基于合作协同演化的大规模黑箱优化的关键问题研究

Large Scale Black-Box Optimization (LSBO) is known as its large number of decision variables, unknown relationships among variables, and complex objective function, which make it very difficult to be solved optimally. Cooperative co-evolution (CC), which is based on the divide-and-conquer strategy, has become the important approach to solve LSBO problem. However, problem decomposition strategy, processing strategy of information interaction among subproblems, and the subproblem optimization algorithm are three bottleneck problems in CC. The project is aimed to take the breakthrough research for these three difficulties. First of all, the local interaction among variables in current search space is studied by the online learning approach in this project. A dynamic problem decomposition strategy is therefore proposed for best reflecting the local interaction. Secondly, for processing the overlapping interaction among the subproblems, the approaches originated from primal/dual decomposition in the convex optimization are proposed, where the independent variables among different subproblems and overlapping variables are optimized in turn in order to realize the rational interactive among the subproblems. Finally, a comprehensive random drift particle swarm optimization (CRDPSO) algorithm is designed in this project in order to improve the optimization effect for the subproblems. The CRDPSO algorithm is enhanced on the global and local search ability based on the RDPSO algorithm. In addition, the importance of all the subproblems are evaluated by the reinforcement learning strategy. Based on the importance of the subproblems, the computational resource can be more efficiently allocated in order to further improve the optimization efficiency. The research results of this project are valuable both in theory and in engineering applications.

大规模黑箱优化由于决策变量数量多、相关性信息未知以及函数性质复杂等特点，给问题的最优化求解带来极大的挑战。基于分治思想的合作协同演化是大规模黑箱优化问题求解的重要手段，但问题分解策略、子问题间信息交互的处理策略以及子问题的优化算法设计仍是其瓶颈问题。本项目旨在针对上述三个难点进行突破性研究。首先，本项目拟通过在线学习获取当前搜索区域的局部变量关系，并据此设计最适合当前局部关系的问题动态分解策略。其次，为处理子问题间的重叠关系，拟借鉴凸优化中的原始与对偶分解方法，通过轮流优化不同子问题内部的独立变量与子问题间重叠的变量来达到子问题间信息的合理交互。最后，为提高子问题的优化效果，拟采用综合随机漂移粒子群优化算法进行更好地全局与局部搜索。另外，本项目还将采用强化学习策略来评估各子问题的重要程度,以期更有效地分配计算资源，从而进一步提高优化效率。本项目的研究成果将具有很好的理论价值和工程应用价值。

大规模黑箱优化(Large Scale Black-box Optimization, LSBO)问题由于决策变量数量多、相关性信息未知以及函数性质复杂等特点，给问题的最优化求解带来极大挑战。LSBO问题中大规模决策变量的存在，使得解空间随着问题规模的增加呈指数级增长，传统的最优化算法已经无法求解。基于分治思想的合作协同演化(Cooperative Co-evolution, CC)是一种通过对问题的分解来求解LSBO问题的算法框架。CC框架能够将LSBO问题分解为优化算法有能力处理的多个中小规模的子问题，其已经成为近年来求解LSBO问题的重要手段。.本项目针对CC框架中的问题分解策略、子问题间信息交互的处理策略以及子问题的优化算法设计等关键问题展开研究。针对差分分组(Differential Grouping，DG)存在的变量关系检测缺失、分组阈值需要人为设定等问题，提出了一种变量分组的自适应DG算法；设计了一种自适应金字塔型计算资源分配算法，提升了算法的计算资源利用率；受CC框架的思想启发，提出了一种LSBO问题的频繁覆盖策略，通过不断的迭代使得产生的搜索子空间交叉叠加，实现子问题间的信息交互并覆盖整个搜索空间，进而搜索得到全局最优值；针对LSBO问题存在的变量重叠导致传统分组算法无法分组的问题，提出了一种基于谱聚类的差分分组算法(DG with Spectral Clustering, DGSC)，通过决策变量间耦合关系设计结构矩阵，并据此作为谱聚类相似性矩阵输入，从而得到对决策变量的聚类结果进而实现模糊分组；为提升DGSC分组算法的精度，提出了一种改进的模糊差分分组算法(DGSC2)，根据目标函数的整体耦合程度自适应地计算对决策变量的分组数目，增强对不同类型函数的适用性，同时考虑决策变量间耦合关系的强弱来提高分组的准确性；为了提升LSBO问题的求解效率，提出了基于CC框架的分布式并行演化算法框架。.基于以上成果，发表学术论文29篇，其中SCI检索论文17篇，包含CCF A类论文1篇，B类论文3篇，JCR1区论文4篇，JCR2区论文6篇；EI检索论文12篇，发表在控制与决策，GECCO，CEC等刊物与会议上；授权中国发明专利2项，申请中国发明专利3项、美国发明专利3项。相关成果获中国商业联合会科学技术奖一等奖1项，江苏省自动化学会科技奖一等奖1项。