单变量边缘分布算法与蚁群算法的混合算法收敛性分析

convergence analysis of the hybrid algorithm with UMDA and AA

智能混杂算法是当前智能优化算法的研究热点,可以融合多种优化算法的优势,提高算法的性能。单变量边缘分布算法具有大范围快速全局搜索能力,但不能很好地利用系统中的反馈信息;蚁群算法是一种并行的分布式正反馈系统算法,但其初期信息素匮乏,求解速度慢。将单变量边缘分布算法与蚁群算法相结合,可以优势互补。基于上述思想,提出一种基于单变量边缘分布算法与蚁群算法混合的算法,并运用马尔科夫随机过程理论对该算法的收敛性进行了分析,结果表明了该算法的优化解满意值序列是单调不增的和收敛的。

The intelligent hybrid algorithm is a current research focus of intelligent optimization algorithms. It can fuse the advantages of many kinds of optimization algorithms to improve performance of the algorithm. The univariate edge distri- bution algorithm （UMDA） has widespread rapid global search capability, but can not use the feedback information in the sys- temquite well. The ant algorithm （AA） is a kind of parallel distributed positive feedback system algorithm, but its initial pheromone is lack and its solving speed is slow. The combination of UMDA and AA can complement each other＇s advantages. Based on the idea mentioned above, a hybrid algorithm based on UMDA and AA is proposed in this paper, and the convergence of the hybrid algorithm is analyzed with Markov random process theory. The result indicates that the optimal solution satisfaction value sequence is drab non-increasing and convergent.