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A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization
We propose a computationally efficient limited memory Covariance Matrix
Adaptation Evolution Strategy for large scale optimization, which we call the
LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for
numerical optimization of non-linear, non-convex optimization problems in
continuous domain. Inspired by the limited memory BFGS method of Liu and
Nocedal (1989), the LM-CMA-ES samples candidate solutions according to a
covariance matrix reproduced from direction vectors selected during the
optimization process. The decomposition of the covariance matrix into Cholesky
factors allows to reduce the time and memory complexity of the sampling to
, where is the number of decision variables. When is large
(e.g., > 1000), even relatively small values of (e.g., ) are
sufficient to efficiently solve fully non-separable problems and to reduce the
overall run-time.Comment: Genetic and Evolutionary Computation Conference (GECCO'2014) (2014
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