A heuristic-search genetic algorithm for multi-stage hybrid flow shop scheduling with single processing machines and batch processing machines

This paper addresses the scheduling problem for a multi-stage hybrid flow shop (HFS) with single processing machines and batch processing machines. Each stage consists of nonidentical machines in parallel, and only one of the stages is composed of batch processing machines. Such a variant of the HFS problem is derived from the actual manufacturing of complex products in the equipment manufacturing industry. Aiming at minimizing the maximum completion time and minimizing the total weighted tardiness, respectively, a heuristic-search genetic algorithm (HSGA) is developed in this paper, which selects assignment rules for parts, sequencing rules for machines (including single processing machines and batch processing machines), and batch formation rules for batch processing machines, simultaneously. Then parts and machines are scheduled using the obtained combinatorial heuristic rules. Since the search space composed of the heuristic rules is much smaller than that composed of the schedules, the HSGA results in lower complexity and higher computational efficiency. Computational results indicate that as compared with meta-heuristics that search for scheduling solutions directly, the HSGA has a significant advantage with respect to the computational efficiency. As compared with combinatorial heuristic rules, other heuristic-search approaches, and the CPLEX, the HSGA provides better optimizational performance and is especially suitable to solve large dimension scheduling problems.