Yasuhiro Tsujimura

A tutorial survey of job-shop scheduling problems using genetic algorithms—I: representation

Abstract Job-shop scheduling problem (abbreviated to JSP) is one of the well-known hardest combinatorial optimization problems. During the last three decades, the problem has captured the interest of a significant number of researchers and a lot of literature has been published, but no efficient solution algorithm has been found yet for solving it to optimality in polynomial time. This has led to recent interest in using genetic algorithms (GAs) to address it. The purpose of this paper and its companion (Part II: Hybrid Genetic Search Strategies) is to give a tutorial survey of recent works on solving classical JSP using genetic algorithms. In Part I, we devote our attention to the representation schemes proposed for JSP. In Part II, we will discuss various hybrid approaches of genetic algorithms and conventional heuristics. The research works on GA/JSP provide very rich experiences for the constrained combinatorial optimization problems. All of the techniques developed for JSP may be useful for other scheduling problems in modern flexible manufacturing systems and other combinatorial optimization problems.

A tutorial survey of job-shop scheduling problems using genetic algorithms, part II: hybrid genetic search strategies

Abstract Job-shop scheduling problem is one of the well-known hardest combinatorial optimization problems. During the last three decades, this problem has captured the interest of a significant number of researchers. A lot of literature has been published, but no efficient solution algorithm has been found yet for solving it to optimality in polynomial time. This has led to recent interest in using genetic algorithms to address the problem. How to adapt genetic algorithms to the job-shop scheduling problems is very challenging but frustrating. Many efforts have been made in order to give an efficient implementation of genetic algorithms to the problem. During the past decade, two important issues have been extensively studied. One is how to encode a solution of the problem into a chromosome so as to ensure that a chromosome will correspond to a feasible solution. The other issue is how to enhance the performance of genetic search by incorporating traditional heuristic methods. Because the genetic algorithms are not well suited for fine-tuning of solutions around optima, various methods of hybridization have been suggested to compensate for this shortcoming. The purpose of the paper is to give a tutorial survey of recent works on various hybrid approaches in genetic job-shop scheduling practices. The research on how to adapt the genetic algorithms to the job-shop scheduling problem provide very rich experiences for the constrained combinatorial optimization problems. All of the techniques developed for the problem are very useful for other scheduling problems in modern flexible manufacturing systems and other difficult-to-solve combinatorial optimization problems.

An efficient approach for large scale project planning based on fuzzy Delphi method

Abstract The goal of this paper is to replace probabilistic or deterministic considerations in the project network analysis by possibilistic ones and to reduce the difficulty arising from the inexact and insufficient information of activity times. The activity times are considered as fuzzy numbers (fuzzy intervals or time intervals) and the fuzzy Delphi method is used to estimate a reliable time interval of each activity. Based on these time estimates, we then propose an efficient methodology for calculating the fuzzy project completion time and the degree of criticality for each path in a project.

Solving job-shop scheduling problems by genetic algorithm

Job-shop scheduling problem (JSP) is one of extremely hard problems because it requires very large combinatorial search space and the precedence constraint between machines. The traditional algorithm used to solve the problem is the branch-and-bound method, which takes considerable computing time when the size of problem is large. We propose a new method for solving JSP using genetic algorithm (GA) and demonstrate its efficiency by the standard benchmark of job-shop scheduling problems. Some important points of GA are how to represent the schedules as an individuals and to design the genetic operators for the representation in order to produce better results.<<ETX>>

Solving fuzzy assembly-line balancing problem with genetic algorithms

Abstract Assembly-line balancing problem is known as one of difficult combinatorial optimization problems. This problem has been solved with linear programming, dynamic programming approaches, but unfortunately these approaches do not lead to efficient algorithms. Recently, genetic algorithm has been recognized as an efficient and usefull procedure for solving large and hard combinatorial optimization problems, such as scheduling problems, travelling salesman problems, transportation problems, and so on. Fuzzy sets theory is frequently used to represent uncertainty of information. In this paper, to treat the data of real-world problems we use a fuzzy number to represent the processing time and show that we can get a good performance in solving this problem using genetic algorithms.

Large-scale 0–1 fuzzy goal programming and its application to reliability optimization problem

Abstract Goal Programming (GP) is one of the most powerful Multiple Objective Decision Making (MODM) methods for Industrial Engineering. In practical MODM problems, many GP models involve a large number of 0–1 decision variables and special structures in the system constraints. In this paper, an efficient algorithm for solving large-scale 0–1 GP problem is proposed, introducing the fuzziness due to judgement of goal accomplishments, with the generalized upper bound structure. Also, the optimization problem of system reliability with several failure modes is demonstrated by using the proposed algorithm. Finally, the effectiveness of the algorithm is illustrated.

An application of fuzzy set theory to inventory control models

A method for solving an inventory control problem, of which input data are described by triangular fuzzy numbers will be presented here. The continuous review model of the inventory control problem with fuzzy input data will be focused in, and a new solution method will be presented. For the reason that the result should be a fuzzy number because of fuzzy input data, and the certain number about order quantity is prefered in the real-world, it is necessary to transform the fuzzy result to crisp one. The interval mean value concept is used here to help to solve this problem. Under the condition of total cost minimum, the interval order quantity maximum can be obtained.

Method for solving multiobjective aggregate production planning problem with fuzzy parameters

Abstract We propose an efficient method that transforms a fuzzy multiple objective linear programming (MOLP) problem model to crisp MOLP model, and an interactive solution procedure that suggest the best compromise aggregate production plans for the multi-period fuzzy multiple objective aggregate production planning (APP) problem.

Entropy-based genetic algorithm for solving TSP

The traveling salesman problem (TSP) is used as a paradigm for a wide class of problems having complexity due to the combinatorial explosion. The TSP has become a target for the genetic algorithm (GA) community, because it is probably the central problem in combinatorial optimization and many new ideas in combinatorial optimization have been tested on the TSP. However, by using GA for solving TSPs, we obtain a local optimal solution rather than a best approximate solution frequently. The goal of the paper is to solve the above mentioned problem about local optimal solutions by introducing a measure of diversity of populations using the concept of information entropy. Thus, we can obtain a best approximate solution of the TSP by using this entropy-based GA.

An effective method for solving flow shop scheduling problems with fuzzy processing times

Abstract This paper show that fuzzy set theory can be useful in modelling and solving flow shop scheduling problems with uncertain processing times and illustrates a methodology for solving job sequencing problem which the opinions of experts greatly disagree in each processing time. Triangular fuzzy numbers (TFNs) are used to represent the processing times of experts. And the comparison methods based on the dominance property is sued to determine the ranking of the fuzzy numbers. By the dominance criteria, for each job, a major TFN and a minor TFN are selected and a pessimistic sequence with major TFNs and an optimistic sequence with minor TFNs are computer. Branch and bound algorithm for makespan in three-machine flow shop is utilized to illustrate the proposed methodology.