Combining Extended Imperialist Competitive Algorithm with...

Research ArticleCombining Extended Imperialist CompetitiveAlgorithm with a Genetic Algorithm to Solve the DistributedIntegration of Process Planning and Scheduling Problem

Shuai Zhang Yangbing Xu Zhinan Yu Wenyu Zhang and Dejian Yu

School of Information Zhejiang University of Finance and Economics No 18 Xueyuan Street Xiasha Hangzhou 310018 China

Correspondence should be addressed to Shuai Zhang zs760914sinacom

Received 30 April 2017 Accepted 1 November 2017 Published 20 November 2017

Academic Editor Marco Mussetta

Copyright copy 2017 Shuai Zhang 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

Distributed integration of process planning and scheduling (DIPPS) extends traditional integrated process planning and scheduling(IPPS) by considering the distributed features of manufacturing In this study we first establish a mathematical model whichcontains all constraints for theDIPPS problemThen the imperialist competitive algorithm (ICA) is extended to effectively solve theDIPPS problem by improving country structure assimilation strategy and adding resistance procedure Next the genetic algorithm(GA) is adapted to maintain the robustness of the plan and schedule after machine breakdown Finally we perform a two-stageexperiment to prove the effectiveness and efficiency of extended ICA and GA in solving DIPPS problem with machine breakdown

1 Introduction

Given the increasing fluctuations of the manufacturingenvironment and the constant need to arrange the processintegrally and dynamically schemes that separately formulatethe plan and schedule no longer accord with the increasinglycomplex requirements Under these environments a modelthat settles the plan and schedule simultaneously that isintegrated process planning and scheduling (IPPS) becomesnecessary In summary the objective of IPPS is to determinean optimal schedule with machine selection for operationand operation sequence for the jobs [1] Beyond the formerstrategy IPPS considers the whole process while enhancingit in terms of dealing with the dynamic environment andmaking the theory consistent with reality

Although IPPS makes a greater degree of progress thanthe former approaches in arranging and programming themanufacturing contents the absence of distributed featureraises a dilemma for this model Against the backdrop ofdistributed production several requirements such as rawmaterial availability and transportation concerns have urgedmanufacturing companies to adopt distributed strategiesTherefore we aim to extend the IPPS and develop a more

advanced model to handle distributed planning and schedul-ing that is distributed integration of process planning andscheduling (DIPPS)

The advantage of DIPPS lies in its feature of coordinatingplanning and scheduling in a distributed environment Thusthe DIPPS is more suitable for the current manufacturingenvironment than IPPS The DIPPS is generalized as follows[2] given 119899 jobs consisting of multiple alternative producingprocesses with different operations in 119906 optional manufac-turing units (MUs) with distinct assembly techniques andequipment we must determine the plans and schedulesincluding units process plans and machines for each job byconsidering the objectives and constraints

On the other hand the robustness of plans and schedulesis of great concern through the manufacturing process Oncemachine breakdown occurs during the manufacturing theprevious plan and schedule are bound to fall short of theiranticipated objectives as a result of the changed context Inthis case an updated plan and schedule that aim to sustainthe constraints and objectives should be structured for theremaining jobs and operations

To deal with the DIPPS problem proposed in this studywe combine an extended imperialist competitive algorithm

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 9628935 13 pageshttpsdoiorg10115520179628935

2 Mathematical Problems in Engineering

(EICA) and a genetic algorithm (GA) together Furthermorethe EICA is utilized to generate plans and schedules thatare implemented before the emergency takes place whileGA is reserved to handle arrangements once a machinebreakdown occurs The traditional imperialist competitivealgorithm (ICA) that simulates competition among empireshas a strong global exploration capability in solving the NP-hard problems In this study we extend the ICA by improvingits country structure assimilation strategy and adding aresistance procedure The EICA has been proved as a moreeffective and efficient algorithm by comparing it with GAand traditional ICA in solving DIPPS problem whereas forGA as a mature and populated evolutionary algorithm itscapability in manufacturing practice has been studied andproved in our previous works [3 4] and many other studiesHere because of the advantage of its structural similarity withEICA and mature application in dealing with planning andscheduling theGA can be easily formulated by implementingthe structure from EICA it therefore responds excellently tothe breakdown emergency and alters the plan and scheduleinto satisfactory states

The remainder of this paper is organized as follows InSection 2 the works relating to ICA and robustness arebriefly introduced In Section 3 amathematicalmodel for theDIPPS problem is established In Section 4 the imperialistcompetitive algorithm is extended to effectively solve theDIPPS problem In Section 5 the GA is adapted to deal withmachine breakdown In Section 6 a two-stage experiment ispresented to prove the effectiveness and efficiency of EICAand GA to solve DIPPS problem in the case of a machinebreakdown Section 7 presents our conclusions

2 Related Work

21 Evolutionary Algorithms GA is an algorithm to searchfor the optimal solution by simulating the natural evolutionprocess And there are some well-known evolutionary algo-rithms inspired by GA such as biogeography based opti-mization [5 6] and genetic swarm optimization [7] In ourprevious work we used GA to optimize the DIPPS in fuzzyenvironment [8] Besides the wide application of GA thereare some other evolutionary algorithms that have been usedfor solving optimization problem For example Rahmat-Samii et al [9] used PSO for antenna design optimizationDorronsoro et al [10] used evolutionary algorithm to modeland solve minimization problems Grimaccia et al [11] usedsocial network optimization to design generators for vehicleenergy harvesting

In addition ICA is a metaheuristic algorithm inspiredby sociopolitical ideology and first proposed by Atashpaz-Gargari and Lucas [12] Generally there are always com-petitions when numerous countries exist By means of warand conquest some powerful countries called imperialistsconquer and colonize others forming empires As time goesby the imperialists assimilate their colonies and conquercolonies belonging to other ones In contrast weaker empiresgradually lose their colonies to more powerful ones andeventually face extinction At the end of competition thereis an ideal state in which the most powerful empire conquers

all lands By simulating the competition above the ICAinnovatively structures its procedure to solve a variety ofoutstanding problemsThrough the last several years severalsignificant works [13ndash15] have sought to strengthen the globalexploration power in order to broaden its application

Since being proposed the ICA has gained popularity andachieved significant performance in solving manufacturingplanning and scheduling problems To settle the optimizationof process planning with various flexibilities Lian et al [16]utilized the ICA to find promising solutions with reasonablecomputational cost under the objective of minimizing totalweighted sum of manufacturing cost Shokrollahpour etal [17] and Seidgar et al [18] both exploited the ICA inassembly flow shop problem while respectively using theTaguchi method and neural network as their own tools inregulating the parameters Additionally in the no-wait two-stage hybrid flow shop Moradinasab et al [19] introduced anew procedure called global war in ICA to avoid the localoptima This step helps to transfuse some new empires ina certain extent and achieves desirable performance in theexperiment In addition in the work of Zhou et al [20] ICAwas adopted to deal with the assembly sequence planningCompared with GA and PSO the ICA performs better inthe experiment and the quality of result is less related tothe initial populations Moreover Madani-Isfahani et al [21]presented an ICA to solve a biobjective unrelated parallelmachine scheduling problemwhere setup times are sequencedependent

Despite the achievements in the specific domain ofmanufacturing arrangement infrequent work has been doneto settle IPPS problems let alone for DIPPS problems Tothe best of our knowledge only Lian et al [22] have appliedthe ICA to solve IPPS while omitting the disposition ofrobustness The scarce adoption of ICA in this area is notcontrary to our expectations Because IPPS and even DIPPSproblem have far more variables and constraints to deal withthey inevitably contain a high magnitude of informationto manage The complexity of simultaneous planning andscheduling also predisposes the process of measure searchingto be handled delicately

22 Robustness Under the constantly changing conditions ofmanufacturing static and unchangeable plans and schedulesare impractical When the initial plans and schedules are putinto effect machine breakdown may take place and disturbthe manufacturing procedure in an uncontrollable way thatinvalidates the former arrangement To keep plans andschedules robust and flexible some extra work is essential

Among the methods applied for replanning andrescheduling right-shifting is the most convenient wayThis corresponds to waiting for the breakdown to be fixedand then carrying on with the work [23] For instance Liuet al [24] used right-shift rescheduling to retain the samesequence of all remaining jobs as that of the predictiveschedule Although this method saves quite a lot of follow-upwork it loses the optimality of planning and scheduling atthe same time Therefore other means have been figuredout Saygin and Kilic [25] adopted a step-by-step mannerby dividing the whole scheduling period into shorter

