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Kouichi MATSUDA, Yukihide TAKAI, Kohsaku YOSHIDA, Masaru NISHIMURA, Mi ...
1995 Volume 31 Issue 5 Pages
544-552
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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This paper describes about cutting stock scheduling system using simulated annealing method. The cutting stock problem is that of combinatorial optimization. The following functions are needed for the cutting stock scheduling system.
1) Balance adjusting function for productivity, yield rate and delivery time.
2) The results of scheduling have to satisfy constraint condition of coil cutting machine.
3) There is time limitation for making cutting stock schedule. To overcome these problem, we realize new cutting stock scheduling system through following methods.
1) Weights for each evaluated item are introduced and sum of these items are minimized by simulated annealing.
2) The new neighborhood structure is developed for this problem which can satisfy constraint condition of coil cutting machine.
3) The adjusting parameter for calculation time is newly introduced for Huang's annealing schedule, so that we can select best solution under the limit of calculation time.
This cutting stock scheduling system is applied to plate plant and used as one of production planning system.
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Yasuo SUGAI
1995 Volume 31 Issue 5 Pages
553-559
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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The improved simulated annealing method which is based on the self-similatiry of cost function is proposed. The simulated annealing method is a stochastic computational algorithm derived from statistical mechanics, and has much success in various fields. However, this method wastes too much computational time to obtain a solution. In practical problems it can be expected that cost functions are statistically self-similar. If cost functions have self-similar property, a quasi reduction of the state space will be achieved, then, computational time can be reduced. Moreover, this procedure can be applied hierarchically by the degree of smoothness. Based on this idea, the proposed method hierarchically repeats the search for the region in which higher quality solutions seem to exist. Finally the standard simulated annealing method is also applied in the highly restricted region of the state space.
The traveling saleman problems are dealt with in this paper. After verifying the cost functions which have statistical self-similar property for the traveling salesman problem, computational experiments for the benchmark data, i. e., the 249-city problem and the 600-city problem will show that the proposed method can achieve much reduction of computational time compared with the standard simulated annealing method.
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Naoyuki KUBOTA, Tsutomu DATE, Toshio FUKUDA
1995 Volume 31 Issue 5 Pages
560-568
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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In this paper, the new genetic algorithm is proposed by introducing the age structure. The genetic algorithm (GA) simulating the process of natural evolutions is an optimization method composed of genetic operators: selection, crossover and mutation. The GA has recently been demonstrated its effectiveness in the scheduling, planning and other optimization issues, but the GA has problems of premature local convergence and the bias by genetic drift, which arise from a loss of diversity in the population of the algorithm. Therefore, first, in this paper, to improve these problems of the GA we propose the genetic algorithm introducing the age structure (ASGA) which is a continuous generation model. Second, the ASGA is applied to the knapsack problem which is one of combinatorial optimization problems and compared with the simple GA (SGA). The results of numerical experiments show the effectiveness of the ASGA better than the SGA. Further, in the ASGA the relation between the lethal age and the rate of crossover is investigated through numerical experiments.
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Hitoshi IIMA, Nobuo SANNOMIYA
1995 Volume 31 Issue 5 Pages
569-576
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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Genetic algorithm (GA) is a new method to solve combinatorial optimization problems by simulating the process of natural evolution. If individuals in GA have constraints, an individual happens to correspond to an infeasible solution, that is, the individual has lethal genes. In this case, GA can not search freely in the solution space. Consequently, the performance of GA may be degraded.
This paper aims at improving the performance for such a GA that many lethal genes are generated in the search process. For this purpose, a modified flowshop schedule problem is considered as a case study. An additional constraint for this problem is that each product has a definite due date to be completed. We show a numerical result for examining the influence of lethal gene on the accuracy of the solution obtained. Furthermore, we propose two procedures for improving GA and compare their effectiveness in the process generating many lethal genes.
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Yasuhiro KIKUCHI
1995 Volume 31 Issue 5 Pages
577-582
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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The new mathematical formalization to describe the dynamics of the stochastic selection GA is presented as a result of introducing the new recombination operator (WF operator) instead of the conventional ones. In this formalization, GA dynamics is expressed by the Markovian process in the hyper-cube. The basic equation (performance equation) which can be used for analyzing GA performance is obtained and the approximation (diffusion process approximation) method to derive the 2-order partial differential equation is proposed. Moreover, the relationship between GA performance and the GA parameter (scaling factor) derived from the analytic solution of the 1-bit problem is discussed.
