Comparing the (1+1)-CMA-ES with a mirrored (1+2)-CMA-ES with sequential selection on the noiseless BBOB-2010 testbed

In this paper, we compare the (1+1)-CMA-ES to the (1+2s m)CMA-ES, a recently introduced quasi-random (1+2)-CMAES that uses mirroring as derandomization technique as well as a sequential selection. Both algorithms were tested using independent restarts till a total number of function evaluations of 104 D was reached, where D is the dimension of the search space. On the non-separable ellipsoid function in dimension 10, 20 and 40, the performances of the (1+2s m)-CMA-ES are better by 17% than the best performance among algorithms tested during BBOB-2009 (for target values of 10−5 and 10−7 ). Moreover, the comparison shows that the (1+2s m)-CMA-ES variant improves the performance of the (1+1)-CMA-ES by about 20% on the ellipsoid, the discus, and the sum of different powers functions and by 12% on the sphere function. Besides, we never observe statistically significant results where the (1+2s m)-CMAES is worse than the (1+1)-CMA-ES. Categories and Subject Descriptors

• Type: Conference
• Year: 2010
• Where: GECCO
• Authors: Anne Auger, Dimo Brockhoff, Nikolaus Hansen
• Keywords: 1+2s M)-CMA-ES, Function Evaluations, GECCO 2010, Non-separable Ellipsoid Function, Optimization