Multiobjective Local Search Algorithm-Based Decomposition for Multiobjective Permutation Flow Shop Scheduling Problem

This paper focuses on the multiobjective solutions of the flow shop scheduling problem with and without sequence dependent setup times. In our case, the two objectives are the minimization of makespan and total flowtime. These problems are solved with a novel multiobjective local search framework-based decomposition, called multiobjective local search based decomposition (MOLSD), which decomposes a multiobjective problem into a number of single objective optimization subproblems using aggregation method and optimizes them simultaneously. First, a problem-specific Nawaz-Enscore-Hoam heuristic is used to initialize the population to enhance the quality of the initial solution. Second, a Pareto local search embedded with a heavy perturbation operator is applied to search the promising neighbors of each nondominated solution found so far. Then, when solving each sub-problem, a single insert-based local search, a multiple local search strategy, and a doubling perturbation mechanism are designed to exploit the new individual. Finally, a restarted method is used to avoid the algorithm trapping into the local optima, which has a significant effect on the performance of the MOLSD. Comprehensive experiments have been conducted by two standard multiobjective metrics: 1) hyper-volume indicator; and 2) set coverage. The experimental results show that the proposed MOLSD provides better solutions that several state of the art algorithms.