求解全局优化问题的正交协方差矩阵自适应进化策略算法

针对协方差矩阵自适应进化策略(CMAES)求解高维多模态函数时存在早熟收敛及求解精度不高的缺陷, 提出一种融合量化正交设计(OD/Q)思想的正交CMAES算法。首先利用小种群的CMAES进行快速搜索, 当算法陷入局部极值时, 依据当前最好解的位置动态选取基向量, 接着利用OD/Q构造的试验向量探测包括极值附近区域在内的整个搜索空间, 从而引导算法跳出局部最优。通过对6个高维多模态标准函数进行测试并与其他算法相比较, 其结果表明, 正交CMAES算法具有更好的搜索精度、收敛速度和全局寻优性能。

Hybrid orthogonal CMAES for solving global optimization problems

In order to overcome the shortcomings of Covariance Matrix Adaptation Evolution Strategy(CMAES),such as premature convergence and low precision,when it is used in high-dimensional multimodal optimization,a hybrid algorithm combined CMAES with Orthogonal Design with Quantization(OD/Q) was proposed.Firstly,the small population CMAES was used to realize a fast searching.When orthogonal CMAES algorithm trapped in local extremum,base vectors for OD/Q were selected dynamically based on the position of current best solution.Then the entire solution space,including the field around extreme value,was explored by trial vectors generated by OD/Q.The proposed algorithm was guided by this process jumping out of the local optimum.The new approach was tested on six high-dimensional multimodal benchmark functions.Compared with other algorithms,the new algorithm has better searching precision,convergence speed and capacity of global search.