2-212 レプリケータ系にもとづくカオス力学系 : ニューラルネットワーク実現からカオス最適化まで

概要

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Studies on constrained global optimization methods using chaos are gaining more interests. They are realized by, i) transforming the constrained decision variable to another unconstrained one by using a certain map, ii) formulating the unconstrained gradient model with respect to the new variable, and iii) generating chaos by discretizing the model with Euler's method and enlarging its sampling parameter enough large so as to unstabilize the equilibrium points. The chaotic trajectories are forced to converge into the global optimum by applying the method called "the chaotic annealing", which stabilize the dynamics by gradually decreasing the sampling parameter. In this paper, we first introduce the gradient model for the optimization problem constrained with the upper and lower bounds, or the model for the constrained problem on the simplex, which has the relationship with the replicator dynamics. They are formulated by applying the map based on the exponential function. On the other hand, we propose a new model for the constrained on the hyper-spherecal surface by using the map based on sine and cosine functions. The efficiency of the global optimization method by using our proposing model is demonstrated with numerical simulations.
社団法人日本機械学会の論文
2002-11-14