Abstract
This paper investigated the impacts of multi-objectivization on solving combinatorial single-objective NK-landscape problems with multiple funnel structures. Multi-objectivization re-formulates a single-objective target problem into a multi-objective problem with a helper problem to suppress the difficulty of the target problem. This paper analyzed the connectivity of two funnels involving global optima in the target and the helper NK-landscape problems via the Pareto local optimal solutions in the multi-objectivized problem. Experimental results showed that multi-objectivization connects the two funnels with global optima of the target and the helper problems as a single bridging domain consisting of the Pareto local optimal solutions. Also, this paper proposed an algorithm named the multi-objectivized local search (MOLS) that searched for the global optimum of the target problem from the global optimum of an artificially generated helper problem via the Pareto local optimal solutions. Experimental results showed that the proposed MOLS achieved a higher success rate of the target single-objective optimization than iterative local search algorithms on target NK-landscape problems with multiple funnels.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aguirre, H.E., Tanaka, K.: Insights on properties of multiobjective MNK-landscapes. In: Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No. 04TH8753), vol. 1, pp. 196–203. IEEE (2004)
Brockhoff, D., Friedrich, T., Hebbinghaus, N., Klein, C., Neumann, F., Zitzler, E.: Do additional objectives make a problem harder? In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, pp. 765–772 (2007)
Deb, K., Saha, A.: Finding multiple solutions for multimodal optimization problems using a multi-objective evolutionary approach. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, pp. 447–454 (2010)
Garza-Fabre, M., Toscano-Pulido, G., Rodriguez-Tello, E.: Multi-objectivization, fitness landscape transformation and search performance: a case of study on the HP model for protein structure prediction. Eur. J. Oper. Res. 243(2), 405–422 (2015)
Jensen, M.T.: Helper-objectives: using multi-objective evolutionary algorithms for single-objective optimisation. J. Math. Modell. Algorithms 3(4), 323–347 (2004)
Kauffman, S., Levin, S.: Towards a general theory of adaptive walks on rugged landscapes. J. Theoret. Biol. 128(1), 11–45 (1987)
Knowles, J.D., Watson, R.A., Corne, D.W.: Reducing local optima in single-objective problems by multi-objectivization. In: Zitzler, E., Thiele, L., Deb, K., Coello Coello, C.A., Corne, D. (eds.) EMO 2001. LNCS, vol. 1993, pp. 269–283. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44719-9_19
Liefooghe, A., Derbel, B., Verel, S., López-Ibáñez, M., Aguirre, H., Tanaka, K.: On pareto local optimal solutions networks. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11102, pp. 232–244. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99259-4_19
McMenemy, P., Veerapen, N., Ochoa, G.: How perturbation strength shapes the global structure of TSP fitness landscapes. In: Liefooghe, A., López-Ibáñez, M. (eds.) EvoCOP 2018. LNCS, vol. 10782, pp. 34–49. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77449-7_3
Ochoa, G., Herrmann, S.: Perturbation strength and the global structure of QAP fitness landscapes. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11102, pp. 245–256. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99259-4_20
Ochoa, G., Tomassini, M., Vérel, S., Darabos, C.: A study of NK landscapes’ basins and local optima networks. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation, pp. 555–562 (2008)
Ochoa, G., Veerapen, N., Daolio, F., Tomassini, M.: Understanding phase transitions with local optima networks: number partitioning as a case study. In: Hu, B., López-Ibáñez, M. (eds.) EvoCOP 2017. LNCS, vol. 10197, pp. 233–248. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-55453-2_16
Thomson, S.L., Daolio, F., Ochoa, G.: Comparing communities of optima with funnels in combinatorial fitness landscapes. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 377–384 (2017)
Thomson, S.L., Ochoa, G.: On funnel depths and acceptance criteria in stochastic local search. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 287–295 (2022)
Vérel, S., Daolio, F., Ochoa, G., Tomassini, M.: Local optima networks with escape edges. In: Hao, J.-K., Legrand, P., Collet, P., Monmarché, N., Lutton, E., Schoenauer, M. (eds.) EA 2011. LNCS, vol. 7401, pp. 49–60. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35533-2_5
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Tanaka, S., Takadama, K., Sato, H. (2023). Multi-objectivization Relaxes Multi-funnel Structures in Single-objective NK-landscapes. In: Pérez Cáceres, L., Stützle, T. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2023. Lecture Notes in Computer Science, vol 13987. Springer, Cham. https://doi.org/10.1007/978-3-031-30035-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-031-30035-6_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-30034-9
Online ISBN: 978-3-031-30035-6
eBook Packages: Computer ScienceComputer Science (R0)