合作协同进化算法的变量相关性学习与成组研究

Benefit by the divide-and-conquer feature, cooperative coevolutionary algorithms (CCEAs) can optimize with high efficiency by dividing a problem into independent components and optimizing them simultaneously. However, whether the problem is properly divided is a key to make full use of the divide-and-conquer feature. The main purpose of this proposal is to provide effective methods for solving large complex optimization problems in the real world. To this end, we use the probabilistic graphical model (PGM) which is powerful for modeling the variables dependency to investigate the methods of learning variables dependency and problem division. There are four issues in this proposal: (1) To design a PGM based CCEA framework so that the resulting CCEA is able to learn the variables' dependency. Besides, an effective information compensation strategy will also be studied to overcome the information loss when dividing the problem into small components, so that the global optimization performance could be guaranteed. (2) To investigate the decentralized Bayesian networks (BNs) learning method within the framework of PGM based CCEA. With this method, the global BN that can describe the relationships of the overall variables could be persistently updated during the evolutionary process. (3) To design the grouping strategy of the variables. At a proper moment, the global BN will be decomposed into some sub-BNs. According to these sub-BNs the variables could be grouped and the self-adaptive problem re-division could be achieved as well. (4) To analyze the proposed algorithms via numerical optimization experiments. Moreover, the problem of system optimization of new concept unmanned underwater vehicles will be used to verify the effectiveness of the proposed algorithms for solving real world applications.

合作协同进化算法（CCEA）"分而治之"的特点，赋予了其高效求解复杂问题的能力。然而，要充分发挥该特点，须确保算法问题分解的正确性。本项目旨在利用概率图形模型对变量关系的建模能力，研究CCEA的变量相关性学习及成组问题，为复杂大规模优化问题的高效求解提供技术手段。主要研究内容包括：①研究基于概率图形模型的CCEA框架，使其具有内在学习能力，并在此框架下研究有效的信息补偿策略，消除由问题分解所至信息丢失对算法全局优化能力的影响；②在概率图形模型CCEA框架下，研究贝叶斯网络模型的分散式构建方法，不断获得能够描述问题变量间关系的全局贝叶斯网络；③研究变量成组策略，适时将全局贝叶斯网络分解为若干子网络，并据此进行变量成组和问题分解，使算法能够自动调整对问题的分解形式。④研究算法的数值实验及分析，并针对新概念水下航行器的总体优化设计问题开展实验分析，验证算法解决实际问题的有效性。

大规模优化在工程和科学领域有着广泛的应用，协同进化算法“分而治之”的特点十分适合用以求解大规模优化问题。本课题的主要研究成果包括：（1）针对协同进化算法在问题分解时，产生的重要进化信息丢失从而导致算法无法收敛到全局最优的问题，提出了使用多模优化进行信息补偿的协同进化算法、使用基于小生境的多模优化和自适应快速聚类的大规模优化算法等，一系列具有信息补偿能力的大规模协同进化算法。（2）针对协同进化算法中变量相关性学习问题，提出了使用边缘概率分布乘积模型建模与最小描述长度准则进行模型选择的统计学习方法，实现变量相关性学习与变量自主成组。（3）在理论研究的基础上，开展了协同进化算法在通信代价敏感的分布式水下无人系统上的应用研究，设计了面向通信代价敏感的动态优化协同进化算法。.本课题在算法设计上取得了多项突破，圆满完成了各项研究任务，实现了预定研究目标。在研究成果方面，本课题共计发表学术论文20篇（期刊论文13篇，会议论文7篇），其中SCI检索论文6篇（SCI二区及以上4篇），出版学术专著一部，申请国防专利4项。在人才培养方面，培养博士3人、硕士5人。在学术合作与交流方面，赴南洋理工大学学术交流一人次，在重要学术会议进行学术报告5人次。