融合自适应分解与单纯形支配的进化超多目标优化算法及其应用

Many-objective optimization problems are involved in science and technology fields. The search efficiency of traditional evolutionary multi-objective optimization (EMO) algorithm greatly degenerates as the number of objectives increases. Therefore, the design of effective evolutionary many-objective optimization algorithm has very important meaning in both theory and real world applications. Considering the deficiency that the existing decomposition-based evolutionary algorithms for many-objective optimization problem don’t easily approach a set of representative Pareto optimal solutions, this project aims at the strategy of hybrid adaptive decomposition and dominating sort for evolutionary many-objective optimization algorithm. Firstly, by learning information from population distribution, the simple and effective method that complex many-objective optimization problem are adaptively decomposed into a number of relatively simple many-objective optimization subproblems will be studied. Secondly, according to the property of simplex, the new dominating relation will be designed for many-objective optimization so that it overcomes weak point of Pareto domination selection pressure rapid decline as objective number increases. Finally, efficient and generalized evolutionary many-objective algorithm will be designed by integrating new relations of domination in subproblems after adaptive decomposition. This project will apply the proposed evolutionary algorithm to the mobile communication and solve the many-objective optimization problem of renewable energy cooperation in OFDM cells.

在科学技术领域，经常会遇到超多目标优化问题。进化多目标算法在求解超多目标优化问题时，随着目标个数的增大，算法搜索效率越来越弱。如何设计出有效的进化超多目标优化算法具有重要的理论和应用价值。该项目针对基于分解和Pareto支配排序的进化超多目标优化算法不容易求出具有代表性的Pareto最优解的不足，研究在进化超多目标优化算法中有效融合自适应分解与新的支配排序的策略。首先，通过对当前种群分布信息的学习，利用统计设计方法研究把超多目标优化问题自适应分解为若干个子问题的简单有效方法；其次，利用单纯形的特性设计出新的支配关系——单纯形支配，以克服基于Pareto支配随着目标增多选择压力急速下降的弱点；最后，在自适应分解的子问题中融入单纯形支配关系，从而设计出高效、具有广泛适应性的进化超多目标优化算法。将该项目提出的进化算法应用于移动通信中求解基于OFDM的小区间可再生能源协作这一超多目标优化问题。

该项目为解决确定性分解超多目标优化进化算法稳健性较差的不足，把解空间自适应划分为若干动态变化的子空间，根据每个子空间中个体的分布，自适应调节权重向量，提出了自适应分解超多目标优化问题的策略。对多目标最优化问题的不均衡性进行了研究，讨论了引起不均衡性的几种类型，并提出了处理这类问题的进化算法。通过把约束转化为目标，结合分区域的方法提出了处理约束单目标和多目标的进化算法。. 提出了一种基于单纯形支配进化多目标算法，把该算法用于求解多系统间可再生能源协作与频谱资源共享机制以提高可再生能源利用效率和频谱效率优化问题。采用提出的基于种群分解的进化多目标算法解决TD-LTE位置区划分问题，及第四代（4G）移动通信网络TD-LTE系统自适应资源调度问题。

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