两层应急抢修系统选址问题的核搜索算法

提出了用于描述两层应急抢修系统选址问题的0-1整数线性规划模型, 该模型能保证整个应急抢修系统的服务质量。设计了求解该问题的两种核搜索算法, 在两种方法中分别根据原问题的线性松弛和拉格朗日松弛确定原问题的核问题和子问题, 从而大大减小了问题的规模。用提出的算法对56个计算实例进行求解, 算例计算结果表明, 与MOSEK软件直接求解得到的结果进行比较, 基于拉格朗日松弛的核搜索算法可以在相对较短的时间内求得较好的解, 这说明拉格朗日松弛对偶问题的最优解能为求解原问题提供非常有效的信息。     

上层含约束条件且具有模糊决策变量的二层多随从线性规划

提出并研究了一类上层含约束条件且具有模糊决策变量的二层多随从线性规划模型,利用结构元理论证明了该模型最优解等价于上层含约束条件的二层多随从线性规划模型最优解,利用Kuhn-Tucker方法得到了该模型最优解,并通过数值算例验证了该方法的可行性。     

灰色二层多目标线性规划问题及其解法

针对二层多目标线性规划问题,结合灰色系统的特性,提出了一般灰色二层多目标线性规划问题,并给出了模型的相关定义和定理.针对漂移型灰色二层多目标线性规划问题,提出一种具有全局收敛性质的求解算法.首先通过线性加权模理想点法把多目标转化为单目标;然后当可行域为非空紧集时,利用库恩塔克条件把双层转化为单层,再利用粒子群算法搜索单目标单层线性规划即可得到原问题的解;最后通过算例表明了该算法的有效性.     

基于单纯形法和局部枚举解混合整数线性规划问题

提出了一种基于单纯形法和局部枚举求解整数线性规划问题的新方法。它通过单纯形法得到松弛问题的最优解并确定变量以及目标函数取值范围,然后基于目标函数,进行局部枚举,从而得到其整数线性规划问题的最优解,与现有方法比较,新解法简单,计算量少,尤其是对于大规模整数线性规划问题,计算量少体现地更明显。     

两阶段求线性规划最优可行解的实现方法

本文对两阶段求线性规划最优可行解的矩阵运算方法作了详实的分析，采用求解矩阵的构造方法、退化可行解的处理方法以及对矩阵行向量和列向量的调整方法，增强求解的可靠性。用算例对程序求线性规划的最优可行解、无界解和无可行解的准确性进行了测试，表明实现方法正确、求解准确。     

求成对线性规划问题的组合最优解的快速算法

本文研究求成对线性规划问题的组合最优解的算法，巧妙地将问题的求解转化成了求西凸多面体间的距离，并给出了求两凸多面体间距离的快速算法，以该算法为核心，一系列的成对线性规划问题的组合最优解的均能在Ｏ时间内求得。     

系数为对称梯形模糊数的模糊线性规划

针对模糊系数的线性规划, 提出了一种系数为对称梯形模糊数的线性规划的方法, 同时得出一些定理、命题以及相应的算法, 并通过实例验证了该方法的有效性. 该方法与常规方法的不同之处在于无须将模糊线性规划转化为经典线性规划就能得到满意的模糊优化解, 因此提出的方法所取得的规划结果更加满足决策者的需要.     

一类非线性两层规划问题的递阶优化解法

提出一种求解一类非线性两层规划问题的新方法．通过引入解耦向量将非线性两层规划问题分解为独立且易于求解的子问题，利用两级递阶结构第1级求解若干优化的子问题，而在第2级利用第1级求解的结果调整解耦向量．所提出的方法借助于分解一协调原理并按迭代方式最终求得问题的最优解．对于含整数的规划问题，通过连续化处理后也可按该方法方便地求解．算例表明所提出的算法是简便而有效的．     

增加约束条件的线性规划问题递推算法研究

首先描述线性规划问题中约束条件增加时的递推求解问题,此问题在线性规划问题中具有广泛的实际背景;然后提出一个基于凸空间思想的快速求解此类问题的递推算法,该算法能快速判断其矛盾约束、冗余约束以及新问题的递推最优解;最后给出了该问题的一个算例,实验仿真结果表明了该方法的有效性.     

不确定两层冲突环境的建模与分析

论文是在简单对策模型的基础上建立了两层超对策模型.并运用这个模型解决两层协商中的冲突问题.通过合理的假设,建立了一个典型的超对策模型,通过引入一种理性行为共生的概念作为其两层超均衡解,并讨论了两层超均衡解存在的条件.     

A computational analysis of LCP methods for bilinear and concave quadratic programming

The use of a sequential linear complementarity problem (SLCP) algorithm for finding a global minimum of bilinear programming problem (BLP) or a concave quadratic program (CQP) is examined. The algorithm consists of solving a sequence of linear complementarity problems (LCP). A branch-and-bound method is also considered in this study. This algorithm is based on the reformulation of a BLP into an LCP with a linear function to minimize. Computational experience with small and medium scale BLPs and CQPs indicates that the SLCP algorithm is quite efficient in finding a global minimum (or at least a solution that is quite near the optimum), but it is, in general, unable to establish that such a solution has been found. An algorithm to find a lower-bound for the BLP can overcome this drawback in some cases. Furthermore the SLCP algorithm is shown to be robust and compares favorably with the branch-and-bound method and another alternative technique.     

