Maximum cut in fuzzy nature: Models and algorithms

Authors:
Rui-Sheng Wang;Li-Min Wang
Affiliations:
Department of Mathematics, Renmin University of China, Beijing 100872, China and Department of Electronics, Information and Communication Engineering, Osaka Sangyo University, Osaka 574-8530, Japa ...;China University of Mining and Technology, Beijing 100083, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The maximum cut (Max-Cut) problem has extensive applications in various real-world fields, such as network design and statistical physics. In this paper, a more practical version, the Max-Cut problem with fuzzy coefficients, is discussed. Specifically, based on credibility theory, the Max-Cut problem with fuzzy coefficients is formulated as an expected value model, a chance-constrained programming model and a dependent-chance programming model respectively according to different decision criteria. When these fuzzy coefficients are represented by special fuzzy variables like triangular fuzzy numbers and trapezoidal fuzzy numbers, the crisp equivalents of the fuzzy Max-Cut problem can be obtained. Finally, a genetic algorithm combined with fuzzy simulation techniques is designed for the general fuzzy Max-Cut problem under these models and numerical experiment confirms the effectiveness of the designed genetic algorithm.