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Tadahiko MURATA, Hisao ISHIBUCHI, Hideo TANAKA
1995 Volume 31 Issue 5 Pages
583-590
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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In this paper, we apply a genetic algorithm to flowshop scheduling problems and examine two hybridizations of a genetic algorithm with other search algorithms. We also propose a genetic algorithm for multi-objective optimization problems. First we examine various genetic operators for the flowshop scheduling problem for minimizing the makespan. By computer simulations, we show that a two-point crossover and a shift change mutation are effective for this problem. Next we compare the genetic algorithm with other search algorithms such as local search, taboo search and simulated annealing. By computer simulations, it is shown that the genetic algorithm is a bit inferior to the others. In order to improve the performance of the genetic algorithm, we examine the hybridization of the genetic algorithm with other search algorithms. Finally, we propose a selection operator and an elitist strategy of the genetic algorithm for multi-objective problems. The high performance of our multi-objective genetic algorithm is demonstrated by computer simulations.
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Yuto MIZUKAMI, Hirokazu MATSUSHITA, Yoshimaro HANAKI, Noboru OHNISHI, ...
1995 Volume 31 Issue 5 Pages
591-597
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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Lathes with two turrets are often used to get high efficiency of turning. To utilize them, it is important to plan a machining sequence considering simultaneous machining by two cutting tools, since combinations of processes influence practical cutting time very much. But it is difficult for users to determine an optimal machining sequence, because the number of the combinations is great.
A method proposed in this paper divides processes into cycles, during which spindle speed is constant, and distributes divided processes to two turrets. Genetic algorithm is applied to divide processes into cycles. Genes are assigned to processes. Values of genes represent identified cycle numbers, and processes with the same cycle number are simultaneously machined. A chromosome is a series of all processes, and constitutes a machining sequence. As a criterion of the first fitness, total cutting time by machining sequences represented by a chromosome is adopted. And as that of the second fitness, difference of cutting time on two turrets for each cycle is adopted. Preserving crossover, arbitrary crossover and mutation are used as genetic operations. Preserving crossover is multipoint crossover to preserve cycles with the good second fitness. Mutation is intended to break cycles with the bad second fitness. Preserving crossover is mainly used in the first stage, and arbitrary crossover and mutation are in the second stage. A simulation showed that proper use of two kinds of crossover and mutation produces good results.
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Keiji MAEKAWA, Hisashi TAMAKI, Hajime KITA, Yoshikazu NISHIKAWA
1995 Volume 31 Issue 5 Pages
598-605
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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The genetic algorithm (GA) is an optimization technique simulating the process of natural evolution, and it has been successfully applied to several optimization problems which are difficult to solve exactly by conventional methods. This paper proposes a new method for solving the traveling salesman problem (TSP) based on the GA. In applications of GA to TSP proposed so far, a coding where the chromosome represents a list of cities arrayed in the visiting order has been mainly used. However, in such a coding, we have to devise a crossover operator that keeps each chromosome to be a permutation, and it inevitably causes a difficulty in inheritance of tour characteristics.
The present paper proposes a new method in which a genetic coding represents edges of the tour, and a crossover operator exchanges the edges of the parent tours. The effectiveness of the proposed method is confirmed through several computational experiments, including a comparison with another typical method. Furthermore, the paper proposes an algorithm which combines GA with the 2-opt method, a local search technique. The effectiveness of this algorithm is also confirmed through a comparison with other methods for solving the TSP.
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Koji MORIKAWA, Takeshi FURUHASHI, Yoshiki UCHIKAWA
1995 Volume 31 Issue 5 Pages
606-614
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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This paper proposes a cooperative scheduling method with the Genetic Algorithm (GA) for the CIM (Computer Integrated Manufacturing) system.
There are many scheduling problems in the CIM, such as design scheduling, production scheduling and transportation scheduling. Recently, the GA has been applied to these problems, and has shown a high performance in scheduling problems. However, the application has been done to an individual problem in the CIM system. Since the scheduling problems have some relations with each other, it is important to consider these problems from the view points of total elapsed time, total cost, total energy consumption, etc.
