Restricted swap-based neighborhood search for the minimum connected dominating set problem

Abstract

The minimum connected dominating set problem (MCDSP) has become increasingly important in recent years due to its applicability to mobile ad hoc networks and sensor grids. This paper presents a restricted swap-based neighborhood (RSN) tailored for solving MCDSP. This novel neighborhood structure is embedded into tabu Search (TS) and a perturbation mechanism is employed to enhance diversification. The proposed RSN-TS algorithm is tested on four sets of public benchmark instances widely used in the literature. The results demonstrate the efficacy of the proposed algorithm in terms of both solution quality and computational efficiency. In particular, the RSN-TS algorithm was able to improve the best known results on 41 out of the 97 problem instances while matching the best known results on all the remaining 56 instances. Furthermore, the article analyzes some key features of the proposed approach in order to identify its critical success factors.

Matheuristics for Variants of the Dominating Set Problem

“…This has led to three publications last year: Dagdeviren et al (2017), who studied the MWCDS problem; Wu et al (2017) and Wang et al (2017) who investigated the MCDS and MWDS problem, respectively. Most of these studies used population-based methods, but these methods can produce a premature convergence, and their computational time can increase quickly with the size of the problem.…”

“…Jovanovic & Tuba (2013) proposed two heuristics based on the ant colony algorithm, the first one is a Min-Max Ant System, while the second one is an ACO with a pheromone correction strategy, which was first proposed in Jovanovic et al (2010) for the MWDS problem. Wu et al (2017) and Li et al (2017) proposed, respectively, a restricted swap-based neighborhood structure and a greedy randomized adaptive search procedure (GRASP) based on a greedy function to solve the MCDS problem. Both methods improve the solutions, by using strategies to forbid cycling in the space search.…”

“…These methods reach good solutions compared to the populationbased method and exact methods. Currently, the work of Wu et al (2017) is the state of the art for the MCDS. We study this problem and show the details of our approach in Chapter 4.…”

“…For the class with few vertices, usually smaller than 50 vertices, we consider the size of the tabu list in 10% of the number vertices (⌊0.1 * |V|⌋) this will ensure that the algorithm is correct, for example, the instances IEEE-14-Bus and IEEE-30-Bus. Table 4.12 presents the results for the instances of the MCDS problem in comparison to the computational results proposed by Gendron et al (2014) and Wu et al (2017). The columns in this table present the results for the following methods: branch-and-cut (columns SABC and IPBC); Benders decomposition (columns SABE and IPBE) and hybrid algorithms (columns SAHY and IPHY).…”

Solving Steiner trees: Recent advances, challenges, and perspectives

“…Both problems are closely related to the minimum connected dominating problem (MCDP) which asks for a connected dominating set of a graph of minimum cardinality. In another Networks article, Wu et al [241] proposed a tabu search approach and highlighted the importance of the MCDP in the design of mobile ad hoc networks and sensor grids. Finally, Gendron et al [105] exploited the connection to the STP to derive an efficient Benders decomposition approach.…”