ホモロジー群による位相の表現とその構造最適化への応用 : 第2報, 遺伝的アルゴリズムにおいて発生する解析不可能な構造に与える位相に基づく評価値とその効果

概要

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Genetic algorithm (GA) is one of the most useful methods to optimize topology of structures. The performance of GA, however, deeply depends upon a rule of cording from a structure to a string (a chromosome), which must be decided before the execution of GA. An improper coding can cause a lot of unanalyzable structures to be generated in the process of optimization, which are separated into several pieces with no supporting or loading points. In this paper, a method to give such unanalyzable structures a fitness value based upon their topology using homology theory is proposed to raise the probability of obtaining the optimum structures. As numerical examples, topology of two dimensional frames and three-dimensional structures consisting of triangular elements supported on a rigid wall and loaded vertically on a point distant from the wall are optimized under a constraint of constant weight. As a result, it was found that the proposed method increased the average fitness value and the number of optimum structures obtained in 100 trials of GA in comparison with other methods that considered unanalyzable structures to be useless.
一般社団法人日本機械学会の論文
1999-08-25