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The weighted independent domination problem: Integer linear programming models and metaheuristic approaches

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  • Pinacho Davidson, Pedro
  • Blum, Christian
  • Lozano, Jose A.

Abstract

This work deals with the so-called weighted independent domination problem, which is an NP-hard combinatorial optimization problem in graphs. In contrast to previous work, this paper considers the problem from a non-theoretical perspective. The first contribution consists in the development of three integer linear programming models. Second, two greedy heuristics are proposed. Finally, the last contribution is a population-based iterated greedy metaheuristic which is applied in two different ways: (1) the metaheuristic is applied directly to each problem instance, and (2) the metaheuristic is applied at each iteration of a higher-level framework – known as construct, merge, solve and adapt – to sub-instances of the tackled problem instances. The results of the considered algorithmic approaches show that integer linear programming approaches can only compete with the developed metaheuristics in the context of graphs with up to 100 nodes. When larger graphs are concerned, the application of the populated-based iterated greedy algorithm within the higher-level framework works generally best. The experimental evaluation considers graphs of different types, sizes, densities, and ways of generating the node and edge weights.

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  • Pinacho Davidson, Pedro & Blum, Christian & Lozano, Jose A., 2018. "The weighted independent domination problem: Integer linear programming models and metaheuristic approaches," European Journal of Operational Research, Elsevier, vol. 265(3), pages 860-871.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:3:p:860-871
    DOI: 10.1016/j.ejor.2017.08.044
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    References listed on IDEAS

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    1. Fanjul-Peyro, Luis & Ruiz, Rubén, 2010. "Iterated greedy local search methods for unrelated parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 207(1), pages 55-69, November.
    2. López-Ibáñez, Manuel & Dubois-Lacoste, Jérémie & Pérez Cáceres, Leslie & Birattari, Mauro & Stützle, Thomas, 2016. "The irace package: Iterated racing for automatic algorithm configuration," Operations Research Perspectives, Elsevier, vol. 3(C), pages 43-58.
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    Cited by:

    1. Yupeng Zhou & Jinshu Li & Yang Liu & Shuai Lv & Yong Lai & Jianan Wang, 2020. "Improved Memetic Algorithm for Solving the Minimum Weight Vertex Independent Dominating Set," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    2. Ma, Yuede & Cai, Qingqiong & Yao, Shunyu, 2019. "Integer linear programming models for the weighted total domination problem," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 146-150.
    3. Parra Inza, Ernesto & Vakhania, Nodari & Sigarreta Almira, José María & Hernández Mira, Frank Angel, 2024. "Exact and heuristic algorithms for the domination problem," European Journal of Operational Research, Elsevier, vol. 313(3), pages 926-936.

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