On the efficiency of Gaussian adaptation
Journal of Optimization Theory and Applications
Completely Derandomized Self-Adaptation in Evolution Strategies
Evolutionary Computation
A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies
Proceedings of the 8th annual conference on Genetic and evolutionary computation
On spectral invariance of randomized hessian and covariance matrix adaptation schemes
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
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We revisit Gaussian Adaptation (GaA), a black-box optimizer for discrete and continuous problems that has been developed in the late 1960’s. This largely neglected search heuristic shares several interesting features with the well-known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) and with Simulated Annealing (SA). GaA samples single candidate solutions from a multivariate normal distribution and continuously adapts its first and second moments (mean and covariance) such as to maximize the entropy of the search distribution. Sample-point selection is controlled by a monotonically decreasing acceptance threshold, reminiscent of the cooling schedule in SA. We describe the theoretical foundations of GaA and analyze some key features of this algorithm. We empirically show that GaA converges log-linearly on the sphere function and analyze its behavior on selected non-convex test functions.