Comparing the (1+1)-CMA-ES with a Mirrored (1+2)-CMA-ES with Sequential Selection on the Noiseless BBOB-2010 Testbed

Anne Auger (1) , Dimo Brockhoff (1) , Nikolaus Hansen (1)

1 TAO - Machine Learning and Optimisation

In this paper, we compare the (1+1)-CMA-ES to the (1+2$_m^s$)-CMA-ES, a recently introduced quasi-random (1+2)-CMA-ES 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 $10^{4} D$ 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+2$_m^s$)-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+2$_m^s$)-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+2$_m^s$)-CMA-ES is worse than the (1+1)-CMA-ES.

Domains: Neural and Evolutionary Computing [cs.NE]

Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Comparing the (1+1)-CMA-ES with a Mirrored (1+2)-CMA-ES with Sequential Selection on the Noiseless BBOB-2010 Testbed. GECCO workshop on Black-Box Optimization Benchmarking (BBOB'2010), Jul 2010, Portland, OR, United States. pp.1543-1550, ⟨10.1145/1830761.1830772⟩. ⟨inria-00502430⟩