This paper proposes a cooperative scheduling method using multi-agent model. Each agent independently solves its own problem using the GA and has a function to tune the parameters for strategic search through interactions with each agent. This system is flexible in coping with the changes of environment, such as the change of scheduling conditions or trouble of some machines. Simulations are done to show the feasibility of proposed method, using Jobshop Scheduling Problem (JSP) and Transportation Problem (TP).
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Isao TAZAWA, Seiichi KOAKUTSU, Hironori HIRATA
1995 Volume 31 Issue 5 Pages
615-621
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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Genetic algorithms (GAs) are search procedures for combinatorial optimization problems. Unlike most of other optimization techniques, GAs search the solution space using a population of solutions. Although GAs have an excellent global search ability, it is not effective for searching the solution space locally due to crossover-based-search. Genetic Immune Recruitment Mechanism (GIRM) makes up for the week point of GAs. In GIRM, new generated solutions take an immune recruitment test. Only those solutions which are similar to the best solution in the population pass the test and survive to the next generation. As a result, GIRM promotes the search around the best solution. In this paper we apply GIRM to the floorplan design problem of VLSI layout and compare the results with the ones of GAs. Especially, we propose new affinity functions in order to evaluate the similarity between floorplans. Computational experiments show that GIRM gives equivalent or better solutions than GAs.
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Takuya WAKUTSU, Eitaro AIYOSHI
1995 Volume 31 Issue 5 Pages
622-630
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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In the solution to combinatorial optimization problems with constraints by using neural networks, the penalty approach is adopted in which the constraint functions are combined with the minimization function. In the transformation of a constrained problem into a unconstrained one, it is feared that a lot of feasible combinatorial states satisfying the constraints corrupt into discrete local optimal solutions in a neighborhood with a radius of one Hamming distance. The paper presents the new fundamentals of the neural network whose states transit so as to satisfy the constraints. The feasibility of the state transition for constraints is kept by the linked transition mode in which some of the neurons change their states cooperatively and simultaneously. In this paper, in order to get off from a local optimum among the feasible states, a stochastic version of the linked state transition rule is proposed as well as deterministic rule. In the stochastic transition, increase of the function value to be minimized is accepted in a ratio. The simulation results for the simple 0-1 combinatorial problems demonstrate effectiveness of these transition manners.
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Takashi NAKAMURA, Eitaro AIYOSHI
1995 Volume 31 Issue 5 Pages
631-639
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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In a pre-stage of the applications of neural networks to combinatorial problems, the problems are formulated as minimization problems with a quadratic or a bilinear function with respect to binaryvalued variables e. g. {0, 1}, and then a neural network are composed of neurons as many as the variables. The solution to the problem is obtained as one of the stationary states of the network. Here, if another femulation is introduced for the same problem by using ternary-valued variables e. g. {-1, 0, 1} to realize reduction of the number of variables, it would be possible to reduce the number of neurons and the total number of states of the neural network.
From the above motivation, the paper presents the fundamentals of the neural network with ternaryvalued neurons whose states transit deterministicly so as to minimize a bi-quadratic function. In the asynchronous state transition, however, the states of neurons are trapped at one of local optima. So, in order to get off from such a local optimum, a manner of operating the state transition stochastically among the ternary values is proposed, in which increase of the function value to be minimized is accepted in a ratio.
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Osamu KATAI, Tadashi HORIUCHI, Shigeo MATSUBARA, Tetsuo SAWARAGI, Sosu ...
1995 Volume 31 Issue 5 Pages
640-649
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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By introducing constraint-oriented notion of fuzziness and the principle of Synergetics, we propose a double-layered system architecture for constraint satisfaction problems involving continuous variables and fuzzy constraints whose upper layer is for structual part of the problems and the lower layer is for elastic part of the problems. The elastic part is treated by decentralized interactive activities among autonomous problem solving units. The structual part is treated by a centralized logic-based symbol processing unit which works concurrently and interactively with the autonomous units for the elastic part. Here decentralization and self-organization is based on Synergetics, and fuzziness is utilized for coding and decomposing complex constraints thus enabling this system architecture. This autonomous decentralized system architecture is then implemented on transputers by using Occam and is applied to design problems showing the effectiveness of our approach.
