Minimum Weight Dominating Set Research Articles

Chemical Reaction Optimization for Minimum Weight Dominating Set

Dominating set of a graph can be defined as the set of vertices that can cover all other vertices of the graph. The minimum weight dominating set (MWDS) is the minimum number of vertices in the dominating set with minimum total weight. In recent times, the chemical reaction optimization algorithm (CRO) has shown its supremacy in solving these types of problems. Therefore in this paper, a novel approach based on CRO has been proposed to solve the MWDS problem. The proposed method uses a repair-based technique to generate a molecule. To make the solution feasible by covering all vertices and to get better results, three supporting operators are implemented along with the CRO operators. Besides this, two repair operators are introduced. In the first repair operator, the searching procedure works based on the scaling properties of vertices, and the second one is a unique method for eliminating common neighbors of vertices of the dominating set. The performance of the proposed method is better than any other existing related algorithms. The performance is measured from different graphs of the benchmark datasets. It can be mentioned that the proposed method takes minimal running time to obtain the minimum weight compared to other benchmark methods.

Improved local search for the minimum weight dominating set problem in massive graphs by using a deep optimization mechanism

The minimum weight dominating set (MWDS) problem is an important generalization of the minimum dominating set problem with various applications. In this work, we develop an efficient local search scheme that can dynamically adjust the number of added and removed vertices according to the information of the candidate solution. Based on this scheme, we further develop three novel ideas to improve performance, resulting in our so-called DeepOpt-MWDS algorithm. First, we use a new construction method with five reduction rules to significantly reduce massive graphs and construct an initial solution efficiently. Second, an improved configuration checking strategy called CC2V3+ is designed to reduce the cycling phenomenon in local search. Third, a general perturbation framework called deep optimization mechanism (DeepOpt) is proposed to help the algorithm avoid local optima and to converge to a new solution quickly.Extensive experiments based on eight popular benchmarks of different scales are carried out to evaluate the proposed algorithm. Compared to seven state-of-the-art heuristic algorithms, DeepOpt-MWDS performs better on random and classic benchmarks and obtains the best solutions on almost all massive graphs. We investigate three main algorithmic ingredients to understand their impacts on the performance of the proposed algorithm. Moreover, we adapt the proposed general framework DeepOpt to another NP-hard problem to verify its generality and achieve good performance.

HSLS: An efficient local search algorithm for the hardware and software partitioning problem

Hardware and software partitioning (HW/SW) is a crucial step in the co-design of embedded systems, which is a typical combinatorial optimisation problem. In practice, HW/SW instances would be of large scale, so it is of significant importance to design effective heuristic algorithms to obtain a high-quality partitioning scheme. Different from previous heuristics, the HW/SW problem is treated as the minimum weight dominating set (MWDS) problem in this letter, and the mature local search framework for solving the MWDS problem is introduced to solve the HW/SW problem. In addition, two suitable vertex selection rules based on scoring function and tabu are proposed. Combined with the introduced local search framework, an efficient local search algorithm named HSLS is obtained. 96 classic benchmark instances are used to evaluate the performance of the HSLS algorithm, and the four latest evolutionary algorithms designed for the HW/SW problem are used as comparison algorithms, which are genetic algorithm, binary particle swarm optimisation, differential evolution, and group theory-based optimisation algorithm. The experimental results show that the HSLS algorithm is far superior to the four comparison algorithms in terms of the optimal solution and obtains optimal solution on 78 benchmark instances, the four comparison algorithms obtain 43, 29, 42, and 41 optimal solutions respectively.

An evolutionary algorithm based hyper-heuristic framework for the set packing problem

In recent years, hyper-heuristics have received massive attention from the research community as an alternative of meta-heuristics. In a hyper-heuristic, generation or selection of an effective heuristic among a pool of heuristics is an important and challenging task in the search process. At each iteration, a suitable heuristic can take the search process toward the global optimal solution. Moreover, some additional factors such as quality and the number of heuristics also affect the performance. In this paper, we propose an evolutionary algorithm based hyper-heuristic framework that incorporates dynamic selection of parameters. To test its generality, effectiveness and robustness, we apply this approach on two different NP-hard problems - set packing problem (SPP) and minimum weight dominating set (MWDS) problem. The proposed approach for the SPP and the MWDS problem has been evaluated respectively on their respective set of benchmark instances. Computational results show that the proposed approach for the SPP and MWDS problem perform much better than their respective state-of-the-art approaches in terms of the solution quality and computational time.

Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function

The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications. This paper proposes a new local search algorithm for the MWDS problem, which is based on two new ideas. The first idea is a heuristic called two-level configuration checking (CC2), which is a new variant of a recent powerful configuration checking strategy (CC) for effectively avoiding the recent search paths. The second idea is a novel scoring function based on the frequency of being uncovered of vertices. Our algorithm is called CC2FS, according to the names of the two ideas. The experimental results show that, CC2FS performs much better than some state-of-the-art algorithms in terms of solution quality on a broad range of MWDS benchmarks.

An Effective Hybrid Memetic Algorithm for the Minimum Weight Dominating Set Problem

The minimum weight-dominating set (MWDS) problem is NP-hard and has a lot of applications in the real world. Several metaheuristic methods have been developed for solving the problem effectively, but suffering from high CPU time on large-scale instances. In this paper, we design an effective hybrid memetic algorithm (HMA) for the MWDS problem. First, the MWDS problem is formulated as a constrained 0-1 programming problem and is converted to an equivalent unconstrained 0-1 problem using an adaptive penalty function. Then, we develop a memetic algorithm for the resulting problem, which contains a greedy randomized adaptive construction procedure, a tabu local search procedure, a crossover operator, a population-updating method, and a path-relinking procedure. These strategies make a good tradeoff between intensification and diversification. A number of experiments were carried out on three types of instances from the literature. Compared with existing algorithms, HMA is able to find high-quality solutions in much less CPU time. Specifically, HMA is at least six times faster than existing algorithms on the tested instances. With increasing instance size, the CPU time required by HMA increases much more slowly than required by existing algorithms.

Hybrid metaheuristic algorithms for minimum weight dominating set

Minimum weight dominating set (MWDS) finds many uses in solving problems as varied as clustering in wireless networks, multi-document summarization in information retrieval and so on. It is proven to be NP-hard, even for unit disk graphs. Many centralized and distributed, greedy and approximation algorithms have been proposed for the MWDS problem. However, all the approximation algorithms are limited to unit disk graphs which are primarily used to model wireless networks. This assumption fails when applied to other domains. In this paper, we present two metaheuristic algorithms – a hybrid genetic algorithm and a hybrid ant colony optimization algorithm – for the problem of computing minimum weight dominating set. We compare our results with that of a greedy heuristic as well as the only other metaheuristic algorithm proposed so far in the literature and show that our algorithms are far better than these algorithms.