基于密切值法的组合赋权多属性决策方法研究

分析主观赋权、客观赋权方法在实际应用中的不足,运用密切值法原理,对多属性决策问题的权重确定采用主观赋权法与客观赋权法相结合的组合赋权思路,完善多属性决策问题的决策方法,并举例说明其合理性.     

基于最大离差和最大联合熵的多方案优选方法

针对多方案优选中指标权重确定问题,提出了基于最小离散和最大广义联合熵的组合赋权方法,建立了组合权系数优化模型。该方法一方面根据评价指标对方案决策所起作用大小赋予不同的权重;另一方面尽量能够消除组合赋权中的不稳定性,使各方法各指标权数赋予平衡因子后广义的联合熵最大,从而使得全局的不确定性最小。最后通过实例说明了此方法合理、稳健。     

基于组合赋权和VIKOR的学术期刊综合评价研究

针对传统学术期刊综合评价中指标权重大多为单一赋权且评价信息难以集结的问题,提出一种新的基于组合赋权和VIKOR的学术期刊综合评价模型.首先,分别利用DEMATEL方法和熵权法确定指标的主观权重和客观权重;然后,利用乘法归一化方法计算指标的组合权重;最后,基于VIKOR方法计算各方案的利益比率值并排序.以教育类期刊为研究对象,结果表明,模型不仅能够充分考虑学术期刊指标间的相互影响关系和指标提供的信息量,还可以有效避免个别较差指标的消极影响被其他指标中和,为学术期刊评价问题提供了一种新思路.     

基于相对熵的多属性决策组合赋权方法

综合各种赋权方法给出的主观和客观属性权重信息,建立了求解多属性决策问题属性权重的优化模型,并改进了文献[11]中模型的求解方法.根据各种主客观赋权法给出的赋权结果的贴近度确定其在权重集成中的加权系数,贴近度通过计算权重向量的相对熵来得到,最后通过应用实例对此方法予以说明.     

基于综合权重的理想模糊物元多属性决策法及应用

研究了属性指标具有不相容性和模糊性及其指标的权重完全未知的模糊多属性决策问题.分析了目前广泛采用的模糊物元分析法以及仅有主观赋权法或客观赋权法确定其指标权重的缺点.根据物元可拓理论和理想解法的思想,定义了理想模糊物元和负理想模糊物元的概念.利用兼顾主观偏好和客观信息的综合权重赋值法,提出了基于综合权重的理想模糊物元多属性决策方法.该法既能充分利用指标本身所包含的客观信息,又能充分发挥决策者的主观能动性.实例研究结果表明该法能反映出决策方案间的细微差别,能对决策方案的优劣做出更准确有效的评价.     

基于秩和比的两阶段多属性决策方法研究

在多属性决策中,方案的数量直接影响了组合赋权和综合评价的复杂度.将多属性决策划分为两个阶段,即方案筛选和组合赋权.基于秩和比法构建了方案筛选步骤,基于综合评价值与主客观评价值偏差最小构建优化模型,并运用算例说明方法的可行性和优越性.     

Fuzzy-TOPSIS法的油田开发方案优选

油田开发方案的优选是一项复杂且重要的工程.基于方法集成的思想,针对备选方案,尽可能列举可能影响油田优选的全部指标,并通过层次模糊赋权法对全部指标按权重大小进行排序,排序靠前的指标对油田开发的影响较大,从而进行筛选得到主要指标.为解决无法量化的模糊指标的评选问题,采用语言评价信息与精确数进行转化,再利用TOPSIS方法依据对象与理想解和负理想解之间的距离计算其贴近度,贴近度越大说明方案越佳.最后以某油田开发项目多个开发方案为实例进行优选.     

基于博弈论和相对熵的基坑支护方案优选

基坑支护方案优选是一项多属性决策,提出了一种基于博弈论组合赋权和相对熵的逼近理想解(TOPSIS)决策模型.首先采用信息熵确定客观权重,运用层次分析法确定主观权重,然后引入博弈论集结模型将主客观权重科学化组合,得到综合权重,最后采用一种基于相对熵的逼近理想解决策方法进行基坑支护方案优选,并结合工程实例进行验证.结果证明:基于相对熵的TOPSIS决策模型在案例中的评价结果与工程实际相吻合.     

