A self-adaptive differential evolution for the permutation flow shop scheduling problem

Since the basic differential evolution (DE) is vulnerable to be trapped in a local optimum, a self-adaptive DE (SDE) is proposed in this paper. Firstly, for the sake of balancing the global and local search ability of DE, chaos theory is introduced to optimize the parameters and a self-adaptive parameter setting strategy according to the individual´s fitness is adopted. Secondly, to increase the population diversity and enhance the global convergence ability of algorithm, the crossover and selection operator of DE are modified. For permutation flow shop problems(PFSP) with the makespan criterion, the largest-order-value rule has been adopted to convert DEs individual to job permutation. Simulations and comparisons of DE, HDE_NOL (hybrid differential evolution without local search) and SDE based on the well-known benchmark problems demonstrate the SDE can balance the local and global search to solve PFSP with the makespan criterion, and there is better global search ability, search efficiency and robusticity for SDE.