Mathematical Problems in Engineering 3

periods and proceeding by overlapping the schedule ofeach period on the previous one to handle the effect ofchanges like breakdowns Jensen [23] proposed a newway of creating robust and flexible solutions for job-shopscheduling problems by busing a robustness measure basedon a neighborhood for schedules Additionally Hasan et al[26] used shifted gap-reduction instead of right-shifting inorder to minimize the effect of interruptions in job-shopscheduling problem

When selectingmethods for dealing withmachine break-down in scheduling and planning the focal points should betargeted at convenience and optimization where the formerpoint pays attention to the adjustment time of replanningand rescheduling while the latter one is concerned with theoptimality of replanning and rescheduling In this study GAis associated with solving the machine breakdown Becauseof the similarity of EICA and GA in representation GA canbe structured and put into work promptly once breakdowntakes place and GA is more effective than ICA in solvingthe problem with small solution space In addition withabundant verification preformed in previous works for IPPSproblems it has a positive reputation for strong and reliableperformance

3 The Mathematical Model forthe DIPPS Problem

As defined in the Introduction DIPPS aims to determinean appropriate manufacturing unit (MU) while selecting theprocess plans and schedules for jobs The so-called MUsare some geographically dispersed units contained in anintegral factory system that have the capability to operateindependently In the DIPPS problem on which we focus inthis study each MU can process all types of jobs that needto be treated However because of the multifarious assemblytechniques and equipment necessitated by differences inconstruction year and purposes among MUs the respectiveoptional process plans and machines are totally differentBased on this situation the arrangement should be settledcautiously Furthermore owing to geographical dispersionthe transportation time for the finished work from MUs tothe central factory is also a significant concern in the courseof scheming

To examine the optimality and rationality of the planand schedule we formulate the relevant objectives and con-straints before formulating them the corresponding indexesare expounded as follows

119880 the quantity of MU119873 the quantity of job

119875119899119906 the quantity of plans of the 119899th job in the 119906thMU

119869119899119906119901 the quantity of operations of the 119901th plan of 119899thjob in the 119906th MU

119872119906 the quantity of machines in the 119906th MU119900119899119906119901119895119898 the 119895th operation of the 119901th plan of the 119899th jobprocessed by the119898th machine in the 119906th MU

it119899119906119901119895119898 the initial time of 119900119899119906119901119895119898it11989911990611990110158401198951015840119898 the initial time of any other operation pro-cessed on the same machine as 119900119899119906119901119895119898ot119899119906119901119895119898 the operating time of 119900119899119906119901119895119898 which contains thesetup time

119900ct119899119906119901119895119898 the completion time of 119900119899119906119901119895119898119895ct119899119906 the completion time of the 119899th job in the 119906thMU

tt119899119906 the transportation time of the 119899th job from the119906th MU to central factory

119883119899119906 the binary variable with 1 representing that the119899th job assigned to the 119906th MU and 0 otherwise

In order to evaluate the excellence of methods for theDIPPS an objective is formulated

Objective Minimize the total makespan 119892tms that is mini-mize the period of time from the very beginning of processingto the end of transportation

119892tms = max119906isin[1119880]

max119899isin[1119873]

[119883119899119906 sdot (119895ct119899119906 + tt119899119906)] (1)

Meanwhile the following constraints are required for the sakeof rationality

Constraint 1 Only one job can be assigned to a single MU

119880

sum119906=1

119883119899119906 = 1 119899 isin [1119873] (2)

Constraint 2Once an operation is under processing no otheroperations can cut in

119900ct119899119906119901119895119898 = it119899119906119901119895119898 + ot119899119906119901119895119898

119899 isin [1119873] 119906 isin [1 119880] 119901 isin [1 119875119899119906] 119895 isin [1 119869119899119906119901 ] 119898 isin [1119872119906] (3)

Constraints 3 Parallel processing for more than one job is notallowed on any machine

it11989911990611990110158401198951015840119898 notin (it119899119906119901119895119898 119900ct119899119906119901119895119898) 119899 isin [1119873] 119906 isin [1 119880] 119901amp1199011015840 isin [1 119875119899119906] 119895amp1198951015840 isin [1 119869119899119906119901 ] 119898 isin [1119872119906] (4)


S [2 25][3 17]

1 [2 23][3 26][4 21]

2

[1 10][4 21]

3 [2 21][4 11]

5

[1 13][3 16]

6

[1 27][2 22]

4

[2 17][3 20]

7

E[1 14][3 16][4 19]

8

S [2 22][3 25]

1[1 18][2 15]

[4 19]

2 [1 29][4 24]

3

[3 17][4 13]

4

[2 12][4 11]

5E[1 15][2 24]

[3 17]

6

S

[2 20][4 24]

1

[1 17][3 15]

2

[1 21][2 27]

5

[1 21][3 28]

3

[2 25][3 22]

4

[3 15][4 10]

6

[2 13][4 11]

7

E[1 14][2 17][3 19]

8

Job 1

Job 2

Job 3

S

[2 17][4 12]

1

[3 13][5 22]

2

[4 18][5 15]

3

[2 14][3 19]

4

[1 25][3 29]

5

[1 24][2 27][3 28]

6

[1 13][5 10]

7

[1 19][4 21]

8

[1 13][2 25]

9E

S [2 23][4 24][5 20]

1[1 19][3 13]

2

[2 17][3 15]

3

[2 27][5 21]

4

[4 22][5 26]

5 [2 15][3 11]

7

[1 13][4 12]

8

[3 17][4 10]

6

E

S [2 27][5 23]

1[4 14][5 18]

2

[1 16][3 19]

3[2 25][3 22]

4 [1 15][4 20]

5

E

Operation

Machine

Operating time

Branch point

Rank 1

Rank 2

[1 14][2 12][3 17]

6

Job 1

Job 2

Job 3

MU 1 MU 2

Rank 1

Rank 1

Rank 2

Rank 2

Rank 2

Rank 2

Rank 2

Rank 2Rank 1

Rank 1

Rank 1

Figure 1 Representation of plans and schedules in MU 1 and MU 2

Constraint 4 The operating sequence of operations of aspecific job cannot be altered once determined

it119899119906119901(119895+1) minus 119900ct119899119906119901119895 ge 0119899 isin [1119873] 119906 isin [1 119880] 119901 isin [1 119875119899119906] 119895 isin [1 119869119899119906119901 ] (5)

In this study with a goal of simplifying the resolvingprocess a simplified example containing two independentMUs and three jobs is structured For the purpose of rep-resenting alternative plans and machines for different jobsand operations in diverse MUs a directed acyclic graph(DAG) is adopted hereThe traditionalDAGcontains verticesand directed edges and is applied throughout mathematicscomputer science and engineering with the capability toclearly represent processes In this study we extend the DAGwith more features to illustrate the information visually andprepare for the subsequent calculation

Specifically Figure 1 exhibits alternative plans and sched-ules for different jobs through different MUs Take the firstDAG in Figure 1 which shows Job 1 alternative plans andschedules in MU 1 for example each vertex and directededge stands for the operation and the processing trendrespectively The black dots named ldquobranch pointsrdquo areattached in the DAG to represent the branch informationthat will be used in the construction of EICA To clarify thestart and end of the plan two virtual operations withoutany operating time labeled ldquoSrdquo and ldquoErdquo are set With regardto valid operations that is the vertices except the starting

and the ending ones each of them represents the optionalmachine number and respective operating times by data setsTracking alongwith the directed edges from the ldquoSrdquo operationto the ldquoErdquo operation without any backtracking one specificplan with a certain sequence and corresponding operationsis determined

4 EICA for the DIPPS Problem

The traditional ICA is introduced in Section 21 Here weillustrate how to extend the traditional ICA to solve theDIPPS problem effectively

41 Country Structure and Initialization The first step ofEICA is to generate the initial population referred to as coun-tries of ICA To clearly represent the information betweenMU plan and operation we devise a three-segment countrystructure (Figure 2)

