1994 IEEE Symposium on
Emerging Technologies & Factory Automation

Genetic Algorithm with Age Structure and Its Applicatio...
Material

Tool providing port

providing port

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I
0
AGV

SELF-ORGANIZING MA'<VFACfURING SYSTEM
The FMS is composed of n...
Population

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3

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2

2

l
Age

Age
Age 0

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Fig.3 Population with age structure in narure
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Molds on the pallet
Fig.5 A genotype of...
which are complicated relatively. The ASGA is perfonned best
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Table I Parameters of each work
Work!

i=='-Job type
Machining per job

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Work2

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5

Number_E~llet

8

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Kubota, n. 1994: genetic algorithm with age structure and its application to self-organising manufacturing system

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Kubota, n. 1994: genetic algorithm with age structure and its application to self-organising manufacturing system

  1. 1. 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 - 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. Abstract 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 Q-7603 -2114-61941$4 .00 © 1994 IEEE. 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 F1S 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 472
  2. 2. Material Tool providing port providing port llo I 0 AGV 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 S0 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. ~I Machining center •• Tool providing port 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. o€';;:.;<ii .i;V 0 0 AGV 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
  3. 3. Population 4 4 3 3 2 2 l Age Age Age 0 t + l Time( Generation) t Fig.3 Population with age structure in narure Fig .4 Press machining line in cluding an AGV of the ASGA is simply as follows. 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. am Step 1 Generation of initial population initialization of age. Step2 Calculation of fitnes s value selection. Step3 Crossover ard mutation . Step4 Increase of age. Step5 Removal of indivtdual amounted to lethal age. Step6 Go to Step2 oro •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 o ut 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. am There are two major differences between the SOA 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 th is case is a series of line, the direction of the flow of jobs is one-way. 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 several types of search well known as a NP-hard problem 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 am
  4. 4. '-. c••<Omm;~,...~-':-;---4- :oo;vi~u.aJ. t2 :-·,-'_ _ _ _ _ _ _ _ _ _ _ _J • .J Molds on the pallet Fig.5 A genotype of individual . Individual Individual 2 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 multipoint 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 Individual I 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 Fig.6 Crossover of multi-chromosome 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, Application to press machining line I 0 types of jobs are entered in sequence from job 1 to job I 0. A As the proposed PML is a flow shop model, the comparison between Work2 and Work3 is to examine variation purpose of the PML is to reorganize the pallet of the PML in to the job type. A comparison among Work4- Work6 is to CKder to shorten makespan, that is defined as the total amount examine variation to the mold type and the number of job. of machining time of the work. Let Fi be the time of job 1 is And the parameters of GA on the numerical simulations are shown in Table 4. We eanied out numerical simulations among finished of all the machining from starting time of first job. Makespan F is as defined eq.(l) and the purpose is to minimize the proposed ASGA with the elitism strategy (ASGA_E) and the SGA ~ GA_E, whose selection is elitism strategy in ofF: stead of roulette strategy in the SGA. A numerical simulation (1) min F =max F; result of Work I is demonstrated in Fig.7 ifii simulation results of 10 runs of Worki-Work6 are demonstrated in Table 5. As Assume that the transportation time of the AGV is ignored in the result of numerical simulations of Work!, The reorganized comparison with the machining time by a press machine and PML, whose makespan is shorter than the makespan of the the loading/unloading time of material is equal without relation previous PML was genemted. Further, The ASGA is performed 10 materials. Fitness function: fitncssx: of individual x is as better than the SGA ifii the GA_E. The performance of the follows: PML applied the ASGA is improved its makespan up to 10% reduction in average. There is no distinctive difference among (2) fitness,= max Fi- sF, three GAs on the Workl-WorkJ. The GA_E ~ the ASGA_E where sis scaling score and it is while constant. are performed better than the SGA on the Work4 and WorkS Crossing site Crmsover rzz ??ZZ/). 475
  5. 5. which are complicated relatively. The ASGA is perfonned best of three GAs on the Work6 which is the most complicated of all the works. [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, CONCLUSIONS In this paper, fi rst, 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: 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 Algorithm s, 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) • 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
  6. 6. Table I Parameters of each work Work! i=='-Job type Machining per job I Work2 10 5 Number_E~llet 8 8 5 5 --- - Job 4 Job 5 Job 6 _ r · Job 7 Job 8 ~j Job 10 ] 5 4 1 1 1 5 --15 7 130 1 4 5 4 ·· 5 4 5 2 4 1 4 5 4 15 135 2 5 I 3 2 Job 1 10 10 Makes pan ~~~ce o_ ~ch~in_g f Job 2 Job 3 Work6 10 10 7 Is Table 2 Job sequence of work I WorkS c-- - 8 Mold type Work4 .. 10 7 12 Work3 ~.-.2? _ i 5 5 2 -3 2 3 5 2 3 2 I 4 3 2 4 I 4 5 I 2 5 5 I 5 4 4 5 2 I 125 120 115 110~------------------------~ 100 50 Generation Fig .7 A simulation result of Work! Table 3 Machining time of each mold Table 5 Simulation resu lts of Work l - Work 6 ASGA E SGA ~- GA E 128 126 I 123 116 Work I Mean 120 116.7 I =o Min 115 114 I 322 1 322 .I Population size Chromosome le ngth Selection strateg~ Crossover rate Mutation ra1e Lethal age Work 3 ASGA E Roulette -- -r--- I 3 Pallet Elite Work 4 I Elite Work 5 0.7 0.001 .... I 322.9 318.6 i 317.9 3 19 315 I 315 487 480 I 480 472.8 470.5 466 466 466 Max Mean Min 295 281.2 271 274 266.2 261 273 264.2 257 276 270 264 262 258.6 258 .2 256 254 254 352 338.6 332 331 Mean il Min -· 100 Number of chromosome ~~~ 114 Max Table 4 Parameters of GA on numerical simu lation GA_E -· -· ·-r 328 Max = I -I Min Work 2 SGA Max 5 Work 6 Mean Min Max Mean Min I - - --- 477 326 325.4 --~ 319 i 470 i-~~~~4

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