进化多目标优化设计满意解的模糊决策

文章提出了一种进化多目标优化满意解的模糊决策方法。首先,根据各个子目标满意度对所有pareto最优解的性能做出模糊评价,并在此基础上将整个pareto解集划分为若干个具有不同性能特征的类;然后根据决策者对目标的模糊偏好,从相应的类中选择最有代表性的个体作为最终的满意解。最后以两杆桁架多目标优化问题为例,说明了该方法的应用。     

A probabilistic model for interactive decision-making

A probabilistic reasoning model is defined where the decision maker (d.m.) is engaged in a sequential information-gathering process facing the trade-off between the reliability of the achieved solution and the associated observation cost. The d.m. is directly involved in the proposed flexible control strategy, which is based on information-theoretic principles. The devised strategy works on a Bayesian belief network that allows the efficient representation and manipulation of the knowledge base relevant to the problem domain. It is shown that this strategy guarantees a constant factor approximate solution with respect to the optimum of the decision problem. Some application examples are also discussed.     

An economical cognitive approach for bi-objective optimization using bliss points, visualization, and interaction

When an optimization problem encompasses multiple objectives, it is usually difficult to define a single optimal solution. The decision maker plays an important role when choosing the final single decision. Pareto-based evolutionary multiobjective optimization (EMO) methods are very informative for the decision making process since they provide the decision maker with a set of efficient solutions to choose from. Despite that the set of efficient solutions may not be the global efficient set, we show in this paper that the set can still be informative when used in an interactive session with the decision maker. We use a combination of EMO and single objective optimization methods to guide the decision maker in interactive sessions.     

多步决策过程中有效解的平稳性

本文首先论述多步决策过程及其性能指标,引进有关信息集、半收敛和强收敛等概念,给出多步决策的含时有效解和定态有效解及其平稳性的定义。然后探讨了集值映射序列在拓扑意义下的收敛和以Pompeiu-Hausdauff距离意义的收敛之间的关系,证明了几个对应关系定理。最后,文章系统地考察了决策过程中有效解的平稳性质。     

递阶优化问题理论及其算法研究与进展

递阶优化问题用来描述具有层次结构的决策问题,两级优化问题是最基本的递阶问题,又称为两层规划或静态Stackelberg问题。这里比较系统地介绍两级以及多级优化问题的模型以及其特征,并探讨了该领域有待研究的几个方向。     

The augmented weighted Tchebychev norm for optimizing a linear function over an integer efficient set of a multicriteria linear program

In this paper, we propose a new exact algorithm, using an augmented weighted Tchebychev norm, for optimizing a linear function on the efficient set of a multiple objective integer linear programming problem. This norm is optimized progressively by improving the value of the linear criteria and going through some efficient solutions. The method produced not only the best efficient solution of the linear objective function but also a subset of nondominated solutions that can help decision makers to select the best decision among a large set of Pareto solutions.     

Application of fuzzy sets to multi-objective project management decisions

In real-world project management (PM) decision problems, input data and/or related parameters are frequently imprecise/fuzzy over the planning horizon owing to incomplete or unavailable information, and the decision maker (DM) generally faces a fuzzy multi-objective PM decision problem in uncertain environments. This work focuses on the application of fuzzy sets to solve fuzzy multi-objective PM decision problems. The proposed possibilistic linear programming (PLP) approach attempts to simultaneously minimise total project costs and completion time with reference to direct costs, indirect costs, relevant activities times and costs, and budget constraints. An industrial case illustrates the feasibility of applying the proposed PLP approach to practical PM decisions. The main advantage of the proposed approach is that the DM may adjust the search direction during the solution procedure, until the efficient solution satisfies the DM's preferences and is considered to be the preferred satisfactory solution. In particular, computational methodology developed in this work can easily be extended to any other situations and can handle the realistic PM decision problems with simplified triangular possibility distributions.     

一种改进混合型多属性决策的求解方法

研究了实数、区间数、模糊数类型相结合的混合型多属性决策问题。通过定义1种新的量化尺度,把各类不同类型属性值在规范化过程中的计算规范到统一的度量空间,然后计算各候选方案与理想方案的贴近度,根据贴近度大小进行决策。最后通过算例进行验证,证明该方法是可行有效的,为解决混合型多属性决策问题提供了1种新方法。     

In the determination of the most efficient decision making unit in data envelopment analysis

In recent years, several mixed integer linear programming (MILP) models have been proposed for determining the most efficient decision making unit (DMU) in data envelopment analysis. However, most of these models do not determine the most efficient DMU directly; instead, they make use of other less related objectives. This paper introduces a new MILP model that has an objective similar to that of the super-efficiency model. Unlike previous models, the new model’s objective is to directly discover the most efficient DMU. Similar to the super-efficiency model, the aim is to choose the most efficient DMU. However, unlike the super-efficiency model, which requires the solution of a linear programming problem for each DMU, the new model requires that only a single MILP problem be solved. Consequently, additional terms in the objective function and more constraints can be easily added to the new model. For example, decision makers can more easily incorporate a secondary objective such as adherence to a publicly stated preference or add assurance region constraints when determining the most efficient DMU. Furthermore, the proposed model is more accurate than two recently proposed models, as shown in two computational examples.