【作者】 王湘中；

【导师】 喻寿益；

【作者基本信息】 中南大学 ， 控制理论与控制工程， 2005， 博士

【摘要】 论文研究进化策略中变异算子的改进。现有的变异算子都使用全基因变异,本文提出单基因变异,通过对变异成功概率、局部收敛速度、全局收敛性能、变异步长控制、计算开销、多种群技术系统地分析比较两种变异方式的优劣,建立基于递减型变异步长单基因变异算子的单种群和多种群进化策略,最后论述进化算法仿真试验平台的构建及其应用。 对进化策略及其变异算子的研究源于变异算子在进化计算中起主导作用的认识。通过对简单遗传算法的改进试验,对交叉算子作用机理的分析,证明了变异算子对交叉算子的局部和全局搜索功能的可替代性,变异算子在算法中起主导作用。 借鉴生物进化理论和基因突变思想的进化策略,其变异算子使用所有基因同时变异的全基因变异方式,本文提出了一次只随机选择其中一个基因发生变异的单基因变异方式。理论分析和仿真试验证明,对于多维优化问题,当变异步长较大时,单基因变异的成功概率大于全基因变异的成功概率,全基因变异存在进化停顿现象,而且计算开销较大,对于高维优化问题尤其突出。 理论分析证明使用Gauss分布的单基因变异算子时,保持成功概率为0.445可以获得最优的局部收敛速度,并提出相应的递减型变异步长控制策略。为了直观分析、比较进化算子的性能,提出了横向仿真技术,并用于单基因变异和全基因变异的局部收敛速度的比较研究。试验证明虽然当变异步长合适时,全基因变异算子的局部收敛速度大于单基因变异,但全基因变异算子要求变异步长较小并且范围很小,而单基因变异算子可以在变异步长较大、且在一个较大的范围内获得良好的局部收敛速度,说明单基因变异算子对变异步长具有良好的鲁棒性。通过两个反例说明Gauss分布递减型步长控制单基因变异算子全局搜索能力的不足,提出了Gauss分布递减型步长单基因变异与均匀分布变异相结合的改进进化策略(μ+λ十κ)-ES,通过一组100维典型测试函数的仿真试验,说明了(μ+λ十κ)-ES良好的局部和全局搜索能力、较少的计算开销。 为了增强(μ+λ十κ)-ES的全局搜索能力、在解多模态优化问题时更多还原

【Abstract】 Improvements of the mutation operator of the evolution strategies (ES) are studied in this paper. All-gene mutation is applied to current mutation operators, single-gene mutation is proposed in the paper. Based on systemic analysis and comparison of the two types of mutation operators in the success probability, local convergence velocity, global convergence performance, mutation step-size control, computation costs, multi-population technique, single-population ES and multi-population ES based on single-gene mutation with descending mutation step-size control strategy are proposed respectively, finally establishment of a platform for evolutionary computation (EC) simulation and the application of the platform are discussed.The study on the ES and its mutation operators is originated from the knowledge that mutation operators play a dominant role in EC. With the experimentation on an improvement of the simple genetic algorithm (SGA) and analysis on the mechanism of crossover operators, it is proven that the local and global searching functions of crossover operators can be replaced by the mutation operators and the later plays a dominant role in EC.Originating from evolutionary theories and gene mutation ideas, the mutation operators of the ES take a manner of all-gene mutation, i.e. all the genes of an individual (or a chromosome) are varied at a time, single-gene mutation in which only one randomly selected gene is varied at a time is proposed in the paper. It is proven through theoretical analysis and simulation that single-mutation has a larger success probability than all-gene mutation under large mutation step-size for high-dimensional optimization, that the all-gene mutation suffers a stagnation of evolution and costs more especially for high-dimensional optimization.It is proven theoretically that when the success probability is about 0.445, the Gaussian distribution single-gene mutation can get the best local searching velocity, and a descending mutation step-size controlstrategy is correspondingly proposed. In order to intuitively analyze and compare the performances of different evolutionary operators, a novel method named as transverse simulation is proposed and is applied to the comparative study on the local convergence velocity of the single-gene mutation and all-gene mutation. It is proven through simulation that all-gene mutation under an appropriate mutation step-size and a small varying range has a lager local convergence velocity than single-gene mutation, and that the single-gene mutation can get a promising convergence velocity under a large mutation step-size and in a large varying range, and that the single-gene mutation operator shares an excellent robustness for the mutation step-size. Two counter examples demonstrate that Gaussian-distribution based single-gene mutation operator with descending step-size control has no enough global searching capability, a uniform-distribution mutation operator is introduced and the both operators are combined in ES, so a novel ES named as (// + X + k) - ES is proposed. Simulations under a set of typical 100-dimensional benchmark demonstrate that (/i + X + k) - ES has promising local and global searching capability and costs less.In order to promote the global searching capability of the({i + X + K)-ES and to solve the multi-modal function optimization (MFO) with multiple optima, a novel multi-population ES mx(ju + X + ic)-ES based on the (// + X + k) - ES is proposed. Sharing-radius is a difficult-determining and key parameter in crowding and (/or) sharing multi-population EC, hill-valley searching method is proposed and determination of the sharing-radius is avoided. A criterion is established to determine the convergence of a sub-population under a given accuracy and confidence, which is an applicable quantitative criterion. Simulations on a set of MFOs demonstrate that mx(jj + x + K)-ES can properly find all the optima.A platform for simulation and application is an important tool for EC, the basic idea and fundamental architecture of the platform is described based on the object-oriented programming (OOP ) and Visual C++. A platform is established and two actual examples -parametersoptimization of an electromechanical system’s speed-control subsystem and optimal control of soccer robots are given to demonstrate the application of the platform and the algorithms proposed in this paper. Finally the future studying topics are given.更多还原