Flow Shop Scheduling Using a General Approach for Differential Evolution

Abstract

This chapter presents a general framework of Differential Evolution algorithm for combinatorial optimization problems. We define the differences between a given pair of solutions in the differential mutation as a set of elementary movements in the discrete search space. In this way, the search mechanism and self-adaptive behavior of the differential evolution is preserved and generalized to combinatorial problems. These ideas are then applied to n-job m-machine flow shop scheduling in order to illustrate its application in an important problem in combinatorial optimization. The method was applied to the 120 Taillard instances of the permutation flow shop scheduling problem, and compared against the results obtained by other metaheuristic algorithms in the literature. Although relying only on the differential mutation and the local search performed on the best individual, dDE ranks fairly well against more sophisticated metaheuristics. The results are promising and illustrate the applicability of the proposed approach for combinatorial optimization using differential evolution. © Springer-Verlag Berlin Heidelberg 2013.