Zbyněk Pitra
ABSTRACT
Surrogate regression models have been shown as a valuable technique in evolutionary optimization to save evaluations of expensive black-box objective functions. Each surrogate modelling method has two complementary components: the employed model and the control of when to evaluate the model and when the true objective function, aka evolution control. They are often tightly interconnected, which causes difficulties in understanding the impact of each component on the algorithm performance. To contribute to such understanding, we analyse what constitutes the evolution control of three surrogate-assisted versions of the state-of-the-art algorithm for continuous black-box optimization --- the Covariance Matrix Adaptation Evolution Strategy. We implement and empirically compare all possible combinations of the regression models employed in those methods with the three evolution controls encountered in them. An experimental investigation of all those combinations allowed us to asses the influence of the models and their evolution control separately. The experiments are performed on the noiseless and noisy benchmarks of the Comparing-Continuous-Optimisers platform and a real-world simulation benchmark, all in the expensive scenario, where only a small budget of evaluations is available.
Supplemental Material
Available for Download
tgz
p528-pitra_suppl.tgz (6.4 MB)
p528-pitra_suppl.tgz
- A. Auger, D. Brockhoff, and N. Hansen. 2013. Benchmarking the Local Metamodel CMA-ES on the Noiseless BBOB'2013 Test Bed. In Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation (GECCO '13 Companion). ACM, New York, NY, USA, 1225--1232.Google Scholar
- A. Auger, M. Schoenauer, and N. Vanhaecke. 2004. LS-CMA-ES: A Second-Order Algorithm for Covariance Matrix Adaptation. In Parallel Problem Solving from Nature - PPSN VIII, Vol. 3242. 182--191.Google Scholar
- M. Baerns and M. Holeňa. 2009. Combinatorial Development of Solid Catalytic Materials. Design of High-Throughput Experiments, Data Analysis, Data Mining. Imperial College Press / World Scientific, London.Google Scholar
- L. Bajer, Z. Pitra, J. Repický, and M. Holeňa. 2019. Gaussian Process Surrogate Models for the CMA Evolution Strategy. Evolutionary Computation 27, 4 (2019), 665--697.Google ScholarDigital Library
- A. J. Booker, J. Dennis, P. D. Frank, D. B. Serafini, Torczon V., and M. Trosset. 1999. A Rigorous Framework for Optimization by Surrogates. Structural Optimization 17 (1999), 1--13.Google ScholarCross Ref
- D. Büche, N. N. Schraudolph, and P. Koumoutsakos. 2005. Accelerating Evolutionary Algorithms with Gaussian Process Fitness Function Models. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 35 (2005), 183--194.Google ScholarDigital Library
- T. Chugh, K. Sindhya, J. Hakanen, and K. Miettinen. 2019. A survey on Handling Computationally Expensive Multiobjective Optimization Problems with Evolutionary Algorithms. Soft Computing 23 (2019), 3137--3166.Google ScholarDigital Library
- M. A. El-Beltagy, P. B. Nair, and A. J. Keane. 1999. Metamodeling Techniques for Evolutionary Optimization of Computationally Expensive Problems: Promises and Limitations. In Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation - Volume 1 (GECCO'99). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 196--203.Google Scholar
- M. Emmerich, K. Giannakoglou, and B. Naujoks. 2006. Single-and Multi-objective evolutionary Optimization assisted by Gaussian Random Field Metamodels,. IEEE Transactions on Evolutionary Computation 10 (2006), 421--439.Google ScholarDigital Library
- M. Emmerich, A. Giotis, M. Özdemir, T. Bäck, and K. Giannakoglou. 2002. Metamodel-Assisted Evolution Strategies, In Parallel Problem Solving from Nature --- PPSN VII. Lecture Notes in Computer Science 2439 (Sept. 2002), 361--370.Google Scholar