基于组合赋权和灰色关联投影法的区域能源供应系统评价研究

通过分析区域能源供应系统综合性能评价影响因素,设计系统评价指标体系,运用层次分析法(AHP)和熵权法结合的组合赋权法确定指标权重,构建加权灰色关联决策矩阵,最终提出了一种基于组合赋权和灰色关联投影法的区域能源供应系统方案优选方法.运用灰色关联投影值对备选方案进行优劣排序,案例分析表明该模型具有程序化、科学实用、便于操作等特点,具有推广和应用价值.     

基于组合赋权法和未确知测度模型的发动机健康状况评估

为了有效评估航空发动机的健康状况,提出一种逼近理想点的组合赋权法和未确知测度模型相结合的评估方法。首先,分别利用序关系分析法、指标相关性赋权法和指标难度赋权法得到各指标的主客观单一权重;利用逼近理想点的组合赋权法并考虑指标权重与重要性的一致性,求解指标组合权重,使赋权结果更具科学性,加大不同类别评价对象的区分度。其次,基于未确知测度模型,利用K-means算法将各指标分为两个对立等级,每个等级又分为两个互补小等级,以减少信息的重叠进一步区分不同类别的评价对象;根据指标属于不同等级的未确知测度、指标组合权重和评分准则,得到评价对象的健康评分。最后,通过航空发动机实例分析以及与其他方法的对比分析,验证此方法的有效性。     

多目标规划的光滑同伦方法

本文给出了求解多目标规划的一种连续同伦方法 .首先 ,运用光滑熵函数将多目标多约束的问题化为单目标单约束的问题 ,然后构造了求解单目标问题的同伦方法 ,并证明了其大范围收敛性 .     

Evaluation of the multiobjective ant colony algorithm performances on biobjective quadratic assignment problems

The difficulty of resolving the multiobjective combinatorial optimization problems with traditional methods has directed researchers to investigate new approaches which perform better. In recent years some algorithms based on ant colony optimization (ACO) metaheuristic have been suggested to solve these multiobjective problems. In this study these algorithms have been reported and programmed both to solve the biobjective quadratic assignment problem (BiQAP) instances and to evaluate the performances of these algorithms. The robust parameter sets for each 12 multiobjective ant colony optimization (MOACO) algorithms have been calculated and BiQAP instances in the literature have been solved within these parameter sets. The performances of the algorithms have been evaluated by comparing the Pareto fronts obtained from these algorithms. In the evaluation step, a multi significance test is used in a non hierarchical structure, and a performance metric (P metric) essential for this test is introduced. Through this study, decision makers will be able to put in the biobjective algorithms in an order according to the priority values calculated from the algorithms’ Pareto fronts. Moreover, this is the first time that MOACO algorithms have been compared by solving BiQAPs.     

On the transformation of lexicographic nonlinear multiobjective programs to single objective programs

This paper deals with multiobjective optimization programs in which the objective functions are ordered by their degree of priority. A number of approaches have been proposed (and several implemented) for the solution of lexicographic (preemptive priority) multiobjective optimization programs. These approaches may be divided into two classes. The first encompasses the development of algorithms specifically designed to deal directly with the initial model. Considered only for linear multiobjective programs and multiobjective programs with a finite discrete feasible region, the second one attempts to transform, efficiently, the lexicographic multiobjective model into an equvivalent model, i.e. a single objective programming problem. In this paper, we deal with the second approach for lexicographic nonlinear multiobjective programs.     

Multiobjective improved spatial fuzzy c-means clustering for image segmentation combining Pareto-optimal clusters

