Abstract
The conflict between computational budget and quality of found solutions is crucial when dealing with expensive black-box optimization problems from the industry. We show that through multi-objective parameter tuning of the Covariance Matrix Adaptation Evolution Strategy on benchmark functions different optimal algorithm configurations can be found for specific computational budgets and solution qualities. With the obtained Pareto front, tuned parameter sets are selected and transferred to a real-world optimization problem from vehicle dynamics, improving the solution quality and budget needed. The benchmark functions for tuning are selected based on their similarity to a real-world problem in terms of Exploratory Landscape Analysis features.
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References
Ait Elhara, O., Auger, A., Hansen, N.: A median success rule for non-elitist evolution strategies: study of feasibility. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, GECCO 2013, Association for Computing Machinery, New York, pp. 415–422 (2013). https://doi.org/10.1145/2463372.2463429
Akiba, T., Sano, S., Yanase, T., Ohta, T., Koyama, M.: Optuna: a next-generation hyperparameter optimization framework. In: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, KDD 2019, Association for Computing Machinery, New York, pp. 2623–2631 (2019). https://doi.org/10.1145/3292500.3330701
Andersson, M., Bandaru, S., Ng, A.H., Syberfeldt, A.: Parameter tuned CMA-ES on the CEC’15 expensive problems. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp. 1950–1957 (2015). https://doi.org/10.1109/CEC.2015.7257124
Bäck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press Inc, Oxford (1996). https://doi.org/10.1093/oso/9780195099713.001.0001
Bäck, T., Foussette, C., Krause, P.: Contemporary Evolution Strategies. Natural Computing Series, 1st edn. Springer, Berlin (2013)
Bartz-Beielstein, T., et al.: Benchmarking in Optimization: Best Practice and Open Issues. Technical report (2020). http://arxiv.org/2007.03488arxiv.org/pdf/2007.03488
Björck, Å.: Numerics of gram-Schmidt orthogonalization. Linear Algebra Appl. 197, 297–316 (1994). https://doi.org/10.1016/0024-3795(94)90493-6
Brockhoff, D., Auger, A., Hansen, N., Arnold, D.V., Hohm, T.: Mirrored sampling and sequential selection for evolution strategies. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 11–21. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15844-5_2
Caraffini, F., Kononova, A.V., Corne, D.: Infeasibility and structural bias in differential evolution. Inf. Sci. 496, 161–179 (2019)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002). https://doi.org/10.1109/4235.996017
Dréo, J.: Using Performance Fronts for Parameter Setting of Stochastic Metaheuristics. In: Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers, pp. 2197–2200. ACM Conferences, Association for Computing Machinery, New York (2009). https://doi.org/10.1145/1570256.1570301
Eiben, A.E., Smit, S.K.: Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm Evol. Comput. 1(1), 19–31 (2011). https://doi.org/10.1016/j.swevo.2011.02.001
Fujii, G., Takahashi, M., Akimoto, Y.: CMA-ES-based structural topology optimization using a level set boundary expression-application to optical and carpet cloaks. Comput. Methods Appl. Mech. Eng. 332, 624–643 (2018). https://doi.org/10.1016/j.cma.2018.01.008
Grefenstette, J.: Optimization of control parameters for genetic algorithms. IEEE Trans. Syst. Man Cybern. 16(1), 122–128 (1986). https://doi.org/10.1109/TSMC.1986.289288
Hansen, N.: CMA-ES with Two-Point Step-Size Adaptation. Technical report RR-6527, INRIA (2008). https://www.hal.inserm.fr/INRIA/inria-00276854
Hansen, N.: The CMA Evolution Strategy: A Tutorial. Technical report (2016). https://arxiv.org/pdf/1604.00772
Hansen, N., Finck, S., Ros, R., Auger, A.: Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions. Technical report RR-6829, INRIA (2009). https://hal.inria.fr/inria-00362633/
Hansen, N., Ostermeier, A.: Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. In: Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 312–317 (1996). https://doi.org/10.1109/ICEC.1996.542381