Generally the first segment represents the MUs whereeach job is assigned The second segment represents theldquobranch informationrdquo The ldquobranch informationrdquo is the spe-cific directed edge that a job selects in each branch pointReferring back to each DAG in Figure 1 we first rank thebranch points individually and assign the former branchpoints higher rankings whereas equivalent-level branchpoints get the same rank From left to right the rank declinesThe upper the branch chosen by the plan the smaller thenatural number assigned to the position For example in this


1

23

11

32

32

21

23

12

13

31

13

12

21

23

1

1 21

2 12

1 11

Job 1

Job 2

Job 3

MU Plan

2

1

OperationJob number

Sequenced machine number

Figure 2 Three-segment country structure in EICA

instance there are up to two branches so the position willbe set as ldquo1rdquo if the upper branch is chosen otherwise it willbe set as ldquo2rdquo By this means when all the branch directionsare decided the plan is fully determined When consideringthe rank number discrepancy of the same job in differentMUs the length of the second segment for a specific job isthe maximum rank number among all MUs and the invalidposition will be omitted in the course of decoding After theabove steps the second segment of the country structurewhere one position represents a branch of the same level isformulatedThus the first two segments form a complete planfor every job

In the third segment we blend the schedules of differentjobs for convenience and every column of this segmentrepresents an operation with the corresponding job numberand machine labeled inside Meanwhile the column of eachjobrsquos operation in this segment manifests its order of prece-dence in processing and its proximity to the left indicateshigher priority The length of this segment is the productof multiplying job quantities by the operation quantities ofthe longest plan among all possible plans For example theexample here has three jobs and the longest plan fromFigure 1consists of five operations thus the third segment here has15 columns Similar to the second segment when the chosenplan has fewer operations than its own maximum one theremaining position will be neglected in the decoding Toavoid illegal schedules in the course of algorithm applicationcandidate machine numbers of an operation are resequencedfrom the lowest one to ldquosubstituted numberrdquo sequenced fromldquo1rdquo For example in Figure 1 Job 3 first operation in MU1 can choose Machines 2 and 4 Therefore the sequencedldquosubstituted numbersrdquo used in the position are 1 and 2

For the purpose of decoding the structure to determinethe specific schedules three strategies explained by Bierwirthand Mattfeld [27] that is active schedule semiactive sched-ule and nondelay schedule are commonly used In this studywe adopt the active schedule

After the countries that is the populations are initializedthe next step is to divide them into imperialists and coloniesand then structure empires Given 119865pop countries 119865impcountries with the most power are selected as imperialistsand the remaining 119865col countries are classified as coloniesaffiliated with imperialists Here we convert the power of Vthcountry into cost 119888V that is the total makespan 119892tms of it (alsoknown as the fitness value) The lower the cost for a countrythe higher its potential to become an imperialist

119888V = 119892Vtms V isin [1 119865pop] (6)

In the subsequent process of determining how manyand which colonies each imperialist owns the cost 119888119890 of 119890thimperialist is transformed into the normalized cost 119862119890

119862119890 = max119894isin[1119865imp]

119888119894 minus 119888119890 119890 isin [1 119865imp] (7)

The normalized power pwr119890 of 119890th imperialist can becalculated as follows

pwr119890 = 119862119890sum119865imp119894=1 119862119894

(8)

Generally the quantity of colonies each imperialist occu-pies is proportionate to its normalized power that is withgreater power come more colonies The initial number NC119890of colonies belonging to the 119899th imperialist is

NC119890 = round pwr119890 sdot 119865col (9)

The colony number of every imperialist is thus workedout and we randomly distribute the corresponding quantityof colonies to the imperialist When the distribution iscomplete the structure of our empires becomes explicit

42 Assimilation Once an imperialist occupies its coloniesand composes its empire it attempts to promote the powerof its affiliated colonies by assimilating them In this stepthe colonies approach the imperialist in a certain form andhave the chance to become more powerful Particularly weimplement a novel assimilation strategy here to transmit apart of the structure of the imperialist to the colonies so asto not only achieve assimilation but also adjust the originalplan and schedule to avoid local optimaThe detailed processis listed as follows (Figure 3)

Step 1 Designate a colony for assimilation and randomlyselect a job (eg Job 2) and ascertain its plan and scheduleinformation in the imperialist

Step 2 Pass down the MU and plan of the selected job in theimperialist that is the corresponding information of this jobin the first two parts to replace the former MU and plan ofthe same job in the colony (denoted by the bold line with anarrow)

Step 3 Randomly select a job in the colony If the job isdifferent from the formerly selected one (eg Job 3) firsttransmit its operations to the positions of the former selectedjobrsquos operations in sequence (denoted by thin lines witharrows) otherwise do nothing


12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

22

11

23

11

32

21

11

32

21

31

12

31

22

12

2 12

1 11

1 12

2 21

2 11

32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

Imperialist

Colony

New colony

21

30

21

Figure 3 Assimilating the colony into imperialist

32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

32

12

32

12

23

31

12

22

31

21

11

22

30

13

2 11

2 12

2 11

Old colony

New colony

21

21

Figure 4 Resisting operation of EICA

Step 4 Transmit the operations of the selected job in Step 1of imperialist to the positions of the latter selected job in thethird part of colony while keeping them in the same order asin the imperialist (denoted by dotted lines with arrows)

43 Resistance In the real world when weak countries areconquered as colonies of more powerful countries some ofthem will make an attempt to resist the domination of theiroccupier by counteracting the assimilation of the imperialistTo broaden the search coverage and prevent a fall into localoptima resistance procedure is added to EICA To allow forthe turbulence of the resisting action we limit the applicationof this step within one job And in this study we set theresistance rate as 005 for each country The concrete processof resistance in this study (Figure 4) is to randomly select ajob and alter the corresponding three parts randomly

44 Position Exchanges After the action of the previous twoparts the costs of the colonies are alteredThere alsomay exista colony whose cost is lower than any other country in itsempire (including the imperialist and colonies) When thissituation occurs the position between the lowest-cost colonyand the imperialist exchanges which means the lowest-costcolony becomes the new imperialist and the former one isrelegated to its vanquished colony In the next assimilation

process other colonies also begin to move towards the newimperialist

45 Competition The competition part indicates the struggleamong imperialists for the colonies of weaker empires Intraditional ICA the strongest empire will take over theweakest colony in the weakest empire However the selectedcolonywill not always be theweakest inwhole country In thisstudy the strategy of elite replacement is introduced into thecompetition which means the strongest imperialist will takeover the weakest country as its colony in every generation Ifthere is only one empire this process will be skipped

46 Elimination and Stop Criterion When an empire isweak enough to cross a certain threshold it moves towardscollapse Its colonies will all be divided and occupied by otherempires and the whole empire is thus eliminated In thisstudy the elimination condition is triggered when an empireloses every colony it owns

In an ideal state all other empires will be eliminated andonly one will survive under the condition that the imperialistand its colonies all have the same cost after repeating theprocess of assimilation and elimination a certain number oftimes However this convergence is too rare to expect underthe practical circumstances Therefore the stop criterion


Job 3 (20)

Job 1 (17)

Job 1 (21)

Job 3 (21)

Job 1 (22)

Job 1 (14)

Job 3 (19)

20 40 60017 (machine 4 breaks down)

Time

Operating time

13

12

31

33

11

Mac

hine

12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

2 12

1 11

21

4

3

2

1

Figure 5 Gantt chart and the chromosomal structure for rescheduling

usually adopts preset iterations or stabilization of the averagefitness values among several generations

5 GA for Machine Breakdown

Machine breakdown occurs occasionally in the course ofa production process and can send the plan and scheduleinto disarray due to the time and cost required for repairIn this study we adapt the GA to reschedule the undoneoperations when breakdown happens Benefiting from thesimilar structure of EICA and GA and the powerful globalexploration capability of the latter algorithm the GA can beeasily formulated by utilizing the structure from EICA ittherefore responds to the breakdown emergency excellentlyand gives consideration to the reschedule with both efficiencyand effectiveness Before elaborating upon the application ofGA the following assumptions and prerequisites are posited

(1) When machine breakdown occurs the remainingoperating time of the operation that is processing on thebroken machine at that time will consequently be discrepantIf the operation waits on the machine to be repaired andresumes immediately after the recovery then it only needsto process the undone part However if the operation istransferred to another machine or it stays on the samemachine but is not the first processed operation after thebreakdown then the process begins fully anew

