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中文摘要：
提出一种求解动态优化问题的多群体单变量边缘分布算法（MUMDA）．首先，利用多个概率模型（对应多个群体）将搜索空间分成几个部分，通过对不同区域的搜索或探索将好解进行迁移，扩大搜索空间，增加种群多样性，跟踪最优解的变化；然后，利用对UMDA收敛性的证明分析了所提出算法的有效性；最后，对两个动态优化问题进行仿真计算，并与传统UMDA和基于随机迁移的UMDA（iUMDA）进行了比较，结果表明，MUMDA能快速适应环境的变化，跟踪最优解．
英文摘要：
An improved multi-population univariate marginal distribution algorithm （MUMDA） is proposed to solve dynamic optimization problems. The search space is divided into several parts by using several probability modals which correspond to several populations. Meanwhile, the algorithm explores and exploits in different regions and the best solutions are migrated. The objective is to enlarge the search space, increase the population diversity and adapt to the change of the environments rapidly. Moreover, the convergence of UMDA is proved, which is used to analyze the validit, y of the proposed algorithm. Finally, an experimental study is carried out to compare the performance of several UMDA. The experimental results show that the MUMDA is effective and can adopt the dynamic environments rapidly.
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