A novel hybrid discrete differential evolution algorithm for blocking flow shop scheduling problems

This paper proposes a novel hybrid discrete differential evolution (HDDE) algorithm for solving blocking flow shop scheduling problems to minimize the maximum completion time (i.e. makespan). Firstly, in the algorithm, the individuals are represented as discrete job permutations, and new mutation and crossover operators are developed for this representation, so that the algorithm can directly work in the discrete domain. Secondly, a local search algorithm based on insert neighborhood structure is embedded in the algorithm to balance the exploration and exploitation by enhancing the local searching ability. In addition, a speed-up method to evaluate insert neighborhood is developed to improve the efficiency of the whole algorithm. Computational simulations and comparisons based on the well-known benchmark instances of Taillard [Benchmarks for basic scheduling problems. European Journal of Operational Research 1993;64:278-285], by treating them as blocking flow shop problem instances with makespan criterion, are provided. It is shown that the proposed HDDE algorithm not only generates better results than the existing tabu search (TS) and TS with multi-moves (TS+M) approaches proposed by Grabowski and Pempera [The permutation flow shop problem with blocking. A tabu search approach 2007;35:302-311], but also outperforms the hybrid differential evolution (HDE) algorithm developed by Qian et al. [An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers. Computers and operations research 2009;36(1):209-233] in terms of solution quality, robustness and search efficiency. Ultimately, 112 out of 120 best known solutions provided by Grabowski and Pempera [The permutation flow shop problem with blocking. A tabu search approach 2007;35:302-311] and Ronconi [A branch-and-bound algorithm to minimize the makespan in a flowshop problem with blocking. Annals of Operations Research 2005;138(1):53-65] are further improved by the proposed HDDE algorithm.