An efficient ILS heuristic for total flow time minimization in a Flow Shop Sequence Dependent Group Scheduling problem

This paper considers the Flow shop Sequence Dependent Group Scheduling (FSDGS) problem with minimization of total flow time criterion. In this problem, the n jobs to be processed on m machines are grouped in families (groups) in a way that a machine setup time is needed between two consecutive jobs of different groups. 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 an Iterated Local Search (ILS) heuristic. Our heuristic operates on a set of reference solutions (high quality and diverse solutions) constructed and updated as done in the Scatter Search metaheuristic. The performance of the proposed heuristic is compared with the best existing metaheuristic (Particle Swarm Optimization - PSO) proposed in the literature for the same problem. The computational results show that our heuristic outperforms the PSO algorithm in terms of solution quality. The results are confirmed by a statistical analysis.