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

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 N P -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, which explores neighborhoods 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. In AIV each perturbation is characterized by removing a job from one machine and inserting it into another machine. AIV was tested using benchmark instances from literature. Statistical analysis of the computational experiments showed that AIV outperformed the algorithms of the literature, setting new