Multiobjective Optimization for FJSP Under Immediate Predecessor Constraints Based OFA and Pythagorean Fuzzy Set

In the flexible job shop scheduling problem (FJSP), immediate predecessor operations have an explicit impact on the scheduling results, and are often ignored. To analyze the influence of immediate predecessor operations on machine tool manufacturing workshops, four forms of immediate predecessor operations with the consideration of uncertain transportation and preparation time are defined. Then, the four forms of immediate predecessor operations are integrated into the FJSP, and a multiobjective FJSP is constructed. An improved optimal foraging algorithm (OFA) and Pythagorean fuzzy set (PFS) are combined to establish a multiobjective optimization algorithm, named PFSOFA. This algorithm is then used to solve the multiobjective FJSP. In PFSOFA, the Pareto fronts are mapped into PFSs. The Pythagorean fuzzy numbers (PFNs) in a PFS are transformed into right triangles, and the distances between the PFNs and the reference PFNs are defined as the distances between their right triangle centroids. Then, all distances of a PFS are integrated by the distance prospect function to obtain a distance prospect value. This value is then used to lead the iteration of PFSOFA. Through extensive experiments, including a real factory application case, the performance of PFSOFA is verified to be better than four classical multiobjective optimization algorithms for solving the multiobjective FJSP constructed in this article. And for the factory case, PFSOFA also obtained the better schemes.