决策信息不明确的多目标模糊优化模型与方法
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摘要
在复杂系统和决策环境中,决策者的知识通常是不完美的,所以无法清楚地表达其偏好,即决策者偏好是不明确的。求解偏好信息不明确的多目标优化问题的关键是:建立能够有效表述不明确信息的优化模型,并在求解过程中正确把握不明确中的确定规律和因素,使得系统最终优化设计结果最大符合决策者的真实意图。本文在此思想指导下,对多种类型不明确决策偏好信息下多目标优化设计问题的建模和求解方法做了进一步的研究和探讨,其主要内容如下:
1)针对传统多目标决策和优化方法需给出无实际物理意义权重的局限,并考虑实际决策和优化过程中存在大量不明确信息的问题,将Messac教授提出了物理规划法推广到模糊多目标决策和优化领域。根据多目标优化问题的建模和决策过程中模糊因素的特点,建立了模糊物理规划决策模型。分析了多种决策环境下的不明确偏好信息在物理规划模型中的表达方法,给出了语言型决策变量和多人决策条件下偏好函数建立过程,重点分析了偏好区间边界值截集水平对偏好函数凸性的影响,给出了偏好函数凸度的检验公式。提出了模糊物理规划决策的简化方法和近似解的有效性条件。该方法将复杂和不确定性的决策问题置于灵活、简单的决策框架中,易于工程设计人员掌握,适用面广。
2)提出了一种适用于模糊偏好结构的交互式多目标优化策略。在利用模糊偏好结构控制向量表达决策者局部偏好信息的基础上,建立了交互式决策框架。根据不明确决策者偏好的不同表达形式,以两类模糊物理规划模型为基础提出了Pareto解集的削减方法,以获得能够有效表示决策者在Pareto曲面上感兴趣的区域的近似解集。该解集具有在Pareto前沿面上任意可达的特性。利用决策者局部偏好信息对近似解集进行评价,以获得满意解。该交互式求解策略广泛适用于求解具有决策者模糊偏好结构的一类多目标优化问题。
3)提出以模糊偏好区间为基础的多目标满意优化模型及求解策略。针对偏好信息不明确的多目标满意优化问题的不同求解条件,提出了基于后验偏好信息的模糊满意决策方法和基于满意度的模糊多目标协同优化方法。以决策者对目标值到其期望值的偏差程度的模糊划分为基础建立满意度函数,该函数是“令人满意准则”指导下的物理规划的偏好函数的扩展形式。根据模糊偏好区间对Pareto解集进行分类,并提出确定各类中心解的方法,依据Pareto解集分类信息所显示的Pareto解的满意水平与折衷性能的关系,实现基于后验偏好信息的满意决策。利用折衷系数对各性能指标改进或牺牲的制约作用,建立改进的协同满意优化模型,决策者可通过对模糊折衷系数及其阈值的调整,实现以兼顾性能指标的相对重要性和冲突程度的可控优化过程。
决策信息不明确的多目标模糊优化设计方法在现实工程应用领域具有重大的现实意义。本文所做工作还处于理论研究和初步应用阶段,还有很多地方值得深入研究。
Under the complex DM environments, the MD's knowledge is usually not perfect and the person could not express clearly for the preference, so MD's preference is undefined. The key factors for solving multi-objective optimization problem with undefined performance are: to effectively express undefined preference and correctly grasp the certain regular and factors for those undefined preference, to achieve the system optimization results meet MD's requirement and expectation. Based on the above thoughts, the paper further develops the models and methods of multi-objective optimization design problems with undefined preference. The main content of this paper includes the following aspects:
1) In view of the limitation that weights and ratings without physical meaning are required to be provided in traditional evaluation methods, physical programming is used in the field of fuzzy multi-objective optimization to deal with the amount of undefined information problems. The fuzzy physical programming model is proposed based on characters of fuzzy factors in multi-objective problem modeling process. The express method of undefined preference in physical programming model is being analyzed under different decision environment. The simplization method and effective conditions of fuzzy physical programming DM also are proposed, which take complex and undefined decision problems into more flexible and simple frames and make it controlled easily by designers and enhance it's suitable range.
2) An interactive multiobjective optimization strategy suitable for fuzzy optimization structure is proposed. With undefined MD preference different forms, the reduce method in Pareto solution has been proposed based on two types of fuzzy physical programming models. The satisfying solution could express clearly the designer's interested ranges on Pearto front and could not be restricted by optimization problem model real action to randomly reach in valid field. The evaluation standard proposed combing qualitative and quantitative is to getting satisfying solution and build interactive decision frame by using fuzzy optimization structure control with the basis of MD's preference. The proposed strategy of interactive solving solution is popularly suitable for the kind of solving multi-objective optimization problem with fuzzy perference model.
3) Multiobjective satisfying optimization model and its solution strategy based on the fuzzy preference range are proposed. To against the different solving solution conditions, fuzzy DM method and coobritive optimization method based on fuzzy satisfying degree are proposed. This function is extension form of preference function of physical programming disign, which is under the direction of satisfying degree standard. Classifying Pareto solution set by fuzzy optimization fields, proposing defined various center solution method, and relying on the relations between the Pareto solution satisfying degree shown by sorting out Pareto solution and compromise performance, the satisfying decision making based on after checking optimization preference can be achieved. Using the restricted impact of various performance target improved or lost by comprise figures and building improved coordinated satisfying optimization model, the designers could adjust the fuzzy comprise figures and its threshold to achieve controllable optimization process taking both relative importance and conflict degree of performance target into the considerations.