(2) The machine breakdown will not disturb the currentprocessing operations on other machines

(3) Considering the transportation time and cost theundone operations cannot be rescheduled to any other MU

(4) If the breakdown occurs in the MU where theremaining operations belong to only one job thenGA is of nouse The rescheduling procedure for this exceptional case isto find the shortest-time-costingmachine for each remainingoperation and then compare the changed plan with the right-shifting plan and choose the better one of the two

51 Initialization The remarkably similar structure betweenthe country and the chromosome makes it possible to formthe initial structure on the basis of the third segment of thecountry (Figure 5) The length of the chromosome that isthe number of genes is in accordance with the quantity ofincomplete operations To preserve the excellence and keepin constancy with the former plan and schedule one ofthe initial chromosomes is directly abstracted from the bestcountry in the last generation while the rest are randomlygenerated

52 Fitness Function and Reproduction Because the resched-uled operations are part of the whole DIPPS to calculate thefitness value of the chromosome and verify the excellenceof the revised schedule the chromosome should be broughtback to the structure of the lowest-cost country and weshouldmeasure the change in cost In other words the fitnessfunction adopted here is the cost of the country

In this study we employ a tournament selection schemefor the reproduction of the chromosome In tournamentselection a number of individuals are selected randomly(dependent on the tournament size typically between 2 and7) from the population and the individual with the best fitnessis chosen for reproduction [28]

53 Crossover and Mutation In the crossover operation weadapt the following strategy (Figure 6)

Step 1 Randomly select two parents from the generation andinitialize two empty offspring

Step 2 Randomly select several jobs (for an even number ofjobs it is 1198732 and for an odd number of jobs it is ((119873 minus1)2)) from jobswhere the unfinished operations belong thenduplicate those jobsrsquo operations from P1 and P2 to the sameposition of O1 and O2 respectively


Table 1 The transportation time fromMU to central factory

MU JobJob 1 Job 2 Job 3 Job 4

MU 1 34 27 36 40MU 2 43 29 25 43

13

12

31

33

11

13

12

32

31

11

32

12

31

11

13

31

12

33

11

13

13

12

31

33

11

P1

P 1

O2

O1

P2

Figure 6 Crossover operation

1

31

23

23

11

1

1

31

23

13

11

1

O1

O1

Figure 7 Mutation operation

Step 3 The remaining genes of P1 and P2 are copied to thesame positions in O2 and O1

Tomutate the chromosome the rapid one-pointmutationis applied here by randomly selecting an operation and thenchanging its sequenced machine number (Figure 7)

6 Experiment

In this section a case study that is simulated based on thereal DIPPS environment is implemented to prove the effec-tiveness of EICA and GA in solving the DIPPS problem withmachine breakdownThe experimental software is developedin the C programming language and implemented on apersonal computer withWindows 7 64-bits an Intel (R) Core240GHz and 4GB RAM

To conduct the experiment we construct a case thatcontains four jobs and two independent MUs The represen-tations of transportation time and plans and schedules indifferent MUs are illustrated in Table 1 and Figures 8 and 9

61 EICA for DIPPS In this section the EICA is appliedto solve the specific DIPPS problem we preestablished Aswe explained in Section 46 the ideal convergence where

Table 2 The partial evolutionary results of EICA

Rank Minimum total makespan Average total makespan(1) 116 14157(2) 118 14891(3) 119 14169(4) 119 14823(5) 120 14062

all other empires move towards elimination and only onesurvives rarely happens in practical circumstances Conse-quently we set another two stop criteria here the iterationstops once either of them is satisfied (1) achieve the maximalgeneration which is set at 300 (2) the relative difference ofaverage costs between two contiguous generations is nomorethan 0005 within four consecutive generations

Because of the stochasticity of evolutionary algorithmswe run EICA 30 times independently and rank them accord-ing to their minimum total makespan values Because of thelimitation of space Table 2 exhibits the partial evolutionaryresults Figure 10 exhibits the evolutionary trajectories ofEICA for the best oneThe blue line and the red line representthe evolution trajectories of average total makespan andminimum total makespan respectively

The best solution after the adoption of EICA is shown inFigure 11 the total makespan of this plan and schedule is 116

We run ICA and GA 30 times and rank them accordingto their minimum total makespan value respectively Table 3exhibits the partial evolutionary results Figure 12 exhibits theevolutionary trajectories of EICA GA and traditional ICAfor the best one respectivelyThe red line black line and pur-ple line represent the evolution trajectories of minimum totalmakespan of EICA traditional ICA and GA respectively

62 GA for Machine Breakdown Through the former stageof the experiment the applicable solution is found by EICAand shown in Figure 11 In the solution Job 1 and Job 4 areprocessed in MU 1 while Job 2 and Job 3 are processed inMU 2 To test and verify the capability of GA to reschedulethe undone operations when machine breakdown occurswe artificially construct two random machine breakdownscenarios for each MU Here in order to measure theinfluence of machine breakdown for single MU the criterionis set as makespan 119891119906119898119904 that is the completion time of the lastoperation in the corresponding MU

119891119906ms = max (119883119899119906 sdot 119895ct119899119906) 119899 isin [1119873] 119906 isin [1 119880] (10)

In this case every generation has 20 chromosomes whilethe crossover and mutation rates are set as 085 and 005respectively Because the search coverage is smaller thanthe former part the GA will terminate when the algorithmachieves the maximal generation And the maximal genera-tion is set at 30

Table 4 shows the information of the breakdownmachines In this experiment we compare GA ICA and


Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan

Averagetotalmakespan

Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E

Figure 8 The representation of four jobsrsquo plans and schedules in MU 1

Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E


AvgTotalMSMinTotalMS

100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation

Figure 10 Evolutionary trajectories of EICA

right-shifting method to get the rescheduling results We runGA and ICA 30 times independently and rank them accord-ing to their minimum total makespan value respectively

Table 5 shows the partial evolutionary results Figures 13(andashd)exhibit the minimum makespan evolutionary trajectories ofGA and ICA for the best one in four cases respectively Theblack line and green line represent the evolution of minimummakespan of GA and ICA respectively The correspondingresults are shown in Table 6 In all four cases theGA generatesmuch better reschedules than the ICA and the right-shiftingplan

63 Robustness Because there exist no benchmarks ofDIPPS we simulate the real DIPPS environment to assessthe optimization capability of EICA In this study we assumethat each operation can randomly select the machine andthe maximum number of machines in the MU is six Wealso assume that the operation time of each machine in anoperation ranges from one to fifty and the transportationtime from MU to central factory ranges from twenty tofifty We do the independent experiments five times andthe average minimum makespan is obtained through GA


Table 4 Machine breakdown information

ID InformationMU Breakdown machine The moment of breakdown Time for repair

(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35

Table 5 The partial evolutionary results of GA and ICA

ID GA ICAMinimum total makespan Average total makespan Minimum total makespan Average total makespan

(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1

Figure 11 Best solution found by EICA

Table 6 Rescheduling results of three methods

Method ID(a) (b) (c) (d)

Right-shifting 101 100 98 110ICA 70 66 69 85GA 69 63 64 79

Table 7 The average minimum makespan obtained by GA andEICA

Experiments GA EICAExperiment a 13023 12700Experiment b 14443 13943Experiment c 13240 12533Experiment d 11663 11373Experiment e 11490 11857

and EICA respectively GA and EICA are run 30 times ineach experiment respectively and the average minimummakespans are exhibited in Table 7 According to Table 7 theproposed EICA performs better than GA in four out of fiveexperiments which strongly prove the EICA is an effectivealgorithm for DIPPS

ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation

Figure 12 Comparisons of evolutionary trajectories of minimummakespan using three algorithms

7 Conclusion

In this study theDIPPSmodel that aims to determine processplans and schedules while selecting the appropriate MUfor jobs is first constructed In contrast with the IPPS theDIPPS discussed here considers the distributed environmentof manufacturing which increases the area of the search


GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA

Figure 13 Comparisons of evolutionary trajectories of minimum makespan using GA and ICA

domain To effectively solve the DIPPS problem and findan optimal or near-optimal plan and schedule the ICA isextended by improving country structure assimilation strat-egy and adding resistance procedure Additionally becauseof the inevitability of machine breakdown in manufacturingprocesses the GA that not only possesses strong globalexploration capability but also has the chromosome whosestructure can be easily extracted from the country structurein EICA is adapted to maintain robustness

