Application of CMSA to the minimum capacitated dominating set problem

Abstract

This work deals with the so-called minimum capacitated dominating set (CAPMDS) problem, which is an NP-Hard combinatorial optimization problem in graphs. In this paper we describe the application of a recently introduced hybrid algorithm known as Construct, Merge, Solve & Adapt (CMSA) to this problem. Moreover, we evaluate the performance of a standalone ILP solver. The results show that both CMSA and the ILP solver outperform current stateof-the-art algorithms from the literature. Moreover, in contrast to the ILP solver, the performance of CMSA does not degrade for the largest problem instances. The experimental evaluation is based on a benchmark dataset containing two different graph topologies and considering graphs with variable and uniform node capacities.

Barrakuda: A Hybrid Evolutionary Algorithm for Minimum Capacitated Dominating Set Problem

“…This is done for the purpose of achieving a balance between the intensification and the diversification of the search process. Recently, Pinacho-Davidson et al [11] developed a construct, merge, solve and adapt (CMSA) approach for the CapMDS. CMSA is a hybrid proposal that integrates a heuristic algorithm and an exact solver to accelerate the solution process, especially thought for the application to large-scale problem instances.…”

“…The first algorithm, labeled CMSA++, is a revised and extended version of the construct, merge, solve and adapt (CMSA) technique presented in prior work [11]. The second algorithm is a new proposal, called BARRAKUDA, which makes use of the algorithmic framework of a biased random key genetic algorithm (BRKGA) [31].…”

“…As mentioned above, CMSA++ is a revised and extended version of the CMSA algorithm from [11]. The extensions concern the following aspects:…”

“…Making the algorithm more robust concerning the parameter values. Note that, in [11], we had to conduct a very fine-grained tuning process in order to achieve a good algorithm performance for all problem instances.…”

“…Nevertheless, keep in mind that the original CMSA from [11] can be obtained by setting the parameter values of CMSA++ in a specific way. In other words, the parameter tuning process may choose this option, if it results better than the newly introduced variations.…”