Abstract
We conduct the first ever statistical comparison between two Local Optima Network (LON) sampling algorithms. These methodologies attempt to capture the connectivity in the local optima space of a fitness landscape. One sampling algorithm is based on a random-walk snowballing procedure, while the other is centred around multiple traced runs of an Iterated Local Search. Both of these are proposed for the Quadratic Assignment Problem (QAP), making this the focus of our study. It is important to note the sampling algorithm frameworks could easily be modified for other domains. In our study descriptive statistics for the obtained search space samples are contrasted and commented on. The LON features are also used in linear mixed models and random forest regression for predicting heuristic optimisation performance of two prominent heuristics for the QAP on the underlying combinatorial problems. The model results are then used to make deductions about the sampling algorithms’ utility. We also propose a specific set of LON metrics for use in future predictive models alongside previously-proposed network metrics, demonstrating the payoff in doing so.
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Change history
04 November 2021
In the originally published version the indexes of some variables in Section 4.1, including Constraint (5) of the model, include a wrong offset of one position. Some errors occurred in notations of variable indexes in Constraint (5) conditions of the model in Section 4.1, together with some ambiguities that may lead to misunderstanding for the reader. This was corrected in the updated version.
References
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. ACM (2008)
Ochoa, G., Veerapen, N.: Mapping the global structure of TSP fitness landscapes. J. Heuristics 24(3), 1–30 (2017)
Herrmann, S., Ochoa, G., Rothlauf, F.: Communities of local optima as funnels in fitness landscapes. In: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, pp. 325–331 (2016)
McMenemy, P., Veerapen, N., Ochoa, G.: How perturbation strength shapes the global structure of TSP fitness landscapes. In: European Conference on Evolutionary Computation in Combinatorial Optimization, pp. 34–49 (2018)
Iclanzan, D., Daolio, F., Tomassini, M.: Data-driven local optima network characterization of QAPLIB instances. In: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation GECCO 2014, pp. 453–460. ACM, New York (2014). http://doi.acm.org/10.1145/2576768.2598275
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
Verel, S., Daolio, F., Ochoa, G., Tomassini, M.: Sampling local optima networks of large combinatorial search spaces: the QAP case. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11102, pp. 257–268. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99259-4_21
Stadler, P.F.: Fitness landscapes. In: Lässig, M., Valleriani, A. (eds.) Biological Evolution and Statistical Physics, vol. 585, pp. 183–204. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45692-9_10
Stützle, T.: Iterated local search for the quadratic assignment problem. Eur. J. Oper. Res. 174(3), 1519–1539 (2006)
Taillard, É.: Robust taboo search for the quadratic assignment problem. Parallel Comput. 17(4–5), 443–455 (1991)
Acknowledgements
This work is supported by the UK’s Engineering and Physical Sciences Research Council (grant number EP/J017515/1). Data generated during this research are available from the Stirling Online Repository for Research Data (http://hdl.handle.net/11667/91).
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Thomson, S.L., Ochoa, G., Verel, S. (2019). Clarifying the Difference in Local Optima Network Sampling Algorithms. In: Liefooghe, A., Paquete, L. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2019. Lecture Notes in Computer Science(), vol 11452. Springer, Cham. https://doi.org/10.1007/978-3-030-16711-0_11
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