导　　师： 刘永清;邓飞其;张丽清

学科专业： 081101

授予学位： 博士

作　　者： ;

机构地区： 华南理工大学

摘　　要： 在科学技术和经济管理等诸多领域，许多问题都可归结为某种函数的最优化这类数学模型。进化算法作为处理复杂函数最优化、全局最优化和多目标最优化问题的一种有效算法，正日益受到人们的重视。本文对带约束的单目标、多目标、分层多目标最优化进化算法进行了研究，提出了新的算法。 针对进化算法计算量大、局部搜索能力弱的不足，把一种数学试验方法——均匀设计用于构造进化算子，使新的进化算子具有相似于传统最优化算法的局部搜索特性，提高了算法的搜索效率。对一组测试函数的数值实验表明新算法计算量少收敛速度快。 对多目标最优化问题，我们构造了一个新的适应值函数，它以规范化后的目标函数乘以一个适当的权重再取最大值作为适应值函数。权重的构造方法与通常的方法不同，它既不限制权重介于0与1之间，也不要求它们之和为1，而只需权重为正且要求它们之积为1。通过广义球面坐标变换选取多组权重向量和均匀设计构方法，保持了种群的多样性，使新算法更易于求出均匀分布的Pareto最优解。该算法的显著特性是不管有效界面是否凸，都能找到足够多均匀分布的有效解。同已有的好算法的数值实验比较也表明了该算法的有效性。 提出了求解约束最优化问题的一种新的进化算法。算法通过把约束优化问题转化为多目标规划，对这个多目标规划，根据带权极小极大策略构造了一个同进化代数有关的变适应值函数。这样定义的变适应值函数能使种群中的容许解逐渐增加并且保持其多样性。该方法能有效处理约束，特别是紧约束。用类似的思想给出了解决约束多目标最优化的一种新的进化算法，计算机仿真显示这种处理单目标、多目标的方法是有效的。 提 In many fields of science and technology, economics and management, etc., there are a lot of problems to can be converted into the kind of mathematical model about certain function optimization. Evolutionary algorithms are one of the effective algorithms for hard optimization, global optimization and multiobjective optimization problems, which are attached more and more importance to. This paper studies evolutionary algorithms for single objective optimization, multiobjective optimization and lexicographically stratified multiobjective optimization and proposes novel evolutionary algorithms. To aim at the shortcoming that evolutionary algorithms spend large amount of computation and is weak at local search, a mathematical experiment method—the uniform design is combined into the evolutionary algorithm operator. The novel evolutionary operator has the local search property similar to that in traditional optimization techniques and explores the search space effectively. The numerical experiments show the effectiveness of the novel algorithm with its less computation, higher convergent speed for a group of benchmark problems. To multiobjective optimization problems, a new fitness function is constructed by maximization of the weighted normalized objectives. The way defining weights is much different from the general ways. Not only the weights defined are not limited between zero and one, but also their sum is not required to be one. The weight vectors are carefully and reasonably designed via generalized sphere coordinate transformation and uniform design. As result, the population can keep the diversity, and the uniform search may be easy. The most important characterization of the proposed algorithm is that it can always find enough uniformly solutions distributed on Pareto frontier no matter whether the Pareto frontier is convex or not. A comparison of numerous preferable evolutionary techniques shows that the proposed algorithm is effective. A novel evolutionary algorithm is propo

关 键 词： 进化算法 多目标最优化 约束最优化 极大极小策略 均匀设计

领　　域： [自动化与计算机技术] [自动化与计算机技术]