Abstract
Permutation flow shop scheduling problems (PFSPs) with many objectives are highly important scheduling problems in operations research. They have attracted substantial attention from enterprise operators and researchers in recent years. In this article, a membership function is used to connect the function values of many-objective optimization problems with a fuzzy membership degree. An approach for mapping function values to fuzzy sets is presented. Thus, the fuzzy relative entropy (FRE) can be employed in many-objective PFSPs. A many-objective PFSP model with four objectives, namely, the makespan, total tardiness, inventory holding cost, and energy consumption cost, is established. The optimal foraging algorithm (OFA) with FRE (OFA/FRE) is proposed for solving many-objective PFSPs. FRE is used as the fitness strategy of OFA. OFA/FRE is evaluated in three classification experiments and compared with five algorithms on the Walking-Fish-Group test suite, PFSP benchmark instances, and a practical PFSP for machine tool components. The results demonstrate that OFA/FRE is a promising tool for many-objective PFSP. The FRE can be used in scheduling problems and in many-objective optimization problems.
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