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

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1、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摘要: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。关键词:协方差矩阵自适应

2、进化策略;正交设计;高维多模态;进化策略;函数优化hybridorthogonalcmaesforsolvingglobaloptimizationproblemshuangya.fei1,2*,liangxi.ming1,chenyi.xiong11.schoolofinformationscienceandengineering,centralsouthuniversity,changshahunan410083,china;2.schoolofelectricandinformationengineering,changshau

3、niversityofscienceandtechnology,changshahunan410114,chinaabstract:inordertoovercometheshortcomingsofcovariancematrixadaptationevolutionstrategy(cmaes),suchasprematureconvergenceandlowprecision,whenitisusedinhigh-dimensionalmultimodaloptimization,anhybridalgorithmcombinedcmaeswitho

4、rthogonaldesignwithquantization(od/q)wasproposedinthisstudy.firstly,thesmallpopulationcmaeswasusedtorealizeafastsearching.whenorthogonalcmaesalgorithmtrappedinlocalextremum,basevectorsforod/qwereselecteddynamicallybasedonthepositionofcurrentbestsolution.thentheentiresolutionspace,

5、includingthefieldaroundextremevalue,wasexploredbytrialvectorsgeneratedbyod/q.theproposedalgorithmwasguidedbythisprocessjumpingoutofthelocaloptimum.thenewapproachistestedonsixhigh-dimensionalmultimodalbenchmarkfunctions.comparedwithotheralgorithms,thenewalgorithmhasbettersearchprec

6、ision,convergentspeedandcapacityofglobalsearch.inordertoovercometheshortcomingsofcovariancematrixadaptationevolutionstrategy(cmaes),suchasprematureconvergenceandlowprecision,whenitisusedinhigh.dimensionalmultimodaloptimization,ahybridalgorithmcombinedcmaeswithorthogonaldesignwithq

7、uantization(od/q)wasproposed.firstly,thesmallpopulationcmaeswasusedtorealizeafastsearching.whenorthogonalcmaesalgorithmtrappedinlocalextremum,basevectorsforod/qwereselecteddynamicallybasedonthepositionofcurrentbestsolution.thentheentiresolutionspace,includingthefieldaroundextremev

8、alue,wasexploredbytrialvectorsgen