不确定规划逼近问题最优解的几乎处处上半收敛性

对不确定规划经验逼近问题的最优解的几乎处处上半收敛性进行了研究。首先将带有约束的不确定规划问题转化成与其等价的无约束的不确定优化问题,然后将经验测度替代不确定测度得到不确定规划的经验逼近模型,并得出逼近问题的目标函数序列的几乎处处上图收敛性,最后利用上图收敛性理论,给出了不确定规划经验逼近最优解集的几乎处处上半收敛性。     

不确定条件下判断和决策的新领域--前景理论

Danel Kahneman诺贝尔经济学奖的主要贡献在于“把心理学的，特别是关于不确定条件下人的判断和决策的研究思想结合到经济科学中”，解释了人类在不确定情况下的判断和决策行为，开创了行为经济学研究的新领域。本阐述Kahneman等人开创的前景理论(Prospect Theory)在实际判断和决策方面偏离传统经济理论预测的内容，重点介绍该理论提出的新的决策模型。并探讨其广泛应用。     

求解不确定型二层线性规划模型的悲观决策方法

基于多参数线性规划理论，将不确定型二层线性规划问题转化为多个关于不确定参数的线性规划问题。利用不确定型决策方法中的悲观准则．从最不利的结果中选择最有利的结果，从而得到不确定型二层线性规划的最优解。数值实例的仿真结果表明，所提出的悲观决策方法对解决诸如不确定供应链的规划与运作等问题不失为一种有效的决策支持工具。     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

鲁棒优化研究综述（英文）

鲁棒优化是解决数据不确定问题的有效方法,其本质是寻找对数据扰动不敏感的解.自2000年以来,鲁棒优化在理论研究和应用方面取得了蓬勃发展.本文介绍了鲁棒优化方法在理论研究方面取得的进展和主要研究结果.     

二(双)层规划综述

二(双)层规划是研究二层决策的递阶优化问题.其理论、方法和应用在过去的30多年取得了很大的发展.本文对二层规划问题的基本概念、性质和算法作了综述,并且对下层规划问题的解不唯一的情况也作了介绍,最后还给出了几种常见的二层规划模型.     

基于SEC准则的油田开发规划不确定优化模型及算法

在油价低迷的国际背景下,上市石油公司进行油田开发规划时越来越重视经营效益。美国证券交易委员会(SEC)要求上市石油公司采用产量法计提折耗,极大地影响了石油公司开发规划方案的制定。油田开发受到自然、技术等多种不确定因素的影响,在制定开发规划时需充分考虑这些不确定性。本文基于不确定理论,考虑措施增油效果和新增投资两类不确定参数,以经营效益最大化和新增投资最小化为目标,构建了基于SEC准则的油田开发规划不确定优化模型,并利用差分进化算法求解,给出措施工作量的帕累托解集。本文以D油田年度规划为例,通过构建模型并求解,给出开发规划方案集,并进一步分析SEC储量的下降对上市石油公司经营效益、新增投资回报率、油气总产量、油气完全成本和措施工作量的影响,为企业制定开发规划方案提供参考。     

（h，φ）-不变广义凸函数的若干性质与（h，φ）-不变广义凸多目标规划的最优性及对偶性

研究了Ben-Tal广义代数运算的若干性质，引进了(h，φ)-不变广义凸函数的概念，讨论了(h，φ)-不变广义凸函数的若干性质，给出了(h，φ)-不变广义凸半无限多目标规划取得有效解(或弱有效解)的充分条件，建立了(h，φ)-不变广义凸多目标规划的Lagrange对偶理论。     

工期-费用权衡问题的两个不确定机会约束规划模型

项目调度问题是指管理者通过资源分配,延长或缩短某些工序的持续时间,达到项目费用和工期之间的平衡。在实际工程项目中,环境的不确定性往往是项目管理者需要考虑的因素之一。本文应用不确定理论描述不确定环境中的项目调度问题,将每道工序的持续时间分为正常持续时间和可变动持续时间。其中,假设工序的正常持续时间为不确定变量,可变动持续时间为决策变量,分别构建在项目费用和项目工期约束下的两个不确定机会约束规划模型。依据不确定变量运算法则,将所建立的不确定规划模型转化为等价的确定模型。最后,通过一个工程实例验证模型的合理性。     

第三届不确定系统年会征文通知

由中国运筹学会不确定系统分会主办,南京理工大学承办的第三届不确定系统年会将于2005年8月12-16日在南京理工大学举行。 本次会议的主题:不确定理论,不确定规划,算法及应用 征文要求: 1)应征论文必须未在正式学术刊物或会议论文集上发表,论文集将在会前正式出版:2)     

