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题名	两层多目标规划理论与方法的研究
作者	赵蔚
学位类别	工学博士
答辩日期	1995-08-01
授予单位	中国科学院自动化研究所
授予地点	中国科学院自动化研究所
导师	何善堉
学位专业	控制理论与控制工程
中文摘要	本文围绕两层多目标规划问题进行了理论与方法两方面的研究。全文 内容共分六个部分。 第一章是综述，介绍了两层规划的一些基本概念及国内外研究概况。 第二章研究了一类非线性两层多目标规划问题，在下层多目标规划问 题的目标函数是严格凸函数，决策变量约束集是凸集的假设下，将两层多 目标规划问题转化成一系列单层多目标规划问题，并给出了这些单层多目 标规划问题与原问题之间的关系，为提出两层多目标规划的算法提供了理 论依据。在单层化的基础上，建立了两层多目标规划的罚函数理论。 第三章提出了一种求解两层多目标规划问题的交互式算法。该算法 的特点是把一个两层多目标规划问题转化成一系列易于求解的单层多目标 规划问题，克服了现有的求解两层多目标规划问题算法的计算上的困难。 该算法在人机交互过程中利用期求水平获取决策者的偏好，对决策者的要 求不高。另外该算法还计算出偏置换率提供给决策者参考，使决策者知道 各目标间的置换信息，从而对非劣点附近非劣面的形状有大致的了解．这 样就能指导决策者设置期求水平。算例说明了算法的有效性。 第四章研究了线性两层多目标规划问题的一些性质。给出了非劣解的 最优性条件，及一个实用的检验可行解是否为非劣解的判定定理。证明了 线性两层多目标规划问题的可行解集是连通闭集，并给出了可行解集的构 造。 第五章将线性两层多目标规划问题转化成一系列单层多目标规划问 题，这些单层多目标规划问题的目标函数都是双线性函数，约束条件也是 线性的。这种单层化方法为线性两层多目标规划问题提供了一条有效的求 解途径。特别地，该方法也适用于下层多人有关联的两层多目标规划问 题。 第六章提出了有待于进一步研究的问题。
英文摘要	This dissertation is concerned with the research on theory and method of bilevel multiobjective programming. It contains six chapters. In Chapter 1, We introduce some basic concepts of bilevel programming and give a comprehensive survey of related literature, both the domestic and overseas. In chapter 2, we study a class of nonlinear bilevel multiobjective programming problems. Under the assumptions that the objective functions are strictly convex and the constraint set of decision variables is convex, the bilevel multiobjective programming problem is transformed into a series of one-level multiobjective programming problems, and the relation between these one-level multiobjective programming problems and the original problem is established, that offers the theoretic basis on which some algorithms for solving bilevel multiobjective programming problems can be developed. Furthermore. The theory about penalty function method of bilevel multiobjective programming is established. In chapter 3, an interactive algorithm for sobAng a class of nonlinear bilevel multiobjective programming problems. The distinguishing feature of this algorithm is that the original bilevel multiobjective programming problem is transformed into a series of one-level multiobjective programming problems that can be solved easily. By doing so. the difficult in computation that exists in the most proposed algorithms for solving bilevel multiobjective programming problems is overcome. Using our algorithm, the preference of the decision maker is obtained by utilizing the aspiration level, so the requirement to the decision maker is rather lenient in the process of manmachine interaction. Moreover, the partial trade-off rates between criteria can be obtained,, so the decision maker knows the relation of trade-off between criteria and the shape of the non-inferior face around the non-inferior point approximately. Then the decision maker can set his aspiration level properly. Numerical example shows the efficiency of the proposed algorithm. In chapter 4,we study; some properties of linear bilevel multiobjective programming problems. An optimality condition for a linear bilevel multiobjective programming problem is presented, and a theorem for the test of a non-inferior solution is given. We illustrate that the feasible set of a linear multiobjective programming problem is connected, and give the structure of the feasible set. In chapter 5, a linear bilevel multiobjective programming problem is transformed into a series of one-level multiobjective programming problems. In each one-level mulfiobjective programming problem, the objective functions are bilinear functions, and the constraint functions are linear functions. This method provides an efficient approach to the solution of bilevel multiobjective programming problems. Particularly, this method can be applied to bilevel multiobjective programming problem with multiple interrelated decision mak
语种	中文
其他标识符	337
内容类型	学位论文
源URL	[http://ir.ia.ac.cn/handle/173211/5652]
专题	毕业生_博士学位论文
推荐引用方式 GB/T 7714	赵蔚. 两层多目标规划理论与方法的研究[D]. 中国科学院自动化研究所. 中国科学院自动化研究所. 1995.

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