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A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization

Ilya Loshchilov 1 
1 Laboratory of Intelligent Systems (LIS)
LIS - Laboratory of Intelligent Systems
Abstract : 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 $m$ 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 $O(mn)$, where $n$ is the number of decision variables. When $n$ is large (e.g., $n$ > 1000), even relatively small values of $m$ (e.g., $m=20,30$) are sufficient to efficiently solve fully non-separable problems and to reduce the overall run-time.
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Submitted on : Monday, April 21, 2014 - 5:29:18 AM
Last modification on : Monday, October 13, 2014 - 3:43:25 PM
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  • HAL Id : hal-00981135, version 1
  • ARXIV : 1404.5520


Ilya Loshchilov. A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization. Genetic and Evolutionary Computation Conference (GECCO'2014), Jul 2014, Vancouver, Canada. ⟨hal-00981135⟩



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