Solving Type-2 Fuzzy Distributed Hybrid Flowshop Scheduling Using an Improved Brain Storm Optimization Algorithm

The distributed hybrid flowshop scheduling (DHFS) problem is a common scheduling problem that has been researched in both academic and industrial fields during recent years. The uncertainty levels in realistic applications are generally too high to be represented by a deterministic value or a triangular fuzzy number (TFN) value. Considering the DHFS problem with type-2 fuzzy processing time and setup time constraints, an improved version of brain storm optimization was developed, where the objective is to minimize the maximum type-2 fuzzy completion time among all factories. The main contributions of this study are as follows: (1) each solution is represented by a two vectors, i.e., a scheduling vector and a factory assignment vector; (2) two realistic constraints, i.e., the type-2 fuzzy processing time in an uncertain environment and the setup time, make the problem more realistic; (3) a novel constructive heuristic based on the Nawaz-Enscore-Ham (NEH) method, called distributed NEH, is proposed; (4) several local search heuristics considering the problem features and the objective are developed to enhance the local search abilities; and (5) a simulated-annealing-based acceptance criterion is embedded to enhance the exploration abilities. The experimental results demonstrate that the proposed algorithm is more efficient and effective for solving the considered type-2 fuzzy DHFS problems in comparison with other recently published efficient algorithms.