Gaussian Adaptation as a unifying framework for continuous black-box optimization and adaptive Monte Carlo sampling

Abstract— We present a unifying framework for continuous optimization and sampling. This framework is based on Gaussian Adaptation (GaA), a search heuristic developed in the late 1960’s. It is a maximum-entropy method that shares several features with the (1+1)-variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The algorithm samples single candidate solutions from a multivariate normal distribution and continuously adapts the first and second moments. We present modifications that turn the algorithm into both a robust continuous black-box optimizer and, alternatively, an adaptive Random Walk Monte Carlo sampler. In black-box optimization, sample-point selection is controlled by a monotonically decreasing, fitness-dependent acceptance threshold. We provide general strategy parameter settings, stopping criteria, and restart mechanisms that render GaA quasi parameter free. We also introduce Metropolis GaA (M-GaA), where samplepoint selection is based on the Me...

• Type: Journal
• Year: 2010
• Where: CEC
• Authors: Christian L. Müller, Ivo F. Sbalzarini
• Keywords: Algorithms, Artificial Intelligence, CEC 2010, Monte Carlo, Random Walk Monte Carlo