1994 IEEE Symposium on Emerging Technologies & Factory Automation

Genetic Algorithm with Age Structure and Its Application to Self-Organizing Manufacturing System

Naoyuki KUBOTA, Toshio FUKUDA, Fumihito ARAI, and Koji SHIMOJIMA

Dept. of Micro System Engineering, Nagoya University, I Furo-cho, Chikusa-ku, Nagoya 464-01, JAPAN

Abstract - This paper deals with the new genetic algorithm with the age structure. The genetic algorithm has been recently demonstrated its effectiveness in optimization issues, but the genetic algorithm has two major problems: a premature local convergence ard a bias by the genetic drift In order to solve these problems, we propose the genetic algorithm introducing the age structure which is a continuous generation model. The genetic algorithm with age structure is applied to the self­organizing manufacturing system, that is, a process self­organizes to the other process in the flexible manufacturing system environment. The effectiveness of the genetic algorithm with the age structure is demonstrated through numerical simulations of the reorganization of the press machining line as an example of the self-organizing manufacturing system.

INTRODUCTION

In recent years, the intelligent manufacturing system, which has been discussed by many researchers, is required alvanced flexible processes in a flexible manufacturing system (FMS) environment[l,2]. We have been proposed self­organizing cellular robotic system (CEBOT) which is composed of a number of autonomous robotic units with simple functions[3]-[6J. The form of the CEBOT is reconfigured dynamically in order to suit to the environment and tasks. Further, as a manufacturing system held the idea of the CEBOT, we propose the self-organizing manufacturing system (SOMS), that is, each process self-organizes effectively to the other process in the FMS. The optimization of each process in the FMS is ne:eCed in <rder to crerue an ideal manufacturing system environment, ard the FMS environment includes many optimization problems which are ill-defined. There are stochastic search methods for these problems such as the simulated annealing, the genetic algorithm(GA}, ard so on . The GA[7]-[9], which simulates the process of natural evolution, is defired as an optimization method with the set, called a population of individuals . Each individual has a fitness

value corresponding with its genotype, ard the next generation of a population is reproduced by selection according to a fitness value of each individual. The simple GA(SGA)[2] as one of the GAs, in general, composes of genetic operators: roulette strategy selection, one-point crossover ard mutation. The GA has been demonsrrated its effectiveness in combinatorial optimization issues, scheduling problems ard so on[JOH13]. However, the GA has two major problems of premature local convergence ard the bias by the genetic drift. These problems occurred when genetic diversity in the population is reduced. Then ways to solve these problems have been proposed following : a fitness scaling, a dynamically conrrol of a mutation rate, a parallelization by subpopulations, and so on . Then, in tl'der to solve these problems, we propose the GA introducing the age structure (ASGA) which is a continuous generation model. In the ASGA, a coexistence of parents and

offspring in a population is pennitted. As optimization problems to compare in the performances among the GAs. most of the GAs are applied fer a scheduling problem or a traveling salesman problem. The job shop scheduling problem (JSSP) is in general refined as an optimization problem to search for optimal scheduling of required works in orckr to shorten makespan performed in the environment composed of several machines[!]. However, in th is JSSP there are many restrictions about transportation methods ard others. lt is required to consider these restrictions in ceder to apply for the FMS. In such a F\1S environment , however, there are lots of flow shop scheduling problem which are defined as a sequencing. The sequence of machining line is effective ' n respect to paths of automated guided vehicles(AGVs) or placemems of belt conveyers, for the di.rection of AGYs are the same. There are many cases that the sequencing of works is optimized according to the several available machines in the FMS environment. In contrast to those cases, there are few cases that the form of machines is optimized according to the sequeoce of given works. Consequently, "e deal with an application for the latter cases. In this popcr, the ASGA is applied to a press machining line (PML) which is capable of

Q-7603-2114-61941$4 .00 © 1994 IEEE. 472

Fig. 1 Self-organizing manufacturing system

reorganizing the machine in itself as an example of the SOMS. However, it is very difficu lt to optimize all manufacturing process for the demanded works. The optimization of the PML is here to reorganize the form of the PML by using the ASGA . The effectiveness of the proposed method is demonstrated through numerical simulations.

