zhandawei / Efficient_Global_Optimization_Algorithms

standard, parallel, constrained, and multiobjective EGO algorithms

A collection of Efficient Global Optimization (EGO) algorithms

Table of Contents

• Requirements
• Standard EGO
• Parallel EGO
• Constrained EGO
• Multiobjecitve EGO
• References

Requirements

1. Windows system.
2. MATLAB 2016b and above.

Standard Efficient Global Optimization algorithm

1. The standard EGO algorithm (EGO_EI.m) ¹. For the Kriging modeling, the Gaussian correlation function is used as the corrlation function and the constant mean is used as the trend function. I refered some codes in the book Engineering design via surrogate modelling: a practical guide ² for the Kriging model. The MATLAB fmincon function is used for maximizing the likehihood function to get the estimated hyperparameters when training the Kriging model. The expected improvement function is maximized by a real-coded genetic algorithm ³.

Parallel Efficient Global Optimization algorithms

1. The Kriging Believer approach (EGO_KB.m) ⁴.
2. The Constant Liar approach (EGO_CL.m) ⁴.
3. The Peseudo Expected Improvement (EGO_Pseudo_EI.m) ⁵ .
4. The Multipoint Expected Improvement (EGO_qEI.m) ⁶. The qEI function is coded according the R code in ⁷.
5. The Fast Multipoint Expected Improvement (EGO_FqEI.m) ⁸.

Constrained Efficient Global Optimization algorithms

1. The Constrained Expected Improvemment (EGO_Constrained_EI.m) ⁹.
2. The Pseudo Constrained Expected Improvement (EGO_Pseudo_Constrained_EI.m) ¹⁰.

Multiobjective Efficient Global Optimization algorithms

1. The ParEGO (Pareto EGO) (ParEGO.m) ¹¹.
2. The Expected Improvement Matrix (EGO_EIM_Euclidean.m,EGO_EIM_Hypervolume.m,EGO_EIM_Maximin.m) ¹².
3. The Expected Hypervolume Improvement (EGO_EHVI.m)¹³. The EHVI criterion is calculated using Monte Carlo approximation.
4. The MOEA/D-EGO (MOEAD_EGO.m)¹⁴. We use all the samples to train the Kriging models instead of using the fuzzy clusting based modeling method used in the original work¹⁴.

References

Footnotes

1. D. R. Jones, M. Schonlau, and W. J. Welch. Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 1998. 13(4): 455-492. ↩

2. A. Forrester and A. Keane. Engineering design via surrogate modelling: a practical guide. 2008, John Wiley & Sons. ↩

3. K. Deb. An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 2000. 186(2): 311-338. ↩

4. D. Ginsbourger, R. Le Riche, and L. Carraro. Kriging Is Well-Suited to Parallelize Optimization, in Computational Intelligence in Expensive Optimization Problems, Y. Tenne and C.-K. Goh, Editors. 2010, 131-162. ↩ ↩²

5. D. Zhan, J. Qian, and Y. Cheng. Pseudo expected improvement criterion for parallel EGO algorithm. Journal of Global Optimization, 2017. 68(3): 641-662. ↩

6. C. Chevalier, and D. Ginsbourger. Fast computation of the multi-points expected improvement with applications in batch selection, in Learning and Intelligent Optimization, G. Nicosia and P. Pardalos, Editors. 2013, 59-69. ↩

7. O. Roustant, D. Ginsbourger, and Y. Deville. DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization. Journal of Statistical Software, 2012. 51(1): 1-55. ↩

8. D. Zhan, Y. Meng and H. Xing. A fast multi-point expected improvement for parallel expensive optimization. IEEE Transactions on Evolutionary Computation, 2022, doi: 10.1109/TEVC.2022.3168060. ↩

9. M. Schonlau. Computer experiments and global optimization. 1997, University of Waterloo. ↩

10. J. Qian, Y. Cheng, J. zhang, J. Liu, and D. Zhan. A parallel constrained efficient global optimization algorithm for expensive constrained optimization problems. Engineering Optimization, 2021. 53(2): 300-320. ↩

11. J. Knowles. ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Transactions on Evolutionary Computation, 2006. 10(1): 50-66. ↩

12. D. Zhan, Y. Cheng, and J. Liu. Expected improvement matrix-based infill criteria for expensive multiobjective optimization. IEEE Transactions on Evolutionary Computation, 2017. 21(6): 956-975. ↩

13. M. T. M. Emmerich, K. C. Giannakoglou, and B. Naujoks. Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels. IEEE Transactions on Evolutionary Computation, 2006, 10(4): 421-439. ↩

14. Q. Zhang, W. Liu, E. Tsang, and B. Virginas. Expensive Multiobjective Optimization by MOEA/D With Gaussian Process Model. IEEE Transactions on Evolutionary Computation, 2010, 14(3): 456-474. ↩ ↩²