Benchmarking the (1,4)-CMA-ES With Mirrored Sampling and Sequential Selection on the Noisy BBOB-2010 Testbed - Archive ouverte HAL Access content directly
Conference Papers Year : 2010

## Benchmarking the (1,4)-CMA-ES With Mirrored Sampling and Sequential Selection on the Noisy BBOB-2010 Testbed

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Anne Auger
• Function : Author
• PersonId : 751513
• IdHAL : anne-auger
Dimo Brockhoff
• Function : Correspondent author
• PersonId : 743680
• IdHAL : dimo-brockhoff

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Nikolaus Hansen

#### Abstract

The Covariance-Matrix-Adaptation Evolution-Strategy (CMA-ES) is a robust stochastic search algorithm for optimizing functions defined on a continuous search space $\R^{D}$. Recently, mirrored samples and sequential selection have been introduced within CMA-ES to improve its local search performances. In this paper, we benchmark the (1,4$_m^s$)-CMA-ES which implements mirrored samples and sequential selection on the BBOB-2010 noisy testbed. Independent restarts are conducted until a maximal number of $10^{4} D$ function evaluations is reached. Although the tested (1,4$_m^s$)-CMA-ES is only a local search strategy, it solves 8 of the noisy BBOB-2010 functions in 20D and 9 of them in 5D for a target of $10^{-8}$. There is also one additional function in 20D and 5 additional functions in 5D where a successful run for at least one of the 15 instances can be reported. Moreover, on 7 of the 8 functions that are solved by the (1,4$_m^s$)-CMA-ES in 20D, we see a large improvement over the best algorithm of the BBOB-2009 benchmarking for the corresponding functions---ranging from an 37% improvement on the sphere with moderate Cauchy noise to a speed-up by a factor of about 3 on the Gallagher function with Cauchy noise.

### Dates and versions

inria-00502441 , version 1 (14-07-2010)

### Identifiers

• HAL Id : inria-00502441 , version 1
• DOI :

### Cite

Anne Auger, Dimo Brockhoff, Nikolaus Hansen. Benchmarking the (1,4)-CMA-ES With Mirrored Sampling and Sequential Selection on the Noisy BBOB-2010 Testbed. GECCO workshop on Black-Box Optimization Benchmarking (BBOB'2010), Jul 2010, Portland, OR, United States. pp.1625-1632, ⟨10.1145/1830761.1830782⟩. ⟨inria-00502441⟩

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