【作者】 邓国强；

【导师】 黄樟灿；

【作者基本信息】 武汉理工大学 ， 应用数学， 2007， 硕士

【摘要】 自20世纪60年代初以来多目标优化问题就受到研究人员越来越多的关注。近些年对演化算法的研究，表明了这种方法比传统的搜索和优化方法更加有效。演化多目标优化(EMO)算法被广泛地应用在各种问题中，在决策和优化领域都引起了研究者极大的重视。本文对当前流行的演化多目标优化算法的基础和不同实现方法中的基本思想进行了综合分析和归纳。阐明当前多目标优化领域的薄弱环节：带有偏好信息的高维多目标优化演化算法和多目标优化算法性能的度量。以此为基础确定了本文的研究方法和目标。具体的工作和创新点如下：1、通过在NSGA-Ⅱ算法中加入新构造的变异算子和偏好算子，提出了基于参考点的演化算法(简称MR-NSGA-Ⅱ算法)，来实现高维多目标优化问题的求解。本文还对算法的时间复杂度和性能进行综合分析，数值实验验证了算法的有效性。2、评价多目标优化算法的性能方法包括测试函数和度量准则两个基本要素，针对标准双目标优化测试问题，系统的分析构造多目标优化测试函数的方法，从理论上证明了构造方法的有效性。对常用的评价多目标优化算法的三个度量准则做了综合分析，提出了评价偏好集的三个新度量准则，即RER、RSP和RGD。最后对本文提出的算法和评价准则做出了总结，并对将来在多目标优化领域的一些可能的发展方向进行了预测。更多还原

【Abstract】 Researchers have more and more paid attention to the multi-objective optimization problems from 1960s. We can conclude that EMO methodologies may provide an advantage over their classical counterparts, such as classical research and optimal methods through the research on Evolutionary Algorithms recently. EMO algorithms have been applied to various problems and attached importance to the researchers in decision and optimal fields.This paper analyzes the foundations of the current popular MOEAs and the basic idea of various methods of MOEAs in general. Demonstrating the weak location of multi-objective optimization field is high-dimension Evolutionary multi-objective optimization algorithms with preference information and the measure of the performance of multi-objective optimization algorithms, so that we ascertain the research method and goal of this paper. The work and creative point of this paper are described as follows:1、Presenting the reference point based evolutionary algorithm (namely MR-NSGA-II algorithm). High-dimension multi-objective optimization problems are solved by NSGA-II algorithm with the new mutation operator and preference operator. Time complexity and the performance of the algorithm are analyzed in general. The effectiveness of the algorithm is tested by the use of high-dimension test functions.2、The measure of the performance of multi-objective optimization algorithms includes test functions and metrics. Analyzing the construction methods of multi-objective optimization test functions. Proving the effect of the construction methods in theory. Analyzing three metrics used in measuring performance of multi-objective optimization algorithms, we presenting three new metrics RER、RSP and RGD to measuring the obtained preferred sets.At last, the algorithm and performance metrics are conclude and some of the most promising future paths of research in multi-objective optimization area are also addressed.更多还原