

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number








20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







20PQEA 6860 6841 6857 6860 833 72 90917CQEA 6860 6860 6860 6860 1000 00 11517FQEA 6860 6860 6860 6860 1000 00 11383

50PQEA 117650 117601 117639 117650 767 211 142567CQEA 117650 117650 117650 117650 1000 00 49067FQEA 117650 117650 117650 117650 1000 00 44883

100PQEA 970300 970201 9702703 970300 700 461 202683CQEA 970300 970300 970300 970300 1000 00 104617FQEA 970300 970201 9702967 970300 967 181 106500

150PQEA 3307950 3307801 33078904 3307950 600 742 273033CQEA 3307950 3307801 33079252 3307950 833 565 208633FQEA 3307950 3307950 3307950 3307950 1000 00 133450

200PQEA 7880600 7880401 78805204 7880600 600 992 297233CQEA 7880600 7880401 78805801 7880600 900 607 223000FQEA 7880600 7880600 7880600 7880600 1000 00 166050

400PQEA 63521200 62847292 63425153 63521200 767 1899322 411483CQEA 63521200 63258981 63512459 63521200 967 478744 344833FQEA 63521200 63521200 63521200 63521200 1000 00 279683

600PQEA 214921800 209608152 212033464 211953199 100 14073464 499633CQEA 214921800 209881401 213598979 214385692 367 15243880 487317FQEA 214921800 214921800 214921800 214921800 1000 00 372017

800PQEA 499089026 488046846 493854763 494709763 00 28503156 500500CQEA 508810386 498371881 504276211 504764499 00 25028902 500500FQEA 510082400 510082400 510082400 510082400 1000 00 451867

1000PQEA 964320421 937999876 951762456 953408640 00 56144299 500500CQEA 979662826 948748605 969462614 972362722 00 87505108 500500FQEA 997003000 994023961 995543257 996005997 67 7703622 500100

84

86

88

90

92

94

96

98

100

102

0 200 400 600 800 1000 1200

Fitn

ess v

alue


times107






596061626364656667686970

1 11 21 31 41 51 61 71 81 91

Obj

fun

c va

lue

Generation number

PQEACQEAFQEA

PQEACQEAFQEA

times102


PQEACQEAFQEA

90

95

100

105

110

115

120

1 21 41 61 81 101 121 141

Obj

fun

c va

lue


times103



75

80

85

90

95

100

1 31 61 91 121 151 181 211 241

Obj

fun

c va

lue

times104

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


26

27

28

29

30

31

32

33

34

1 51 101 151 201 251 301 351 401 451

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number






62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



119894 divided by 119873 (as


119891119875-PEAKS( 119909) =

1

119873max1le119894le119901



165170175180185190195200205210215220

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


38

40

42

44

46

48

50

52

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number








20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




596061626364656667686970

1 11 21 31 41 51 61 71 81 91

Obj

fun

c va

lue

Generation number

PQEACQEAFQEA

PQEACQEAFQEA

times102


PQEACQEAFQEA

90

95

100

105

110

115

120

1 21 41 61 81 101 121 141

Obj

fun

c va

lue


times103



75

80

85

90

95

100

1 31 61 91 121 151 181 211 241

Obj

fun

c va

lue

times104

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


26

27

28

29

30

31

32

33

34

1 51 101 151 201 251 301 351 401 451

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number






62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



119894 divided by 119873 (as


119891119875-PEAKS( 119909) =

1

119873max1le119894le119901



165170175180185190195200205210215220

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


38

40

42

44

46

48

50

52

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number








20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




62

64

66

68

70

72

74

76

78

80

1 61 121 181 241 301 361 421 481 541

Obj

fun

c va

lue

times105

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


48505254565860626466

1 101 201 301 401 501 601 701 801 901

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



119894 divided by 119873 (as


119891119875-PEAKS( 119909) =

1

119873max1le119894le119901



165170175180185190195200205210215220

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times106

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


38

40

42

44

46

48

50

52

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number








20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







20PQEA 0982 0958 0970 0971 00 0006 150050CQEA 1000 0977 0988 0987 67 0007 149448FQEA 1000 1000 1000 1000 1000 0000 82393

50PQEA 0986 0956 0970 0969 00 0009 150050CQEA 0998 0956 0980 0981 00 0009 150050FQEA 1000 1000 1000 1000 1000 0000 84097

100PQEA 0986 0952 0970 0972 00 0008 150050CQEA 0999 0971 0985 0984 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 93028

