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Benchmarking the Local Metamodel CMA-ES on the Noiseless BBOB'2013 Test Bed

Anne Auger 1 Dimo Brockhoff 2 Nikolaus Hansen 1
1 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
2 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
Abstract : This paper evaluates the performance of a variant of the local-meta-model CMA-ES (lmm-CMA) in the BBOB 2013 expensive setting. The lmm-CMA is a surrogate variant of the CMA-ES algorithm. Function evaluations are saved by building, with weighted regression, full quadratic metamodels to estimate the candidate solutions' function values. The quality of the approximation is appraised by checking how much the predicted rank changes when evaluating a fraction of the candidate solutions on the original objective function. The results are compared with the CMA-ES without meta-modeling and with previously benchmarked algorithms, namely BFGS, NEWUOA and saACM. It turns out that the additional meta-modeling improves the performance of CMA-ES on almost all BBOB functions while giving significantly worse results only on the attractive sector function. Over all functions, the performance is comparable with saACM and the lmm-CMA often outperforms NEWUOA and BFGS starting from about 2D^2 function evaluations with D being the search space dimension.
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Submitted on : Friday, May 24, 2013 - 4:47:57 PM
Last modification on : Tuesday, October 5, 2021 - 11:48:01 AM
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  • HAL Id : hal-00825840, version 1


Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Benchmarking the Local Metamodel CMA-ES on the Noiseless BBOB'2013 Test Bed. GECCO (Companion), workshop on Black-Box Optimization Benchmarking (BBOB'2013), Jul 2013, Amsterdam, Netherlands. ⟨hal-00825840⟩



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