Flow Shop Scheduling Using a General Approach for Differential Evolution

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. Frederico Gadelha Guimarães · Rodrigo César Pedrosa Silva · Oriane Magela Neto Departamento de Engenharia Elétrica, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil e-mail: [email protected], [email protected], [email protected] Ricardo Sérgio Prado Instituto Federal Minas Gerais, Ouro Preto, Brazil e-mail: [email protected] Donald David Davendra Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VB-Technical University of Ostrava, Czech Republic e-mail: [email protected] I. Zelinka et al. (Eds.): Handbook of Optimization, ISRL 38, pp. 597–614. springerlink.com c © Springer-Verlag Berlin Heidelberg 2013 598 F.G. Guimarães et al.