A Hybrid Discrete Memetic Algorithm for Solving Flow-Shop Scheduling Problems

Abstract

Flow-shop scheduling problems are classic examples of multi-resource and multi-operation scheduling problems where the objective is to minimize the makespan. Because of the high complexity and intractability of the problem, apart from some exceptional cases, there are no explicit algorithms for finding the optimal permutation in multi-machine environments. Therefore, different heuristic approaches, including evolutionary and memetic algorithms, are used to obtain the solution—or at least, a close enough approximation of the optimum. This paper proposes a novel approach: a novel combination of two rather efficient such heuristics, the discrete bacterial memetic evolutionary algorithm (DBMEA) proposed earlier by our group, and a conveniently modified heuristics, the Monte Carlo tree method. By their nested combination a new algorithm was obtained: the hybrid discrete bacterial memetic evolutionary algorithm (HDBMEA), which was extensively tested on the Taillard benchmark data set. Our results have been compared against all important other approaches published in the literature, and we found that this novel compound method produces good results overall and, in some cases, even better approximations of the optimum than any of the so far proposed solutions.