Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions
Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions
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DOI：
10.1145/3040718.3040720
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
Youhei Akimoto;A. Auger;N. Hansen
中科院分区：
文献类型：
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作者：
Youhei Akimoto;A. Auger;N. Hansen
我们研究了一般凸二次函数的加权重组进化策略。我们得到了在无限维极限下的渐近质量增益，并得到了最优重组权和最优步长。本文的工作是对前人工作的推广，在无限维球函数上得到了加权重组进化策略的渐近质量增益。此外，对于有限维搜索空间，我们得到了一般二次函数的质量增益的严格界。它们揭示了质量增益在海森矩阵的特征值分布中和对重组权重的依赖关系。将搜索空间的维取到无穷大，证明了最优重组权与海森矩阵无关，即对球函数最优的重组权对凸二次函数也是最优的。
We investigate evolution strategies with weighted recombination on general convex quadratic functions. We derive the asymptotic quality gain in the limit of the dimension to infinity, and derive the optimal recombination weights and the optimal step-size. This work is an extension of previous works where the asymptotic quality gain of evolution strategies with weighted recombination was derived on the infinite dimensional sphere function. Moreover, for a finite dimensional search space, we derive rigorous bounds for the quality gain on a general quadratic function. They reveal the dependency of the quality gain both in the eigenvalue distribution of the Hessian matrix and on the recombination weights. Taking the search space dimension to infinity, it turns out that the optimal recombination weights are independent of the Hessian matrix, i.e., the recombination weights optimal for the sphere function are optimal for convex quadratic functions.