EVOLUTIONARY ALGORITHMS FOR JOB-SHOP SCHEDULING

This paper explains how to use Evolutionary Algorithms (EA) to deal with a flexible job shop scheduling problem, especially minimizing the makespan. The Job-shop Scheduling Problem (JSP) is one of the most difficult problems, as it is classified as an NP-complete one (Carlier and Chretienne, 1988; Garey and Johnson, 1979). In many cases, the combination of goals and resources exponentially increases the search space, and thus the generation of consistently good scheduling is particularly difficult because we have a very large combinatorial search space and precedence constraints between operations. Exact methods such as the branch and bound method and dynamic programming take considerable computing time if an optimum solution exists. In order to overcome this difficulty, it is more sensible to obtain a good solution near the optimal one. Stochastic search techniques such as evolutionary algorithms can be used to find a good solution. They have been successfully used in combinatorial optimization, e.g. in wire routing, transportation problems, scheduling problems, etc. (Banzhaf et al., 1998; Dasgupta and Michalewicz, 1997). Our objective is to establish a practical relationship between the development in the EA area and the reality of a production JSP by developing, on the one hand, two effective genetic encodings, such as parallel job and parallel machine representations of the chromosome, and on the other, genetic operators associated with these representations. In this article we deal with the problem of flexible job-shop scheduling which presents two difficulties: the first is the assignment of each operation to a machine, and the other is the scheduling of this set of operations in order to minimize our criterion (e.g. the makespan).