A discrete filled function algorithm for approximate global solutions of max-cut problems

Authors:
Ai-Fan Ling;Cheng-Xian Xu;Feng-Min Xu
Affiliations:
Department of Mathematics, Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, PR China;Department of Mathematics, Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, PR China and SKLMSE Lab., Xi'an Jiaotong University, PR China;Department of Mathematics, Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

A discrete filled function algorithm is proposed for approximate global solutions of max-cut problems. A new discrete filled function is defined for max-cut problems and the properties of the filled function are studied. Unlike general filled function methods, using the characteristic of max-cut problems, the parameters in proposed filled function need not be adjusted. This greatly increases the efficiency of the filled function method. By combining a procedure that randomly generates initial points for minimization of the filled function, the proposed algorithm can greatly reduce the calculation cost and be applied to large scale max-cut problems. Numerical results on different sizes and densities test problems indicate that the proposed algorithm is efficient and stable to get approximate global solutions of max-cut problems.