The Weighted Independent Domination Problem: ILP Model and Algorithmic Approaches

Pinacho-Davidson, Pedro; Blum, Christian; Lozano, José A.

doi:10.1007/978-3-319-55453-2_14

Cited by 4 publications

(4 citation statements)

References 11 publications

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“…We may say that instances with the edge densities from 0.1 to 0.4 are likely to be more difficult than others. In fact, the experiments in [5,14] mainly deal with random graphs with the edge densities in this range.…”

Section: Phase Transition Of Difficultymentioning

confidence: 99%

“…Laforest and Phan [14] proposed an exact algorithm based on clique partition, and made empirical comparison with one of the Liu and Song's algorithms, in terms of the computation time. Davidson et al [5] proposed an integer linear optimization model for the weighted version of the MinIDS problem (i.e., weights are given to edges as well as vertices, and the weight of an edge vx is counted as cost if the edge vx is used to assign a non-solution vertex v to a solution vertex x; every non-solution vertex v is automatically assigned to an adjacent solution vertex x such that the weight of vx is the minimum) and performed experimental validation for random graphs. Recently, Wang et al [20] proposed a tabu-search based memetic algorithm and Wang et al [21] proposed a metaheuristic algorithm based on GRASP (greedy randomized adaptive search procedure).…”

Section: Introductionmentioning

confidence: 99%

“…They showed their effectiveness on DIMACS instances, in comparison with CPLEX12.6 and LocalSolver5. 5.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Local Search for the Minimum Independent Dominating Set Problem

Haraguchi

2018

Preprint

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In the present paper, we propose an efficient local search for the minimum independent dominating set problem. We consider a local search that uses k-swap as the neighborhood operation. Given a feasible solution S, it is the operation of obtaining another feasible solution by dropping exactly k vertices from S and then by adding any number of vertices to it. We show that, when k = 2, (resp., k = 3 and a given solution is minimal with respect to 2-swap), we can find an improved solution in the neighborhood or conclude that no such solution exists in O(n∆) (resp., O(n∆ 3 )) time, where n denotes the number of vertices and ∆ denotes the maximum degree. We develop a metaheuristic algorithm that repeats the proposed local search and the plateau search iteratively, where the plateau search examines solutions of the same size as the current solution that are obtainable by exchanging a solution vertex and a non-solution vertex. The algorithm is so effective that, among 80 DIMACS graphs, it updates the best-known solution size for five graphs and performs as well as existing methods for the remaining graphs.

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Section: Phase Transition Of Difficultymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Efficient Local Search for the Minimum Independent Dominating Set Problem

Haraguchi

2018

Preprint

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“…The WID problem was initially introduced in [2]. Three integer linear programming (ILP) models and a population-based iterated greedy (PBIG) algorithm were presented in [5,6]. In this work we make use of one of the two solution construction heuristics used by the PBIG algorithm in order to define an intelligent decoder for a so-called biased random key genetic algorithm (BRKGA).…”

Section: Introductionmentioning

confidence: 99%

A biased random key genetic algorithm for the weighted independent domination problem

Corominas

Blum

Blesa

2019

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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This work deals with an N P-hard problem in graphs known as the weighted independent domination problem. We propose a biased random key genetic algorithm for solving this problem. The most important part of the proposed algorithm is a decoder that translates any vector of real-values into valid solutions to the tackled problem. The experimental results, in comparison to a state-of-theart population-based iterated greedy algorithm from the literature, show that our proposed approach has advantages over the state-ofthe-art algorithm in the context of the more dense graphs in which edges have higher weights than vertices.

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