不确定多层规划及其应用

Multilevel programming is used to deal with decentralized decision making problem in which multiple decision makers are arranged within a hierarchical administrative structure and have their own decision variables, objectives and constraints. The upper-level decision maker first makes decision to optimize his own objective. According to that, the lower-level decision makers make decisions to optimize their own objectives...So far, multilevel programming models involving random variables and fuzzy variables have been well studied, and some algorithms have also been designed to solve those models. However, some quantities in the daily life are uncertain variables rather than random variables or fuzzy variables. In order to deal with decentralized planning problem involving uncertain variables, we will develop uncertain multilevel programming model...Sometimes, the objective function has no analytic form, but is determined by uncertain inference rules in the constraint functions. This optimization problem can be modeled by uncertain logic programming. In this project, we will combine uncertain logic programming and uncertain multileval programming, and propose an uncertain logic multilevel programming model...This project is interdisciplinary among operations research, mathematical programming, information science and computer science. The research work consists of theory and application. Emphasis is put on uncertain multilevel programming model as well as its algorithms and applications in management, engineering, energy, logistics and so on.

多层规划主要用于解决分散决策问题，即在一个系统中有多个处于一定等级的决策者，他们拥有各自的决策变量、目标和约束，并且上层决策者可以通过他的决策变量来影响下层决策者的策略。目前，含有随机变量和模糊变量的多层规划模型及其算法已经得到了长足的发展。然而，大量的调研表明实际生活中的许多变量既不是随机变量也不是模糊变量，而是不确定变量。为了解决含有不确定变量的分散决策问题，本项目组将研究不确定多层规划。另外，目标函数的表达式有时也不是明确的，而是由约束条件中的不确定推理规则决定。为此本项目组将探索不确定逻辑规划模型，并将它和不确定多层规划相结合,提出基于不确定逻辑的多层规划模型。本项目为运筹学、数学规划、信息科学以及计算机科学的交叉项目，研究内容涉及理论和应用两个方面，包括如何建立不确定多层规划模型、设计智能算法以及在管理、工程、能源、物流等领域中的应用。

大量的调研表明实际生活中的许多变量既不是随机变量也不是模糊变量，而是不确定变量。为了解决含有不确定变量的分散决策问题，本项目组研究了不确定多层规划，不确定多层规划是用于解决在不确定环境下一个多层系统的具有多个决策者的分散决策问题。本项目提出了三类基本模型，即期望值模型，机会约束规划模型及其相关机会规划模型。另外，本项目还完善了不确定微分方程理论。文献表明，本项目的研究成果已经被应用到管理、工程、能源、物流等领域中。