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A discrete filled function algorithm embedded with continuous approximation for solving max-cut problems

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  • Ling, Ai-Fan
  • Xu, Cheng-Xian
  • Xu, Feng-Min

Abstract

In this paper, a discrete filled function algorithm embedded with continuous approximation is proposed to solve max-cut problems. A new discrete filled function is defined for max-cut problems, and properties of the function are studied. In the process of finding an approximation to the global solution of a max-cut problem, a continuation optimization algorithm is employed to find local solutions of a continuous relaxation of the max-cut problem, and then global searches are performed by minimizing the proposed filled function. Unlike general filled function methods, characteristics of max-cut problems are used. The parameters in the proposed filled function need not to be adjusted and are exactly the same for all max-cut problems that greatly increases the efficiency of the filled function method. Numerical results and comparisons on some well known max-cut test problems show that the proposed algorithm is efficient to get approximate global solutions of max-cut problems.

Suggested Citation

  • Ling, Ai-Fan & Xu, Cheng-Xian & Xu, Feng-Min, 2009. "A discrete filled function algorithm embedded with continuous approximation for solving max-cut problems," European Journal of Operational Research, Elsevier, vol. 197(2), pages 519-531, September.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:519-531
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    References listed on IDEAS

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    1. Chengxian Xu & Jianzhong Zhang, 2001. "A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 213-234, March.
    2. Francisco Barahona & Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1988. "An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design," Operations Research, INFORMS, vol. 36(3), pages 493-513, June.
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    Cited by:

    1. Geng Lin & Wenxing Zhu, 2012. "A discrete dynamic convexized method for the max-cut problem," Annals of Operations Research, Springer, vol. 196(1), pages 371-390, July.
    2. Md Rafiqul Islam & Md Shahidul Islam & Pritam Khan Boni & Aldrin Saurov Sarker & Md Asif Anam, 2024. "Solving the maximum cut problem using Harris Hawk Optimization algorithm," PLOS ONE, Public Library of Science, vol. 19(12), pages 1-34, December.
    3. Wenxing Zhu & Geng Lin & M. M. Ali, 2013. "Max- k -Cut by the Discrete Dynamic Convexized Method," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 27-40, February.

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