Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1443–1459 | Cite as

Surrogate-based global optimization using an adaptive switching infill sampling criterion for expensive black-box functions

RESEARCH PAPER
First Online:
Received:
Revised:
Accepted:
  • 111 Downloads

Abstract

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.

Keywords

Surrogate-based global optimization Infill sampling criterion Expensive black-box function Sequential approximate optimization 
This is a preview of subscription content, log in to check access

Notes

Acknowledgements

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).

References

  1. Bjorkman M, Holmstrom K (2000) Global optimisation of costly nonconvex functions using radial basis functions. Optim Eng 1:373–397MathSciNetCrossRefMATHGoogle Scholar
  2. 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
  3. Dong H, Song B, Dong Z, Wang P (2016) Multi-start space reduction (MSSR) surrogate-based global optimization method. Struct Multidisc Optim 54:907–926CrossRefGoogle Scholar
  4. Evers G (2016) Particle swarm optimization research toolbox (Version 20160308), M.S. thesis code. http://www.georgeevers.org/pso_research_toolbox.htm
  5. Garg H (2014) Solving structural engineering design optimization problems using an artificial bee colony algorithm. J Ind Manag Optim 10(3):777–794MathSciNetCrossRefMATHGoogle Scholar
  6. Gaviano M, Kvasov DE, Lera D, Sergeyev YD (2003) Algorithm 829: software for generation of classes of test functions with known local and global minima for global optimization. ACM Trans Math Softw 29(4):469–480MathSciNetCrossRefMATHGoogle Scholar
  7. Gutmann HM (2001) A radial basis function method for global optimization. J Glob Optim 19:201–227MathSciNetCrossRefMATHGoogle Scholar
  8. Iman RL (2008) Latin hypercube sampling, encyclopedia of quantitative risk analysis and assessment. Wiley, New YorkGoogle Scholar
  9. Jie H, Wu Y, Ding J (2015) An adaptive metamodel-based global optimization algorithm for black-box type problems. Eng Optim 47(11):1459–1480MathSciNetCrossRefGoogle Scholar
  10. Johnson ME, Moore LM, Ylvisaker D (1990) Minimax and maximin distance designs. J Stat Plann Inference 26:131–148MathSciNetCrossRefGoogle Scholar
  11. Jones DR (2001) A taxonomy of global optimization methods based on response surfaces. J Glob Optim 21:345–383MathSciNetCrossRefMATHGoogle Scholar
  12. Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:455–492MathSciNetCrossRefMATHGoogle Scholar
  13. 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
  14. Liu H, Xu S, Ma Y, Wang X (2015) Global optimization of expensive black box functions using potential Lipschitz constants and response surfaces. J Glob Optim 63(2):229–251MathSciNetCrossRefMATHGoogle Scholar
  15. Liu H, Xu S, Chen X, Wang X, Ma Q (2017) Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy. Struct Multidiscip Optim 55:155–177MathSciNetCrossRefGoogle Scholar
  16. Long T, Wu D, Guo X, Wang GG, Liu L (2015) Efficient adaptive response surface method using intelligent space exploration strategy. Struct Multidiscip Optim 51:1335–1362CrossRefGoogle Scholar
  17. Molga M, Smutnicki C (2005) Test functions for optimization needs. Available at http://new.zsd.iiar.pwr.wroc.pl/files/docs/functions.pdf
  18. Orr MJL (1996) Introduction to radial basis function networks. Centre for Cognitive Science, University of Edinburgh, EdinburghGoogle Scholar
  19. Park JS (1994) Optimal latin-hypercube designs for computer experiments. J Stat Plann Inference 39:95–111MathSciNetCrossRefMATHGoogle Scholar
  20. 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
  21. Parr JM, Forrester AIJ, Keane AJ, Holden CME (2012) Enhancing infill sampling criteria for surrogate-based constrained optimization. J Comput Methods Sci Eng 12:25–45MathSciNetMATHGoogle Scholar
  22. 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
  23. Regis RG, Shoemaker CA (2007) Improved strategies for radial basis function methods for global optimization. J Glob Optim 37:113–135MathSciNetCrossRefMATHGoogle Scholar
  24. Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4(4):409–423MathSciNetCrossRefMATHGoogle Scholar
  25. Sasena MJ (2002) Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations, Dissertation, University of MichiganGoogle Scholar
  26. Schonlau M (1997) Computer experiments and global optimization, Dissertation, University of WaterlooGoogle Scholar
  27. Shewry MC, Wynn HP (1987) Maximum entropy sampling. J Appl Stat 14:165–170CrossRefGoogle Scholar
  28. Sobester A, Leary SJ, Keane AJ (2005) On the design of optimization strategies based on global response surface approximation models. J Glob Optim 33:31–59MathSciNetCrossRefMATHGoogle Scholar
  29. Xu X, Meng Z, Sun J, Huang L, Shen R (2012) A second-order smooth penalty function algorithm for constrained optimization problems. Comput Optim Appl 55:155–172MathSciNetCrossRefMATHGoogle Scholar
  30. Yang XS (2010) Nature inspired metaheuristic algorithms, 2nd edn. Luniver Press, United KingdomGoogle Scholar
  31. Ye KQ, Li W, Sudjianto A (2000) Algorithmic construction of optimal symmetric Latin hypercube designs. J Stat Plann Inference 90:145–159MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringHanyang UniversitySeoulSouth Korea
  2. 2.Advanced module engineering team, LG Chem R&D CampusGwacheonSouth Korea

Personalised recommendations