A new Lagrangian net algorithm for solving max-bisection problems

Authors:
Fengmin Xu;Xusheng Ma;Baili Chen
Affiliations:
School of Science and Department of Computer Science and Technology, Xi'an Jiaotong University, Xi'an, 710049, PR China;School of Science, Xi'an Jiaotong University, Xi'an, 710049, PR China;School of Science, Xi'an Jiaotong University, Xi'an, 710049, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

The max-bisection problem is an NP-hard combinatorial optimization problem. In this paper, a new Lagrangian net algorithm is proposed to solve max-bisection problems. First, we relax the bisection constraints to the objective function by introducing the penalty function method. Second, a bisection solution is calculated by a discrete Hopfield neural network (DHNN). The increasing penalty factor can help the DHNN to escape from the local minimum and to get a satisfying bisection. The convergence analysis of the proposed algorithm is also presented. Finally, numerical results of large-scale G-set problems show that the proposed method can find a better optimal solutions.