Abstract
Local Optima Networks (LON) model combinatorial landscapes as graphs, where nodes are local optima and edges transitions among them according to given move operators. Modelling landscapes as networks brings a new rich set of metrics to characterize them. Most of the previous works on LONs fully enumerate the underlying landscapes to extract all local optima, which limits their use to small instances. This article proposes a sound sampling procedure to extract LONs of larger instances and estimate their metrics. The results obtained on two classes of Quadratic Assignment Problem (QAP) benchmark instances show that the method produces reliable results.
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Notes
- 1.
Here an adaptive walk means that from a given point the walk goes to a randomly chosen neighbor if the neighbor’s fitness is better, otherwise it tries another random neighbor.
References
Richter, H., Engelbrecht, A.E.: Recent Advances in the Theory and Application of Fitness Landscapes. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-41888-4
Ochoa, G., Tomassini, M., Verel, S., Darabos, C.: A study of NK landscapes’ basins and local optima networks. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2008, pp. 555–562. ACM (2008)
Tomassini, M., Verel, S., Ochoa, G.: Complex-network analysis of combinatorial spaces: the NK landscape case. Phys. Rev. E 78(6), 066114 (2008)
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
Chicano, F., Luque, G., Alba, E.: Autocorrelation measures for the quadratic assignment problem. Appl. Math. Lett. 25(4), 698–705 (2012)
Reidys, C., Stadler, P.: Combinatorial landscapes. SIAM Rev. 44(1), 3–54 (2002)
Ochoa, G., Verel, S., Tomassini, M.: First-improvement vs. best-improvement local optima networks of NK landscapes. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 104–113. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15844-5_11
Kauffman, S., Levin, S.: Towards a general theory of adaptive walks on rugged landscapes. J. Theor. Biol. 128, 11–45 (1987)
Koopmans, T.C., Beckmann, M.: Assignment problems and the location of economic activities. Econometrica 25(1), 53–76 (1957)
Daolio, F., Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of the permutation flow-shop problem. In: Legrand, P., Corsini, M.-M., Hao, J.-K., Monmarché, N., Lutton, E., Schoenauer, M. (eds.) EA 2013. LNCS, vol. 8752, pp. 41–52. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11683-9_4
Knowles, J., Corne, D.: Instance generators and test suites for the multiobjective quadratic assignment problem. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds.) EMO 2003. LNCS, vol. 2632, pp. 295–310. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36970-8_21
Taillard, E.D.: Comparison of iterative searches for the quadratic assignment problem. Locat. Sci. 3(2), 87–105 (1995)
Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Trans. Evol. Comput. 15(6), 783–797 (2011)
Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Barthélemy, M., Barrat, A., Pastor-Satorras, R., Vespignani, A.: Characterization and modeling of weighted networks. Phys. A 346, 34–43 (2005)
Newman, M.E.: Assortative mixing in networks. Phys. Rev. Lett. 89(20), 208701 (2002)
Goodman, L.: Snowball sampling. Ann. Math. Stat. 32(1), 148–170 (1961)
Chicano, F., Daolio, F., Ochoa, G., Vérel, S., Tomassini, M., Alba, E.: Local optima networks, landscape autocorrelation and heuristic search performance. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012. LNCS, vol. 7492, pp. 337–347. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32964-7_34
Daolio, F., Verel, S., Ochoa, G., Tomassini, M.: Local optima networks and the performance of iterated local search. In: Genetic and Evolutionary Computation Conference, GECCO 2012, pp. 369–376. ACM Press (2012)
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Verel, S., Daolio, F., Ochoa, G., Tomassini, M. (2018). Sampling Local Optima Networks of Large Combinatorial Search Spaces: The QAP Case. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11102. Springer, Cham. https://doi.org/10.1007/978-3-319-99259-4_21
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