Black-box optimization benchmarking of IPOP-saACM-ES and BIPOP-saACM-ES on the BBOB-2012 noiseless testbed

In this paper, we study the performance of IPOP-saACM-ES and BIPOP-saACM-ES, recently proposed self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategies. Both algorithms were tested using restarts till a total number of function evaluations of 10^6D was reached, where D is the dimension of the function search space. We compared surrogate-assisted algorithms with their surrogate-less versions IPOP-aCMA-ES and BIPOP-CMA-ES, two algorithms with one of the best overall performance observed during the BBOB-2009 and BBOB-2010. The comparison shows that the surrogate-assisted versions outperform the original CMA-ES algorithms by a factor from 2 to 4 on 8 out of 24 noiseless benchmark problems, showing the best results among all algorithms of the BBOB-2009 and BBOB-2010 on Ellipsoid, Discus, Bent Cigar, Sharp Ridge and Sum of different powers functions.

[1]  Bernhard Sendhoff,et al.  Efficient evolutionary optimization using individual-based evolution control and neural networks: A comparative study , 2005, ESANN.

[2]  Michèle Sebag,et al.  Comparison-Based Optimizers Need Comparison-Based Surrogates , 2010, PPSN.

[3]  F. Hoffmann,et al.  Controlled Model Assisted Evolution Strategy with Adaptive Preselection , 2006, 2006 International Symposium on Evolving Fuzzy Systems.

[4]  Michèle Sebag,et al.  Self-adaptive surrogate-assisted covariance matrix adaptation evolution strategy , 2012, GECCO '12.

[5]  Anne Auger,et al.  Investigating the Local-Meta-Model CMA-ES for Large Population Sizes , 2010, EvoApplications.

[6]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[7]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[8]  Nikolaus Hansen,et al.  Benchmarking a BI-population CMA-ES on the BBOB-2009 function testbed , 2009, GECCO '09.

[9]  Oliver Kramer,et al.  Covariance Matrix Self-Adaptation and Kernel Regression - Perspectives of Evolutionary Optimization in Kernel Machines , 2010, Fundam. Informaticae.

[10]  K. Price.  Differential evolution vs. the functions of the 2/sup nd/ ICEO , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[11]  Edmund K. Burke,et al.  Parallel Problem Solving from Nature - PPSN IX: 9th International Conference, Reykjavik, Iceland, September 9-13, 2006, Proceedings , 2006, PPSN.

[12]  Andreas Zell,et al.  Evolution strategies assisted by Gaussian processes with improved preselection criterion , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[13]  N. Hansen,et al.  Real-Parameter Black-Box Optimization Benchmarking: Experimental Setup , 2010 .

[14]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[15]  Michèle Sebag,et al.  Alternative Restart Strategies for CMA-ES , 2012, PPSN.

[16]  Anne Auger,et al.  Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions , 2009 .

[17]  Francisco Herrera,et al.  A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization , 2009, J. Heuristics.

[18]  Nikolaus Hansen,et al.  Compilation of Results on the 2005 CEC Benchmark Function Set , 2005 .

[19]  Thomas Philip Runarsson.  Ordinal Regression in Evolutionary Computation , 2006, PPSN.

[20]  Thomas Philip Runarsson,et al.  Sampling strategies in ordinal regression for surrogate assisted evolutionary optimization , 2011, 2011 11th International Conference on Intelligent Systems Design and Applications.

[21]  Raymond Ros,et al.  Benchmarking a weighted negative covariance matrix update on the BBOB-2010 noiseless testbed , 2010, GECCO '10.

[22]  Dirk V. Arnold,et al.  Improving Evolution Strategies through Active Covariance Matrix Adaptation , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[23]  Petros Koumoutsakos,et al.  Local Meta-models for Optimization Using Evolution Strategies , 2006, PPSN.