A Two-Population Cooperative Multiobjective Differential Evolution Algorithm for Batching Scheduling Problem

Abstract

Batch processing machine (BPM) scheduling problem is a NP hard problem for it includes machine allocation, job grouping, and batch scheduling. In this paper, to address the BPM scheduling problem with unrelated parallel machine, a multiobjective algorithm based on multipopulation coevolution is proposed to minimize the total energy consumption and the completion time simultaneously. Firstly, the mixed integer programming model of the problem is established, and four heuristic decoding rules are proposed. Secondly, to improve the diversity and convergence of the algorithm, the population is divided into two populations: each of the populations evolves independently by using different decoding rules, and the two populations will communicate through a common external archive set every certain number of generations. Thirdly, an initialization strategy and a variable neighborhood search algorithm (VNS) are proposed to improve the overall performance of the algorithm. Finally, in order to evaluate the proposed algorithm, a large number of comparative experiments with the state-of-the-art multiobjective algorithms are carried out, and the experimental results proved the effectiveness of the proposed algorithm.