自适应折叠混沌优化方法

An Adaptive Iterative Chaos Optimization Method

针对传统混沌优化方法中优化结果对搜索初始值要求极高以及搜索效率较低的问题,提出一种自适应折叠混沌优化方法。该方法首先提出一种新型无限折叠混沌映射,并证明了该映射无有理数不动点;根据映射关系式建立混沌模型求解Lyapunov指数,并基于该混沌模型对搜索初值采用大幅度改变和小幅度改变两种方式来考察映射对初值的依赖程度。采用所提映射取代传统的有限折叠映射作为混沌产生器,提高了混沌的动态优化性能,通过在优化过程中不断缩小优化变量的搜索空间来提高搜索效率和精度。实验结果表明,该方法的优化结果不依赖于初始值位置,具有搜索效率高的特点。与Logistic映射和Tent映射优化方法相比,平均搜索效率分别提高了71.6%和62.6%。

A new adaptive iterative chaos optimization method is proposed to improve the problems that the optimal results generated from the existing chaotic optimization methods rely on initial points and that search efficiency of these methods is lower. It is proved that the chaotic map has no rational number fixed point, then the mapping relational formula is used to establish a chaotic model that is used to solve the Lyapunov exponent, and the sensitivity of chaotic maps to initial values is investigated under large variation and small variation on initial starting points. The chaotic map is then used to establish chaotic generator to replace the finite-collapse map, and to improve the dynamic performance of chaotic optimization. The method improves the search efficiency by continuously reducing the searching space of variables and enhancing search precision. Numerical results show that the optimal results generated by the proposed method do not depend on the initial value, and the search efficiency is high. Comparisons with the Logistic mapping and the Tent mapping optimization method show that the average search efficiency of the proposed method improves about 71.6% and 62.6%, respectively.