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001). https://doi.org/10.1162/106365601750190398
Hernández, A.M., van Nieuwenhuyse, I., Rojas-Gonzalez, S.: A survey on multi-objective hyperparameter optimization algorithms for Machine Learning. ArXiv (2021). https://arxiv.org/pdf/2111.13755.pdf
International Organization for Standardization: ISO 21994:2007 - Passenger cars - Stopping distance at straight-line braking with ABS - Open-loop test method (2007)
Jankovic, A., Eftimov, T., Doerr, C.: Towards feature-based performance regression using trajectory data. In: Castillo, P.A., Jiménez Laredo, J.L. (eds.) EvoApplications 2021. LNCS, vol. 12694, pp. 601–617. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-72699-7_38
Jastrebski, G.A., Arnold, D.V.: Improving evolution strategies through active covariance matrix adaptation. In: IEEE International Conference on Evolutionary Computation, pp. 2814–2821 (2006). https://doi.org/10.1109/CEC.2006.1688662
Kerschke, P., Preuss, M., Wessing, S., Trautmann, H.: Detecting funnel structures by means of exploratory landscape analysis. In: Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, pp. 265–272. ACM Digital Library, Association for Computing Machinery, New York (2015). https://doi.org/10.1145/2739480.2754642
Kerschke, P., Trautmann, H.: Comprehensive feature-based landscape analysis of continuous and constrained optimization problems using the r-package flacco. In: Bauer, N., Ickstadt, K., Lübke, K., Szepannek, G., Trautmann, H., Vichi, M. (eds.) Applications in Statistical Computing. SCDAKO, pp. 93–123. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25147-5_7
Koch-Dücker, H.-J., Papert, U.: Antilock braking system (ABS). In: Reif, K. (ed.) Brakes, Brake Control and Driver Assistance Systems. BPAI, pp. 74–93. Springer, Wiesbaden (2014). https://doi.org/10.1007/978-3-658-03978-3_6
Kochenderfer, M.J., Wheeler, T.A.: Algorithms for Optimization. The MIT Press, Cambridge and London (2019)
Kokoska, S., Zwillinger, D.: CRC Standard Probability and Statistics Tables and Formulae, CRC Press, Boca Raton (2000). https://doi.org/10.1201/b16923
Long, F.X., van Stein, B., Frenzel, M., Krause, P., Gitterle, M., Bäck, T.: Learning the characteristics of engineering optimization problems with applications in automotive crash. In: Proceedings of the Genetic and Evolutionary Computation Conference. GECCO 2022, Association for Computing Machinery, New York, (2022). https://doi.org/10.1145/3512290.3528712
Loshchilov, I., Hutter, F.: CMA-ES for Hyperparameter Optimization of Deep Neural Networks (2016). https://arxiv.org/abs/1604.07269
Lunacek, M., Whitley, D.: The dispersion metric and the CMA evolution strategy. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, p. 477. Association for Computing Machinery (2006). https://doi.org/10.1145/1143997.1144085
Mersmann, O., Bischl, B., Trautmann, H., Preuss, M., Weihs, C., Rudolph, G.: Exploratory landscape analysis. In: Lanzi, P.L. (ed.) Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, ACM Conferences, ACM, New York, pp. 829–836 (2011). https://doi.org/10.1145/2001576.2001690
Mersmann, O., Preuss, M., Trautmann, H.: Benchmarking evolutionary algorithms: towards exploratory landscape analysis. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 73–82. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15844-5_8
Muñoz, M.A., Kirley, M., Halgamuge, S.K.: Exploratory landscape analysis of continuous space optimization problems using information content. IEEE Trans. Evol. Comput. 19(1), 74–87 (2015). https://doi.org/10.1109/TEVC.2014.2302006
Niemz, T.: Reducing Braking Distance by Control of Semi-Active Suspension. Dissertation, Technische Universität Darmstadt (2007). https://tuprints.ulb.tu-darmstadt.de/912/
de Nobel, J., Vermetten, D., Wang, H., Doerr, C., Bäck, T.: Tuning as a Means of Assessing the Benefits of New Ideas in Interplay with Existing Algorithmic Modules. Technical report (2021). https://arxiv.org/pdf/2102.12905
