Main Vector Adaptation: A CMA Variant with Linear Time and Space Complexity

The covariance matrix adaptation (CMA) is one of the most powerful self adaptation mechanisms for Evolution Strategies. However, for increasing search space dimension N , the performance declines, since the CMA has space and time complexity O(N2). Adapting the main mutation vector instead of the covariance matrix yields an adaptation mechanism with space and time complexity O(N). Thus, the main vector adaptation (MVA) is appropriate for large-scale problems in particular. Its performance ranges between standard ES and CMA and depends on the test function. If there is one preferred mutation direction, then MVA performes as well as CMA.