To verify the ability of EICA and GA we conduct atwo-stage experiment In the first stage the EICA withoutconsidering machine breakdown is applied in a case withfour jobs and two MUs in the second stage the GA istested through four machine breakdown cases The results ofthis two-stage experiment demonstrate the effectiveness andefficiency of extended ICA andGA in solvingDIPPS problemwith machine breakdown

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

The work has been supported by National Natural Sci-ence Foundation of China (no 51475410 no 51375429)and Zhejiang Natural Science Foundation of China (noLY17E050010)

References

[1] C Moon J Kim and S Hur ldquoIntegrated process planningand scheduling with minimizing total tardiness in multi-plantssupply chainrdquoComputers and Industrial Engineering vol 43 no1-2 pp 331ndash349 2002

[2] S Zhang Z N Yu W Y Zhang D J Yu and D P ZhangldquoDistributed integration of process planning and schedulingusing an enhanced genetic algorithmrdquo International Journal ofInnovative Computing Information amp Control vol 11 no 5 pp1587ndash1602 2015

[3] W Y Zhang S Zhang M Cai and J X Huang ldquoA newmanufacturing resource allocation method for supply chainoptimization using extended genetic algorithmrdquo InternationalJournal of Advanced Manufacturing Technology vol 53 no 9-12 pp 1247ndash1260 2011


[4] J Wu W Y Zhang S Zhang Y N Liu and X H Meng ldquoAmatrix-based Bayesian approach for manufacturing resourceallocation planning in supply chainmanagementrdquo InternationalJournal of Production Research vol 51 no 5 pp 1451ndash1463 2013

[5] D Simon ldquoBiogeography-based optimizationrdquo IEEE Transac-tions on Evolutionary Computation vol 12 no 6 pp 702ndash7132008

[6] H P Ma D Simon P Siarry and M R Fei ldquoBiogeography-based optimization a 10-year reviewrdquo IEEE Transactions onEmerging Topic in Computational Intelligence vol 1 no 5 pp391ndash407 2017

[7] F GrimacciaMMussetta P Pirinoli andR R Zich ldquoGeneticalswarm optimization (GSO) a class of population-based algo-rithms for antenna designrdquo inProceedings of the 1st InternationalConference on Communications and Electronics pp 467ndash471Hanoi Vietnam 2006

[8] S Zhang Z N Yu W Y Zhang D J Yu and Y B Xu ldquoAnextended genetic algorithm for distributed integration of fuzzyprocess planning and schedulingrdquo Mathematical Problems inEngineering vol 2016 no 3 pp 1ndash13 2016

[9] Y Rahmat-Samii D Gies and J Robinson ldquoParticle swarmoptimization (PSO) a novel paradigm for antenna designsrdquoUrsiRadio Science Bulletin vol 76 no 3 pp 14ndash22 2017

[10] B Dorronsoro P Ruiz G Danoy Y Pinge and P BouvryEvolutionary algorithms for mobile ad hoc networks WileyPublishing 2014

[11] F Grimaccia G Gruosso M Mussetta A Niccolai and RE Zich ldquoDesign of tubular permanent magnet generatorsfor vehicle energy harvesting by means of social networkoptimizationrdquo IEEE Transactions on Industrial Electronics no99 p 1 2017

[12] E Atashpaz-Gargari and C Lucas ldquoImperialist competitivealgorithm an algorithm for optimization inspired by imperial-istic competitionrdquo IEEE Congress on Evolutionary Computationpp 4661ndash4667 2007

[13] H Bahrami M Abdechiri and M R Meybodi ldquoImperialistcompetitive algorithmwith adaptive coloniesmovementrdquo Inter-national Journal of Intelligent Systems amp Applications vol 4 no2 pp 49ndash57 2012

[14] J L Lin H C Chuan Y H Tsai and C W Cho ldquoImprovingimperialist competitive algorithm with local search for globaloptimizationrdquo in Proceedings of the Asia Modelling Symposiumpp 61ndash64 2013

[15] A Marto M Hajihassani D Jahed Armaghani E TonnizamMohamad and A M Makhtar ldquoA novel approach for blast-induced flyrock prediction based on imperialist competitivealgorithm and artificial neural networkrdquo Scientific World Jour-nal vol 2014 Article ID 643715 11 pages 2014

[16] K Lian C Zhang X Shao and L Gao ldquoOptimization ofprocess planning with various flexibilities using an imperialistcompetitive algorithmrdquo The International Journal of AdvancedManufacturing Technology vol 59 no 5-8 pp 815ndash828 2012

[17] E Shokrollahpour M Zandieh and B Dorri ldquoA novel impe-rialist competitive algorithm for bi-criteria scheduling of theassembly flowshop problemrdquo International Journal of Produc-tion Research vol 49 no 11 pp 3087ndash3103 2011

[18] H Seidgar M Kiani M Abedi and H Fazlollahtabar ldquoAnefficient imperialist competitive algorithm for scheduling in thetwo-stage assembly flow shop problemrdquo International Journal ofProduction Research vol 52 no 4 pp 1240ndash1256 2014

[19] N Moradinasab R Shafaei M Rabiee and P RamezanildquoNo-wait two stage hybrid flow shop scheduling with genetic

and adaptive imperialist competitive algorithmsrdquo Journal ofExperimental amp Theoretical Artificial Intelligence vol 25 no 2pp 207ndash225 2013

[20] W Zhou J Yan Y Li C Xia and J Zheng ldquoImperialist compet-itive algorithm for assembly sequence planningrdquo InternationalJournal of AdvancedManufacturing Technology vol 67 no 9-12pp 2207ndash2216 2013

[21] M Madani-Isfahani E Ghobadian H Iranitekmehdash RTavakkoli-Moghaddam and M Naderi-Beni ldquoAn imperial-ist competitive algorithm for a bi-objective parallel machinescheduling problem with load balancing considerationrdquo Inter-national Journal of Industrial Engineering Computations vol 4no 2 pp 191ndash202 2013

[22] K L Lian C Y Zhang L Gao and X Y Li ldquoIntegrated processplanning and scheduling using an imperialist competitivealgorithmrdquo International Journal of Production Research vol 50no 15 pp 4326ndash4343 2012

[23] M T Jensen ldquoGenerating robust and flexible job shop schedulesusing genetic algorithmsrdquo IEEE Transactions on EvolutionaryComputation vol 7 no 3 pp 275ndash288 2003

[24] L Liu H Y Gu and Y G Xi ldquoRobust and stable schedulingof a single machine with random machine breakdownsrdquo Inter-national Journal of AdvancedManufacturing Technology vol 31no 7-8 pp 645ndash654 2007

[25] C Saygin and S E Kilic ldquoIntegrating flexible process planswith scheduling in flexible manufacturing systemsrdquo The Inter-national Journal of AdvancedManufacturing Technology vol 15no 4 pp 268ndash280 1999

[26] S M K Hasan R Sarker and D Essam ldquoGenetic algorithmfor job-shop scheduling withmachine unavailability and break-downsrdquo International Journal of Production Research vol 49 no16 pp 4999ndash5015 2011

[27] C Bierwirth and D C Mattfeld ldquoProduction scheduling andrescheduling with genetic algorithmsrdquo Evolutionary computa-tion vol 7 no 1 pp 1ndash18 1999

[28] X Y Li X Y Shao L Gao andW R Qian ldquoAn effective hybridalgorithm for integrated process planning and schedulingrdquoInternational Journal of Production Economics vol 126 no 2pp 289ndash298 2010

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Journal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


(EICA) and a genetic algorithm (GA) together Furthermorethe EICA is utilized to generate plans and schedules thatare implemented before the emergency takes place whileGA is reserved to handle arrangements once a machinebreakdown occurs The traditional imperialist competitivealgorithm (ICA) that simulates competition among empireshas a strong global exploration capability in solving the NP-hard problems In this study we extend the ICA by improvingits country structure assimilation strategy and adding aresistance procedure The EICA has been proved as a moreeffective and efficient algorithm by comparing it with GAand traditional ICA in solving DIPPS problem whereas forGA as a mature and populated evolutionary algorithm itscapability in manufacturing practice has been studied andproved in our previous works [3 4] and many other studiesHere because of the advantage of its structural similarity withEICA and mature application in dealing with planning andscheduling theGA can be easily formulated by implementingthe structure from EICA it therefore responds excellently tothe breakdown emergency and alters the plan and scheduleinto satisfactory states

