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Solving large scale Max Cut problems via tabu search

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Abstract

In recent years many algorithms have been proposed in the literature for solving the Max-Cut problem. In this paper we report on the application of a new Tabu Search algorithm to large scale Max-cut test problems. Our method provides best known solutions for many well-known test problems of size up to 10,000 variables, although it is designed for the general unconstrained quadratic binary program (UBQP), and is not specialized in any way for the Max-Cut problem.

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References

  • Boros, E., Hammer, P.: The Max-Cut problem and quadratic 0-1 optimization; polyhedral aspects, relaxations and bounds. Ann. Oper. Res. 33, 151–180 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • Burer, S., Monteiro, D., Zang, Y.: Rank-two relaxation heuristic for Max-Cut and other binary quadratic programs. SIAM J. Optim. 12, 503–521 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • Choi, C., Ye, Y.: Solving sparse semidefinite programs using the dual scaling algorithm with an iterative solver. Working Paper, Department of Management Sciences, The University of Iowa (2000)

  • Festa, P., Pardalos, P., Resende, M., Ribeiro, C.: Randomized heuristics for the Max-Cut problem. Optim. Methods Softw. 7, 1033–1058 (2002)

    Article  MathSciNet  Google Scholar 

  • Glover, F., Lü, Z., Hao, J.K.: Diversification-driven tabu search for unconstrained binary quadratic problems. 4OR, Q. J. Oper. Res. (2010). doi:10.1007/s10288-009-0115-y

    Google Scholar 

  • Goemans, M., Williamson, D.: Improved approximation algorithms for Max-Cut and satisfiability problems using Semidefinite programming. J. ACM 42, 1115–1145 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Helmberg, C., Rendl, F.: Solving quadratic (0-1) problems by semidefinite programs and cutting planes. Working Paper, Technische Universitat Graz (1996)

  • Karish, S., Rendl, F., Clausen, J.: Solving graph bisection problems with semidefinite programming. SIAM J. Comput. 12, 177–191 (2000)

    Google Scholar 

  • Krishnan, K., Mitchell, J.: A semidefinite programming based polyhedral cut and price approach for the Max-Cut problem. Comput. Optim. Appl. 33, 51–71 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Marti, R., Duarte, A., Laguna, M.: Advanced scatter search for the Max-Cut problem. INFORMS J. Comput. 21, 26–38 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Rendl, F., Rinaldi, G., Wiegele, A.: Solving Max-Cut to optimality by intersecting semidefinite and polyhedral relaxations. Math. Program. 121, 307–335 (2008)

    Article  MathSciNet  Google Scholar 

  • Poljak, S., Tuza, Z.: The Max-Cut problem: a survey. In: Cook, W., Lovasz, L., Seymour, P. (eds.) Special Year on Combinatorial Optimization. DIMACS Series in Discrete Mathematics and Computer Science. Am. Math. Soc., Providence (1995)

    Google Scholar 

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Correspondence to Fred Glover.

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Kochenberger, G.A., Hao, JK., Lü, Z. et al. Solving large scale Max Cut problems via tabu search. J Heuristics 19, 565–571 (2013). https://doi.org/10.1007/s10732-011-9189-8

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  • DOI: https://doi.org/10.1007/s10732-011-9189-8

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