Pareto-optimality approach for flexible job-shop scheduling problems: hybridization of evolutionary algorithms and fuzzy logic

Most scheduling problems are complex combinatorial problems and very difficult to solve [Manage. Sci. 35 (1989) 164; F.S. Hillier, G.J. Lieberman, Introduction to Operations Research, Holden-Day, San Francisco, CA, 1967]. That is why, lots of methods focus on the optimization according to a single criterion (makespan, workloads of machines, waiting times, etc.). The combining of several criteria induces additional complexity and new problems. In this paper, we propose a Pareto approach based on the hybridization of fuzzy logic (FL) and evolutionary algorithms (EAs) to solve the flexible job-shop scheduling problem (FJSP). This hybrid approach exploits the knowledge representation capabilities of FL [Fuzzy Sets Syst. 1 (1989)] and the adaptive capabilities of EAs. The integration of these two methodologies for the multi-objective optimization has become an increasing interest. The objective considered is to minimize the overall completion time (makespan), the total workload of machines and the workload of the most loaded machine. Many examples are presented to illustrate some theoretical considerations and to show the efficiency of the suggested methodology.