【作者】 赵瑞；

【导师】 林丹；

【作者基本信息】 天津大学 ， 运筹学与控制论， 2005， 硕士

【摘要】 多目标优化问题一直是科学和工程研究领域的一个难题和热点问题,在遗传算法应用到这一领域以前,已经产生了许多经典的方法,经典方法在处理大维数、多模态等复杂问题上存在许多不足。多目标遗传算法具有处理大的问题空间的能力,在一次进化过程中可以得到多个可行解曲面,对问题域的先验知识没有要求,对函数定义域的凸性不敏感,这正是经典算法所不具备的。所以,应用遗传算法求解多目标优化问题,是这一领域的发展趋势。本文在广泛深入地查阅国内外文献的基础上,对遗传算法及其面向多目标优化问题的基础理论和基本方法进行了深入的理论研究和实验分析,主要内容如下:1.系统、详尽的介绍了遗传算法的一般流程和基本理论、方法,以及面向多目标优化问题的遗传算法的基本理论方法。对经典的方法进行了分析和比较,指出了经典方法的应用范围、成功实例、不足之处。2.提出了一种新的多目标遗传算法。针对随机权重多目标遗传算法提出了三点改进:(1)精华保留,从临时Pareto解集中选出个拥挤距离最大的个体作为精华保留,从而使当前周围个体密度小的Pareto解占优,对保持种群的多样性有利;(2)采用追踪权值的方法,记录下选择过程中选出的个体所对应的权重;(3)产生一部分固定的权值用于选择操作,找出当前拥挤距离最大的Pareto解,在其对应的权值附近产生一些权值用于选择操作,从而使Pareto解在Pareto前沿的分布更均匀。实验结果表明,新的算法具有更好效果。Nelite3.简要回顾了递阶优化问题的发展历史,归纳总结了递阶优化问题的特点,论述了递阶优化问题的研究现状。4.针对现有方法求解一种上层为0—1变量,下层为多目标的两层决策问题的不足,提出了一种更符合实际决策过程的新方法,旨在为上、下决策者在二者的偏好之间给出一定数量的最优解;并且针对该问题设计了一种多种群协同进化的遗传算法。通过多个子种群同时进化,每个子种群对应的下层目标函数的偏好不同,在进化的过程中采用一定的信息交换原则,使求解基于不同偏好最优解的过程在整个群体的一次进化过程中实现。文中给出的算例说明了算法的有效性。更多还原

【Abstract】 Using Evolutionary Algorithms (EAs) to solve global optimization problems, i.e.Evolutionary Optimization (EO), is always the most important research and applica-tion domain of EAs. Although having been successfully applied in many practicalproblems, EAs not only lack steady theoretical foundations, but expose many shortco-mings in practical applications. 1. We introduce related biology knowledge and give a brief review of the deve-lopment history of EAs. Then we conclude the main characters of EAs and sum up thepresent situation of the theories and applications of EAs. 2. This paper provides a new multi-objective genetic algorithm that improves onthe random weight multi-objective genetic algorithm from three parts as follow:(1) Reserving elite. Choosing individuals whose crowding distances are themost ones from temporary Pareto solution set as the elite to reserve. Therefore, thePareto solution whose individual density is small around currently is better than theothers, that is profit for holding the variety of the genus group;(2) Applying themethod of tracing weight to record the weights according to the individuals chosen inthe choosing progress;(3) Generating members of fixed weights to choose theoperation and find out the Pareto solution whose crowding distance is the biggest.Then generating some weights around the weight according to such solution to choosethe operation and make the Pareto solution to distribute in the Pareto former edgemore uniformly. The result of the test shows that the new algorithm has the bettereffect.Nelite3. We give a brief review on the development history of hierarchical optimalsystems, then we conclude the main characters of hierarchical optimal systems, statethe survey of hierarchical optimal systems.4. Towards the shortage of the present methods that solve the situation wherethere are upper level 0-1 decision variables and lower level multi-objective functions ,we propose anew method which accord with the actual demands. In this paper, wediscussed the situation where there are upper level 0-1 decision variables and lowerlevel multi-objective functions, which leads to certain amount of optimal valuesbetween preferences of the upper and lower level decision makers. We furtherconstruct a multi-population co-evolution genetic algorithm. Multiple subpopulationevolve simultaneously. The preferences of the lower level objective functions of eachsubpopulation are different and we use the information exchanging principle to solvethe optimal values in different preferences in one process of the evolution in thewhole population. The examples in our paper show the efficiency of this algorithm.更多还原