二层多目标规划问题的算法设计与应用研究

项目名称： 二层多目标规划问题的算法设计与应用研究

项目编号： No.11201039

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 吕一兵

作者单位： 长江大学

项目金额： 22万元

中文摘要： 作为描述管理部门多个阶层关系和全面体现决策者意愿的一种有力工具，二层多目标规划展现出了广阔的应用前景，并日益引起了研究者的重视。值得指出的是，目前有关二层多目标规划的研究，主要集中在理论研究，有数值实验结果的算法研究还很欠缺。本项目拟设计两类二层多目标规划问题较为有效的求解算法，同时拓展其新的应用领域。主要内容包括：（1）设计线性二层多目标规划的平衡点方法，分析其收敛性，并编程予以实现。（2）一类非线性二层多目标规划（NLBMP）的罚函数方法以及神经网络方法。①构造该类NLBMP的罚问题，研究罚函数的精确性以及罚问题的最优性条件，设计该类NLBMP的精确罚函数算法；②构造该类NLBMP的神经网络模型，分析其收敛性和稳定性，编程实现神经网络模型，并进行仿真计算。（3）构建排污权市场交易的二层多目标规划模型，设计出较为有效的求解算法，同时以实例研究验证模型的可行性和有效性。

中文关键词： 二层多目标规划；罚函数；神经网络；粒子群算法；排污权

英文摘要： As a powerful instrument to describe the hierarchical relationships in managerial department and reflect the wills of the decision maker comprehensively, the bilevel multiobjective programming(BMP) has shown the vast applications prospects and been drawing much attention of the researchers. It is worth pointing out that the existing research on the BMP problem mainly focuses on its theoretical aspects, and the algorithms with numerical experiment results are rare relatively. The program would propose more effective algorithms for two classes of BMP problems and expend the new applications filed of BMP. Particularly, its contents include: (1) An equilibrium point approach for the linear BMP is proposed, and the convergence of the algorithm is analyzed. Then the algorithm is realized by making programs. (2) Penalty function approach and neural network approach for a class of nonlinear BMP problem, in which the lower level is convex multiobjective programming. ① a new penalized problem is constructed, and the exactness of the penalty function and the optimality condition suitable for realizing algorithm are analyzed. Finally, an exact penalty function algorithm is proposed; ② A neural network model of the above nonlinear BMP problem is constructed. The convergence and stability are analyzed based on the theory of

英文关键词： bilevel multiobjective programming；penalty function；neural network；particle swarm algorithm；emission permits