- A. Forrester, A. Sobester, and A. Keane. 2008. Engineering Design via Surrogate Modelling: A Practical Guide. John Wiley & Sons, Ltd.Google ScholarCross Ref
- H.-M. Gutmann. 2001. A Radial Basis Function Method for Global Optimization. Journal of Global Optimization 19 (2001), 201--227.Google ScholarDigital Library
- N. Hansen. 2006. The CMA Evolution Strategy: A Comparing Review. In Towards a New Evolutionary Computation. Studies in Fuzziness and Soft Computing, Vol. 192. Springer, Berlin, Heidelberg, 75--102.Google Scholar
- N. Hansen. 2019. A Global Surrogate Assisted CMA-ES. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '19). ACM, New York, NY, USA, 664--672.Google ScholarDigital Library
- N. Hansen, A. Auger, S. Finck, and R. Ros. 2012. Real-Parameter Black-Box Optimization Benchmarking 2012: Experimental Setup. Technical Report. INRIA.Google Scholar
- N. Hansen, A. Auger, R. Ros, O. Merseman, T. Tušar, and D. Brockhoff. 2020. COCO: a Platform for Comparing Continuous Optimizers in a Black-Box Setting. Optimization Methods and Software 36, 1 (Aug. 2020), 114--144.Google Scholar
- N. Hansen, S. Finck, R. Ros, and A. Auger. 2009. Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions. Technical Report RR-6829. INRIA. Updated February 2010.Google Scholar
- N. Hansen, S. Finck, R. Ros, and A. Auger. 2009. Real-Parameter Black-Box Optimization Benchmarking 2009: Noisy Functions Definitions. Research Report RR-6869. INRIA.Google Scholar
- N. Hansen and A. Ostermeier. 2001. Completely Derandomized Self-Adaptation in Evolution Strategies. Evolutionary Computation 9, 2 (June 2001), 159--195.Google ScholarDigital Library
- S. Hosder, L. Watson, and B. Grossman. 2001. Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport. Optimization and Engineering 2 (2001), 431--452.Google ScholarCross Ref
- Y. Jin, M. Hüsken, M. Olhofer, and Sendhoff B. 2005. Neural Networks for Fitness Approximation in Evolutionary Optimization. In Knowledge Incorporation in Evolutionary Computation, Y. Jin (Ed.). Springer, 281--306.Google Scholar
- Y. Jin, M. Olhofer, and B. Sendhoff. 2001. Managing approximate models in evolutionary aerodynamic design optimization. In CEC 2001. 592--599.Google Scholar
- Y. Jin, M. Olhofer, and B. Sendhoff. 2002. A Framework for Evolutionary Optimization with Approximate Fitness Functions. IEEE Transactions on Evolutionary Computation 6 (2002), 481--494.Google ScholarDigital Library
- S. Kern, N. Hansen, and P. Koumoutsakos. 2006. Local Metamodels for Optimization Using Evolution Strategies. In PPSN IX. 939--948.Google Scholar
- J.W. Kruisselbrink, M.T.M. Emmerich, A.H. Deutz, and T. Bäck. 2010. A Robust Optimization Approach Using Kriging Metamodels for Robustness Approximation in the CMA-ES. In IEEE CEC. 1--8.Google Scholar
- S.J. Leary, A. Bhaskar, and A.J. Keane. 2004. A Derivative Based Surrogate Model for Approximating and Optimizing the Output of an Expensive Computer Simulation. Journal of Global Optimization 30 (2004), 39--58.Google ScholarDigital Library
- I. Loshchilov, M. Schoenauer, and M. Sebag. 2012. Self-Adaptive SurrogateAssisted Covariance Matrix Adaptation Evolution Strategy. In GECCO'12. ACM, 321--328.Google Scholar
- I. Loshchilov, M. Schoenauer, and M. Sebag. 2013. Intensive Surrogate Model Exploitation in Self-Adaptive Surrogate-Assisted CMA-ES (saACM-ES). In GECCO'13. 439--446.Google Scholar
- J. Lu, B. Li, and Y. Jin. 2013. An Evolution Strategy Assisted by an Ensemble of Local Gaussian Process Models. In GECCO'13. 447--454.Google Scholar
