带软约束的模糊二次规划问题研究

发布时间：2018-04-26 16:49

本文选题：模糊二次规划 + 二次隶属函数　；参考：《广州大学》2017年硕士论文

【摘要】：带软约束的模糊二次规划问题,由一个二次目标函数和若干线性约束条件在模糊环境中组合而成。求解方法需要先将模糊约束转化为隶属度形式,此处通常采用线性隶属函数描述。考虑到线性函数形式单一,无法充分保证决策者的意愿。若改用非线性函数描述其满意度,又会增加处理的难度。可见,寻找一类既能最大限度地保留决策者意愿,又能轻松求解的隶属函数具有相当的现实意义。采用可调节二次隶属函数可以做到这一点。为此,论文主要针对带软约束的模糊二次规划问题,改用二次隶属函数或者正态隶属函数刻画模糊约束的满意度,分别建立了两种含不同隶属函数的模糊二次规划模型。由于正态函数在表达形式上的复杂性,进一步提出用二次函数在关键点处近似替代正态函数,从而简化了含正态隶属函数模型的求解。论文的主要内容包括:1、针对带软约束的模糊二次规划问题,以总结几种基于线性隶属函数的求解方法为依托,分析和探讨模型的其它解法。2、提出了一类可调节二次隶属函数供决策者选择,建立了含二次隶属函数的模糊二次规划模型,比较了扩展线性方法和参数规划法两类求解方法,从中找出一些规律性的东西。3、基于正态函数建构含正态隶属函数的模糊二次规划模型,研究用二次函数在关键点处近似替代正态函数来简化模型的求解问题,讨论替换前后最优解的变化情况。4、通过简单实例,给出了目标函数的等值线为圆形和抛物形两类简单的模糊二次规划的图解法,获得了较满意的结果。论文所用的方法优势在于,二次隶属函数与该模型的目标函数在表达形式上相一致。函数的形态可以随意调节,避免了采用其它非线性隶属函数对求解的影响。该方法续写了模糊二次规划的内容,也为决策者解决模糊环境下的规划问题,提供了更丰富的途径。
[Abstract]:The fuzzy quadratic programming problem with soft constraints is composed of a quadratic objective function and some linear constraints in a fuzzy environment. It is necessary to transform fuzzy constraint into membership form, which is usually described by linear membership function. Considering the single form of linear function, the will of decision maker can not be fully guaranteed. If the nonlinear function is used to describe its satisfaction, it will increase the difficulty of processing. Therefore, it is of practical significance to find a kind of membership function which can not only retain the will of the decision maker to the maximum extent, but also solve the membership function easily. This can be achieved by using adjustable quadratic membership function. To solve the problem of fuzzy quadratic programming with soft constraints, this paper uses quadratic membership function or normal membership function to describe the satisfaction of fuzzy constraints, and establishes two fuzzy quadratic programming models with different membership functions. Due to the complexity of normal function in expression form, it is further proposed that the quadratic function be used to approximate the normal function at the key point, thus simplifying the solution of the model of membership function containing normal state. The main contents of this paper include: 1. Aiming at the fuzzy quadratic programming problem with soft constraints, we summarize several solving methods based on linear membership function. Based on the analysis and discussion of other solutions of the model, a class of adjustable quadratic membership function is proposed for decision makers to choose. A fuzzy quadratic programming model with quadratic membership function is established. The extended linear method and parametric programming method are compared. Based on the normal function, the fuzzy quadratic programming model with normal membership function is constructed, and the problem of solving the model is simplified by using quadratic function to approximate replace normal function at the key point. The variation of the optimal solution before and after substitution is discussed. By a simple example, the graphic method of two simple fuzzy quadratic programming, which the objective function is circular and parabolic, is given, and the satisfactory results are obtained. The advantage of the method is that the quadratic membership function is consistent with the objective function of the model. The shape of the function can be adjusted at will to avoid the influence of other nonlinear membership functions on the solution. The method extends the content of fuzzy quadratic programming and provides a more abundant way for decision makers to solve the planning problem in fuzzy environment.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221

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