非线性函数全局最优化的一种混沌优化混合算法

混沌优化方法是近年出现的利用混沌的遍历性、随机性作为全局优化机制的一种优化技术。已有的混沌优化方法都是利用Logistic映射作为混沌序列发生器,而由Logistic映射产生的混沌序列的概率密度函数服从两头多、中间少的切比雪夫型分布,这种分布特性会严重影响混沌优化全局搜索能力和效率。利用Logistic映射的特点,在混沌搜索时预先筛选掉劣质点,建立改进的混沌BFGS混合优化算法。复杂非线性测试函数计算结果表明,与文献中不加改进的混沌混合算法相比,本算法以同样的混沌搜索次数找到全局最优解的概率提高了10-30%,而以概率1获得全局最优解的最大混沌搜索次数减少了8-10倍。另外,还将细搜索策略引入到改进的混沌BFGS混合算法中,对具有较大边界约束范围的非线性函数进行了优化计算。

A HYBRID CHAOS OPTIMAZATION ALGORITHM FOR GLOBAL OPTIMIZATION OF NONLINEAR FUNCTIONS

The chaos optimization technique proposed in recent years searches the global optimum, using the properties of ergodicity and randomness of the chaos sequence. The chaos optimization algorithms in the literature are all based on Logistic map. However, it is noticed that the probability density function of chaotic sequence of Logistic map is Chebyshev-type function, which may affect the global searching capacity and computational efficiency of chaos optimization algorithm severely. In this paper, considering the property of probability density function of chaotic sequence, an improved hybrid chaos-BFGS optimization algorithm is established by eliminating the bad design points during the chaos searching process. Numerical results of the improved chaos-BFGS algorithm for the nonlinear test functions show that the probability of getting the global optimum increases by 10-30 % for the same number of chaos search, and the number of chaos search reduces 8-10 times with the probability of 1.0 for obtaining the global optimum, compared to the results in the reference. In addition, the fine search strategy is introduced into the hybrid algorithm so that it can optimize the nonlinear functions with large boundary constraints.