吴方法在多目标规划问题中的应用

【作者】 吕占美；

【导师】 陈小松；

【作者基本信息】 中南大学 ， 计算数学， 2011， 硕士

【摘要】 针对一般多目标规划问题,提出了一种求解多目标优化问题Pareto-最优解的一个新的方法,该方法基于计算代数与代数几何的理论.任选其中一个目标函数作为主目标函数,其余目标函数通过引入参量,化为约束条件,将多目标问题化为带有参量的单目标规划问题,然后运用代数系统全局优化的吴有限核定理,求出有限核,并对有限核进行简要的参量分析,得到多目标优化问题Pareto-最优解.全文由三章组成.第一章为绪论,简要介绍了多目标规划问题的研究背景和研究进展,吴文俊方法,MMP软件以及本文的主要工作.第二章为预备知识,主要介绍了吴方法的基本理论及其应用所需要的基本的代数学知识,并详细介绍了吴特征列方法.第三章为吴方法在多目标规划中的应用,是本文的核心内容,提出了一种用吴方法求解多目标规划的算法,并通过线性和非线性多目标规划的实例验证了该方法的有效性.更多还原

【Abstract】 The paper deals with the general multi-objective programming problem, and proposes a new method for abtaining the Pareto-optimal solution of a multi-objective optimization problem, which is based on computational algebra and algebraic geometry theory. In the beginning we choose one of the objective functions as the main objective function, and convert the rest of the objective functions into the constraints by introducing parameters. Thus, the multi-objective problem is transformed into a single objective programming problem with parameters. Then we can get the finite kernel by applying the Wu’s finite kernel theorem of global optimization of the algebraic systems and obtain the Pareto-optimal solution of multi-objective optimization problem by a brief parametric Analysis. This thesis is composed of three chapters.The first chapter is an introduction, a brief introduction of multi-objective programming background and research progress, Wu Wenjun’s method, MMP software and the paper’s work.Chapter II to prepare for the knowledge used in the paper, mainly introduces the basic theory of Wu’s method and the required knowledge of basic algebra in its applications, and introduces the Wu’s characteristic set method in detail. The third chapter, the core of this article, is an application of Wu’s method in multi-objective programming. Here, we put forward a new algorithm for solving multi-objective planning, and through linear and nonlinear multi-objective programming examples demonstrate that the method is effective.更多还原