Owen, A.B.: Scrambling sobol’ and niederreiter-xing points. J. Complex. 14(4), 466–489 (1998). https://doi.org/10.1006/jcom.1998.0487
Pacejka, H.B., Bakker, E.: The magic formula tyre model. Veh. Syst. Dyn. 21(sup001), 1–18 (1992). https://doi.org/10.1080/00423119208969994
Piad-Morffis, A., Estévez-Velarde, S., Bolufé-Röhler, A., Montgomery, J., Chen, S.: Evolution strategies with thresheld convergence. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp. 2097–2104 (2015). https://doi.org/10.1109/CEC.2015.7257143
Preuss, M.: Improved topological niching for real-valued global optimization. In: Chio, C., et al. (eds.) EvoApplications 2012. LNCS, vol. 7248, pp. 386–395. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29178-4_39
Sala, R., Müller, R.: Benchmarking for metaheuristic black-box optimization: perspectives and open challenges. In: 2020 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2020). https://doi.org/10.1109/CEC48606.2020.9185724
Siemens Digital Industries Software: Tire Simulation & Testing (2020). https://www.plm.automation.siemens.com/global/en/products/simulation-test/tire-simulation-testing.html
Sobol’, I.M.: On the distribution of points in a cube and the approximate evaluation of integrals. Comput. Math. Math. Phys. 7(4), 86–112 (1967). https://doi.org/10.1016/0041-5553(67)90144-9
The MathWorks Inc: Simulink (2015). https://www.mathworks.com/’
Thomaser, A., Kononova, A.V., Vogt, M.E., Bäck, T.: One-shot optimization for vehicle dynamics control systems: towards benchmarking and exploratory landscape analysis. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 2036–2045. Association for Computing Machinery, New York (2022). https://doi.org/10.1145/3520304.3533979
van Rijn, S., Wang, H., van Leeuwen, M., Bäck, T.: Evolving the structure of evolution strategies. In: 2016 IEEE Symposium Series on Computational Intelligence (SSCI), pp. 1–8 (2016). https://doi.org/10.1109/SSCI.2016.7850138
van Rijn, S., Wang, H., van Stein, B., Bäck, T.: Algorithm configuration data mining for cma evolution strategies. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2017, Association for Computing Machinery, New York, pp. 737–744 (2017). https://doi.org/10.1145/3071178.3071205
Wang, H., Emmerich, M., Bäck, T.: Mirrored orthogonal sampling with pairwise selection in evolution strategies. In: Proceedings of the 29th Annual ACM Symposium on Applied Computing, SAC 2014, Association for Computing Machinery, New York, pp. 154–156 (2014). https://doi.org/10.1145/2554850.2555089
Wang, H., Emmerich, M., Bäck, T.: Mirrored orthogonal sampling for covariance matrix adaptation evolution strategies. Evol. Comput. 27(4), 699–725 (2019). https://doi.org/10.1162/evco_a_00251
Ye, F., Doerr, C., Wang, H., Bäck, T.: Automated configuration of genetic algorithms by tuning for anytime performance. IEEE Trans. Evol. Comput. 26(6), 1526–1538 (2022). https://doi.org/10.1109/TEVC.2022.3159087
Zhao, M., Li, J.: Tuning the hyper-parameters of CMA-ES with tree-structured Parzen estimators. In: 2018 Tenth International Conference on Advanced Computational Intelligence (ICACI), pp. 613–618 (2018). https://doi.org/10.1109/ICACI.2018.8377530
Acknowledgements
This paper was written as part of the project newAIDE under the consortium leadership of BMW AG with the partners Altair Engineering GmbH, divis intelligent solutions GmbH, MSC Software GmbH, Technical University of Munich, TWT GmbH. The project is supported by the Federal Ministry for Economic Affairs and Climate Action (BMWK) on the basis of a decision of the German Bundestag.
The authors would like to thank Jacob de Nobel and Diederick Vermetten for their support with the modular CMA-ES implementation.
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Thomaser, A., Vogt, ME., Kononova, A.V., Bäck, T. (2023). Transfer of Multi-objectively Tuned CMA-ES Parameters to a Vehicle Dynamics Problem. In: Emmerich, M., et al. Evolutionary Multi-Criterion Optimization. EMO 2023. Lecture Notes in Computer Science, vol 13970. Springer, Cham. https://doi.org/10.1007/978-3-031-27250-9_39
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