Benchmarking the local metamodel CMA-ES on the noiseless BBOB'2013 test bed

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 meta-models 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 2 times D2 function evaluations with D being the search space dimension.