求解全局優(yōu)化問題的正交協(xié)方差矩陣自適應(yīng)進(jìn)化策略算法.doc

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1、求解全局優(yōu)化問題的正交協(xié)方差矩陣自適應(yīng)進(jìn)化策略算法摘要:針對(duì)協(xié)方差矩陣自適應(yīng)進(jìn)化策略(cmaes)求解高維多模態(tài)函數(shù)時(shí)存在早熟收斂及求解精度不高的缺陷,提出一種融合量化正交設(shè)計(jì)(od/q)思想的正交cmaes算法。首先利用小種群的cmaes進(jìn)行快速搜索,當(dāng)算法陷入局部極值時(shí),依據(jù)當(dāng)前最好解的位置動(dòng)態(tài)選取基向量,接著利用od/q構(gòu)造的試驗(yàn)向量探測包括極值附近區(qū)域在內(nèi)的整個(gè)搜索空間,從而引導(dǎo)算法跳出局部最優(yōu)。通過對(duì)6個(gè)高維多模態(tài)標(biāo)準(zhǔn)函數(shù)進(jìn)行測試并與其他算法相比較,其結(jié)果表明,正交cmaes算法具有更好的搜索精度、收斂速度和全局尋優(yōu)性能。

2、關(guān)鍵詞:協(xié)方差矩陣自適應(yīng)進(jìn)化策略;正交設(shè)計(jì);高維多模態(tài);進(jìn)化策略;函數(shù)優(yōu)化hybridorthogonalcmaesforsolvingglobaloptimizationproblemshuangya.fei1,2*,liangxi.ming1,chenyi.xiong11.schoolofinformationscienceandengineering,centralsouthuniversity,changshahunan410083,china;2.schoolofelectricandinformat

3、ionengineering,changshauniversityofscienceandtechnology,changshahunan410114,chinaabstract:inordertoovercometheshortcomingsofcovariancematrixadaptationevolutionstrategy(cmaes),suchasprematureconvergenceandlowprecision,whenitisusedinhigh-dimensionalmultimodaloptimization

4、,anhybridalgorithmcombinedcmaeswithorthogonaldesignwithquantization(od/q)wasproposedinthisstudy.firstly,thesmallpopulationcmaeswasusedtorealizeafastsearching.whenorthogonalcmaesalgorithmtrappedinlocalextremum,basevectorsforod/qwereselecteddynamicallybasedonthepositiono

5、fcurrentbestsolution.thentheentiresolutionspace,includingthefieldaroundextremevalue,wasexploredbytrialvectorsgeneratedbyod/q.theproposedalgorithmwasguidedbythisprocessjumpingoutofthelocaloptimum.thenewapproachistestedonsixhigh-dimensionalmultimodalbenchmarkfunctions.co

6、mparedwithotheralgorithms,thenewalgorithmhasbettersearchprecision,convergentspeedandcapacityofglobalsearch.inordertoovercometheshortcomingsofcovariancematrixadaptationevolutionstrategy(cmaes),suchasprematureconvergenceandlowprecision,whenitisusedinhigh.dimensionalmulti

7、modaloptimization,ahybridalgorithmcombinedcmaeswithorthogonaldesignwithquantization(od/q)wasproposed.firstly,thesmallpopulationcmaeswasusedtorealizeafastsearching.whenorthogonalcmaesalgorithmtrappedinlocalextremum,basevectorsforod/qwereselecteddynamicallybasedontheposi

8、tionofcurrentbestsolution.thentheentiresolutionspace,includingthefieldaroundextremevalue,wasexploredbytrialvectorsgen