It has significant and realistic applications in real engineering field for fuzzy multi-objective optimization method with indetermincy of DM. This paper is working at the initial theories application study stage else.
1)针对传统多目标决策和优化方法需给出无实际物理意义权重的局限,并考虑实际决策和优化过程中存在大量不明确信息的问题,将Messac教授提出了物理规划法推广到模糊多目标决策和优化领域。根据多目标优化问题的建模和决策过程中模糊因素的特点,建立了模糊物理规划决策模型。分析了多种决策环境下的不明确偏好信息在物理规划模型中的表达方法,给出了语言型决策变量和多人决策条件下偏好函数建立过程,重点分析了偏好区间边界值截集水平对偏好函数凸性的影响,给出了偏好函数凸度的检验公式。提出了模糊物理规划决策的简化方法和近似解的有效性条件。该方法将复杂和不确定性的决策问题置于灵活、简单的决策框架中,易于工程设计人员掌握,适用面广。
2)提出了一种适用于模糊偏好结构的交互式多目标优化策略。在利用模糊偏好结构控制向量表达决策者局部偏好信息的基础上,建立了交互式决策框架。根据不明确决策者偏好的不同表达形式,以两类模糊物理规划模型为基础提出了Pareto解集的削减方法,以获得能够有效表示决策者在Pareto曲面上感兴趣的区域的近似解集。该解集具有在Pareto前沿面上任意可达的特性。利用决策者局部偏好信息对近似解集进行评价,以获得满意解。该交互式求解策略广泛适用于求解具有决策者模糊偏好结构的一类多目标优化问题。
3)提出以模糊偏好区间为基础的多目标满意优化模型及求解策略。针对偏好信息不明确的多目标满意优化问题的不同求解条件,提出了基于后验偏好信息的模糊满意决策方法和基于满意度的模糊多目标协同优化方法。以决策者对目标值到其期望值的偏差程度的模糊划分为基础建立满意度函数,该函数是“令人满意准则”指导下的物理规划的偏好函数的扩展形式。根据模糊偏好区间对Pareto解集进行分类,并提出确定各类中心解的方法,依据Pareto解集分类信息所显示的Pareto解的满意水平与折衷性能的关系,实现基于后验偏好信息的满意决策。利用折衷系数对各性能指标改进或牺牲的制约作用,建立改进的协同满意优化模型,决策者可通过对模糊折衷系数及其阈值的调整,实现以兼顾性能指标的相对重要性和冲突程度的可控优化过程。
决策信息不明确的多目标模糊优化设计方法在现实工程应用领域具有重大的现实意义。本文所做工作还处于理论研究和初步应用阶段,还有很多地方值得深入研究。
Under the complex DM environments, the MD's knowledge is usually not perfect and the person could not express clearly for the preference, so MD's preference is undefined. The key factors for solving multi-objective optimization problem with undefined performance are: to effectively express undefined preference and correctly grasp the certain regular and factors for those undefined preference, to achieve the system optimization results meet MD's requirement and expectation. Based on the above thoughts, the paper further develops the models and methods of multi-objective optimization design problems with undefined preference. The main content of this paper includes the following aspects:
1) In view of the limitation that weights and ratings without physical meaning are required to be provided in traditional evaluation methods, physical programming is used in the field of fuzzy multi-objective optimization to deal with the amount of undefined information problems. The fuzzy physical programming model is proposed based on characters of fuzzy factors in multi-objective problem modeling process. The express method of undefined preference in physical programming model is being analyzed under different decision environment. The simplization method and effective conditions of fuzzy physical programming DM also are proposed, which take complex and undefined decision problems into more flexible and simple frames and make it controlled easily by designers and enhance it's suitable range.
2) An interactive multiobjective optimization strategy suitable for fuzzy optimization structure is proposed. With undefined MD preference different forms, the reduce method in Pareto solution has been proposed based on two types of fuzzy physical programming models. The satisfying solution could express clearly the designer's interested ranges on Pearto front and could not be restricted by optimization problem model real action to randomly reach in valid field. The evaluation standard proposed combing qualitative and quantitative is to getting satisfying solution and build interactive decision frame by using fuzzy optimization structure control with the basis of MD's preference. The proposed strategy of interactive solving solution is popularly suitable for the kind of solving multi-objective optimization problem with fuzzy perference model.
3) Multiobjective satisfying optimization model and its solution strategy based on the fuzzy preference range are proposed. To against the different solving solution conditions, fuzzy DM method and coobritive optimization method based on fuzzy satisfying degree are proposed. This function is extension form of preference function of physical programming disign, which is under the direction of satisfying degree standard. Classifying Pareto solution set by fuzzy optimization fields, proposing defined various center solution method, and relying on the relations between the Pareto solution satisfying degree shown by sorting out Pareto solution and compromise performance, the satisfying decision making based on after checking optimization preference can be achieved. Using the restricted impact of various performance target improved or lost by comprise figures and building improved coordinated satisfying optimization model, the designers could adjust the fuzzy comprise figures and its threshold to achieve controllable optimization process taking both relative importance and conflict degree of performance target into the considerations.
It has significant and realistic applications in real engineering field for fuzzy multi-objective optimization method with indetermincy of DM. This paper is working at the initial theories application study stage else.
引文
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