随机关系结构及应用

提出了随机结构空间的一般性概念，从而引出了随机关系结构的概念，建立了概率优选与概率排序的应用模型．     

随机模拟型综合评价模式及其求解算法

针对类似于“球队实力”比较的评价问题,通常很难以一次的比赛给出绝对的评价结论,提出了随机模拟型的综合评价模式。即通过参数设置的方式,可将传统评价模式转化为随机模式,求解得到方案之间优劣关系比较的可能性排序结论。可能性排序结论是对绝对形式评价结论的拓展。首先,对随机模拟型评价模式进行了介绍;然后,分析了传统评价方法向随机模拟型评价模式转化的一般思路;在此基础上,基于“在提升排序链出现的可能性基础上,进一步保证排序链的稳定性”的规则,给出了求解可能性排序结论的两种方法。最后,通过算例对随机模拟型评价模式的应用进行了说明,并将其与绝对形式评价结论进行了比较。该评价模式是对传统评价模式的拓展,可进一步拓宽综合评价理论的实际应用范围。     

二阶段随机规划问题基于随机模拟的遗传算法

利用遗传算法不过多依赖目标函数性质．适应于全局搜索的特点．提出了求解二阶段随机规划的基于随机模拟的遗传算法，算法采用随机模拟技术利用样本均值近似代替期望值，使计算得以简化，计算实例表明该算法是有效和可行的。     

一个求概率约束规划的随机拟次梯度算法

概率约束规划是经常费到的一类规划，但其约束函数含有概率，在一般场合下，很难求出，随机拟次梯度法无须计算约束值与导数值，只要构造出约束函数目标函数的随机拟次梯度即可，本文给出了一个求解概率约束规划的随机拟次梯度算法，并证明了有关的定量及性质。     

普遍型模糊随机规划

本文提出了一种求解多目标模糊随机规划问题的普遍方法。这种方法在同一个理论框架内处理约束与目标中的随机性和模糊性,因此它具有相当的普遍性。确定性规划,模糊规划和随机规划都可看成是它的特例。     

二层随机规划基于随机模拟的遗传算法

本提出了二层随机规划模型，给出了求解二层随机规划问题的基于随机模拟的遗传算法。实际算例表明算法是可行的、有效的。     

带随机过程的随机规划问题最优解集的过程特性与稳定性

本文证明了带随机过程的随机规划问题最优解集做为集值随机过程的可测性、可测最优解选择过程的存在性。研究了最优解集过程的平稳性、马氏性以及最优值过程的鞅性和最优解集过程的集值鞅性。最后，讨论了在有限维分布意义下最优解集过程对所含随机过程参数的连续性以及最优值过程的稳定性。     

随机偏爱群体决策的随机Borda数法

对于具随机偏爱信息的群体决策问题，本文引入供选方案的随机Borda数和供选方案集上的随机Borda数映射概念．在讨论了随机Borda数映射满足随机偏爱公理的基础上，给出一个对所有供选方案进行群体排序的方法．     

具有优先约束的单机随机排序问题

讨论工件的加工时间为常数,机器发生随机故障的单机随机排序问题,目标函数极小化工件的加权完工时间和的数学期望最小.考虑两类优先约束模型.在第一类模型中,设工件间的约束为串并有向图.证明了模块M的ρ因子最大初始集合I中的工件优先于模块中的其它工件加工,并且被连续加工所得的排序为最优排序,从而将Lawler用来求解约束为串并有向图的单机加权总完工时间问题的方法推广到机器发生随机故障的情况.在第二类模型中,设工件间的约束为出树优先约束.证明了最大家庭树中的工件优先于家庭树中其它的工件加工,并且其工件连续加工所得到的排序为最优排序并给出了最优算法.     

带随机过程的随机规划问题最优解过程的平稳性与马氏性

证明了带随机过程的随机规划问题其最优争集中至少存在一列最优解均为可测的随机过程；且如果问题中的随机过程具有平稳性与马氏性，则此时间问题的最优解过程亦具有相应的特性。     

The relationship between integer and real solutions of constrained convex programming

We prove the following theorem which gives a bound on the proximity of the real and the integer solutions to certain constrained optimization programs.     

An O(n 2) Active Set Algorithm for Solving Two Related Box Constrained Parametric Quadratic Programs

Recently, O(n ²) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x Dx–a x+| x–c| and (1/2)x Dx–a x+(/2)( x–c)², respectively, subject to lxb, for all nonnegative values of the parameter . Here, D is a positive diagonal n×n matrix, and a are arbitrary n-vectors, c is an arbitrary scalar; l and b are arbitrary n-vectors such that lb. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs withno additional computational cost.     

Binary fuzzy goal programming

Goal programming is an important technique for solving many decision/management problems. Fuzzy goal programming involves applying the fuzzy set theory to goal programming, thus allowing the model to take into account the vague aspirations of a decision-maker. Using preference-based membership functions, we can define the fuzzy problem through natural language terms or vague phenomena. In fact, decision-making involves the achievement of fuzzy goals, some of them are met and some not because these goals are subject to the function of environment/resource constraints. Thus, binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches. This paper proposes a new idea of how to program the binary fuzzy goal programming model. The binary fuzzy goal programming model can then be solved using the integer programming method. Finally, an illustrative example is included to demonstrate the correctness and usefulness of the proposed model.     

Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach

In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formulation of the problem; so also are the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels. Then the fuzzy goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtain the most satisfactory solution for all decision makers.     

On ℓp programming

Our paper treats the primal and dual program of ?_p programming. ?_p programming is a generalization of ?_p approximation problems. There is a strict connection between ?_p programming and geometrical programming, because in both of them geometrical inequality plays a fundamental role. The structure of our paper follows that of Klafszkys [1].In the first Sections duality theorems are proved, which play an important role in mathematical programming. Most of these results can be found in Petersons and Eckers [3,4,5], but our proofs are much more simple and we show these fundamental properties more detailed.Afterwards the relation between the Lagrange function and the optimal solution pair is investigated. Regularity is investigated as well and we show the marginal value of ?_p programming. In the end linear programming ?_p constrained ?_p approximation problems, the quadratically constrained quadratic programming and compromise programming are shown as special cases of ?_p programming.     

Composite geometric programming

Geometric programming is based on functions called posynomials, the terms of which are log-linear. This class of programs is extended from the composition of an exponential and a linear function to an exponential and a convex function. The resulting duality theory for composite geometric programs retains many of the qualities of geometric programming duality, while at the same time encompassing new areas of application. As an application, composite geometric programming is applied to exponential geometric programming. A pure dual is developed for the first time and used to solve a problem from the literature.This research was supported by the Air Force Office of Scientific Research, Grant No. AFOSR-83-0234.     

A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs

We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors.     

On dual solutions of the linear assignment problem

For the linear assignment problem we describe how to obtain different dual solutions. It turns out that a shortest path algorithm can be used to compute such solutions with several interesting properties that enable to do better post-optimality analysis.Two examples illustrate how different dual solutions can be used in the context of the traveling salesman problem.     

An O(n) algorithm for quadratic knapsack problems

An algorithm is presented which solves bounded quadratic optimization problems with n variables and one linear constraint in at most O(n) steps. The algorithm is based on a parametric approach combined with well-known ideas for constructing efficient algorithms. It improves an O(n log n) algorithm which has been developed for a more restricted case of the problem.