Abstract
Both, Construct, Merge, Solve and Adapt (CMSA) and Large Neighborhood Search (LNS), are hybrid algorithms that are based on iteratively solving sub-instances of the original problem instances, if possible, to optimality. This is done by reducing the search space of the tackled problem instance in algorithm-specific ways which differ from one technique to the other. In this paper we provide first experimental evidence for the intuition that, conditioned by the way in which the search space is reduced, LNS should generally work better than CMSA in the context of problems in which solutions are rather large, and the opposite is the case for problems in which solutions are rather small. The size of a solution is hereby measured by the number of components of which the solution is composed, in comparison to the total number of solution components. Experiments are conducted in the context of the multi-dimensional knapsack problem.
This work was funded by project TIN2012-37930-C02-02 (Spanish Ministry for Economy and Competitiveness, FEDER funds from the European Union) and project SGR 2014-1034 (AGAUR, Generalitat de Catalunya). Evelia Lizárraga acknowledges funding from the Mexican National Council for Science and Technology (CONACYT, doctoral grant number 253787).
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References
Talbi, E. (ed.): Hybrid Metaheuristics. Studies in Computational Intelligence, vol. 434. Springer, Heidelberg (2013)
Blum, C., Raidl, G.R.: Hybrid Metaheuristics - Powerful Tools for Optimization. Springer, Heidelberg (2016)
Boschetti, M.A., Maniezzo, V., Roffilli, M., Bolufé Röhler, A.: Matheuristics: optimization, simulation and control. In: Blesa, M.J., Blum, C., Gaspero, L., Roli, A., Sampels, M., Schaerf, A. (eds.) HM 2009. LNCS, vol. 5818, pp. 171–177. Springer, Heidelberg (2009). doi:10.1007/978-3-642-04918-7_13
Pisinger, D., Ropke, S.: Large neighborhood search. In: Gendreau, M., Potvin, J.-Y. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 146, pp. 399–419. Springer, New York (2010)
Caserta, M., Voß, S.: A corridor method based hybrid algorithm for redundancy allocation. J. Heuristics 22(4), 405–429 (2016)
Lalla-Ruiz, E., Voß, S.: POPMUSIC as a matheuristic for the berth allocation problem. Ann. Math. Artif. Intell. 76(1–2), 173–189 (2016)
Fischetti, M., Lodi, A.: Local branching. Math. Program. 98(1), 23–47 (2003)
Blum, C., Pinacho, P., López-Ibáñez, M., Lozano, J.A.: Construct, merge, solve & adapt: a new general algorithm for combinatorial optimization. Comput. Oper. Res. 68, 75–88 (2016)
Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130(3), 449–467 (2001)
Chu, P.C., Beasley, J.E.: A genetic algorithm for the multidimensional knapsack problem. Discret. Appl. Math. 49(1), 189–212 (1994)
Leung, S., Zhang, D., Zhou, C., Wu, T.: A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack problem. Comput. Oper. Res. 39(1), 64–73 (2012)
Kong, X., Gao, L., Ouyang, H., Li, S.: Solving large-scale multidimensional knapsack problems with a new binary harmony search algorithm. Comput. Oper. Res. 63, 7–22 (2015)
Hanafi, S., Freville, A.: An efficient tabu search approach for the 0–1 multidimensional knapsack problem. Eur. J. Oper. Res. 106(2–3), 659–675 (1998)
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)
Blum, C., Blesa, M.J.: Construct, merge, solve and adapt: application to the repetition-free longest common subsequence problem. In: Chicano, F., Hu, B., García-Sánchez, P. (eds.) EvoCOP 2016. LNCS, vol. 9595, pp. 46–57. Springer, Heidelberg (2016). doi:10.1007/978-3-319-30698-8_4
Lizárraga, E., Blesa, M.J., Blum, C., Raidl, G.R.: Large neighborhood search for the most strings with few bad columns problem. Soft Comput. (2016, in press)
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Lizárraga, E., Blesa, M.J., Blum, C. (2017). Construct, Merge, Solve and Adapt Versus Large Neighborhood Search for Solving the Multi-dimensional Knapsack Problem: Which One Works Better When?. 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_5
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