Title :
A deterministic annealing algorithm for a combinatorial optimization problem by the use of replicator equations
Author :
Tsuchiya, Kazuo ; Nishiyama, Takehiro ; Tsujita, Katsuyoshi
Author_Institution :
Dept. of Aeronaut. & Astronaut., Kyoto Univ., Japan
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
Keywords :
bifurcation; combinatorial mathematics; simulated annealing; approximate solution; bifurcation characteristics; combinatorial optimization problem; deterministic annealing algorithm; equilibrium solutions; pitchfork bifurcations; replicator equations; uniform solution; Aerodynamics; Algorithm design and analysis; Approximation methods; Bifurcation; Cities and towns; Equations; Optimization methods; Performance analysis; Postal services; Simulated annealing;
Conference_Titel :
Systems, Man, and Cybernetics, 1999. IEEE SMC '99 Conference Proceedings. 1999 IEEE International Conference on
Conference_Location :
Tokyo
Print_ISBN :
0-7803-5731-0
DOI :
10.1109/ICSMC.1999.814099
