Efficient multi-objective algorithm for the lot-streaming hybrid flowshop with variable sub-lots

Recent years, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been researched and applied for numerous optimization problems. In this study, we propose an improved version of MOEA/D with problem-specific heuristics, named PH-MOEAD, to solve the hybrid flowshop scheduling (HFS) lot-streaming problems, where the variable sub-lots constraint is considered to minimize four objectives, i.e., the penalty caused by the average sojourn time, the energy consumption in the last stage, as well as the earliness and the tardiness values. For solving this complex scheduling problem, each solution is coded by a two-vector-based solution representation, i.e., a sub-lot vector and a scheduling vector. Then, a novel mutation heuristic considering the permutations in the sub-lots is proposed, which can improve the exploitation abilities. Next, a problem-specific crossover heuristic is developed, which considered solutions with different sub-lot size, and therefore can make a solution feasible and enhance the exploration abilities of the algorithm as well. Moreover, several problem-specific lemmas are proposed and a right-shift heuristic based on them is subsequently developed, which can further improve the performance of the algorithm. Lastly, a population initialization mechanism is embedded that can assign a fit reference vector for each solution. Through comprehensive computational comparisons and statistical analysis, the highly effective performance of the proposed algorithm is favorably compared against several presented algorithms, both in solution quality and population diversity.