求解完整Pareto前沿的多目标优化新方法研究

项目名称： 求解完整Pareto前沿的多目标优化新方法研究

项目编号： No.61472041

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 胡小兵

作者单位： 北京师范大学

项目金额： 72万元

中文摘要： 寻找Pareto前沿对解决各种多目标优化问题意义重大。现有的多目标优化方法大都只能寻找近似的Pareto前沿，目前还鲜有能够求解完整Pareto前沿的理论和方法。本项目将全面深入地研究一种利用前k个最好单目标解求解完整（而不是近似或部分）Pareto前沿的理论和方法。首先要充分研究能确保找到完整Pareto前沿的理论条件。然后将以涟漪扩散算法为重点，研究可适用于一些重要类型的离散多目标优化问题的求解完整Pareto前沿的方法。还将以海平面上升算法为重点，研究可适用于连续多目标优化问题的方法。新理论和新方法将被用于求解三个真实的多目标优化问题（即：湖南省农业风险防范优化，北京市朝阳区灾害情况下疏散路径优化，和北京机场飞机进离港与停机位分配优化）的完整Pareto前沿。预期研究成果不仅是对多目标优化理论的一个重要的创新和拓展，而且能够为更好支持现实生活中多目标优化决策提供一套全新的方法和工具。

中文关键词： 算法设计；精确算法；组合优化；算法分析；进化计算

英文摘要： Calculating Pareto front plays a crucial role in multi-objective optimization problem (MOP). Most existing methods only provide approximation of Pareto front, and there lacks research literature on calculating complete Pareto front. This project will carry out a comprehensive study on a new theory and method to calculate complete Pareto front by making use of the k best single-objective solutions. First, some theoretical conditions will be developed to guarantee the finding of complete Pareto front. Then, mainly based on ripple-spreading algorithm, some new methods will be designed to calculate complete Pareto front for some kinds of discrete MOP. And mainly according to sea level rising algorithm, some new methods will be developed to find complete Pareto front for continuous MOP. At last, new methods will be applied to 3 real-world MOPs (agriculture risk governance in Hunan Province, evacuation route optimization in disaster situations in Beijing Chaoyang District, and air traffic management at Beijing Capital Airport). This project will significantly contribute to the advance in optimization theories, and also provide a useful decision-making support tool for real-world MOPs.

英文关键词： Algorithm Design;Deterministic Algorithm;Combinatorial Optimization;Algorithm Analysis;Evolutionary Computation