模糊随机双层规划的精确建模及高效算法研究

Fuzzy random bilevel programming is a suitable model which describes hierarchical decision-making problems under fuzzy random environments. How to construct exact models, define reasonable concepts of the optimal solution and design efficient algorithms are the critical issues and research hot spots in the domain of fuzzy random bilevel programming. On the basis of fuzzy random theory and the theory of deterministic bilevel programming, this project intends to firstly construct more comprehensive and objective fuzzy random bilevel programming exact models under various decision-making backgrounds. Secondly, define new concepts of the only optimal solution, which can satisfy different requirements of the decision makers under different decision-making situations in terms of the concepts of the measure or the ranking methods of fuzzy random variable; and give a notion of the optimal solution set from a new perspective, which is able to provide more information for the decision makers in a wider range by means of the Pareto optimality concept of multi-objective programming. Finally, for fuzzy random bilevel programming involving particular types of fuzzy random variable, construct its determined equivalent models with special structures and good characteristics, and on this basis, design novel traditional algorithms with much less computations and higher computational efficiency; and for the models with general kinds of fuzzy random variable or larger scale problems, design intelligent algorithms based on fuzzy random simulation, which can work out the optimal solution within reasonable computation and time consumption. This project’s achievements will enrich the research on the theories and methods in fuzzy random bilevel programming domain, and promote the practical application of fuzzy random bilevel programming.

模糊随机双层规划是刻画模糊随机环境下递阶决策问题的合适模型。如何为其建立精确的模型、定义恰当的最优解概念、设计高效的求解算法是当前研究此类规划的难点和热点。本项目拟以模糊随机理论和确定双层规划理论为基础开展研究。首先，建立多种决策背景下更全面和客观的模糊随机双层规划精确模型。其次，拟利用模糊随机变量测度概念或排序方法定义新的唯一最优解概念，满足不同决策情形下决策者不同需求；借助多目标优化问题Pareto最优解概念从新角度定义最优解集合概念，在更大范围内为决策者提供更多信息。最后，对含特殊类型模糊随机变量模型，提出结构特殊和性质良好的确定等价模型，以此设计计算量更小和计算效率更高的新型传统算法；对含一般模糊随机变量或规模较大模型，拟利用模糊随机模拟技术设计在合理计算量和时间内找到最优解的高效智能算法。相关成果将丰富和完善模糊随机双层规划的理论和方法研究，为其应用到实际问题中起到积极推动作用。

模糊随机双层规划是考虑双重不确定性的两层递阶决策问题的模型，它是非常复杂和难以处理、但应用前景十分广阔的一类不确定双层规划。本项目以经典双层规划理论与方法以及模糊随机理论与方法为基础，针对上下层目标函数和约束函数中不确定系数均为模糊随机变量的模糊随机双层规划开展研究。在具体决策背景下着重从满足决策者各种特定需求角度定义不同最优解概念，这些最优解概念更符合不确定环境下实际复杂决策要求，而且针对不确定程度较高的模糊随机双层规划所定义的一对近似最优解还能为决策者提供更多有效信息。借助于便于运算的模糊随机变量比较和排序方法或优秀的去模糊化去随机化方法，构建模型结构复杂度低和变形过程运算量小的中间转化模型，给出结构特殊和性质优良的最终确定等价模型。这些中间转化双层规划模型含有较少的新增约束和变量，简化了转化函数形式复杂性和减少了转化过程计算量，基于此获得了形式简单和容易处理的最终确定等价双层规划模型。此外，对于上下层目标函数和约束函数中不确定系数都是区间数的区间双层规划，基于优秀的区间数比较和排序方法以及运算简便的区间不等式约束等价变形技术，结合决策者多种具体需求引入不同最优解概念，给出结构简便和便于求解的最终确定等价双层规划模型。结合模型结构特点，通过可行有效的传统算法或混合智能算法求解最终确定等价双层规划模型获得两类不确定双层规划的最优解。本项目对于模糊随机双层规划的研究丰富了此类不确定双层规划理论和方法的研究，也为其应用到解决模糊随机环境下实际多层嵌套决策问题起到积极作用，同时对其他类型不确定双层规划的研究也有一定的促进作用。另外关于区间双层规划的研究也为从新的视角研究模糊随机双层规划提供了新途径和新思路。