An Adaptive Large Neighborhood Search with Learning Automata for the Unrelated Parallel Machine Scheduling Problem

This work deals with the Unrelated Parallel Machine Scheduling Problem with Setup Times, with the objective of minimizing the makespan. It is proposed an Adaptive Large Neighborhood Search (ALNS) metaheuristic using Learning Automata (LA) to adapt the probabilities of using removal and insertion heuristics and methods. A computable function in the LA updates the probability vector for selecting the actions, corresponding to six removal and six insertion methods. We also propose a new insertion method based on Hungarian algorithm, which is applied to solve subproblems optimally. Computational experiments are performed to verify the performance of the proposed method. A set of instances available in the literature with problems up to 150 jobs and 10 machines is employed in the experiments. The proposed LA-ALNS is compared against three other algorithms from the literature. The results suggest that our algorithm has better performance in most of cases (88%) under the defined conditions of experiments. Statistical tests also suggest that LA-ALNS is better than the other algorithms from the literature. The proposed method is able to automatically choose the most suitable heuristics for the instance of the problem, through adaptation and learning in the Learning Automata.