The remainder of this paper is organized as follows InSection 2 the works relating to ICA and robustness arebriefly introduced In Section 3 amathematicalmodel for theDIPPS problem is established In Section 4 the imperialistcompetitive algorithm is extended to effectively solve theDIPPS problem In Section 5 the GA is adapted to deal withmachine breakdown In Section 6 a two-stage experiment ispresented to prove the effectiveness and efficiency of EICAand GA to solve DIPPS problem in the case of a machinebreakdown Section 7 presents our conclusions

2 Related Work

21 Evolutionary Algorithms GA is an algorithm to searchfor the optimal solution by simulating the natural evolutionprocess And there are some well-known evolutionary algo-rithms inspired by GA such as biogeography based opti-mization [5 6] and genetic swarm optimization [7] In ourprevious work we used GA to optimize the DIPPS in fuzzyenvironment [8] Besides the wide application of GA thereare some other evolutionary algorithms that have been usedfor solving optimization problem For example Rahmat-Samii et al [9] used PSO for antenna design optimizationDorronsoro et al [10] used evolutionary algorithm to modeland solve minimization problems Grimaccia et al [11] usedsocial network optimization to design generators for vehicleenergy harvesting

In addition ICA is a metaheuristic algorithm inspiredby sociopolitical ideology and first proposed by Atashpaz-Gargari and Lucas [12] Generally there are always com-petitions when numerous countries exist By means of warand conquest some powerful countries called imperialistsconquer and colonize others forming empires As time goesby the imperialists assimilate their colonies and conquercolonies belonging to other ones In contrast weaker empiresgradually lose their colonies to more powerful ones andeventually face extinction At the end of competition thereis an ideal state in which the most powerful empire conquers

all lands By simulating the competition above the ICAinnovatively structures its procedure to solve a variety ofoutstanding problemsThrough the last several years severalsignificant works [13ndash15] have sought to strengthen the globalexploration power in order to broaden its application

Since being proposed the ICA has gained popularity andachieved significant performance in solving manufacturingplanning and scheduling problems To settle the optimizationof process planning with various flexibilities Lian et al [16]utilized the ICA to find promising solutions with reasonablecomputational cost under the objective of minimizing totalweighted sum of manufacturing cost Shokrollahpour etal [17] and Seidgar et al [18] both exploited the ICA inassembly flow shop problem while respectively using theTaguchi method and neural network as their own tools inregulating the parameters Additionally in the no-wait two-stage hybrid flow shop Moradinasab et al [19] introduced anew procedure called global war in ICA to avoid the localoptima This step helps to transfuse some new empires ina certain extent and achieves desirable performance in theexperiment In addition in the work of Zhou et al [20] ICAwas adopted to deal with the assembly sequence planningCompared with GA and PSO the ICA performs better inthe experiment and the quality of result is less related tothe initial populations Moreover Madani-Isfahani et al [21]presented an ICA to solve a biobjective unrelated parallelmachine scheduling problemwhere setup times are sequencedependent

Despite the achievements in the specific domain ofmanufacturing arrangement infrequent work has been doneto settle IPPS problems let alone for DIPPS problems Tothe best of our knowledge only Lian et al [22] have appliedthe ICA to solve IPPS while omitting the disposition ofrobustness The scarce adoption of ICA in this area is notcontrary to our expectations Because IPPS and even DIPPSproblem have far more variables and constraints to deal withthey inevitably contain a high magnitude of informationto manage The complexity of simultaneous planning andscheduling also predisposes the process of measure searchingto be handled delicately

22 Robustness Under the constantly changing conditions ofmanufacturing static and unchangeable plans and schedulesare impractical When the initial plans and schedules are putinto effect machine breakdown may take place and disturbthe manufacturing procedure in an uncontrollable way thatinvalidates the former arrangement To keep plans andschedules robust and flexible some extra work is essential

Among the methods applied for replanning andrescheduling right-shifting is the most convenient wayThis corresponds to waiting for the breakdown to be fixedand then carrying on with the work [23] For instance Liuet al [24] used right-shift rescheduling to retain the samesequence of all remaining jobs as that of the predictiveschedule Although this method saves quite a lot of follow-upwork it loses the optimality of planning and scheduling atthe same time Therefore other means have been figuredout Saygin and Kilic [25] adopted a step-by-step mannerby dividing the whole scheduling period into shorter

















119892tms = max119906isin[1119880]

max119899isin[1119873]

[119883119899119906 sdot (119895ct119899119906 + tt119899119906)] (1)



119880

sum119906=1

119883119899119906 = 1 119899 isin [1119873] (2)


119900ct119899119906119901119895119898 = it119899119906119901119895119898 + ot119899119906119901119895119898





S [2 25][3 17]

1 [2 23][3 26][4 21]

2

[1 10][4 21]

3 [2 21][4 11]

5

[1 13][3 16]

6

[1 27][2 22]

4

[2 17][3 20]

7

E[1 14][3 16][4 19]

8

S [2 22][3 25]

1[1 18][2 15]

[4 19]

2 [1 29][4 24]

3

[3 17][4 13]

4

[2 12][4 11]

5E[1 15][2 24]

[3 17]

6

S

[2 20][4 24]

1

[1 17][3 15]

2

[1 21][2 27]

5

[1 21][3 28]

3

[2 25][3 22]

4

[3 15][4 10]

6

[2 13][4 11]

7

E[1 14][2 17][3 19]

8

Job 1

Job 2

Job 3

S

[2 17][4 12]

1

[3 13][5 22]

2

[4 18][5 15]

3

[2 14][3 19]

4

[1 25][3 29]

5

[1 24][2 27][3 28]

6

[1 13][5 10]

7

[1 19][4 21]

8

[1 13][2 25]

9E

S [2 23][4 24][5 20]

1[1 19][3 13]

2

[2 17][3 15]

3

[2 27][5 21]

4

[4 22][5 26]

5 [2 15][3 11]

7

[1 13][4 12]

8

[3 17][4 10]

6

E

S [2 27][5 23]

1[4 14][5 18]

2

[1 16][3 19]

3[2 25][3 22]

4 [1 15][4 20]

5

E

Operation

Machine

Operating time

Branch point

Rank 1

Rank 2

[1 14][2 12][3 17]

6

Job 1

Job 2

Job 3

MU 1 MU 2

Rank 1

Rank 1

Rank 2

Rank 2

Rank 2

Rank 2

Rank 2

Rank 2Rank 1

Rank 1

Rank 1












1

23

11

32

32

21

23

12

13

31

13

12

21

23

1

1 21

2 12

1 11

Job 1

Job 2

Job 3

MU Plan

2

1

OperationJob number







119888V = 119892Vtms V isin [1 119865pop] (6)


119862119890 = max119894isin[1119865imp]

119888119894 minus 119888119890 119890 isin [1 119865imp] (7)


pwr119890 = 119862119890sum119865imp119894=1 119862119894

(8)









12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

22

11

23

11

32

21

11

32

21

31

12

31

22

12

2 12

1 11

1 12

2 21

2 11

32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

Imperialist

Colony

New colony

21

30

21


32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

32

12

32

12

23

31

12

22

31

21

11

22

30

13

2 11

2 12

2 11

Old colony

New colony

21

21










Job 3 (20)

Job 1 (17)

Job 1 (21)

Job 3 (21)

Job 1 (22)

Job 1 (14)

Job 3 (19)


Time

Operating time

13

12

31

33

11

Mac

hine

12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

2 12

1 11

21

4

3

2

1


















MU 1 34 27 36 40MU 2 43 29 25 43

13

12

31

33

11

13

12

32

31

11

32

12

31

11

13

31

12

33

11

13

13

12

31

33

11

P1

P 1

O2

O1

P2


1

31

23

23

11

1

1

31

23

13

11

1

O1

O1




6 Experiment















Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan


Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




















119892tms = max119906isin[1119880]

max119899isin[1119873]

[119883119899119906 sdot (119895ct119899119906 + tt119899119906)] (1)



119880

sum119906=1

119883119899119906 = 1 119899 isin [1119873] (2)


119900ct119899119906119901119895119898 = it119899119906119901119895119898 + ot119899119906119901119895119898





