Iterated Local Search with Path Relinking for Solving Parallel Machines Scheduling Problem with Resource-Assignable Sequence Dependent Setup Times

This paper addresses the unrelated parallel machine problem with machine and job sequence dependent setup. In this problem, the amount of the setup time does not only depend on the machine and job sequence, but also on a number of resources assigned, which can vary between a minimum and a maximum. The goal is to find a schedule that minimizes the linear combination of the total resources assigned and the total completion time. The problem is NP-hard in the strong sense. The NP-hardness of the problem motivates us to develop a new Iterated Local Search (ILS) heuristic to obtain near-optimal solutions. The heuristic uses an intensification strategy based on the Path Relinking technique which generates new solutions by exploring trajectories that connect high-quality solutions. Computational tests are carried out on a set of benchmark instances and the results obtained by the proposed ILS improve the best known results from the literature by a significant margin.