Comparative Performance of Three Metaheuristic Approaches for the Maximally Diverse Grouping Problem

Abstract

Given a set of elements and a symmetric matrix representing dissimilarities between them, the maximally diverse grouping problem asks to find a partitioning of the elements into a fixed number of restricted size-groups such that the sum of pairwise dissimilarities between elements in the same group is maximized. We present multistart simulated annealing, hybrid genetic and variable neighborhood search algorithms for solving this problem. We report on computational experiments that compare the performance of these algorithms on benchmark instances of size up to 2000 elements.

Maximally diverse grouping: an iterated tabu search approach

“…In order to reach such solutions, the VNS technique for instances of size 2000 required very long computation times. In general, it was discovered from the experiments that all the methods investigated by Palubeckis et al (2011) did not perform very well for large problem instances. The authors have concluded that there remains a lot of room for improvement in the heuristics for solving the MDGP.…”

“…The current paper is an important extension of our recent work (Palubeckis et al, 2011) on metaheuristics for solving the MDGP. The previous study by Palubeckis et al (2011) has investigated computationally the applicability of three quite different metaheuristics to the MDGP, namely, simulated annealing (SA), HGA and variable neighbourhood search (VNS).…”

“…The previous study by Palubeckis et al (2011) has investigated computationally the applicability of three quite different metaheuristics to the MDGP, namely, simulated annealing (SA), HGA and variable neighbourhood search (VNS). Since the CPU time-based stopping criterion was used, the SA procedure was run in a multistart mode.…”

“…Certainly, in this case, the index k can be dropped everywhere. Computational experience shows that the MDGP is a substantially more difficult problem than the MDP (Palubeckis, 2007;Palubeckis et al, 2011;Martí et al, 2013). An important special case of the MDGP is the K r -factor problem (Guruswami et al, 2001), which asks for the existence of a partition of the vertex set of a graph into copies of the complete graph on r vertices, denoted K r .…”

“…As expected, the performance of the pure genetic algorithm, that is HGA without the LS component, is very poor compared with the proposed HGA implementation. The third algorithm considered by Palubeckis et al (2011) is based on the VNS scheme. As the experiments show, for the largest problem instances in the test set, this algorithm performed better than both SA and HGA.…”