A Wale Optimization Algorithm for Distributed Flow Shop with Batch Delivery

Abstract In this study, a distributed flow shop scheduling problem with batch delivery constraints is investigated. The objective is to minimize the makespan and energy consumptions simultaneously. To this end, a hybrid algorithm combining the wale optimization algorithm (WOA) with local search heuristics is developed. In the proposed algorithm, each solution is represented by three vectors, namely a job scheduling sequence vector, batch assignment vector, and a factory assignment vector. Then, an efficient neighborhood structure is applied in the proposed algorithm to enhance search abilities. Furthermore, the simulated annealing algorithm and clustering method are embedded to improve the global search abilities of the algorithm. Finally, 30 instances are generated based on realistic application to test the performance of the algorithm. After detailed comparisons with three efficient algorithms, i.e., ABC-Y, ICA-K, and IWOA NS , the superiority of the proposed algorithm is verified.