多目标优化论文：多目标优化 多目标进化算法 网格机制 自
适应网格
【中文摘要】进化算法求解多目标优化问题已经成为多目标优化领域研究的热点之一,现实中的优化问题通常具备两个或两个以上相互冲突的目标。跟单目标优化问题有唯一的最优解不同,多目标优化问题的最优解是一组折中解,通常称为Pareto最优解集。多目标进化算法是模拟生物自然选择的随机搜索算法,并且在求解高度复杂的非线性多目标优化问题有很大的优势,因此,在过去的二十年里引起了学术界众多学者的关注,同时得到快速的发展。然而,大部分算法在处理MOPs和CMOPs时,很少考虑从已有的信息(如:种群信息、进化轨迹、优良个体分布等)中进行学习、交流。另外,已有的算法没有考虑种群全局信息对进化的作用。实际上这些信息对进化种群的影响也是非常重要的,进化种群必须在特定的信息中才能更好的进化。另一方面,自适应网格技术其难点在于每维目标上单元网格的尺寸很难确定,如果其尺寸确定后,即网格总数相应的确定。一般情况下,种群中的个体所占的网格数目是非常少,导致分布性在一定程序上受到影响。本文主要针对网格机制多目标进化算法进行研究,所做的主要工作包括下面两个方面:第一,提出一种网格激励机制的约束多目标进化算法(C-GIEA)。大多数约束多目标进化算法没有考虑种群中的信息交流,缺乏指导性的搜索。C-GIEA利用网格保存各种信息和约束条件来引导种群进化。一方面,对约束空间有很强的搜索能力,使其向更优的搜索区域逼近,最终向最优解靠近;另一方面,通过种群状态调整网格中
其它信息,实现种群与这些信息相互学习和共同进化。并反过来实现对种群的促进、导向功能。通过与2个著名算法的对比实验,结果表明C-GIEA在解集的收敛性、分布广泛性和分布均匀性有良好的性能。第二,提出混合自适应网格进化算法(HAGA)。自适应网格算法中的单元网格在每个目标上的尺寸很难确定。如果尺寸选择不恰当,将会使得解集的分布性很差。HAGA将局部搜索因子、修剪因子和差分进化算子加到自适应网格中,并辅助网格算法搜索更优解。此方法的主要思想通过等分每个目标值将解的搜索空间均匀地划分成若干网格,并在种群的进化过程中随机剔除一个个体,它所在的网格中包含了最多的个体。然后,通过加入局部搜索因子、修剪因子和差分进化算子,一方面提高算法的收敛性,另一方面提高解集的分布性。通过与3个著名算法在21个测试问题上3方面的对比实验,表明了HAGA良好的性能。
【英文摘要】Multi-objective optimization which is solved by evolutionary algorithms is the principle research area in optimization method. Most real-world problems have two or more conflicting objectives. Different from the single objective optimization problems which have the only optimum solution, the optimum solutions of multi-objective optimization problems are a group of trade-off solutions, namely Pareto optimum solutions set. Multi-objective evolutionary algorithm is a kind of random search algorithm which simulates the nature selection and
evolution. It specializes in solving highly sophisticated and nonlinear multi-objective optimization problems. It appeals many researchers so that it develops rapidly. However, a great amount of evolutionary algorithms did not consider the used information such as the information of population, the proceeding of evolutionary and the spread of elitist when dealing with the MOPs as well as CMOPs. In addition, the presence algorithms did not regard the impacts of evolutionary on the global knowledge. Actually, it has an important impact on the population and that population does more progress in the proceeding of evolutionary in a unique position. On the other hand the adaptive grid algorithm have difficult in the cell size of each dimension for the size is fixed, and then the amount of the grid is also fixed. In generally, the individuals occupied a small number of the grid, so the distribution is affected. The research work in this paper focus on the grid mechanism for multi-objective evolutionary algorithm and the contribution of this work contains the following two folds:First, a constrained multi-objective evolutionary algorithm base on grid incentives (denoted as C-GIEA) is proposed. Most of the constrained multi-objective evolutionary algorithms do not consider the exchange of information among
多目标优化论文：多目标优化多目标进化算法网格机制自适应网格
