【作者】 唐文艳；

【导师】 顾元宪；

【作者基本信息】 大连理工大学 ， 工程力学， 2002， 博士

【摘要】 结构优化设计不仅可以降低结构重量和材料成本，而且能够改进结构的强度、刚度、振动特性、屈曲稳定性等性能，是计算力学以及现代设计制造领域的重要研究方向。 本文的研究工作由两部分组成：1．在研究分析基本的遗传算法原理和综合近期关于遗传算法研究进展的基础上，针对结构优化问题的特殊性质和要求，对遗传算法提出了若干改进措施。2．在若干类型的结构优化问题中应用本文改进的遗传算法，通过大量算例的数值试验和算法比较表明，遗传算法在结构优化的某些困难问题中具有其特点，本文的改进措施是可行和有效的。 各章节的内容安排如下： 第一章首先论述了遗传算法的研究进展。内容包括遗传算法的发展历史和特点、理论的研究、约束处理及适应值评价和标定及遗传算法会议与研讨会等。接着阐述了遗传算法的应用，着重叙述了遗传算法在结构优化中的应用，并且指出了存在的问题。最后概述了本文的研究工作。 第二章介绍了标准遗传算法的基本过程及其基本原理。首先介绍遗传算法的基本术语，即生物界中染色体、基因、等位基因、基因座、基因型和表现型与遗传算法中的对应关系。然后介绍了标准遗传算法的基本过程及其经验的参数选择。最后介绍了遗传算法的基本原理，即模式定理。而积木块假设却说明了遗传算法具备寻找到全局最优解的能力。同时还分析了遗传算法的隐含并行性和收敛性。 第三章提出了对遗传算法的改进，是本文理论算法研究的重要部分。在研究分析基本的遗传算法原理和综合近期关于遗传算法研究进展的基础上，本文针对结构优化问题的特殊性质和要求，对遗传算法提出了若干改进措施。主要包括：(1)凝聚约束处理；(2)约束凝聚选择算子；(3)用复合形法对匹配池中个体进行可行性改进；(4)竞争最优保留；(5)编码机制的研究；(6)二进制编码交叉操作的改进。 以下四章的内容都是在有代表性的结构优化问题中应用改进的遗传算法，计算结果表明本文研究提出的改进遗传算法是可行的、有效的。 第四章研究了遗传算法在桁架结构连续变量和离散变量尺寸优化中的应用。对连续变量的桁架尺寸优化问题，比较了遗传算法与传统方法得到的结果，进而说明本文的算法能够得到比较满意的结果，其改进方法可行、有效。同时也说明了本文算法对惩罚因子的选择不敏感；竞争最优保留方法能够给优良基因更大的机会遗传给后代；复合形法改进个体的可行性能够加速算法的收敛。对离散变量的桁架尺寸优化问题，本文首次采用整数编码，并且与二进制编码进行了比较。通过算例表明，整数编码的遗传算法是有效的，而且在二进制编码所能表示的离散值个数与变量的可选离散值数目不能一一对应 大连理工大学博士学位论文一时，整数编码显示了它的优势，在相同的控制参数下，能够得到比二进制编码更优的结果。 第五章研究了遗传算法在具有混合变量的析架形状优化和具有奇异现象的拓扑优化中的应用。对于混合变量的析架形状优化问题，本文提出了混合编码策略，即二进制和实数混合编码、整数和实数混合编码。通过算例，对二进制编码和两种混合编码方法进行了比较，说明混合编码方式得到的结果比二进制编码好，其中整数和实数编码方式得到最优解是最好的。对于具有奇异现象的拓扑优化问题，本文通过引入拓扑变量，提出了新的数学列式。大量的算例表明，遗传算法能够得到问题的全局最优解。还将本文算法应用于杆截面积固定的（0，1）规划拓扑优化问题，算例的结果表明遗传算法能够很方便地处理这类问题。 第六章研究了遗传算法在具有不连通可行域问题中的应用。采用二进制编码的遗传算法，求解了可行域不连通的结构优化问题，具体包括具有局部屈曲约束的拓扑优化和动力响应优化这两类问题。算例的结果表明，遗传算法不需要任何其它的辅助手段能够求解这类问题。 第七章研究了遗传算法在复合材料铺层顺序优化中的应用。首先给出了复合材料基本理论。接着阐述了遗传算法的实现过程。通过复合材料铺层顺序优化的算例，结果表明本文算法是可行的。 第八章总结全文的工作，并展望了进一步的研究工作。 本文的研究工作是国家重点基础研究专项经费（G1999032805）和高等学校骨干教师资助计划资助课题的一部分。更多还原

【Abstract】 By means of structural optimization, not only the weight of structures can be reduced, but also the strength, stiffness, vibration behavior, buckling stability, and other performances of structures can be improved efficiently. Structural optimization is an important research direction in the computational mechanics and modern design field.The research work in the dissertation consists of two major parts. The first part proposes several improved measures on GA based on the analysis of the GA’s theory and recent research of GA according to special property and requirements of structural optimization problems. The second part describes application of improved GA in all types of structural optimization problems. The numerical test and algorithmic comparison show that improved measures on GA are feasible and efficient.The research work will be introduced as follows:In chapter 1, the research developments of GA are surveyed, which include the history of development and characteristic for GA, research of the theory, evaluation of constraint handling and fitness function value, conference and forum. In the following section, applications of GA are discussed, especially in structural optimization. Existent problems applied to structural optimization are pointed out. In the last section, the main contents of the research in this dissertation are presented.In chapter 2, the process and fundament of simple GA are introduced. The basic terms are presented firstly, which include the relationships of chromosome, gene, alleles, locus, genetype, phenotype between the biology and GA. Then the process and experiential parametric selections of GA are given. Finally schema theorem is described. Building block hypothesis shows that GA has ability of finding the global optimum solution. Implicit parallelism and convergence are analyzed.In chapter 3, improvements on GA are investigated. Surrogate constraint handling, surrogate reproduction, improvement on individuals in mating pool by complex method, competitive elitist model, investigation of coded mechanism and improvement on crossover operator for binary coding are proposed.The contents of the following four chapters show that the improvements in this dissertation are feasible and effective by all kinds of typical examples.In chapter 4, GA is applied to sizing optimization of truss with continuous and discrete variables. In sizing optimization of truss with continuous variables, solutions between GA and the traditional methods are compared, which reveals that satisfying solutions are achieved, and that improved GA are feasible and effective. Improved GA doesn’t depend on choice of penalty factor, competitive elitist model can provide more opportunity to be inherited to offspring for excellent genes, and individual feasibility improved with complex method canaccelerate convergence. In sizing optimization of truss with discrete variables, integer coding is used and compared with binary coding. The numerical solutions show the integer-coded GA is effective. When number of the discrete value between representation for binary coding and in discrete list can’t be corresponded by one-to-one, integer coding is predominant, and better solutions are achieved under the same parameters.In chapter 5, GA is applied to configuration optimization of truss with mixed variables and topology optimization of truss with singularity. In configuration optimization of truss with mixed variables, mixed coded strategies are proposed which are binary and floating coding, integer and floating coding. Comparing the numerical solutions of binary coding and mixed coding, better solutions are obtained with the mixed coding, and the numerical solutions in most examples with integer and floating coding are best. In topology optimization of truss with singularity, a new mathematic formula with the topological variables is proposed. The numerical examples prove that the global optimum can be gained. In addition, GA is applied to (0,1) programming topology optimization of truss, when the c更多还原