SELF-ORGANIZING MA'<VFACfURING SYSTEM

The FMS is composed of numerically controlled machines , machining centers, assembling stations arrl robots, <l1d so on. Further, as automatic transportation methods, belt conveyors, transportation vehicles, monorail cars are handled in this system. The purpose of the FMS is to automatically carry out the process which is composed of design, machining , control, ard management by integrating flexible machines ard

computerized control. The effectiveness of the FMS is an ability to correspond to high variety. Then in order to create an ideal manufacturing system environment, we propose the S 0 M S, that is, a process self-organizes in accordance with the other process in the such FMS environment(Fig.l ). The self­organization of SOMS is to reorganize hardware as well as software of manufacturing system. As an example of the SOMS, assuming that there is a manufacturing system composed of machining centers which is capable of reorganizing for itself and a number of AGVs(Fig.2). Machining centers are equipped exchangeable tools according to required machining. AGVs carry not only materials/products but also tools which are equipped machining center. In this system, machining control and manufacturing management is performed not by the centralization but by the decentralization.

Material providing port

llo Tool providing port

o€';;:.;<iii.i;V

I ~I 0 AGV

0 Machining center

0 AGV •

Tool providing port

• 0 oil~~~ Product providing port

Fig.2 An example of manufacturing system

The machining information about each material is held by the bucket kept materials. Therefore, each AGV carries bucket to the machining center according to machining information. The flow of processes is generally summarized as follows: designing of the machining center, planning of the manufacturing schedule, ard producing products actually according to its schedule. In these processes, it is important to reduce manufacturing cost and makespan to optimize all the manufacturing system as is demanded However, it is very difficult, ard the optimized system is vulnerable to breakdown of system or delays of schedules. Therefore, the self­organization according to other process such as the SOMS is effective with regard to the flexibility of all the manufacturing system.

AGE STRUCfURED GENETIC ALGORITIIM

In this chapter, we propose the ASGA as one of improvements to maintain genetic diversity in a population. A typical population with age structure in nature[ 14, 15] is presented in Fig.3. The ASGA simulates simply this population in nature. In this paper, one generation is defined as a unit of the dis~Tete time. Each individual in the ASGA is introduced the parameter called an age ard is removed from a population when its age amounts to the fixed lethal age. All the offspring, which are generated from parents by the crossover an:l mutation operator, are at age 0. Further, the next generation of a population is reproduced by the selection among the population included parents m those offspring. The procedure

473

Population

4 3 2

l

Age

t

4 3 2

Age

Age 0

t + l Time( Generation)

Fig.3 Population with age structure in narure

of the ASGA is simply as follows.

Step 1 Generation of initial population am initialization of age.

Step2 Calculation of fitnes s value oro selection.

Step3 Crossover ard mutation .

Step4 Increase of age.

Step5 Removal of indivtdual amounted to lethal age.

Step6 Go to Step2

There are two major differences between the SOA am the ASGA. First , the parents of the last generation is capable

of e<isting in the next generation by the selection of the

ASO A. That is, the parents are pemnitted coexistence with their

offspring. Second, in the ASGA e<JCh individual is removed

from a population when its age amounts to the lethal age

without considering fitness value. Therefore, the ASOA is

capable of better regulation of the number of the same

individual.

APPLICATION TO PRESS MACHINING LINE

Press manufacturing line

The ASGA is applied for the PML(Fig.4), which is capable of reorganizing the system in itself as an example of

the SOMS . In this PML, the number of press machine is

bigger than the number of the machining process per job, for

to give the PML further redundancy is flexible to manufacture several types of products at one line . As the PML in this case is a series of line, the direction of the flow of jobs is one-way.

Fig .4 Press machining line in cluding an AGV

The material of each job is transported from the place for

material to the press machine am after perfomned machining the

product is cransported to the place for the product by an AGV.

That is, in th is line the flow shop scheduling is carried out.

The assumptions of the PML in thi s case are written as follows.

•A worlc is composed of n jobs.

•The sequence of given jobs is fixed.

•Each job requires operations by m molds a-d its

machining sequence is thed.

•It is able to attach up to three mold in each pallet

on the press machine.

•The mold, which is required on the job. is

automatically selected am the machining is carried

out by its required mold.

•When a press machine in front of the AGV is in

process, the AOV stands by in from of the press

machine till finishing the machining. •When the pallet of the press machine in front of

the AGV does not include the mold required in the

next operation of the job, the AGV passes it by.

In this PML, there are optimization of flow shop

scheduling of jobs on the work, reorganizing press machine, a

path planning of AGVs an:! so on. The scheduling problem is well known as a NP-hard problem am several types of search

algorithms for the scheduling problem have been proposed.

However, as described before. reorganization of the PML is

dealt in this paper. Consequently, the optimization of the attachment, i.e. mold type of the PML to suit with the given

work is dealt.

474

'-. c••<Omm;~,...~-':-;-t -2-4- :oo;vi~u.aJ.

:-·,-' ____________ J

• .J

Molds on the pallet

Fig.5 A genotype of individual

Individual Individual 2 .

Crossing site Crmsover

Individual I

rzz ??ZZ/).

