AIV: A Heuristic Algorithm based on Iterated Local Search and Variable Neighborhood Descent for Solving the Unrelated Parallel Machine Scheduling Problem with Setup Times

Abstract

This paper deals with the Unrelated Parallel Machine Scheduling Problem with Setup Times (UPMSPST). The objective is to minimize the maximum completion time of the schedule, the so-called makespan. This problem is commonly found in industrial processes like textile manufacturing and it belongs to NP-Hard class. It is proposed an algorithm named AIV based on Iterated Local Search (ILS) and Variable Neighborhood Descent (VND). This algorithm starts from an initial solution constructed on a greedy way by the Adaptive Shortest Processing Time (ASPT) rule. Then, this initial solution is refined by ILS, using as local search the Random VND procedure, exploring neighborhood structures based on swaps and multiple insertions. In this procedure, here called RVND, there is no fixed sequence of neighborhoods, because they are sorted on each application of the local search. The perturbations of ILS consist in reinserting jobs from one machine to another. AIV was tested using benchmark instances from literature and statistical analysis of the computational experiments showed that AIV outperformed the algorithms of the literature, setting new improved solutions.