有效生成饰带群混沌吸引子参数的改进优生遗传算法

Search of Chaotic Attractor Parameter Vectors with Frieze Groups By Improved Eugenic Genetic Algorithm

本文将蒙特卡罗搜索法与优生遗传算法应用于构造饰带群等价映射模型p112与模型p1a1混沌吸引子,并针对“遗传漂移”现象提出了改进的优生遗传算法.研究表明,在参数空间中引入空间距离的限制,可以由初始种群参数向量搜索出无重复参数向量的子代参数集合.在进化的种群中,也无重复混沌吸引子参数向量,从而避免了原有优生遗传算法在种群中出现的“遗传漂移”现象.新算法实现了种群中的参数无重复地不断更新,利用更新的种群在参数空间上能够持续地搜索出无重复图形结构的混沌吸引子参数向量,解决了原优生遗传算法无法持续有效生成新的混沌吸引子参数向量的问题.

Chaotic parameter vectors in the multi-parameter space can be randomly searched by the Monte Carlo search algorithm and eugenic genetic algorithm. These two algorithms are used to construct chaotic attractors of p112- and p1a1-equivariant mappings of frieze groups, and an improved eugenic genetic algorithm is presented for avoiding “genetic drift” phenomenon from the eugenic genetic algorithm. It is showed that introduction of the limit of space distance in parameter space can build a generation parameter vector set, in which the parameter vectors are chaotic and differ from each other, by an initial father parameter vector set which can be updated continuously and without overlap by a new child parameter vector successfully-constructed.