(

Fig.6 Crossover of multi-chromosome

Application to press machining line

As the proposed PML is a flow shop model, the

purpose of the PML is to reorganize the pallet of the PML in

CKder to shorten makespan, that is defined as the total amount

of machining time of the work. Let Fi be the time of job 1 is

finished of all the machining from starting time of first job. Makespan F is as defined eq.(l) and the purpose is to minimize

ofF:

min F =max F; (1)

Assume that the transportation time of the AGV is ignored in comparison with the machining time by a press machine and the loading/unloading time of material is equal without relation 10 materials. Fitness function: fitncssx: of individual x is as

follows:

fitness,= max Fi- sF, (2)

where sis scaling score and it is while constant.

Each individual of population has three chromosomes

whose length is the number of pallet on the PML. As for

coding of the GA, the strings of each gene are defined as the

number of mold type and the number of locus is defined as the numerical Olrler of the pallet. That is. the set of the i-th locus

genes of the chromosomes in the iooividual refer 10 the set of

the molds included in the i-th pallet(Fig.5). Further, the overlap

of same mold type on the pallet is not permitted . The multi­

point crossover is handled as the crossover operator ~ the crossover is performed between the same number of

chromosome of each individual(Fig.6). The mutation operator replaces a string with other strings except strings on the pallet.

The transposition operator is an operator to replace position of

chromosome in the individual. The reproduction of the next

population is performed by selection: the roulette

strategy(SGA), elitism strategy(GA_E, ASGA_E).

Numerical simulations

In this section, numerical simulations among the GAs

concerning selection operator are shown. The purpose of the

proposed PML is to shorten makespan. The numericill simulation is performed by 6 type of works. The parameters of

these works are shnwn in Table I.

The purpose of Workl is a comparison of the makespam between the previous PML with the PML after the

reorganization of the PML. Its job sequence and machining

time of ea::h mold is shown in Table 2 and Table 3. The

sequence of machining of each job on the Work2-Work6 and a

machining time of each mold arc randomly generated on each work( machining time limit to 20 discrete time). In the Work I, I 0 types of jobs are entered in sequence from job 1 to job I 0. A

comparison between Work2 and Work3 is to examine variation

to the job type. A comparison among Work4- Work6 is to

examine variation to the mold type and the number of job.

And the parameters of GA on the numerical simulations are

shown in Table 4. We eanied out numerical simulations among

the proposed ASGA with the elitism strategy (ASGA_E) and the SGA ~ GA_E, whose selection is elitism strategy in

stead of roulette strategy in the SGA. A numerical simulation

result of Work I is demonstrated in Fig.7 ifii simulation results of 10 runs of Worki-Work6 are demonstrated in Table 5. As

the result of numerical simulations of Work!, The reorganized

PML, whose makespan is shorter than the makespan of the

previous PML was genemted. Further, The ASGA is performed better than the SGA ifii the GA_E. The performance of the

PML applied the ASGA is improved its makespan up to 10% reduction in average. There is no distinctive difference among

three GAs on the Workl-WorkJ. The GA_E ~ the ASGA_E

are performed better than the SGA on the Work4 and WorkS

475

which are complicated relatively. The ASGA is perfonned best of three GAs on the Work6 which is the most complicated of all the works.

CONCLUSIONS

In this paper, fi rs t, we proposed the self-organizing manufacturing system. The proposed system organizes the manufacturing system in itself. Second, we proposed the genetic algorithm introduced the age structure. As one of the self-organi:dng manufacturing system, the genetic algorithm with age structure is applied for a reorganization of a press machining line . Through the simulation the effectiveness of the proposed system is demonstrated. Further subjects are as follows:

• As we only dealt with a specialized case that sequences for work is given and the purpose of the optimization is to determine the reorganization to shonen makespan of the press machining line, it is required for the proposed system to extend the job shop scheduling problem in order to apply for actual systems .

• In Older to show the effectiveness of the proposed system, we reed to deal with several types of self-organization of other processes according to the interaction between process.

• In order to adjust the proposed system to breakdown of the system <n1 delays of schedule, we reed to extend the proposed system to the autonomous distributed system.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. Y. Kawauchi for many useful comments and suggestions .

