Flexible job shop scheduling using hybrid differential evolution algorithms

Keywords: Scheduling Flexible job shop Differential evolution Local search Neighborhood structure Makespan a b s t r a c t This paper proposes hybrid differential evolution (HDE) algorithms for solving the flexible job shop scheduling problem (FJSP) with the criterion to minimize the makespan. Firstly, a novel conversion mechanism is developed to make the differential evolution (DE) algorithm that works on the continuous domain adaptive to explore the problem space of the discrete FJSP. Secondly, a local search algorithm based on the critical path is embedded in the DE framework to balance the exploration and exploitation by enhancing the local searching ability. In addition, in the local search phase, the speed-up method to find an acceptable schedule within the neighborhood structure is presented to improve the efficiency of whole algorithms. Extensive computational results and comparisons show that the proposed algorithms are very competitive with the state of the art, some new best known solutions for well known benchmark instances have even been found. The job shop scheduling problem (JSP) is one of most important and difficult problems in the field of production scheduling. The flexible job shop scheduling problem (FJSP) is an extension of the classical JSP, in which operations are allowed to be processed by any machine from a given set, rather than one specified machine. Generally, the FJSP is much closer to a real production environment and has more practical applicability. However, the FJSP is more complex than the JSP because of its additional decision to assign each operation to the appropriate machine (routing) besides sequencing operations on machines. It has been proved that the FJSP is strongly NP-hard even if each job has at most three operations and there are two machines (Garey et al., 1976). Although exact algorithms based on a disjunctive graph representation of the problem have been developed, but they are not applicable for instances with more than 20 jobs and 10 machines (Pinedo, 2002). So, metaheuristics for the FJSP, which aim to find the near-optimal schedule with acceptable computational time, have gained increasing attention in the past decades. Among them, tabu search (TS), genetic algorithm (GA), particle swarm optimization (PSO) were most frequently adopted to solve the FJSP. As for TS, Brandimarte (1993) proposed a hybrid TS heuristic with some known dispatching rules to solve the FJSP. Hurink et al. (1994) presented a TS procedure in which routing and sequencing are regarded as …