Local search heuristics for the Flowshop Sequence Dependent Group Scheduling problem

This paper considers the Flowshop Sequence Dependent Group Scheduling (FSDGS) problem In this problem, the n jobs to be processed on m machines are grouped in families (or groups) in a way that a machine setup time is needed between two consecutive jobs of different groups. The purpose of this problem is to determine the sequence of the groups and the sequence of the jobs within each group in order to minimize the total flow time. The FSDGS problem is classified as NP-hard, thus, efficient heuristics are needed to obtain near-optimal solutions in reasonable computational time. In this work, we propose a hybrid heuristic based on Variable Neighborhood Descent (VND) and Iterated Local Search (ILS) metaheuristic. Our heuristic operates with three neighborhood structures and new starting solutions are obtained by applying a perturbation procedure on the current best solution. The computational results show that our heuristic outperforms, in terms of solution quality, an algorithm proposed in the literature. The results are confirmed by a statistical analysis.