Abstract
We have proposed an optimization method for a combinatorial optimization problem based on successive bifurcation characteristics of a replicator equation, and to obtain a good approximate solution of the optimization problem, a deterministic annealing algorithm has been applied. During the annealing process, bifurcations of equilibrium solutions occur and the bifurcation structure affects the performance of the deterministic annealing algorithm. In the paper, the bifurcation structure of the proposed dynamic system is analyzed in detail. It is shown that only pitchfork bifurcations occur in the annealing process, and the solution obtained by the annealing is the branch uniquely connected with the uniform solution. In many cases, the solution corresponds to a good approximate solution of the optimization problem.
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