Metaheuristics to solve grouping problems: A review and a case study

Grouping problems are a special type of combinatorial optimization problems that have gained great relevance because of their numerous real-world applications. The solution process required by some grouping problems represents a high complexity, and currently, there is no algorithm to find the optimal solution efficiently in the worst case. Consequently, the scientific community has classified such problems as NP-hard. For the solution of grouping problems, numerous elaborate procedures have been designed incorporating different techniques. The specialized literature includes enumerative methods, neighborhood searches, evolutionary algorithms as well as swarm intelligence algorithms. In this study, a review of twenty-two NP-hard grouping problems is carried out, considering seventeen metaheuristics. The state-of-the-art suggests that Genetic Algorithms (GM) have shown the best performance in most of the cases, and the group-based representation scheme can be used to improve the performance of different metaheuristics designed to solve grouping problems. Finally, a case study is presented to compare the performance of three metaheuristic algorithms with different representation schemes for the Parallel-Machine Scheduling problem with unrelated machines, including the GA with extended permutation encoding, the Particle Swarm Optimization (PSO) with machine-based encoding, and the GA with group-based encoding. Experimental results suggest that the GA with the group-based encoding is the best option to address this problem.