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Constraint handling in efficient global optimization

Published: 01 July 2017 Publication History

Abstract

Real-world optimization problems are often subject to several constraints which are expensive to evaluate in terms of cost or time. Although a lot of effort is devoted to make use of surrogate models for expensive optimization tasks, not many strong surrogate-assisted algorithms can address the challenging constrained problems. Efficient Global Optimization (EGO) is a Kriging-based surrogate-assisted algorithm. It was originally proposed to address unconstrained problems and later was modified to solve constrained problems. However, these type of algorithms still suffer from several issues, mainly: (1) early stagnation, (2) problems with multiple active constraints and (3) frequent crashes. In this work, we introduce a new EGO-based algorithm which tries to overcome these common issues with Kriging optimization algorithms. We apply the proposed algorithm on problems with dimension d ≤ 4 from the G-function suite [16] and on an airfoil shape example.

References

[1]
I. H. A. Abbot and A. E. von Doenhoff. 1959. Theory of wing sections, including a summary of airfoil data. Dover Publications, New York.
[2]
C. Audet, A. J. Booker, Dennis, Jr, P. D. Frank, and D. W. Moore. 2000. A Surrogate-Model-Based Method For Constrained Optimization. In AIAA/ISSMO. 2000--4891.
[3]
S. Bagheri, W. Konen, and T. Bäck. 2016. Online selection of surrogate models for constrained black-box optimization. In IEEE SSCI'2016. 1--8.
[4]
A. J. Booker, J. E. Dennis, P. D. Frank, D. B. Serafini, V. Torczon, and M. W. Trosset. 1999. A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization 17, 1 (1999), 1--13.
[5]
M. Drela. 1989. XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils. In Conference on Low Reynolds Number Airfoil Aerodynamics. University of Notre Dame. http://web.mit.edu/drela/Public/papers/xfoil_sv.pdf
[6]
M. Drela and M. B. Giles. 1987. Viscous-Inviscid Analysis of Transonic and Low Reynolds Number Airfoils. AIAA Journal 25, 10 (Oct. 1987), 1347--1355.
[7]
C. Durantin, J. Marzat, and M. Balesdent. 2016. Analysis of multi-objective Kriging-based methods for constrained global optimization. Computational Optimization and Applications 63, 3 (2016), 903--926.
[8]
A. I. Forrester and A. J. Keane. 2009. Recent advances in surrogate-based optimization. Progress in Aerospace Sciences 45, 1 (2009), 50--79.
[9]
K.C. Giannakoglou. 2002. Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Progress in Aerospace Sciences 38, 1 (2002), 43 -- 76.
[10]
R. B. Gramacy and H. K. H. Lee. 2011. Optimization under unknown constraints. In Bayesian Statistics. Vol. 9. 229--247.
[11]
R. Hicks and P. A. Henne. 1978. Wing Design by Numerical Optimization. Journal of Aircraft 15, 7 (1978), 407--412.
[12]
R. Hussein and K. Deb. 2016. A Generative Kriging Surrogate Model for Constrained and Unconstrained Multi-objective Optimization. In GECCO '16. ACM, New York, NY, USA, 573--580.
[13]
E. Iuliano and D. Quagliarella. 2015. Evolutionary Optimization of Benchmark Aerodynamic Cases using Physics-based Surrogate Models. In AIAA SciTech. American Institute of Aeronautics and Astronautics, 1721--1736.
[14]
D. R. Jones, M. Schonlau, and W. J. Welch. 1998. Efficient Global Optimization of Expensive Black-Box Functions. J. of Global Optimization 13, 4 (Dec. 1998), 455--492.
[15]
D. G. Krige. 1951. A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Southern African Institute of Mining and Metallurgy 52, 6 (1951), 119--139.
[16]
J. Liang, T. P. Runarsson, E. Mezura-Montes, M. Clerc, P. Suganthan, C. Coello, and K. Deb. 2006. Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. Journal of Applied Mechanics 41, 8 (2006).
[17]
J. Mockus. 1977. On Bayesian Methods for Seeking the Extremum and their Application. In IFIP Congress. 195--200.
[18]
J. Parr, C. M. Holden, A. I. Forrester, and A. J. Keane. 2010. Review of efficient surrogate infill sampling criteria with constraint handling. In 2nd International Conference on Engineering Optimization. 1--10.
[19]
J. M. Parr, A. J. Keane, A. I. Forrester, and C. M. Holden. 2012. Infill sampling criteria for surrogate-based optimization with constraint handling. Engineering Optimization 44, 10 (2012), 1147--1166.
[20]
Victor Picheny. 2014. A stepwise uncertainty reduction approach to constrained global optimization. In International Conference on Artificial Intelligence and Statistics. Reykjavik, Iceland, 787--795.
[21]
D. Quagliarella, G. Petrone, and G. Iaccarino. 2014. Optimization Under Uncertainty Using the Generalized Inverse Distribution Function. In AISTATS, W. Fitzgibbon (Ed.). Computational Methods in Applied Sciences, Vol. 34. Springer, NL, 171--190.
[22]
R. G. Regis. 2014. Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points. Engineering Optimization 46, 2 (2014), 218--243.
[23]
T. P. Runarsson and X. Yao. 2000. Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation 4, 3 (2000), 284--294.
[24]
T. P. Runarsson and X. Yao. 2005. Search biases in constrained evolutionary optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 35, 2 (2005), 233--243.
[25]
M. J. Sasena, P. Papalambros, and P. Goovaerts. 2002. Exploration of meta-modeling sampling criteria for constrained global optimization. Engineering optimization 34, 3 (2002), 263--278.
[26]
M. J. Sasena, P. Y. Papalambros, and P. Goovaerts. 2001. The Use of Surrogate Modeling Algorithms to Exploit Disparities in Function Computation Time within Simulation-Based Optimization. In 4th World Congress of Structural and Multidisciplinary Optimization. 5--11.
[27]
M. Schonlau, W. J. Welch, and D. R. Jones. 1998. Global versus local search in constrained optimization of computer models. Lecture Notes-Monograph Series, Vol. 34. Institute of Mathematical Statistics, Hayward, CA, 11--25.
[28]
D. Villanueva, R. Le Riche, G. Picard, and R. Haftka. 2012. Surrogate-based agents for constrained optimization. In AIAA Non-Deterministic Approaches Conference. 1935--1951.

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cover image ACM Conferences
GECCO '17: Proceedings of the Genetic and Evolutionary Computation Conference
July 2017
1427 pages
ISBN:9781450349208
DOI:10.1145/3071178
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Published: 01 July 2017

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Author Tags

  1. EGO
  2. Gaussian processes
  3. constraint optimization
  4. expensive optimization
  5. kriging
  6. surrogate models

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GECCO '17 Paper Acceptance Rate 178 of 462 submissions, 39%;
Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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