In this paper, we propose a grayscale image segmentation method based on a multiobjective optimization approach that optimizes two complementary criteria (region and edge based). The region-based fitness used is the improved spatial fuzzy c-means clustering measure that is shown performing better than the standard fuzzy c-means (FCM) measure. The edge-based fitness used is based on the contour statistics and the number of connected components in the image segmentation result. The optimization algorithm used is the multiobjective particle swarm optimization (MOPSO), which is well suited to handle continuous variables problems, the case of FCM clustering. In our case, each particle of the swarm codes the centers of clusters. The result of the multiobjective optimization technique is a set of Pareto-optimal solutions, where each solution represents a segmentation result. Instead of selecting one solution from the Pareto front, we propose a method that combines all solutions to get a better segmentation. The combination method takes place in two steps. The first step is the detection of high-confidence points by exploiting the similarity between the results and the membership degrees. The second step is the classification of the remaining points by using the high-confidence extracted points. The proposed method was evaluated on three types of images: synthetic images, simulated MRI brain images and real-world MRI brain images. This method was compared to the most widely used FCM-based algorithms of the literature. The results demonstrate the effectiveness of the proposed technique.     

多目标规划问题的强均衡解

用可变权方法引进了多目标规划问题的强均衡解并证明它是多目标规划的Pareto解,通过求解可变权综合问题而获得任一单目标都不会最小的Pareto解,这种解在可持续发展规划中具有重要意义。     

Multiobjective mathematical programming via the Multiplex model and algorithm

The increased interest in the existence and consideration of multiple objectives has made itself evident in the significant growth in the development and implementation of multiobjective mathematical programming. Unfortunately, it is our opinion that this field is now characterized by such a diversity of philosophies, models, approaches and terminology that any unifying theme is obscured. In fact, rather than stressing the (substantial) degree of inherent commonality between multiobjective models and methods, most presentations seem to focus on their real, or imagined, differences. We believe that such treatment can be counterproductive and thus propose, herein, what we hope is a more unified treatment of multiobjective mathematical programming via the use of the multiphase simplex, or Multiplex model and algorithm. While none of the components and concepts of the Multiplex method are, in themselves, new, we do believe that the specific arrangement of these ideas, in the form presented, does serve to clarify the close relationships between the models and (simplex based) algorithms for most forms of multiobjective mathematical programming (and, in turn, their relationship to ‘conventional,’ single objective programming).     

η-Approximation Method for Non-convex Multiobjective Variational Problems

In this paper, we use the η-approximation method for a class of non-convex multiobjective variational problems with invex functionals. In this approach, for the considered multiobjective variational problem, the associated η-approximated multiobjective variational problem is constructed at the given feasible solution. The equivalence between (weakly) e?cient solutions in the original multiobjective variational problem and its associated η-approximated multiobjective variational problem is established under invexity hypotheses.     

Bundle-based descent method for nonsmooth multiobjective DC optimization with inequality constraints

Multiobjective DC optimization problems arise naturally, for example, in data classification and cluster analysis playing a crucial role in data mining. In this paper, we propose a new multiobjective double bundle method designed for nonsmooth multiobjective optimization problems having objective and constraint functions which can be presented as a difference of two convex (DC) functions. The method is of the descent type and it generalizes the ideas of the double bundle method for multiobjective and constrained problems. We utilize the special cutting plane model angled for the DC improvement function such that the convex and the concave behaviour of the function is captured. The method is proved to be finitely convergent to a weakly Pareto stationary point under mild assumptions. Finally, we consider some numerical experiments and compare the solutions produced by our method with the method designed for general nonconvex multiobjective problems. This is done in order to validate the usage of the method aimed specially for DC objectives instead of a general nonconvex method.     

基于变权系数的人才聘用模型

主要是将招聘模型化成标准的指派问题,运用匈牙利算法进行处理.模型一:通过设置一虚拟部门通过上述方法得到最优分配方案.模型二:构建了偏差函数与变权函数,同样构造成一指派问题,得到七种分配方案,然后从中找出最优解.此模型还可推广到多人应聘多个部门的模型.     

多目标协商模型的标量化方法

多目标协商问题是协商理论的一个新的研究领域.本文讨论了由Bronisz和Krus提出的多目标协商模型和Bronisz-Krus-协商解概念,构造了由Bronisz-Krus多目标协商模型诱导的单目标协商模型并对其提出了一套公理系统和引入了Raiffa-协商解概念,讨论了诱导结局空间的性质,给出了Bronisz-Krus多目标协商模型与其诱导的单目标协商模型在某种意义下的等价性,即Bronisz-Krus-协商解与Raiffa-协商解可以互相确定,并给出了这种相互确定的关系式.