MMES: Mixture Model-Based Evolution Strategy for Large-Scale Optimization

This work provides an efficient sampling method for the covariance matrix adaptation evolution strategy (CMA-ES) in large-scale settings. In contract to the Gaussian sampling in CMA-ES, the proposed method generates mutation vectors from a mixture model, which facilitates exploiting the rich variable correlations of the problem landscape within a limited time budget. We analyze the probability distribution of this mixture model and show that it approximates the Gaussian distribution of CMA-ES with a controllable accuracy. We use this sampling method, coupled with a novel method for mutation strength adaptation, to formulate the mixture model-based evolution strategy (MMES)-a CMA-ES variant for large-scale optimization. The numerical simulations show that, while significantly reducing the time complexity of CMA-ES, MMES preserves the rotational invariance, is scalable to high dimensional problems, and is competitive against the state-of-the-arts in performing global optimization.

Automated summary

This study introduces an efficient sampling method for CMA-ES in large-scale settings by generating mutation vectors from a mixture model. The proposed MMES variant significantly reduces the time complexity of CMA-ES while preserving rotational invariance and scalability to high dimensional problems, showing competitiveness in global optimization.