Fixed set search application for minimizing the makespan on unrelated parallel machines with sequence-dependent setup times

This paper addresses the problem of minimizing the makespan on unrelated parallel machines with sequence-dependent setup times. The term unrelated machines is used in the sense that there is no correlation between the processing times for jobs between different machines. Due to the NP-hardness of this problem, a wide range of metaheuristics has been developed to find near-optimal solutions. Out of such methods, the ones based on constructive greedy algorithms like the Greedy Randomized Adaptive Search Procedure (GRASP), Ant Colony Optimization (ACO) and Worm Optimization (WO) proved to be most efficient. The Fixed Set Search (FSS) is a novel population-based metaheuristic of this type that adds a learning mechanism to the GRASP. The basic concept of FSS is to avoid focusing on specific high quality solutions but on parts or elements that such solutions have. This is done through fixing a set of elements that exist in such solutions and dedicating computational effort to finding near-optimal solutions for the underlying subproblem. In this work, the FSS is applied to the problem of interest. Computational experiments show that the FSS manages to significantly outperform the GRASP, ACO and WO on the standard benchmark instances when the quality of found solutions is considered without an increase in computational cost. This application of the FSS is significant as it shows that it can also be applied to scheduling type problems, in addition to covering and routing ones.