Smart General Variable Neighborhood Search with Local Search based on Mathematical Programming for Solving the Unrelated Parallel Machine Scheduling Problem

This work addresses the Unrelated Parallel Machine Scheduling Problem in which machine and job sequencedependent setup time are considered. The objective is to minimize the makespan. For solving it, a Smart General Variable Neighborhood Search algorithm is proposed. It explores the solution space through five strategies: swap of jobs in the same machine, insertion of job in the same machine, swap of jobs between machines, insertion of jobs to different machines and an application of a Mixed Integer Linear Programming formulation to obtain optimum scheduling on each machine. The first four strategies are used as shaking mechanism, while the last three are applied as local search through the Variable Neighborhood Descent method. The proposed algorithm was tested in a set of 810 instances available in the literature and compared to three state-of-the-art algorithms. Although the SGVNS algorithm did not statistically outperform them in these instances, it was able to outperform them in 79 instances.