A probability maximization model based on rough approximation and its application to the inventory problem

In the present paper, we concentrate on dealing with a class of multi-objective programming problems with random coefficients and present its application to the multi-item inventory problem. The P-model is proposed to obtain the maximum probability of the objective functions and rough approximation is applied to deal with the feasible set with random parameters. The fuzzy programming technique and genetic algorithm are then applied to solve the crisp programming problem. Finally, the application to Auchan’s inventory system is given in order to show the efficiency of the proposed models and algorithms.     

Uncertain programming: a unifying optimization theory in various uncertain environments

By uncertain programming we mean the optimization theory in generally uncertain (random, fuzzy, fuzzy random, grey, etc.) environments. Three broad classes of uncertain programming are expected value models and chance-constrained programming as well as dependent-chance programming. In order to solve general uncertain programming models, a simulation-based genetic algorithm is also documented. Finally, some applications and further research problems appearing in this area are posed.     

Uncertain random programming with applications

Uncertain random variable is a tool to deal with a mixture of uncertainty and randomness. This paper presents an operational law of uncertain random variables, and shows an expected value formula by using probability and uncertainty distributions. This paper also provides a framework of uncertain random programming that is a type of mathematical programming involving uncertain random variables. Finally, some applications of uncertain random programming are discussed.     

A class of multiobjective linear programming models with random rough coefficients

In the present paper, we concentrate on dealing with a class of multiobjective programming problems with random rough coefficients. We first discuss how to turn a constrained model with random rough variables into crisp equivalent models. Then an interactive algorithm which is similar to the interactive fuzzy satisfying method is introduced to obtain the decision maker’s satisfying solution. In addition, the technique of random rough simulation is applied to deal with general random rough objective functions and random rough constraints which are usually hard to convert into their crisp equivalents. Furthermore, combined with the techniques of random rough simulation, a genetic algorithm using the compromise approach is designed for solving a random rough multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.     

离散型区间概率随机变量和模糊概率随机变量的数学期望

研究离散型区间概率随机变量和离散型第二类模糊概率随机变量数学期望的性质及求解方法．利用模糊分解定理,把求模糊概率随机变量的数学期望问题化为求一系列区间概率随机变量的数学期望．求区间概率随机变量的数学期望是一个典型的线性规划问题,用单纯形方法推导了求区间概率随机变量数学期望的一个很实用的计算公式．算例表明,用该计算公式得到的结果和用数学规划方法得到的结果完全吻合,但计算过程相对简单．     

A new methodology for crisp equivalent of fuzzy chance constrained programming problem

This paper deals with a chance constrained programming model, where both fuzziness and randomness are present in the objective function and constraints. The concept of fuzzy random variable, mean and variance of fuzzy random variable, minimum of fuzzy numbers are used in the model. The methodology is verified through a numerical example.     

On some optimisation models in a fuzzy-stochastic environment

This paper is on fuzzy stochastic optimisation, an area that is quickly coming to the forefront of mathematical programming under uncertainty. An even stronger motivating factor for the growing interest in this area can be found in the ubiquitous nature of decision problems involving hybrid imprecision. More precisely, we consider a range of situations in which random factors and fuzzy information co-occur in an optimisation setting. Related hybrid optimisation models are discussed and converted into deterministic terms through appropriate tools like probabilistic set, uncertain probability, and fuzzy random variable, making good use of uncertainty principles. We also discuss ways to deal with the resulting problems. Numerical examples carried out using class optimisation software demonstrate the efficiency of the proposed approaches. We shall end this article by pointing out some of the challenges that currently occupy researchers in this emerging field.     

基于遗传算法的随机模糊立体运输问题

随机模糊立体运输问题的研究是为了解决现实生活中双因素不确定性问题,在遗传算法的基础上,运用可信性理论建立随机模糊运输问题的机会约束规划模型.通过算例进行VC++编程模拟计算,验证了此模型的可行性,最终提出了基于遗传算法解决随机模糊立体运输问题的模型.     

模糊密度随机变量的数学描述

研究了由于概率密度函数的模糊性而引起的模糊概率随机变量问题。给出了区间密度函数、模糊密度函数、模糊密度随机变量及其分布函数和模糊密度随机变量的模糊数学期望、模糊方差等基本概念及定义和计算方法,并证明了有关定理。