500PQEA 0981 0954 0968 0968 00 0007 150050CQEA 0994 0966 0982 0983 00 0007 150050FQEA 1000 1000 1000 1000 1000 0000 95803

1000PQEA 0977 0948 0965 0966 00 0008 150050CQEA 0994 0969 0982 0984 00 0006 150050FQEA 1000 1000 1000 1000 1000 0000 94495

75

80

85

90

95

100

1 101 201 301 401 501 601 701 801 901 1001

Obj

fun

c va

lue

times107

PQEACQEAFQEA

PQEACQEAFQEA

Generation number



0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119891 (119909) = sum pt119894lowast 119909119894

(6)


sumwt119894lowast 119909119894lt 119862 (7)

where119909119894= (1199091 119909

119872)119909119894is 0 or 1 pt




119894= 0 and 119894 = 1 119872


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


0

02

04

06

08

1

12

1 301 601 901 1201 1501 1801 2101 2401 2701 3001

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number





119895= wt119895+119896119898where







pt119895= wt







10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






10

200PQEA 24222 23423 23965 24022 2140 112880CQEA 24319 23722 23991 24021 1362 127532FQEA 24322 24220 24314 24321 255 73515

5000PQEA 559926 551617 555315 555546 19857 499348CQEA 557944 550326 554411 554773 20157 498905FQEA 592810 590092 591494 591494 8066 498223

5

200PQEA 15008 14605 14804 14857 1274 139992CQEA 15108 14608 14871 14907 1348 121588FQEA 15108 15008 15104 15108 183 91160

5000PQEA 334680 328120 331565 331569 15093 499008CQEA 330892 325231 327619 327652 15249 498883FQEA 363587 359984 362343 362450 9921 498093

2

200PQEA 8398 7801 8147 8199 1828 165077CQEA 8400 7601 8154 8149 1652 172823FQEA 8400 8300 8321 8301 402 137615

5000PQEA 174665 168139 171836 171895 14620 499140CQEA 169071 162886 166073 166359 16543 498625FQEA 197443 192821 195912 196074 11185 498843

1

200PQEA 5497 4899 5285 5299 1426 291117CQEA 5497 4899 5334 5396 1394 297235FQEA 5498 5399 5484 5497 340 255655

5000PQEA 104861 101268 103519 103694 9991 498967CQEA 100787 95661 98035 98054 12262 498928FQEA 124745 122104 123315 123145 6708 499153






157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




157167177187197207217227237247257

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number

times102


36213721382139214021412142214321442145214621

1 301 601 901 1201

Obj

fun

c va

lue

times102

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




119895= 119886[wt

119895119886] The parameter 119886

8

9

10

11

12

13

14

15

16

1 301 601 901 1201

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


181

201

221

241

261

281

301

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number







1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






1000

200PQEA 10113 10095 10104 10104 53 208817CQEA 10116 10092 10105 10104 51 256945FQEA 10137 10122 10130 10131 38 165498

5000PQEA 249807 249684 249753 249750 332 491542CQEA 249723 249627 249688 249687 222 491412FQEA 250521 250395 250474 250478 317 485267

500

200PQEA 5070 5049 5060 5061 56 190365CQEA 5070 5049 5061 5061 55 198847FQEA 5091 5073 5082 5082 45 127020

5000PQEA 125028 124944 124993 124994 239 483715CQEA 125004 124929 124964 124962 203 482153FQEA 125553 125448 125504 125505 264 488277

200

200PQEA 2040 2025 2030 2028 41 238790CQEA 2040 2022 2032 2033 45 239368FQEA 2052 2034 2044 2043 47 153933

5000PQEA 50103 50040 50070 50066 194 475055CQEA 50097 50028 50059 50066 171 477915FQEA 50436 50346 50389 50390 200 485703

100

200PQEA 1023 1014 1017 1017 29 197130CQEA 1026 1014 1018 1017 27 252298FQEA 1032 1014 1023 1023 45 243558

5000PQEA 25086 25029 25060 25059 137 472835CQEA 25077 25026 25054 25053 118 471443FQEA 25329 25236 25281 25278 218 491103

