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

• Type: Conference
• Year: 2007
• Where: GECCO
• Authors: James N. Knight, Monte Lunacek
• Keywords: Algorithm, Covariance Matrix, GECCO 2007, Time Complexity