S [2 25][3 17]

1 [2 23][3 26][4 21]

2

[1 10][4 21]

3 [2 21][4 11]

5

[1 13][3 16]

6

[1 27][2 22]

4

[2 17][3 20]

7

E[1 14][3 16][4 19]

8

S [2 22][3 25]

1[1 18][2 15]

[4 19]

2 [1 29][4 24]

3

[3 17][4 13]

4

[2 12][4 11]

5E[1 15][2 24]

[3 17]

6

S

[2 20][4 24]

1

[1 17][3 15]

2

[1 21][2 27]

5

[1 21][3 28]

3

[2 25][3 22]

4

[3 15][4 10]

6

[2 13][4 11]

7

E[1 14][2 17][3 19]

8

Job 1

Job 2

Job 3

S

[2 17][4 12]

1

[3 13][5 22]

2

[4 18][5 15]

3

[2 14][3 19]

4

[1 25][3 29]

5

[1 24][2 27][3 28]

6

[1 13][5 10]

7

[1 19][4 21]

8

[1 13][2 25]

9E

S [2 23][4 24][5 20]

1[1 19][3 13]

2

[2 17][3 15]

3

[2 27][5 21]

4

[4 22][5 26]

5 [2 15][3 11]

7

[1 13][4 12]

8

[3 17][4 10]

6

E

S [2 27][5 23]

1[4 14][5 18]

2

[1 16][3 19]

3[2 25][3 22]

4 [1 15][4 20]

5

E

Operation

Machine

Operating time

Branch point

Rank 1

Rank 2

[1 14][2 12][3 17]

6

Job 1

Job 2

Job 3

MU 1 MU 2

Rank 1

Rank 1

Rank 2

Rank 2

Rank 2

Rank 2

Rank 2

Rank 2Rank 1

Rank 1

Rank 1












1

23

11

32

32

21

23

12

13

31

13

12

21

23

1

1 21

2 12

1 11

Job 1

Job 2

Job 3

MU Plan

2

1

OperationJob number







119888V = 119892Vtms V isin [1 119865pop] (6)


119862119890 = max119894isin[1119865imp]

119888119894 minus 119888119890 119890 isin [1 119865imp] (7)


pwr119890 = 119862119890sum119865imp119894=1 119862119894

(8)









12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

22

11

23

11

32

21

11

32

21

31

12

31

22

12

2 12

1 11

1 12

2 21

2 11

32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

Imperialist

Colony

New colony

21

30

21


32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

32

12

32

12

23

31

12

22

31

21

11

22

30

13

2 11

2 12

2 11

Old colony

New colony

21

21










Job 3 (20)

Job 1 (17)

Job 1 (21)

Job 3 (21)

Job 1 (22)

Job 1 (14)

Job 3 (19)


Time

Operating time

13

12

31

33

11

Mac

hine

12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

2 12

1 11

21

4

3

2

1


















MU 1 34 27 36 40MU 2 43 29 25 43

13

12

31

33

11

13

12

32

31

11

32

12

31

11

13

31

12

33

11

13

13

12

31

33

11

P1

P 1

O2

O1

P2


1

31

23

23

11

1

1

31

23

13

11

1

O1

O1




6 Experiment















Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan


Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





S [2 25][3 17]

1 [2 23][3 26][4 21]

2

[1 10][4 21]

3 [2 21][4 11]

5

[1 13][3 16]

6

[1 27][2 22]

4

[2 17][3 20]

7

E[1 14][3 16][4 19]

8

S [2 22][3 25]

1[1 18][2 15]

[4 19]

2 [1 29][4 24]

3

[3 17][4 13]

4

[2 12][4 11]

5E[1 15][2 24]

[3 17]

6

S

[2 20][4 24]

1

[1 17][3 15]

2

[1 21][2 27]

5

[1 21][3 28]

3

[2 25][3 22]

4

[3 15][4 10]

6

[2 13][4 11]

7

E[1 14][2 17][3 19]

8

Job 1

Job 2

Job 3

S

[2 17][4 12]

1

[3 13][5 22]

2

[4 18][5 15]

3

[2 14][3 19]

4

[1 25][3 29]

5

[1 24][2 27][3 28]

6

[1 13][5 10]

7

[1 19][4 21]

8

[1 13][2 25]

9E

S [2 23][4 24][5 20]

1[1 19][3 13]

2

[2 17][3 15]

3

[2 27][5 21]

4

[4 22][5 26]

5 [2 15][3 11]

7

[1 13][4 12]

8

[3 17][4 10]

6

E

S [2 27][5 23]

1[4 14][5 18]

2

[1 16][3 19]

3[2 25][3 22]

4 [1 15][4 20]

5

E

Operation

Machine

Operating time

Branch point

Rank 1

Rank 2

[1 14][2 12][3 17]

6

Job 1

Job 2

Job 3

MU 1 MU 2

Rank 1

Rank 1

Rank 2

Rank 2

Rank 2

Rank 2

Rank 2

Rank 2Rank 1

Rank 1

Rank 1












1

23

11

32

32

21

23

12

13

31

13

12

21

23

1

1 21

2 12

1 11

Job 1

Job 2

Job 3

MU Plan

2

1

OperationJob number







119888V = 119892Vtms V isin [1 119865pop] (6)


119862119890 = max119894isin[1119865imp]

119888119894 minus 119888119890 119890 isin [1 119865imp] (7)


pwr119890 = 119862119890sum119865imp119894=1 119862119894

(8)









12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

22

11

23

11

32

21

11

32

21

31

12

31

22

12

2 12

1 11

1 12

2 21

2 11

32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

Imperialist

Colony

New colony

21

30

21


32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

32

12

32

12

23

31

12

22

31

21

11

22

30

13

2 11

2 12

2 11

Old colony

New colony

21

21










Job 3 (20)

Job 1 (17)

Job 1 (21)

Job 3 (21)

Job 1 (22)

Job 1 (14)

Job 3 (19)


Time

Operating time

13

12

31

33

11

Mac

hine

12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

2 12

1 11

21

4

3

2

1


















MU 1 34 27 36 40MU 2 43 29 25 43

13

12

31

33

11

13

12

32

31

11

32

12

31

11

13

31

12

33

11

13

13

12

31

33

11

P1

P 1

O2

O1

P2


1

31

23

23

11

1

1

31

23

13

11

1

O1

O1




6 Experiment















Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan


Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





1

23

11

32

32

21

23

12

13

31

13

12

21

23

1

1 21

2 12

1 11

Job 1

Job 2

Job 3

MU Plan

2

1

OperationJob number







119888V = 119892Vtms V isin [1 119865pop] (6)


119862119890 = max119894isin[1119865imp]

119888119894 minus 119888119890 119890 isin [1 119865imp] (7)


pwr119890 = 119862119890sum119865imp119894=1 119862119894

(8)









12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

22

11

23

11

32

21

11

32

21

31

12

31

22

12

2 12

1 11

1 12

2 21

2 11

32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

Imperialist

Colony

New colony

21

30

21


32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

32

12

32

12

23

31

12

22

31

21

11

22

30

13

2 11

2 12

2 11

Old colony

New colony

21

21










Job 3 (20)

Job 1 (17)

Job 1 (21)

Job 3 (21)

Job 1 (22)

Job 1 (14)

Job 3 (19)


Time

Operating time

13

12

31

33

11

Mac

hine

12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

2 12

1 11

21

4

3

2

1


















MU 1 34 27 36 40MU 2 43 29 25 43

13

12

31

33

11

13

12

32

31

11

32

12

31

11

13

31

12

33

11

13

13

12

31

33

11

P1

P 1

O2

O1

P2


1

31

23

23

11

1

1

31

23

13

11

1

O1

O1




6 Experiment















Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan


Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

22

11

23

11

32

21

11

32

21

31

12

31

22

12

2 12

1 11

1 12

2 21

2 11

32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

Imperialist

Colony

New colony

21

30

21


32

11

32

11

23

31

11

22

31

21

12

22

30

12

1 12

2 12

2 11

32

12

32

12

23

31

12

22

31

21

11

22

30

13

2 11

2 12

2 11

Old colony

New colony

21

21










Job 3 (20)

Job 1 (17)

Job 1 (21)

Job 3 (21)

Job 1 (22)

Job 1 (14)

Job 3 (19)


