Reducing the space-time complexity of the CMA-ES

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Reducing the space-time complexity of the CMA-ES
A limited memory version of the covariance matrix adaptation evolution strategy (CMA-ES) is presented. This algorithm, L-CMA-ES, improves the space and time complexity of the CMA-ES algorithm. The L-CMA-ES uses the m eigenvectors and eigenvalues spanning the m-dimensional dominant subspace of the n-dimensional covariance matrix, C, describing the mutation distribution. The algorithm avoids explicit computation and storage of C resulting in space and time savings. The L-CMA-ES algorithm has a space complexity of O(nm) and a time complexity of O(nm2 ). The algorithm is evaluated on a number of standard test functions. The results show that while the number of objective function evaluations needed to find a solution is often increased by using m < n the increase in computational efficiency leads to a lower overall run time. Categories and Subject Descriptors I.2.8 [Artificial Intelligence]: Problem Solving, Control
James N. Knight, Monte Lunacek
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Authors James N. Knight, Monte Lunacek
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