Surrogate-based global optimization using an adaptive switching infill sampling criterion for expensive black-box functions
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Surrogate-based global optimization algorithms use a surrogate model along with a sampling criterion. The AMP-SBGO algorithm sequentially samples points to gradually find the global optimum. The sampling criterion used to decide where to sample in each iteration dominates the algorithm and directly impacts its efficiency and robustness. This paper presents a method that uses multiple criteria for each phase of sampling, with conditions for switching from one criterion to another. Such behavior can improve the performance of the algorithm by allowing the optimization process to be less influenced by the initial sample points. Each phase, referred to as the global search phase and local search phase, utilizes different techniques. For the global search, a weighted maximin distance metric is proposed that is more efficient than ordinary maximin distance searches, and for the local search, the surrogate is optimized using a multi-start gradient-based optimizer. The algorithm was tested on 9 unconstrained mathematical test functions and 4 classes of GKLS functions along with 5 constrained test problems, which included 4 engineering design problems, and showed significant improvements compared to existing surrogate-based global optimization algorithms. The algorithm was then implemented to optimize the shape of a flange shaft in a washing machine.
KeywordsSurrogate-based global optimization Infill sampling criterion Expensive black-box function Sequential approximate optimization
This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20164010200860) and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Korea government, Ministry of Science, ICT & Future Planning (NRF-2017R1A2B1006384).
- Dixon LCW, Szego GP (1978) The global optimisation problem: an introduction. In: Dixon LCW and Szego GP (eds) Towards Global Optimisation 2, North-Holland Amsterdam, pp 1–15Google Scholar
- Evers G (2016) Particle swarm optimization research toolbox (Version 20160308), M.S. thesis code. http://www.georgeevers.org/pso_research_toolbox.htm
- Iman RL (2008) Latin hypercube sampling, encyclopedia of quantitative risk analysis and assessment. Wiley, New YorkGoogle Scholar
- Liang JJ, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan PN, Coello CAC, Deb K (2006) Problem definitions and evalutation criteria for the CEC 2006 special session on constrained real-parameter optimization. J Appl Mech 41:8Google Scholar
- Molga M, Smutnicki C (2005) Test functions for optimization needs. Available at http://new.zsd.iiar.pwr.wroc.pl/files/docs/functions.pdf
- Orr MJL (1996) Introduction to radial basis function networks. Centre for Cognitive Science, University of Edinburgh, EdinburghGoogle Scholar
- Park D, Chung IB, Choi DH (2018) Surrogate based global optimization using adaptive switching infill sampling criterion. In: Schumacher A, Vietor T, Fiebig S, Bletzinger KU, Maute K (eds) Advances in structural and multidisciplinary optimization. WCSMO 2017. Springer, Cham, pp 692-699Google Scholar
- Regis RG (2013) Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points. Eng Optim. https://doi.org/10.1080/0305215X.2013.765000
- Sasena MJ (2002) Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations, Dissertation, University of MichiganGoogle Scholar
- Schonlau M (1997) Computer experiments and global optimization, Dissertation, University of WaterlooGoogle Scholar
- Yang XS (2010) Nature inspired metaheuristic algorithms, 2nd edn. Luniver Press, United KingdomGoogle Scholar