A two-phase evolutionary algorithm for multi-objective distributed assembly permutation flowshop scheduling problem

In recent years, multi-objective optimization problems have received extensive attention. This paper proposes a two-phase evolutionary algorithm (TEA) to solve the multi-objective distributed assembly permutation flowshop scheduling problem with total flowtime and total tardiness criteria. The first phase of the TEA uses a novel two-population structure to simultaneously optimize the two criteria. According to the characteristics of the structure, two construction heuristics are designed to obtain solutions with both high quality and diversity. Four crossover and two mutation operators are presented. The interaction between the two populations increases the diversity within each population. The second phase integrates the previous two populations and uses the method of normalized objective function to enhance efficiency. Two new crossover operators are proposed to improve the performance of the algorithm. The TEA first finds several approximate front solutions to provide ideal feasible areas, and then continuously expands the solutions to the Pareto front. It embodies convergence, diversity and uniformity in different phases. Finally, through 810 benchmark instances, the TEA is compared with five classical and popular algorithms. The effectiveness of the two mechanisms in the TEA is analyzed. Experimental results demonstrate the superior performance of the TEA in terms of distribution and coverage of solutions.