- R.H. Myers, D.C. Montgomery, and C.M. Anderson-Cook. 2009. Response Surface Methodology: Proces and Product Optimization Using Designed Experiments. John Wiley and Sons, Hoboken.Google Scholar
- L. Na, Q. Feng, Z. Liang, and W.M. Zhong. 2012. Gaussian Process Assisted Coevolutionary Estimation of Distribution Algorithm for Computationally Expensive Problems. Journal of Central South University of Technology 19 (2012), 443--452.Google ScholarCross Ref
- Y.S. Ong, P.B. Nair, A.J. Keane, and K.W. Wong. 2005. Surrogate-assisted evolutionary optimization frameworks for high-fidelity engineering design problems. In Knowledge Incorporation in Evolutionary Computation, Y. Jin (Ed.). Springer, 307--331.Google Scholar
- Z. Pitra, J. Repický, and M. Holeňa. 2019. Landscape Analysis of Gaussian Process Surrogates for the Covariance Matrix Adaptation Evolution Strategy. In GECCO'19. ACM, 691--699.Google Scholar
- K. Rasheed, X. Ni, and S. Vattam. 2005. Methods for Using Surrogate Modesl to Speed Up Genetic Algorithm Oprimization: Informed Operators and Genetic Engineering. In Knowledge Incorporation in Evolutionary Computation, Y. Jin (Ed.). Springer, 103--123.Google Scholar
- C. E. Rasmussen and C. K. I. Williams. 2006. Gaussian Processes for Machine Learning. MIT Press.Google ScholarDigital Library
- A. Ratle. 2001. Kriging as a Surrogate Fitness Landscape in Evolutionary Optimization. Artificial Intelligence for Engineering Design, Analysis and Manufacturing 15 (2001), 37--49.Google ScholarDigital Library
- H. Ulmer, F. Streichert, and A. Zell. 2003. Evolution Strategies Assisted by Gaussian Processes with Improved Pre-Selection Criterion. In IEEE CEC. 692--699.Google Scholar
- V. Volz, G. Rudolph, and B. Naujoks. 2017. Investigating Uncertainty Propagation in Surrogate-Assisted Evolutionary Algorithms. In GECCO'17. 881--888.Google Scholar
- J. Wu, S. Shekh, N. Y. Sergiienko, B. S. Cazzolato, B. Ding, F. Neumann, and M. Wagner. 2016. Fast and Effective Optimisation of Arrays of Submerged Wave Energy Converters. In Proceedings of the Genetic and Evolutionary Computation Conference 2016 (GECCO '16). Association for Computing Machinery, New York, NY, USA, 1045--1052.Google Scholar
- Z.Z. Zhou, Y.S. Ong, P.B. Nair, A.J. Keane, and K.Y. Lum. 2007. Combining Global and Local Surrogate Models to Accellerate Evolutionary Optimization. IEEE Transactions on Systems, Man and Cybernetics. Part C: Applications and Reviews 37 (2007), 66--76.Google ScholarDigital Library
Index Terms
- Interaction between model and its evolution control in surrogate-assisted CMA evolution strategy
Recommendations
CMA evolution strategy assisted by kriging model and approximate ranking
The covariance matrix adaptation evolution strategy (CMA-ES) is a competitive evolutionary algorithm (EA) for difficult continuous optimization problems. However, expensive function evaluation of many real-world optimization problems poses a serious ...
Intensive surrogate model exploitation in self-adaptive surrogate-assisted cma-es (saacm-es)
GECCO '13: Proceedings of the 15th annual conference on Genetic and evolutionary computationThis paper presents a new mechanism for a better exploitation of surrogate models in the framework of Evolution Strategies (ESs). This mechanism is instantiated here on the self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategy ...
Self-adaptive surrogate-assisted covariance matrix adaptation evolution strategy
GECCO '12: Proceedings of the 14th annual conference on Genetic and evolutionary computationThis paper presents a novel mechanism to adapt surrogate-assisted population-based algorithms. This mechanism is applied to ACM-ES, a recently proposed surrogate-assisted variant of CMA-ES. The resulting algorithm, s*ACM-ES, adjusts online the ...
Comments