Completely derandomized self-adaptation in evolution strategies
Completely derandomized self-adaptation in evolution strategies
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DOI：
10.1162/106365601750190398
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发表时间：
2001-06-01
影响因子：
6.8
通讯作者：
Ostermeier, A
中科院分区：
文献类型：
--
作者：
Hansen, N;Ostermeier, A
本文提出了两种有用的突变分布自适应方法——非随机化和累积的概念。综述了突变策略、参数控制和两级非随机化概念的主要缺点。提出了任意（正态）突变分布自适应的基本要求。应用任意的正态突变分布相当于应用一般的线性问题编码。突变策略参数控制的基本目标大致是在未来偏爱先前选择的突变步骤。如果严格追求这一目标，则会产生完全非随机化的自适应方案，该方案可适应任意正态突变分布。该方案被称为协方差矩阵自适应（CMA），满足了上述要求。它仍然可以通过累积得到很大的改进——利用进化路径而不是单个搜索步骤。通过对各种测试函数的仿真，揭示了具有和不具有协方差矩阵自适应的进化策略的局部和全局搜索特性。它们的性能只有在完全缩放的函数上才可以比较。在严重缩放的、不可分离的函数上，通常观察到几个数量级的加速因子。对于适度错误缩放的函数，可以预期加速因子为3到10。
This paper puts forward two useful methods for self-adaptation of the mutation distribution - the concepts of derandomization and cumulation. Principle shortcomings of the concept of mutative strategy parameter control and two levels of derandomization are reviewed. Basic demands on the self-adaptation of arbitrary (normal) mutation distributions are developed. Applying arbitrary, normal Mutation distributions is equivalent to applying a general, linear problem encoding.The underlying objective of mutative strategy parameter control is roughly to favor previously selected mutation steps in the future. If this objective is pursued rigorously, a completely derandomized self-adaptation scheme results, which adapts arbitrary normal mutation distributions. This scheme, called covariance matrix adaptation (CMA), meets the previously stated demands. It can still be considerably improved by cumulation - utilizing an evolution path rather than single search steps.Simulations on various test functions reveal local and global search properties of the evolution strategy with and without covariance matrix adaptation. Their performances are comparable only on perfectly scaled functions. On badly scaled, nonseparable functions usually a speed up factor of several orders of magnitude is observed. On moderately mis-scaled functions a speed up factor of three to ten can be expected.