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A new discrete filled function method for solving large scale max-cut problems

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Abstract

The global optimization method based on discrete filled function is a new method that solves large scale max-cut problems. We first define a new discrete filled function based on the structure of the max-cut problem and analyze its properties. Unlike the continuous filled function methods, by the characteristic of the max-cut problem, the parameters in the proposed filled function does not need to be adjusted. By combining a procedure that randomly generates initial points for minimization of the proposed filled function, the proposed algorithm can greatly reduce the computational time and be applied to large scale max-cut problems. Numerical results and comparisons with several heuristic methods indicate that the proposed algorithm is efficient and stable to obtain high quality solution of large scale max-cut problems.

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Authors and Affiliations

  1. School of Finance, Jiangxi University of Finance & Economics, Nanchang, 330013, People’s Republic of China

    Ai-fan Ling

  2. Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Ai-fan Ling

  3. Hangzhou Institute of Service Engineering, Hangzhou Normal University, Hangzhou, 310036, People’s Republic of China

    Cheng-xian Xu

Authors
  1. Ai-fan Ling
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  2. Cheng-xian Xu
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Correspondence to Ai-fan Ling.

Additional information

This work is supported by National Natural Science Foundations of China (71001045, 10971162), Jiangxi Educational Committee Science Foundation for Youths (GJJ10114) and Jiangxi University of Finance and Economics Support Program funds for outstanding youths.

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Ling, Af., Xu, Cx. A new discrete filled function method for solving large scale max-cut problems. Numer Algor 60, 435–461 (2012). https://doi.org/10.1007/s11075-011-9522-1

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