Time

Operating time

13

12

31

33

11

Mac

hine

12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

2 12

1 11

21

4

3

2

1


















MU 1 34 27 36 40MU 2 43 29 25 43

13

12

31

33

11

13

12

32

31

11

32

12

31

11

13

31

12

33

11

13

13

12

31

33

11

P1

P 1

O2

O1

P2


1

31

23

23

11

1

1

31

23

13

11

1

O1

O1




6 Experiment















Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan


Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Job 3 (20)

Job 1 (17)

Job 1 (21)

Job 3 (21)

Job 1 (22)

Job 1 (14)

Job 3 (19)


Time

Operating time

13

12

31

33

11

Mac

hine

12

31

13

23

22

12

31

21

33

11

31

22

12

30

1 21

2 12

1 11

21

4

3

2

1


















MU 1 34 27 36 40MU 2 43 29 25 43

13

12

31

33

11

13

12

32

31

11

32

12

31

11

13

31

12

33

11

13

13

12

31

33

11

P1

P 1

O2

O1

P2


1

31

23

23

11

1

1

31

23

13

11

1

O1

O1




6 Experiment















Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan


Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







MU 1 34 27 36 40MU 2 43 29 25 43

13

12

31

33

11

13

12

32

31

11

32

12

31

11

13

31

12

33

11

13

13

12

31

33

11

P1

P 1

O2

O1

P2


1

31

23

23

11

1

1

31

23

13

11

1

O1

O1




6 Experiment















Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan


Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Table3Th

epartia

levolutio

nary

results

ofICAandGA

ICA

GA

Rank

Minim

umtotalm

akespan


Rank

Minim

umtotalm

akespan


(1)120

15228

(1)117

12313

(2)122

14072

(2)121

13098

(3)128

14570

(3)123

1272

8(4)

131

1478

8(4)

123

12531

(5)132

14467

(5)124

1312

7


S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





S1

[1 33][2 25][4 13][6 29][7 37][8 19]

[1 16][3 32][4 28][5 24]

[7 35]

[2 17][3 26][6 21][8 12]

[3 30][4 20][5 15][6 35]

[8 24]

[2 17][3 39][4 25][5 33][6 20][8 14]

[1 12][2 29][5 18][7 23]

[3 21][4 15][5 30][6 10]

[1 19][3 25][4 13][8 30] [2 31][4 25]

[5 18][7 34]

[1 32][3 37][5 19][6 24]

[7 15]

Job 12

4

3

5

6

9

7

810

E [1 13][3 40][5 29][6 20]

[7 32]

[1 13][2 31][3 22][4 28][6 33][8 17]

[1 17][4 33][5 25][6 10]

[8 20]

[2 27][3 33][5 40][8 17]

[3 19][4 30][5 12][7 28]

[8 41]

[3 38][6 25][7 27][8 18]

[4 16][6 29][7 40][8 35]

[1 34][3 27][4 20][5 12]

[7 38]

[2 28][4 17][5 40][6 35]

[8 22]

[2 19][3 27][4 35][5 33]

[6 13]

Job 2

S1

3

4

10E

2

5

69

7

8

[1 15][2 30][3 27][5 11][6 36][8 20]

[4 41][5 23][6 13][7 31]

[2 18][4 31][7 24][8 37]

[4 15][5 26][6 10][8 33]

[3 28][4 13][6 34][8 20]

[3 33][4 10][5 17][7 39]

[8 22]

[2 13][3 20][4 34][5 42]

[7 25]

[1 26][3 18][4 14][5 44]

[7 35][3 24][4 37][6 12][7 45]

[8 19]

Job 3

S1

2

3

4

5

6 8

7

9

E

[1 34][3 17][4 26][5 41][6 41][8 20] [1 14][2 23]

[3 34][5 11][7 40][8 28]

[2 35][3 24][7 13][8 19]

[2 34][3 27][5 16][7 22]

[3 18][4 43][7 26][8 32]

[2 27][4 16][6 39][7 32]

[1 21][2 39][5 12][6 15]

[9 33]

[2 16][3 35][4 27][5 20]

[7 32]

Job 4

S

1

2

3

4

5 6

7 8E


Job 1 Job 2

S1

3

11E

2

6

5

Job 3

S

1

4

2

5

3 8

6

9

E

[1 14][2 36][3 22][4 27][6 19][7 33]

[1 17][2 38][5 25][6 11][7 28][8 13]

[1 26][2 39][5 15][8 20]

[2 30][4 40][6 25][7 18]

[2 17][3 31][5 10][6 25][7 38][8 14]

[2 13][4 23][6 37][8 27]

[9 34]

[4 17][5 28][7 40][9 10]

[2 31][3 10][5 35][8 19]

[9 25]

[1 30][3 12][4 20][6 14]

[8 26][3 32][4 19][5 25][7 14]

[9 37]7

10[2 17][3 25][5 12][6 38][8 32][9 27]

[2 40][3 27][5 14][6 23][8 31][9 35]

[1 19][2 35][4 25][7 13][8 30][9 28]

[1 26][3 34][4 15][5 10]

[7 21]

[2 15][5 20][6 27][8 37]

[9 33]

[4 33][5 25][6 17][7 10]

[9 40]

[1 19][2 10][3 25][7 30]

[8 37]

[1 9][3 26][5 15][6 18]

[9 32]

[1 13][3 24][5 16][7 33]

[1 43][2 10][4 18][5 26]

[4 13][6 23][7 40][8 34]

[1 39][3 12][4 25][5 27][7 20][9 33]

4

8

7

9

10

12

[3 21][4 13][5 42][7 37]

[8 25]

[2 32][3 20][5 12][7 45]

[8 16]

[3 41][4 10][6 23][7 31]

[8 16]

[2 28][4 39][7 20][9 13]

[2 38][3 27][5 13][8 18]

[1 25][2 30][5 13][9 42]

[1 27][3 10][6 19][9 38]

[4 15][5 20][6 37][9 28]

[1 30][3 40][5 23][6 9]

[8 19][9 15]

[2 13][3 31][4 25][5 19][8 36][9 40]

S

1

2 4

6

7

3 5

9

8

10E

[2 25][3 13][5 17][6 39]

[9 30]

[2 18][4 23][5 35][7 27]

[9 10]

[1 39][4 15][6 27][8 19]

[9 30]

[2 11][3 22][7 25][8 40]

[9 30]

[1 35][2 20][5 27][6 16]

[8 12]

[1 40][3 28][4 35][5 19][8 12][9 23][1 33][4 29]

[5 18][6 21][7 13][9 43]

[1 20][3 38][5 11][6 33][7 26][8 45]

[4 31][6 18][7 27][8 21]

[2 43][4 17][5 30][9 24]

Job 4

S

1

2 5

3

6 7

8

49

10

E



100110120130140150160170180190200210220230240250

Tota

l mak

espa

n

1 3719 73 9155 253

289

163

181

199

217

235

127

271

145

109

Generation








(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







(a) 1 4 11 27(b) 1 7 17 30(c) 2 2 15 28(d) 2 4 15 35



(a) 69 6955 70 817569 7105 72 7895

(b) 63 6300 66 668563 6345 69 6900

(c) 64 6540 75 795072 7200 87 8700

(d) 79 7900 85 888079 7915 89 9480

46

34

31

26

44

13

21

32

25

31

44

24

44

23

2 11

1 22

2 22

41

2 11

32

12

11

31

41

16

21

11

12

2

1

1

1








ICAGAEICA

105110115120125130135140145150155160165170175180

Min

tota

l mak

espa

n

1 37 55 73 9119 127

145

199

181

217

289

235

253

271

163

109

Generation


7 Conclusion



GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





GAICA

60

65

70

75

80

85

90

95

100M

in m

akes

pan

55

60

65

70

75

80

85

90

Min

mak

espa

n

75

80

85

90

95

100

105

110

115

Min

mak

espa

n

60

65

70

75

80

85

90

95

100

105

Min

mak

espa

n

5 9 13 17 21 25 291Generation (c)

5 9 13 17 21 25 291Generation (d)

5 9 13 17 21 25 291Generation (b)

5 9 13 17 21 25 291Generation (a)

GAICA

GAICA

GAICA






Acknowledgments


References






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Combining Extended Imperialist Competitive Algorithm with...

Documents

Transcript of Combining Extended Imperialist Competitive Algorithm with...