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A Binary Representation Approach
Hisashi TAMAKI, Yoshishige HASEGAWA, Junji KOZASA, Mituhiko ARAKI
1995 Volume 31 Issue 5 Pages
650-657
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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In this paper, a scheduling problem in a plastics forming plant is studied. This problem basically belongs to the class of unrelated parallel machine problems, but includes several restrictions which originate from the necessity to use auxiliary equipment. Thus it can be regarded as an example of complex scheduling problems arising in industries. The paper presents a new scope for the study of practical scheduling problems by proposing a method to solve them without relying upon dispatching rules. First, we transform the scheduling problem to a mathematical programming problem, and represent feasible schedules by binary strings. This formulation enables to use the search methods (such as simulated annealing methods, genetic algorithms, etc.). We actually coded several search methods and carried out computational experiments for the problems of practical size. Results indicate that our methods can give satisfactory solutions to the considered scheduling problem.
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Jinliang CHENG, Hiroshi KISE, Hironori MATSUMOTO
1995 Volume 31 Issue 5 Pages
658-665
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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This paper deals with a scheduling problem of minimizing the maximum completion time (i. e., the makespan) for an automated manufacturing system such as FMS and FMC that consists of three machining centers with sufficient buffers, an AGV (automated guided vehicle) and loading and unloading stations. First, the problem is formulated exactly, and is shown to be approximately reduced to the classical 4-machine flowshop scheduling problem (4 FSP). Second, an approximation algorithm that utilizes a fuzzy inference based on a dominance relation for the 4 FSP is proposed. Third, a branch-and-bound (BAB) algorithm that utilizes the fuzzy approximation is proposed. Finally, extensive numerical experiments demonstrate that the BAB algorithm can solve problem instances With up to 500 jobs in reasonable time with a quite high possibility.
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Tsuyoshi SATAKE, Katsumi MORIKAWA, Nobuto NAKAMURA
1995 Volume 31 Issue 5 Pages
666-674
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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In this study we propose a heuristic scheduling approach to the minimization of maximum completion time of the general job-shop scheduling problems. The fundamental idea of this approach is based on the ability of human scheduler's pattern recognition, and we have tried to construct the similar manner in our heuristic procedure. We firstly divide the jobs into job groups based on the similarity of their flow patterns, and then generate sub-schedules for each job group separately. Finally we integrate the sub-schedules into the final global schedule with the aid of eliminating procedure of the operation conflicts. In order to test the effectiveness of the proposed approach, we have conducted the computational experiment varying the number of jobs from six to twenty, and the number of machines from five to fifteen. By comparison experiments with neural network approach and simulated annealing, the proposed approach has produced good solutions in reasonable computing times.
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Yuichi MIYAMOTO, Yoshimitsu KUROSAKI, Masato HAYASHI, Kenji OZAKI, Tak ...
1995 Volume 31 Issue 5 Pages
675-681
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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This paper discusses an effective method for solving a combinatorial discrete optimization problems and considers a physical distribution problem, which consists of an assignment problem and a routing problem of automated guided vehicles, as one of the conbinatorial discrete optimization problems. Namely, when requests for traveling occur, the proposed method assigns them to available vehicles and determines a route for each of the vehicles without interference with realtime. The algorithm used to solve this problem utilizes knowledge processing which consists of a logic programming and a constraint processing, because this problem is regarded as a constraint satisfaction problem. The constraint processing is used to avoid the interference among vehicles which is an important element in an effective physical distribution. Finally, the capability of the proposed method is shown by discrete-event simulation results for a closed-loop traveling model.
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Manabu TAKEMURA, Shigeo TANAKA, Hidenori HASHIGUCHI, Katsuaki ONOGI, Y ...
1995 Volume 31 Issue 5 Pages
682-684
Published: May 31, 1995
Released on J-STAGE: March 27, 2009
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We proposed a heuristic algorithm for combinatorial optimization problems using partially identifying approximation. However, if the original problem is large, we must use approximation methods in it. This paper discusses the effects of the use of approximation methods on the effectiveness of this method.
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