基于演化计算多峰函数

多峰函数(multimodal function),即含有多个局部最优解或全局最优解的函数。在数学、建筑、工程、机械等众多实际领域都需要将所研究的不足转化为多峰函数不足进行求解,如神经网络的结构优化以及权值优化不足,复杂系统参数及结构辨识不足等。这些现实不足的求解也就转化成了多峰函数全局优化不足的求解。对于多峰函数,寻求全部最优解的研究已经成为热点,并已经取得了很多不同方向的成果。针对多峰函数的特点,利用演化计算的可并行性、高效性以及原理的简洁性进行研究是本文的主要思路。以下为主要的研究工作:(1)针对多峰函数不足求解的多种策略,从传统策略和演化计算两个方面对其进行了研究以及近况浅析浅析。(2)对演化计算的发展、种类及其各自的特点以及应用领域做了浅析浅析研究。(3)在已有的多种优化策略的基础上,提出了一种针对多峰函数的多层次、全方位的演化计算策略(GSGL算法)。GSGL算法根据共享型遗传算法模型原理引入性能、地域离散度概念对初始种群进行预处理,保证种群初始解的多样性从而避开种群的早熟。(4)算法采用模糊聚类的策略将种群分块,每个小块被看作是一个小的种群,接着在小块内部实行迭代,并在此过程中引入最优解档案以及入档案的判定条件,使得能找到的所有的最优解以数组形式作为结果输出。GSGL算法将遗传共享、全局搜索和局部搜索等能力集中于一体,在求解多峰函数上有较好的效果。(5)将GSGL算法应用于几个典型的多峰函数不足求解中,对实验结果进行了浅析浅析总结并对今后的研究工作做出了展望。

【Abstract】wWw.shuoshilunwen.com Multimodal function is containing more than one local optimal solutions and global optimal solutions. There are many research questions need to be tranormed into multi-modal function problems in mathematics, architecture, engineering, mechanical and other practical areas. Such as neural network structure and weights optimization, complex system parameters and structure identification problems etc. solving these realities nature of the problem and the solution will be turned into a multimodal function global optimization problems. Which has become a hot spot and is made a lot of different directions results.This paper focus on the paralleli, efficiency and simplicity of the evolutionary computation for solving these questions, the main research tasks as follows:(1)Research a variety of methods for multi-modal function from traditional methods and evolutionary computation and make a status analysis about it.(2) Make research and analysis on the development, type and respective characteristics of evolutionary computation.(3)This paper put over a new multi-level and omni-bearing method (GSGL algorithm) for multimodal function solving based on the evolutionary computation already referred. Firstly this algorithm processing of the initial population based on shared genetic algorithm models, which could ensure the diversity of species thus oid the premature population.(4) The algorithm use the fuzzy clustering method to populate sub-blocks, each piece is seen as a all population and internal implementation made simultaneously. In the process, the explored optimal solution is added into the file based on the decision condition. This algorithm he the combination ability of Shared genetic algorithm, global search and local search, so it has better results than many others in solving multimodal function.(5) GSGL algorithm is applied to several typical problems of multi-modal function and though analyzing and summarizing experimental results got the algorithm traits. The papers also make the prospect for the future.

【关键词】 多峰函数;演化计算;模糊聚类;遗传算法;种群多样性;
【Key words】 multimodal function;evolutionary algorithm;fuzzy clustering;genetic algorithm;population diversity;

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