【作者】 余林琛；

【导师】 王卫华；

【作者基本信息】 武汉理工大学 ， 应用数学， 2004， 硕士

【摘要】 不论在科学实验还是在工程设计中，很多实际问题都可转化为优化问题，因此优化计算已越来越得到人们的重视。但是当搜索空间非常大时，传统算法无法在一个合理的计算时间内得出用户可接受的次优解，而演化算法作为一种随机搜索优化技术，却能解决这类复杂的问题，并已广泛应用于求解实际问题。 但是传统演化策略中存在一定的半盲目性，使得种群进化缺乏方向性，导致求解效率与效果不能达到平衡，因此本文研究基于个体相似性的演化优化算法以求解决这一问题。围绕这一目的本文进行了如下工作： 本文主要由理论研究和应用实践两部分组成。第一部份是理论研究：介绍演化算法的一般理论和概念，提出了基于个体间相似性的自适应变异算子的思想。采用单亲繁殖方式，结合所设计的变异算子，提出一种新的演化算法。第二部分是应用实践：将所提出的演化算法应用于工程优化中的下料问题，与传统算法的结果进行比较，显示出本文所设计算法的优良性能。本文的具体内容如下： 第一章介绍了研究背景，指出本文研究要解决的关键技术问题及研究策略。 第二章介绍了演化计算的一般理论，包括演化计算的基本概念、基本特征及设计演化算法所应遵循的基本原则等。 第三章阐述了作者对基于个体间相似性变异算子以及自适应演化算法的研究。在系统研究了演化优化、单亲遗传等的基础上，定义了个体距离、相似性和邻域等概念(用距离反映个体间的差异程度，用相似性描述个体间对应基因位的类似程度，用邻域实现对种群按相似性分割)，提出了基于个体相似性的单亲变异算子，在变异过程中引入分级策略，设计出基于相似性的自适应演化算法。从而使得变异算子具有了很强的导向性，避免了传统达尔文演化策略的半盲目性，使计算结果更稳定地收敛到所求解问题的全局最优解。 第四章描述了对算法进行数值试验的效果。应用上述新的演化算法解决一维下料问题时，运算结果证明了新算子和新算法的优良性能。 最后对全文进行了总结。更多还原

【Abstract】 Many problems can be classified into optimization problems, whether from science test or from engineering design. But in reasonable computational time, traditional algorithms can not obtain approximate satisfied optima for large scale problem. However, evolutionary algorithms is competent for these problems, and is used widely to work out the with large scale optimization problems in practice.But traditional evolutionary scheme, which has the semi-blindness when producing offspring, can’t achieve the balance between the efficiency and result. To solve the problem, we did the research as following:The dissertation consists of two parts: in the first part we study on the theory of evolutionary computation: A survey is made on the general theory of evolutionary computation. We proposed a new adaptive mutation operator based on the similitude between individuals. Based on the systematical survey on the One-Parent Genetic Algorithm, a new adaptive evolutionary algorithm using this operator is proposed. In the second part, we talk about the application of the new evolutionary algorithm to solving one-dimensional cutting stock problems. The experimental results show the advantageous performance of the algorithm. The main research work is listed as follows:In the first chapter, we give a brief introduction to the research content of evolutionary computation .Then we point out the key problem that must be solved in our research work.In the second chapter, we discuss the general theory of evolutionary computation, including its basic concepts, basic characteristics and fundamental procedure that one has to follow when designing evolutionary algorithms.The third chapter presents our research on real-code adaptive mutation operator based on the similitude between individuals. Based on the systematical survey on evolutionary optimization and One-Parent Genetic Algorithm, we propose a One-Parent mutation operator based on the similitude between real-code individuals. First of all, we defined the distance, similitude and neighborhoods of individual.Distance can reflect the difference between individuals, and similitude is designed to reflect how close two individuals are, and neighborhoods are used to realize the division of population. We proposed a new adaptive evolutionary algorithm based on similitude which has several characteristics. Firstly, it is capable for mutation operator to acquire "insight jumps" of the fitness; secondly, it can avoid the "semi-blind" of conventional Darwinian-type evolutionary computation. Thirdly, it ensures the stable converge of the algorithm into global optimum.The fourth chapter presents our application research on using the new evolutionary algorithm to solve one-dimensional cutting stock problems. The experimental results show the advantageous performance of the algorithmAt last, the research work in the dissertation is summarized, we suggests that more research work in this area should be done in the future and predicts bright prospect of future research.更多还原