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 theoretical work from the literature, this paper considers the problem from an algorithmic perspective. The first contribution consists in the development of an integer linear programming model and a heuristic that makes use of this model. Second, two greedy heuristics are proposed. Finally, the last contribution is a population-based iterated greedy algorithm that takes profit from the better one of the two developed greedy heuristics. The results of the compared algorithmic approaches show that small problem instances based on random graphs are best solved by an efficient integer linear programming solver such as CPLEX. Larger problem instances are best tackled by the population-based iterated greedy algorithm. The experimental evaluation considers random graphs of different sizes, densities, and ways of generating the node and edge weights.
This work was supported by project TIN2012-37930-C02-02 (Spanish Ministry for Economy and Competitiveness, FEDER funds from the European Union).
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Notes
- 1.
In this problem, given an undirected graph with node weights, the goal is to find an independent dominating set for which the sum of the weights of the nodes is minimal.
- 2.
Note that Greedy2 is chosen over Greedy1 because, as it will be shown later, Greedy2 generally works better than Greedy1.
References
Chang, S.C., Liu, J.J., Wang, Y.L.: The weighted independent domination problem in series-parallel graphs. In: Proceedings of ICS 2014 - The International Computer Symposium of Intelligent Systems and Applications, vol. 274, pp. 77–84. IOS Press (2015)
Chang, G.J.: The weighted independent domination problem is NP-complete for chordal graphs. Discrete Appl. Math. 143(1), 351–352 (2004)
Wang, Y., Li, R., Zhou, Y., Yin, M.: A path cost-based GRASP for minimum independent dominating set problem. Neural Comput. Appl. (2016, in press)
Potluri, A., Singh, A.: Hybrid metaheuristic algorithms for minimum weight dominating set. Appl. Soft Comput. 13(1), 76–88 (2013)
Chaurasia, S.N., Singh, A.: A hybrid evolutionary algorithm with guided mutation for minimum weight dominating set. Appl. Intell. 43(3), 512–529 (2015)
Bouamama, S., Blum, C.: A hybrid algorithmic model for the minimum weight dominating set problem. Simul. Model. Practice Theor. 64, 57–68 (2016)
Lin, G., Zhu, W., Ali, M.M.: An effective hybrid memetic algorithm for the minimum weight dominating set problem. IEEE Trans. Evol. Comput. (2016, in press)
Ruiz, R., Stützle, T.: A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. Eur. J. Oper. Res. 177(3), 2033–2049 (2007)
Fanjul-Peyro, L., Ruiz, R.: Iterated greedy local search methods for unrelated parallel machine scheduling. Eur. J. Oper. Res. 207(1), 55–69 (2010)
Bouamama, S., Blum, C., Boukerram, A.: A population-based iterated greedy algorithm for the minimum weight vertex cover problem. Appl. Soft Comput. 12(6), 1632–1639 (2012)
Porta, J., Parapar, J., Doallo, R., Barbosa, V., Santé, I., Crecente, R., Díaz, C.: A population-based iterated greedy algorithm for the delimitation and zoning of rural settlements. Comput. Environ. Urban Syst. 39, 12–26 (2013)
López-Ibáñez, M., Dubois-Lacoste, J., Pérez Cáceres, L., Birattari, M., Stützle, T.: The irace package: iterated racing for automatic algorithm configuration. Oper. Res. Perspect. 3, 43–58 (2016)
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Davidson, P.P., Blum, C., Lozano, J.A. (2017). The Weighted Independent Domination Problem: ILP Model and Algorithmic Approaches. In: Hu, B., López-Ibáñez, M. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2017. Lecture Notes in Computer Science(), vol 10197. Springer, Cham. https://doi.org/10.1007/978-3-319-55453-2_14
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