An opposition-based differential evolution algorithm for permutation flow shop scheduling based on diversity measure

The permutation flow shop problem (PFSSP) is an NP-hard problem of wide engineering and theoretical background. In this paper, a differential evolution (DE) based memetic algorithm, named ODDE, is proposed for PFSSP. First, to make DE suitable for PFSSP, a new LRV rule based on random key is introduced to convert the continuous position in DE to the discrete job permutation. Second, the NEH heuristic was combined the random initialization to the population with certain quality and diversity. Third, to improve the global optimization property of DE, a DE approach based on measure of population's diversity is proposed to tuning the crossover rate. Fourth, to improve the convergence rate of DE, the opposition-based DE employs opposition-based learning for the initialization and for generation jumping to enhance the global optimal solution. Fifth, the fast local search is used for enhancing the individuals with a certain probability. Sixth, the pairwise based local search is used to enhance the global optimal solution and help the algorithm to escape from local minimum. Additionally, simulations and comparisons based on PFSSP benchmarks are carried out, which show that our algorithm is both effective and efficient. We have also evaluated our algorithm with the well known DMU problems. For the problems with the objective of minimizing makespan, the algorithm ODDE obtains 24 new upper bounds of the 40 instances, and for the problems with the objective of maximum lateness, ODDE obtains 137 new upper bounds of the 160 instances. These new upper bounds can be used for future algorithms to compare their results with ours. (C) 2012 Elsevier Ltd. All rights reserved.