【作者】 杨光；

【导师】 徐涛；

【作者基本信息】 吉林大学 ， 固体力学， 2015， 博士

【摘要】 对于科技的进步、各行各业的发展,优化是永恒的课题之一。事实表明,需要解决的优化问题大部分是多目标优化问题,这些问题广泛存在于工业设计、经济决策、交通规划、企业管理等有价值的工作中。多目标优化及其应用的研究是必要的,而且极具实际意义。本文基于2012年吉林省科技发展计划重大项目及配套的中国第一汽车集团公司技术中心项目,结合国家自然基金项目的研究成果,对多目标优化方法及其在车身抗撞性优化中的应用进行了深入研究。主要工作包括:(1)多目标优化算法及其应用的总结详细介绍多目标优化算法的研究现状。描述多目标优化算法的分类情况,以求解模式作为常规的分类标准,多目标优化算法一般分为数值多目标优化算法和智能多目标优化算法。分别描述两类中典型多目标优化算法的原理,以及发展历程。研究多目标优化在实际中应用的现状,详细描述了智能多目标算法广泛应用的原因,及其在计算效率方面不可忽视的缺陷。最后,简明的介绍了多目标优化算法的设计目标,以及设计数值多目标优化算法时必须的几种典型的最优化方法。本部分工作可以作为研究基础。(2)提出牛顿法加权和法首先介绍无约束多目标优化问题的标准数学模型,以及帕累托最优解、帕累托最优前端的概念。基于牛顿法和线性加权和法提出一种求解无约束多目标优化问题的算法,称为牛顿加权和法(NWSA)。在求解精度方面,对采用这种算法所求出的解为帕累托最优解进行证明。在求解效率方面,当目标函数为连续二次可微凸函数时,对牛顿加权和法在求解时具有超线性收敛进行证明;当目标函数为二次可微凸函数且满足利普希兹连续时,对牛顿加权和法在求解中表现出超二次收敛性能进行证明。(3)讨论了牛顿法加权和法求解性能分别介绍了牛顿加权和法在求解两个目标、三个目标的优化问题时权重因子的设置方法,并将这种模式推广到更多目标情况。设计出牛顿加权和法的三种初值选择方式:随机初值、同一初值和最优初值。通过算例验证不同初值选择方式下的计算结果精度和计算效率。选择最优初值作为牛顿加权和法的初值选择方式,从而进一步提高了其计算效率。将已发表论文中的多目标优化算例选为测试问题,分别使用多目标遗传算法和牛顿加权和法对其进行计算。从结果精度、帕累托前端分布质量和计算效率三个方面对测试结果进行对比,得出牛顿加权和法在无约束多目标优化中具有较高的计算效率和计算精度,但帕累托前端分布质量一般。(4)提出牛顿法加权和弗里希法对于工程中大量存在的不等式约束多目标优化问题,在牛顿加权和法(NWSA)的基础上加入约束处理方法,提出牛顿加权和弗里希法(NWSFA)。选择两个标准算例,分别采用MATLAB软件遗传算法工具箱中的多目标遗传算法和牛顿加权和弗里希法对其进行计算,对比计算结果的质量,验证牛顿加权和弗里希法在求解不等式约束多目标优化问题的可行性和高效性。最后,基于牛顿加权和弗里希法,提出一种先求解后选择的工程多目标优化求解理念,并通过工程算例对其进行展示。(5)前纵梁截面多目标尺寸优化对汽车正面碰撞进行描述,说明从力学的角度,汽车碰撞问题本质上是对接触问题的研究。详细的概括了接触碰撞非线性有限元法的基本原理以及计算方法。介绍了碰撞仿真分析常用的软件和软件的基本操作过程。基于试验设计方法和有限元仿真分析结果,建立了前纵梁碰撞性能关于其截面尺寸的代理模型。然后,采用牛顿加权和弗里希法对多目标优化模型进行计算,获得前纵梁碰撞帕累托最优前端,并将其与原结构性能对比,寻找优化设计参考方案,实现前纵梁结构的多目标优化。最后,对改进后的结构进行碰撞仿真分析,验证前纵梁碰撞性能的提高。更多还原

