A hybrid differential evolution method for permutation flow-shop scheduling

The permutation flow-shop scheduling problem (PFSSP) is a typical combinational optimization problem, which is of wide engineering background and has been proved to be strongly NP-hard. In this paper, a hybrid algorithm based on differential evolution (DE), named HDE, is proposed for the single-objective PFSSPs. Firstly, to make DE suitable for solving PFSSPs, a largest-order-value (LOV) rule is presented to convert the continuous values of individuals in DE to job permutations. Secondly, after the DE-based exploration, a simple but efficient local search, which is designed according to the PFSSPs' landscape, is applied to emphasize exploitation. Thus, not only does the HDE apply the parallel evolution mechanism of DE to perform effective exploration (global search), but it also adopts problem-dependent local search methodology to adequately perform exploitation (local search). Based on the theory of finite Markov chains, the convergence property of the HDE is analyzed. Then, the HDE is extended to a multi-objective HDE (MHDE) to solve the multi-objective PFSSPs. Simulations and comparisons based on benchmarks for both single-objective and multi-objective PFSSPs are carried out, which show the effectiveness, efficiency, and robustness of the proposed HDE and MHDE.