A Comparative Analysis of Two Matheuristics by Means of Merged Local Optima Networks

Abstract

We present a comparative analysis of two hybrid algorithms for solving combinatorial optimisation problems. The first one is a specific variant of an established family of techniques known as large neighbourhood search (LNS). The second one is a much more recent algorithm known as construct, merge, solve & adapt (CMSA). Both approaches generate, in different ways, reduced sub-instances of the tackled problem instance at each iteration. The experimental analysis is conducted on two NP-hard combinatorial subset selection problems: the multidimensional knapsack problem and minimum common string partition. The results support the intuition that CMSA has advantages over the LNS variant in the context of problems for which solutions contain rather few items. Moreover, they show that the opposite may be the case for problems in which solutions contain rather many items. The analysis is supported by a new way of visualising the trajectories of the compared algorithms in terms of merged monotonic local optima networks.