Abstract
Simulation-driven optimization problems are often computationally-expensive, an aspect which has motivated the use of metamodels as they provide approximate function values more economically. To further improve the prediction accuracy the use of ensembles has been explored in which predictions from multiple metamodels are combined. However, the optimal ensemble topology, namely, which types of metamodels it includes, is typically not known, while using a fixed topology may degrade the prediction accuracy and search effectiveness. To address this issue this paper proposes a metamodel-assisted algorithm which autonomously adapts the ensemble topology online during the search such that an optimal topology is used throughout. An extensive performance analysis shows the effectiveness of the proposed algorithm and approach.
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References
Y. Tenne and C. K. Goh, eds., Computational Intelligence in Expensive Optimization Problems, vol. 2 of Evolutionary Learning and Optimization, Springer, Berlin, 2010.
X. Dinh and K. K. Ann, “Radial basis function neural network based adaptive fast nonsingular terminal sliding mode controller for piezo positioning stage,” International Journal of Control, Automation, and Systems, vol. 15, no. 6, pp. 2892–2905, 2017.
C. Wang, J.-H. Wang, S.-S. Gu, X. Wang, and Y.-X. Zhang, “Elongation prediction of steel-strips in annealing furnace with deep learning via improved incremental extreme learning machine,” International Journal of Control, Automation, and Systems, vol. 15, no. 3, pp. 1466–1477, 2017.
F. A. C. Viana, R. T. Haftka, and L. T. Watson, “Efficient global optimization algorithm assisted by multiple surrogate technique,” Journal of Global Optimization, vol. 56, no. 2, pp. 669–689, 2013.
J. Muller and C. A. Shoemaker, “Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems,” Journal of Global Optimization, vol. 60, no. 2, pp. 123–144, 2014.
T. Wortmann, A. Costa, G. Nannicini, and T. Schroepfer, “Advantages of surrogate models for architectural design optimization,” Artificial Intelligence for Engineering Design, Analysis and Manufacturing, vol. 29, no. 4, pp. 471–481, 2015.
B. Talgorn, S. L. Digabel, and M. Kokkolaras, “Statistical surrogate formulations for simulation-based design optimization,” Journal of Mechanical Design, vol. 137, no. 2, Paper number MD-14-1128, 2015.
Y. Tenne, “A simulated annealing based optimization algorithm,” Computational Optimization in Engineering -Paradigms and Applications (H. Peyvandi, ed.), ch. 3, pp. 47–67, IN-TECH Publishing, 2017.
R. G. Regis and C. A. Shoemaker, “A quasi-multistart framework for global optimization of expensive functions using response surface models,” Journal of Global Optimization, vol. 56, no. 3, pp. 1719–1753, 2013.
Y. Jin, “Surrogate-assisted evolutionary computation: Recent advances and future challenges,” Swarm and Evolutionary Computation, vol. 1, pp. 61–70, 2011.
A. R. Conn and S. L. Digabel, “Use of quadratic models with mesh-adaptive direct search for constrained black-box optimization,” Optimization Methods and Software, vol. 28, no. 1, pp. 139–158, 2013.
S. Grarton and L. N. Vicente, “A surrogate management framework using rigorous trust-region steps,” Optimization Methods and Software, vol. 29, no. 1, pp. 10–23, 2014.
I. Couckuyt, F. De Turck, T. Dhaene, and D. Gorissen, “Automatic surrogate model type selection during the optimization of expensive black-box problems,” Proceedings of the 2011 Winter Simulation Conference-WSC 2011 (S. Jain, R. R. Creasey, J. Himmelspach, K. P. White, and M. Fu, eds.), (Phoenix, AZ, USA), IEEE, 2011.
D. Gorissen, L. D. Tommasi, J. Croon, and T. Dhaene, “Automatic model type selection with heterogeneous evolution: An application to RF circuit block modeling,” Proceedings of the IEEE Congress on Evolutionary Computation (CEC), (Piscataway, New Jersey), pp. 989-996, IEEE, 2008.
Y. Tenne, “An optimization algorithm employing multiple metamodels and optimizers,” International Journal of Automation and Computing, vol. 10, no. 3, pp. 227–241, 2013.
B. G. M. Husslage, G. Rennen, E. R. van Dam, and D. den Hertog, “Space-filling latin hypercube designs for computer experiments,” Optimization and Engineering, vol. 12, no. 4, pp. 611–630, 2011.
R. V. Joseph and Y. Hung, “Orthogonal-maximin latin hypercube designs,” Statistica Sinica, vol. 18, pp. 171–186, 2008.
P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. P. Chen, A. Auger, and S. Tiwari, “Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization,” Technical Report Kan-GAL 2005005, Nanyang Technological University, Singapore and Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology Kanpur, India, 2005.
A. Ratle, “Optimal sampling strategies for learning a fitness model,” Proc. of the IEEE Congress on Evolutionary Computation-CEC 1999, (Piscataway, New Jersey), pp. 2078–2085, IEEE, 1999.
D. Büche, N. N. Schraudolph, and P. Koumoutsakos, “Accelerating evolutionary algorithms with Gaussian process fitness function models,” IEEE Transactions on Systems, Man, and Cybernetics-Part C, vol. 35, no. 2, pp. 183–194, 2005.
D. J. Sheskin, Handbook of Parametric and Nonparametric Statistical Procedures, Boca Raton, Florida: Chapman and Hall, 4th ed 2007.
Y.-S. Ong, P. B. Nair, A. J. Keane, and K. W. Wong, “Surrogate-assisted evolutionary optimization frameworks for high-fidelity engineering design problems,” in Knowledge Incorporation in Evolutionary Computation (Y. Jin, ed.) in Studies in Fuzziness and Soft Computing, vol. 167, pp. 307–332, Springer, Berlin, Heidelberg, 2005.
S. L. Padula, C. R. Gumbert, and W. Li, “Aerospace applications of optimization under uncertainty,” Engineering Optimization, vol. 7, pp. 317–328, 2006.
R. M. Hicks and P. A. Henne, “Wing design by numerical optimization,” Journal of Aircraft, vol. 15, no. 7, pp. 407–412, 1978.
H.-Y. Wu, S. Yang, F. Liu, and H.-M. Tsai, “Comparison of three geometric representations of airfoils for aerodynamic optimization,” Proc. of the 16th AIAA Computational Fluid Dynamics Conference, (Reston, Virginia), pp. 1–11, American Institute of Aeronautics and Astronautics, 2003.
M. Drela and H. Youngren, XFOIL 6.9 User Primer. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 1 ed., 2001.
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Yoel Tenne received his Ph.D. in Mechanical Engineering from Sydney University in 2007. He was an Australian Endeavour postdoctoral fellow at KAIST, Korea in 2009 and a JSPS postdoctoral fellow at Kyoto University, Japan during 2010-2011. His research interests include computational intellligence and applied optimization.
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Tenne, Y. Online Ensemble Topology Selection in Expensive Optimization Problems. Int. J. Control Autom. Syst. 18, 955–965 (2020). https://doi.org/10.1007/s12555-018-0356-7
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DOI: https://doi.org/10.1007/s12555-018-0356-7