Analysis of stochastic local search methods for the unrelatedparallel machine scheduling problem.

Abstract

This work addresses the unrelated parallel machine scheduling problem with sequence-dependent setup times,in which a set of jobs must be scheduled for execution by one of the several available machines. Each jobhas a machine-dependent processing time. Furthermore, given multiple jobs, there are additional setup times,which vary based on the sequence and machine employed. The objective is to minimiz e the schedule’s com-pletion time (makespan). The problem is NP-hard and of significant practical relevance. The present paperinvestigates the performance of four different stochastic local search (SLS) methods designed for solvingthe particular scheduling problem: simulated annealing, iterated local search, late acceptance hill-climbing,and step counting hill-climbing. The analysis focuses on design questions, tuning effort, and optimizationperformance. Simple neighborhood structures are considered. All proposed SLS methods performed signifi-cantly better than two state-of-the-art hybrid heuristics, especially for larger instances. Updated best-knownsolutions were generated for 901 of the 1000 large benchmark instances considered, demonstrating that par-ticular SLS methods are simple yet powerful alternatives to current approaches for addressing the problem.Implementations of the contributed algorithms have been made available to the research community.