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A new Lagrangian net algorithm for solving max-bisection problems. (English) Zbl 1220.05029
Summary: The max-bisection problem is an $$N$$P-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.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05C85 Graph algorithms (graph-theoretic aspects) 90C27 Combinatorial optimization
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