Abstract
The max-cut problem is to partition the vertices of a weighted graph G = (V,E) into two subsets such that the weight sum of the edges crossing the two subsets is maximized. This paper presents a memetic max-cut algorithm (MACUT) that relies on a dedicated multi-parent crossover operator and a perturbation-based tabu search procedure. Experiments on 30 G-set benchmark instances show that MACUT competes favorably with 6 state-of-the-art max-cut algorithms, and for 10 instances improves on the best known results ever reported in the literature.
Keywords
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
Benlic, U., Hao, J.K.: A multilevel memetic approach for improving graph k-partitions. IEEE Transactions on Evolutionary Computation 15(5), 624–642 (2011)
Burer, S., Monteiro, R.D.C., Zhang, Y.: Rank-two relaxation heuristics for max-cut and other binary quadratic programs. SIAM Journal on Optimization 12, 503–521 (2001)
Falkenauer, E.: Genetic algorithms and grouping problems. Wiley, New York (1998)
Festa, P., Pardalos, P.M., Resende, M.G.C., Ribeiro, C.C.: Randomized heuristics for the max-cut problem. Optimization Methods and Software 7, 1033–1058 (2002)
Frieze, A., Jerrum, M.: Improved approximation algorithm for max k-cut and max-bisection. Algorithmica 18, 67–81 (1997)
Galinier, P., Boujbel, Z., Fernandes, M.C.: An efficient memetic algorithm for the graph partitioning problem. Annals of Operations Research 191(1), 1–22 (2011)
Galinier, P., Hao, J.K.: Hybrid evolutionary algorithms for graph coloring. Journal of Combinatorial Optimization 3(4), 379–397 (1999)
Gao, L., Zeng, Y., Dong, A.: An ant colony algorithm for solving Max-cut problem. Progress in Natural Science 18(9), 1173–1178 (2008)
Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the Association for Computing Machinery 42(6), 1115–1145 (1995)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thacher, J.W. (eds.) Complexity of Computer Computation, pp. 85–103. Plenum Press (1972)
Karish, S., Rendl, F., Clausen, J.: Solving graph bisection problems with semidefinite programming. SIAM Journal on Computing 12, 177–191 (2000)
Kim, S.H., Kim, Y.H., Moon, B.Y.: A Hybrid Genetic Algorithm for the MAX CUT Problem. In: Genetic and Evolutionary Computation Conference, pp. 416–423 (2001)
Kochenberger, G., Hao, J.K., Lü, Z., Wang, H., Glover, F.: Solving large scale max cut problems via tabu search. Accepted to Journal of Heuristics (2012)
Krishnan, K., Mitchell, J.: A semidefinite programming based polyhedral cut and price approach for the Max-Cut problem. Computational Optimization and Applications 33, 51–71 (2006)
Marti, R., Duarte, A., Laguna, M.: Advanced scatter search for the max-cut problem. INFORMS Journal on Computing 21(1), 26–38 (2009)
Palubeckis, G.: Application of multistart tabu search to the MaxCut problem. Information Technology and Control 2(31), 29–35 (2004)
Porumbel, D.C., Hao, J.K., Kuntz, P.: An evolutionary approach with diversity guarantee and well-informed grouping recombination for graph coloring. Computers and Operations Research 37(10), 1822–1832 (2010)
Rendl, F., Rinaldi, G., Wiegele, A.: Solving Max-Cut to optimality by intersecting semidefinite and polyhedral relaxations. Mathematical Programming 121, 307–335 (2008)
Shylo, V.P., Shylo, O.V.: Solving the maxcut problem by the global equilibrium search. Cybernetics and Systems Analysis 46(5), 744–754 (2010)
Wang, J.: An Improved Maximum Neural Network Algorithm for Maximum Cut Problem. Neural Information Processing 10(2), 27–34 (2006)
Wang, Y., Lü, Z., Glover, F., Hao, J.K.: Probabilistic GRASP-tabu search algorithms for the UBQP problem. Accepted to Computers and Operations Research (2012), http://dx.doi.org/10.1016/j.cor.2011.12.006
Wu, Q., Hao, J.K.: Memetic search for the max-bisection problem. Accepted to Computers and Operations Research (2012), http://dx.doi.org/10.1016/j.cor.2012.06.001
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wu, Q., Hao, JK. (2012). A Memetic Approach for the Max-Cut Problem. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds) Parallel Problem Solving from Nature - PPSN XII. PPSN 2012. Lecture Notes in Computer Science, vol 7492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32964-7_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-32964-7_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32963-0
Online ISBN: 978-3-642-32964-7
eBook Packages: Computer ScienceComputer Science (R0)