基于向量角分解的高维多目标进化算法

选择是进化的主要驱动力,也是多目标进化算法的关键特征,然而,在处理高维多目标问题时,随着目标维数的增加种群的收敛性和分布性的冲突加剧,传统多目标进化算法中的选择算子已难以有效地维持种群的收敛性与分布性之间的平衡.针对该问题,提出一种基于向量角分解的高维多目标进化算法.首先,将个体本身作为参考向量,利用目标向量之间的夹角作为个体的相似度测度估计种群分布性,以减轻算法预先指定权重向量的负担;然后,利用成绩标量函数作为个体的收敛性测度,该收敛测度在引导种群走向Pareto最优前沿方面发挥着重要作用;最后,提出一种基于向量角分解的精英选择策略,其在环境选择过程中利用向量角信息将目标空间动态分解,并利用成绩标量函数从分布性较好的区域中挑选较好的个体进入下一代,能够动态地平衡种群的收敛性和分布性.对比实验结果表明,所提出算法具有较强的竞争力,其在保持种群分布性的同时具有足够的选择压力,能够有效地引导高维目标空间的搜索.

Many-objective evolutionary algorithm based on vector angle decomposition

Selection is the main driving force of evolution and is a key feature of multi-objective evolutionary algorithms. However, when dealing with many-objective optimization problems, with the incease of objective dimensions, the conflicts between convergence and distribution will intensify, and the selection operators in the traditional multi-objective evolutionary algorithms is difficult to effectively maintain the balance between the convergence and distribution of population. To solve this problem, this paper proposes a many-objective evolution algorithm based on vector angle decomposition (VAD). Firstly, the individuals themself are used as a reference vector, and the angles between the target vectors are used as the similarity measure to estimate the population distribution, which reduces the burden of the algorithm pre-specifying the weight vectors. Then, the achievement scalarizing function is used as the convergence measure of the individual, which plays an important role in guiding the population towards the Pareto optimal front. Finally, an elite selection strategy based on vector angle decomposition is proposed, which uses vector angle information to dynamically decompose the objective space in the process of environment selection, and then uses the achievement scalarizing function to select better individuals from better distributed regions into the next generation, so as to dynamically balance the convergence and distribution of population. Comparative experiments results indicate a highly competitive performance of the proposed approach. And it has sufficient selection pressure while maintaining the diversity of the population, which can effectively guide the search of high-dimensional objective space.