3436384042444648505254

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


735

745

755

765

775

785

795

805

815

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




18

20

22

24

26

28

30

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number


30

35

40

45

50

55

60

65

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

times103

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




10055

10065

10075

10085

10095

10105

10115

10125

10135

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


249180

249280

249380

249480

249580

249680

249780

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




5015

5025

5035

5045

5055

5065

5075

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

Generation number


1244

1245

1246

1247

1248

1249

1250

1 301 601 901 1201 1501 1801

Obj

fun

c va

lue

PQEACQEAFQEA

PQEACQEAFQEA

times102

Generation number



2009

2014

2019

2024

2029

2034

2039

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number


49830

49880

49930

49980

50030

50080

1 301 601 901 1201 1501 1801 2101 2401 2701

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number














1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






1000

200PQEA 31583 30647 31180 31221 1938 119295CQEA 31587 30811 31265 31257 2060 116388FQEA 31587 31581 31586 31587 18 73537

5000PQEA 708392 697953 703964 704143 24204 499152CQEA 703183 692142 697451 696994 29457 498935FQEA 764159 758628 761728 761963 15265 498415

500

200PQEA 19049 18142 18682 18747 1962 134142CQEA 19046 18462 18772 18774 1257 138005FQEA 19049 19046 19048 19049 07 84348

5000PQEA 411918 405428 408012 407759 17533 499310CQEA 401861 393326 398180 398439 19371 498628FQEA 452412 446621 449780 449917 12961 498718

200

200PQEA 9613 9044 9413 9420 1591 214528CQEA 9621 9118 9477 9519 1380 198957FQEA 9621 9558 9611 9621 211 139205

5000PQEA 198546 194542 196730 196844 9493 498778CQEA 191986 186153 188308 188099 15303 498763FQEA 223217 219368 220820 220720 10801 498860

100

200PQEA 5802 5198 5534 5555 1524 303258CQEA 5802 5210 5591 5613 1429 318865FQEA 5802 5638 5784 5802 467 258733

5000PQEA 112605 107915 110401 110440 10364 499048CQEA 107044 102173 104741 104807 12488 498433FQEA 129271 126639 128167 128285 7365 499162

995

1000

1005

1010

1015

1020

1025

1 501 1001 1501 2001 2501 3001 3501 4001 4501

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number



24910249152492024925249302493524940249452495024955

1 301 601 901 1201

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




18

20

22

24

26

28

30

32

34

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number


415

435

455

475

495

515

535

555

575

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number



92

112

132

152

172

192

212

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


211

231

251

271

291

311

331

351

1 301 601 901 1201 1501 1801 2101 2401

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




38434853586368737883

1 201 401 601 801 1001 1201 1401 1601 1801

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number


855

875

895

915

935

955

975

1 301 601 901 1201 1501

Obj

fun

c va

lue

PQEACQEAFQEA

times102

Generation number




20

25

30

35

40

45

50

55

60

1 501 1001 1501 2001 2501 3001 3501 4001

Obj

fun

c va

lue

PQEACQEAFQEA

Generation number

times102


44

45

46

47

48

49

50

51

1 501 1001 1501 2001

Obj

fun

c va

lue

PQEACQEAFQEA

times103

Generation number






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






KP-1 CSISFLA 7475 7467 7473 7474 16FQEA 7498 7473 7494 7497 77

KP-2 CSISFLA 9865 9837 9856 9858 72FQEA 10040 10039 10040 10040 05

KP-3 CSISFLA 15327 15248 15297 15302 185FQEA 15378 15370 15375 15376 25

KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 59596 59338 59427 59409 769



5 Conclusions




KP-7 CSISFLA 60779 60264 60443 60420 1306FQEA 61831 61811 61820 61820 61

KP-14 CSISFLA 52403 52077 52267 52264 862FQEA 52538 52518 52526 52526 58

KP-19 CSISFLA 60562 60539 60549 60550 57FQEA 60570 60550 60560 60560 60

KP-24 CSISFLA 72151 72070 72112 72111 212FQEA 72232 72192 72202 72192 137

KP-29 CSISFLA 51399 51390 51396 51396 31FQEA 51405 51390 51398 51399 42

KP-34 CSISFLA 84244 84099 84175 84181 384FQEA 85090 85016 85041 85035 257




Acknowledgments


References














































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



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