Hybrid matheuristics for the multi-capacitated clustering problem

Abstract

The capacitated clustering problem is a well-known and largely studied combinatorial optimization problem with several industrial applications. Although a great attention has been paid to this problem in the literature, the deeming of the problem with clients of multiple types and clusters with multiple capacities is quite limited. We introduce a novel variant of capacitated clustering problems named multi-capacitated clustering problem (MCCP), a NP-hard optimization problem in which there are several clients that must be grouped into different sets that have different capacities for different types of clients. It is taken into account the distance between each one of these clients and the potential clusters to which they can be allocated, aiming to minimize the sum of such distances. It is presented an integer programming model for this problem, which it is shown to have limited application solving large-sized instances. As solution procedures, we present the following algorithms. We propose a greedy heuristic to generate a feasible solution within a negligible computational effort. We adapt a size-reduction (SR) matheuristic to solve the problem under study. Furthermore, we introduce an innovative matheuristic that hybridizes the well-known GRASP algorithm with the SR algorithm. Also, we develop a variable fixing (VF) heuristic, which is an extension of the matheuristic presented by Martinez-Gavara et al. \cite{martinez2017randomized}. Finally, we propose a hybrid matheuristic based on the SR and VFH algorithms. Computational results over a set of 100 randomly generated test instances point out the quality of the solutions found by the proposed algorithms. Our proposals are among the best heuristics developed for this problem.