REFERENCE

[I I P . Pu, J.Hughes, "Integrating AGV Schedules in a Scheduling System for a Flexible Manufacturing Environment", Proc. of IEEE International Conference on Robotics ;nt Automation, 3149/3154 (1994) [2] R.Macchiaroli, S.Riemma, "Clustering Methods for Production Planning ;nt Scheduling in a Flexible Manufacturing System", Proc. of IEEE International Conference on Robotics and Automation, 315513I60 (1994)

476

[3]T.Fukuda, T.Ueyama, "Cellular Robotics n1 Micro Robotic Systems", World Scientific Series in Robotic m Automated Systems Vol.IO, World Scientific (1994) [4] T . Fukuda, T. Ueyama, "Self-Evolutionary Robotic System -Sociobiology ;nt Social Robotics-" , Journal of Robotics m Mechatronics, Vol.4, No.2, 96/103 (1992) [5] Y. Kawauchi, T. Fukuda, "Genetic System and Evolution", Journal of Robotics and Mechatronics. Vo1.4, No.2, 108/114 (1992) 161 T . Ueyama, T. Fukuda, "Self-Organization of Hierarchical Structure on Cellular Robotic System". Proc . of IEEE International Conference on Robotics and Automation, 3224/3229, (1994) 17] J. H. Holland, "Adaptation in Natural and Ani tidal Systems", University of Michigan Press (1975) [8] D. E. Goldberg, "Genetic Algorithm -in Search,

Optimization, and Machine Learning-", Addison Wesley Publishing Company, Inc. (1989) [9] G. Syswerda, "A Study of Reprodu ction in Generational and Steady-State Genetic Algorithms", Foundation of Genetic Algorithms, Morgan Kaufmarnn, 94/101 (1991) [10] K. Juliff, "A multi-chromosome Genetic Algorithm for Pallet Loading", Proc. of the Fifth International Conference on Genetic Algorithms, 467/473 (1993) [II] A. Homaifar, S. Guan, G. E. Liepins, "A New Approach on the Traveling Salesman Problem by Genetic Algorithms", Proc. of the Fifth International Conference on Genetic Algorithms, 460/466 (1993) [12] K. Shimojima, T. Fukuda, F . Arai, Y. Hasegawa, "Unsupervised/Supervised Learning for RBF-Fuzzy Inference -Adaptive Rules ;n! Membership Function and Hierarchical Structure by Genetic Algorithm-", Proc. of the IEEE World Wisemen/women Workshop, 97/104 (1994) [13] N. Baba, N. Kubota, "Collision Avoidance Planning of a Robot Manipulator by Using Genetic Algorithm -A Consideration for the Problem in Which Moving Obstacles and/or Several Robots Are Included in the Workspace-", Proc. of The First IEEE Conference on Evolutionary Computation, 714nJ9 (1994) [14] J. F. Crow, "Basic Concepts in Population, Quantitative, ;n! Evolutionary Genetics", W. H. Freeman m Company, New York (1986) [15] A. A. Berryman, "Population systems , A General Introduction", Plenum Press, New York (IY81)

Table I Parameters of each work

Work! I Work2 Work3 Work4 WorkS Work6 i=='-- c-- - .. Job type 10 ~.-.2?_ 10 10 10 -Machining per job 5 5

Number_E~llet 8 8

Mold type 5 5

Table 2 Job sequence of work I

~~~ce o_f ~ch~in_g

Job 1 2 5 I 3 2

Job 2 1 4 5 4 2 --- -- ·· - --Job 3 5 4 5 2 3

Job 4 4 1 4 5 2

Job 5 4 3 5 2 3 Job 6 _

r · 5 2 I 4 3

Job 7 4 2 4 I 4

Job 8 1 5 I 2 5

~j 1 5 I 5 4

Job 10 ] 1 4 5 2 I

Table 3 Machining time of each mold

Table 4 Parameters of GA on numerical simu lation

. I SGA I GA_E ASGA E

Population size 100

Number of chromosome 3 Chromosome length Pallet

Selection strateg~ Roulette I Elite I Elite

Crossover rate 0.7 - - -Mutation ra1e -r--- 0.001

Lethal age I 5

i 5

8

Is

Makes pan 135

130

125

120

115

7

12

7

10 10

15 15 -- -5 7

110~------------------------~

477

50 100 Generation

Fig .7 A simulation result of Work!

Table 5 Simulation resu lts of Work l - Work 6

SGA GA E ASGA E

~- 128 126 I 123

Work I Mean 120 116.7 I 116

Min 115 114 I 114 =o -I -· -· · -r 322 Max 328 322 1

Work 2 ~~~ 322.9 318.6 i 317.9

Min 319 315 I 315 =

Max 487 480 I 480

Work 3 Mean il 472.8 470.5 i 470

Min 466 466 466 - ·

Max 295 274 273

Work 4 Mean 281.2 266.2 264.2

Min 271 261 257

Max 276 264 262

Work 5 Mean 270 258.6 258 .2

Min 256 254 254 .... Max 352 332 331

Work 6 Mean 338.6 325.4 i -~~~~4 - - ----- --~

Min I 326 319