【Abstract】 For technological advances and the development of all industry, optimization is one consistent theme. It turns out that most of the optimization problems that need to be solved are the multi-objective optimization problems, which exist in many valuable jobs such as industrial design, economic decisions, traffic plans and business management. The research on the multi-objective optimization and its application is necessary and has practical significance.The article supported by Science and Technology Development Plan of Jilin Province and its assorted project, FAW Group Combined Action Plan,carries out research deeply on the multi-objective optimization method and its application in extent optimization of car body. The main work includes as follows.(1) A summary of the multi-objective optimization and its applicationThe details of the research status of the multi-objective optimization are presented. The classification of the multi-objective optimization which is based on the solution mode is described. The multi-objective optimization algorithms are divided into the numerical one and the intelligent one. The principles of these two typical multi-objective optimization algorithms and their development processes are described, respectively. The application status in practice of the multi-objective optimization is studied and the reasons why the multi-objective optimization is popular in practice and the defects on computational efficiency that should not be neglected are described. Finally, the design goals of the multi-objective optimization and some typical multi-objective optimization algorithms which are necessary in designing the numerical multi-objective optimization are explained briefly. This section can be the basis of the research.(2) Proposing the Newton Weighted Sum AlgorithmFirstly, the standard mathematical model of the unconstrained multi-objective optimization problem and the concepts of Pareto optimal solution and Pareto optimal front points are introduced. An algorithm is based on the Newton method and the linear weighted sum method which can solve the unconstrained multi-objective optimization problem, which is called the Newton Weighted Sum Algorithm(NWSA), are proposed. In respect of solving efficiency, when the objective function is the twice continuously differentiable and convex, the Newton Weighted Sum Algorithm is super linearly convergent; when the objective function is quadratic differential convex and satisfies the Lipschitz continuity, the Newton Weighted Sum Algorithm is super quadratic convergent.(3) Discussing the solving properties of the Newton Weighted Sum AlgorithmThe set methods of weighting factors when solving the optimization problems having two and three objects using the Newton Weighted Sum Algorithm are introduced, respectively. Then this mode is extended to the situation in which there’s more objects. Three selection processes are designed for the initial values of the Newton Weighted Sum Algorithm: random initial values, same initial values and optimal initial values. It is confirmed that the precision of the results is almost the same and computational efficiency is different significantly calculated by different initials values using examples. The computing time and average iteration speed under the optimal initial values way are far smaller than other ways. The optimal initial values are selected as the initial values of the Newton Weighted Sum Algorithm, which can further improving the computational efficiency. The multi-objective optimization examples are selected from published papers as testing problems, and, the Multi-objective Genetic Algorithms and the Newton Weighted Sum Algorithm are utilized to make calculations, respectively. Test results are compared from the view of the result accuracy, Pareto front distributed quality and calculation efficiency, drawing conclusions that the Newton Weighted Sum Algorithm has higher calculation efficiency and accuracy in the unconstrained multi-objective optimization, while the Pareto front distributed quality is general.(4) Proposing Newton Weighted Sum Frisch AlgorithmThere are many multi-objective optimization problems with inequality constrains. As a result, Newton Weighted Sum Frisch Algorithm is proposed by adding a method to handle constraints to the Newton Weighted Sum Algorithm. Two standard examples are chose, and the Multi-objective Genetic Algorithms from the genetic algorithm toolbox in MATLAB and the Newton Weighted Sum Algorithm are utilized to make calculations. The results are compared, validating the feasibility and high-efficiency of using the Newton Weighted Sum Frisch Algorithm to solve inequality constrained multi-objective optimization. Finally, based on the Newton Weighted Sum Frisch Algorithm, a concept of first solving then selecting to solve engineering multi-objective optimization is proposed and it is displayed by an engineering example.(5) The multi-objective optimization in the sectional of the front railThe vehicle front impact is described, showing that in the view of mechanics, the automobile impact problem is essentially the research on the contact problems. The fundamentals and computing methods of nonlinear finite element method of contact impact are summarized. The common impact simulation software as also as the basic operating process of the software is introduced. Based on the experiment design method and results of finite element simulation analysis, an agent model of the sectional structure of the impact properties is built. Then Newton Weighted Sum Frisch Algorithm is utilized to compute the multi-objective optimization problem, resulting in the optimal Pareto front of the front rail impact. Then the properties of the original structure are compared with the Pareto front. Seeking for the referenced scheme of optimized design, the multi-objective optimization of the front rail structure is achieved. Finally, by the simulation of the improved structure impact results, the improvement of the front rail impact properties is verified.更多还原