Abstract
This paper presents a simple iterated local search metaheuristic incorporating a k-opt local search (KLS), called Iterated KLS (IKLS for short), for solving the maximum clique problem (MCP). IKLS consists of three components: LocalSearch at which KLS is used, a Kick called LEC-Kick that escapes from local optima, and Restart that occasionally diversifies the search by moving to other points in the search space. IKLS is evaluated on DIMACS benchmark graphs. The results showed that IKLS is an effective algorithm for the MCP through comparisons with multi-start KLS and state-of-the-art metaheuristics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Applegate, D., Cook, W., Rohe, A.: Chained Lin-Kernighan for large traveling salesman problems. INFORMS Journal on Computing 15(1), 82–92 (2003)
Battiti, R., Protasi, M.: Reactive local search for the maximum clique problem. Algorithmica 29(4), 610–637 (2001)
Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: Du, D.-Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization (suppl. Vol. A), pp. 1–74. Kluwer, Dordrecht (1999)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Hansen, P., Mladenović, N., Urošević, D.: Variable neighborhood search for the maximum clique. Discrete Applied Mathematics 145(1), 117–125 (2004)
Håstad, J.: Clique is hard to approximate within n 1 − ε. Acta. Mathematica 182, 105–142 (1999)
Johnson, D.S., McGeoch, L.A.: The traveling salesman problem: A case study. In: Aarts, E., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 215–310. John Wiley & Sons, New York (1997)
Johnson, D.S., Trick, M.A.: Cliques, Coloring, and Satisfiability. Second DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society (1996)
Katayama, K., Hamamoto, A., Narihisa, H.: An effective local search for the maximum clique problem. Information Processing Letters 95(5), 503–511 (2005)
Katayama, K., Narihisa, H.: Iterated local search approach using genetic transformation to the traveling salesman problem. In: Proc. of the Genetic and Evolutionary Computation Conference, pp. 321–328 (1999)
Katayama, K., Tani, M., Narihisa, H.: Solving large binary quadratic programming problems by effective genetic local search algorithm. In: Proc. of the Genetic and Evolutionary Computation Conference, pp. 643–650 (2000)
Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal 49, 291–307 (1970)
Khot, S.: Improved inapproximability results for maxclique, chromatic number and approximate graph coloring. In: Proceedings of the 42nd IEEE symposium on Foundations of Computer Science, pp. 600–609 (2001)
Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling salesman problem. Operations Research 21, 498–516 (1973)
Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57, pp. 321–353. Kluwer Academic Publishers, Norwell (2003)
Marchiori, E.: Genetic, iterated and multistart local search for the maximum clique problem. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoIASP 2002, EvoWorkshops 2002, EvoSTIM 2002, EvoCOP 2002, and EvoPlan 2002. LNCS, vol. 2279, pp. 112–121. Springer, Heidelberg (2002)
Merz, P., Freisleben, B.: Fitness landscapes, memetic algorithms and greedy operators for graph bi-partitioning. Evolutionary Computation 8(1), 61–91 (2000)
Merz, P., Katayama, K.: Memetic algorithms for the unconstrained binary quadratic programming problem. BioSystems 78(1–3), 99–118 (2004)
Moscato, P., Cotta, C.: A gentle introduction to memetic algorithms. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57, pp. 105–144. Kluwer Academic Publishers, Norwell (2003)
Östergård, P.R.J.: A fast algorithm for the maximum clique problem. Discrete Applied Mathematics 120(1–3), 197–207 (2002)
Pullan, W., Hoos, H.H.: Dynamic local search for the maximum clique problem. Journal of Artificial Intelligence Research 25, 159–185 (2006)
Singh, A., Gupta, A.K.: A hybrid heuristic for the maximum clique problem. Journal of Heuristics 12(1-2), 5–22 (2006)
Tomita, E., Seki, T.: An efficient branch-and-bound algorithm for finding a maximum clique. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds.) DMTCS 2003. LNCS, vol. 2731, pp. 278–289. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Katayama, K., Sadamatsu, M., Narihisa, H. (2007). Iterated k-Opt Local Search for the Maximum Clique Problem. In: Cotta, C., van Hemert, J. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2007. Lecture Notes in Computer Science, vol 4446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71615-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-71615-0_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71614-3
Online ISBN: 978-3-540-71615-0
eBook Packages: Computer ScienceComputer Science (R0)