カオス特性を有する多値ヒステリシスマシンによる整数計画法

抄録

Asynchronous Neural Networks as optimizing machines for the 0-1 combinatorial optimization problems have the problem that state transition is trapped at one of local optimal solutions in a neighborhood with a radius of one hamming distance. In order to get off such local minima, the Boltzmann Machine which state transition is probabilistic was proposed. On the other hand, the Hysteresis Machine which state transition acceptes increase of the minimizing function value within a certain range deterministically was developed. Moreover, according to the schedule to search global optimal solution, the Annealed Hysteresis Machine, which hysteretic width decreases monotonously, and the Chaotic Hysteresis Machine, which hysteretic width fluctuates chaotically, were proposed, and effectiveness for a few 0-1 combinatorial optimization problems was demonstrated. In this article, the chaotic hysteresis is introduced in the Multi-Valued Neural Network for integer programming problems. Moreover, the simulation results for a few integer programming problems demonstarate effectiveness of the Multi-Valued Chaotic Hysteresis Machine.