摘要
近年来,基于混沌的初值敏感性、伪随机性、遍历性以及自相似分形等非线性动力学特性所发展的混沌优化方法,是一种有潜力的工程全局优化新工具,已广泛应用于科学与工程技术的各学科领域。根据混沌优化方法的发展历程,以算法基本思想和工程应用研究状况为重点,评述了混沌神经网络优化方法、第一类混合混沌优化算法(基于混沌搜索)、第二类混合混沌优化算法(混沌序列代替随机序列)以及混沌分形优化四种主要混沌优化算法。混沌映射最早被引入神经网络,发展了混沌神经网络优化方法,可解决复杂的组合优化等全局优化问题。遗传算法及粒子群等启发式随机算法虽具全局搜索能力,但易出现早熟并陷入局部最优。然后,出现了混沌搜索的概念,研究者将其嵌入启发式算法建立了第一类混合混沌优化算法,可有效克服原启发式算法早熟收敛的缺点。随后,利用混沌映射产生的混沌序列代替启发式算法中的随机参数形成了第二类混合混沌优化算法。混合混沌优化算法有益于实现快速全局收敛和提高计算精度。最后,利用混沌分形特性,从分形理论出发提出一类新颖的混沌分形优化算法,可搜索到优化问题的所有全局最优解。此外,对混沌优化算法研究的几个发展方向进行了展望,诸如加强混沌优化算法的参数设计、处理大规模优化、多目标优化问题以及使用代理模型等。
In recent years, a new potential tool for global optimization, namely, chaos optimization algorithm （COA）,which is based on nonlinear dynamics characteristics such as the sensitivity on initial value,pseudo-randomness, ergodicity and self-similar fractals of chaos etc, has been widely applied in various disciplinary areas of science and technology. According to the development history of COA,this paper reviews four kinds of major COAs focusing on their basic ideas and the research situations of engineering application： chaotic neural network optimization method, the first type of hybrid C0A （based on chaotic search） , the second type of hybrid COA （chaotic sequence instead of random sequence） and chaos and fractal optimization algorithm. Chaotic map was firstly introduced to neural network, and chaotic neural network optimization method was developed, which can solve the complex problems of global optimization, such as combinatorial optimization. The heuristic random algorithms like genetic algorithm and particle swarm algorithm have the capability of global searching, but they are prone to prematurity and falling into local optima. After the chaotic search concept appeared, researchers estab- lished the first type of hybrid COA which embeds chaotic search into heuristic algorithm,and can over- come effectively the shortcoming of premature convergence of original heuristic algorithm. Subsequently, replacing random parameters of heuristic algorithm with chaotic sequences of chaotic maps, the second type of hybrid COA is formed. Hybrid chaos optimization algorithms facilitate to achieve rapid global convergence and improve the computational accuracy. Finally, using the chaotic and fractal characteris- tics,the chaos and fractal optimization algorithm, as a novel approach proposed from the fractal theory,is proposed and can search for all the global optimum solutions of the optimization problem. In addition, several research directions of COA are presented,including enhancing parameter design of COA, handing large scale optimization and multi-objective optimization problem,and utilizing the surrogate models and SO on.
出处
《计算力学学报》
CAS
CSCD
北大核心
2016年第3期269-286,共18页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(51478086
11332004)资助项目
关键词
全局优化
混沌优化算法
混沌序列
混沌神经网络
混沌搜索
混沌分形优化
global optimization
chaos optimization algorithms
chaotic sequence
chaotic neural network
chaotic search
chaos and fractal optimization
