An efficient constrained global optimization algorithm with a clustering-assisted multiobjective infill criterion using Gaussian process regression for expensive problems. (English) Zbl 1534.90120
Summary: Constrained optimization problems trouble engineers and researchers because of their high complexity and computational cost. When the objective function and constraints are both expensive black-box problems, there are many difficulties in solving them due to the unknown mathematical expressions and limited computational resources. To address these difficulties, we propose an efficient constrained global optimization algorithm. In the proposed algorithm, Gaussian process regression models are used to approximate the expensive objective function and constraints. Differential evolution (DE) is adopted to find the minimum value of the constrained lower confidence bounding (LCB). To further improve the accuracy of the Gaussian process regression models for the objective and constraints simultaneously, a clustering-assisted multiobjective infill criterion is proposed. The multiobjective infill criterion is utilized to balance the exploration between the objective and constraints. The clustering selection method is used to maintain the diversity of the sample points. The experimental results show that the proposed algorithm is better than or at least comparable to classic algorithms and other state-of-the-art algorithms
MSC:
| 90C26 | Nonconvex programming, global optimization |
Keywords:
global optimization; expensive constrained optimization; Gaussian process; clustering method; multiobjective infill criterionReferences:
| [1] | Ahmadianfar, I.; Bozorg-Haddad, O.; Chu, X., Gradient-based optimizer: A new metaheuristic optimization algorithm, Inf. Sci., 540, 131-159 (2020) · Zbl 1474.90517 |
| [2] | Wang, B.-C.; Feng, Y.; Li, H.-X., Individual-dependent feasibility rule for constrained differential evolution, Inf. Sci., 506, 174-195 (2020) · Zbl 1456.90160 |
| [3] | Drucker, H.; Burges, C. J.; Kaufman, L.; Smola, A.; Vapnik, V., Support vector regression machines, Adv. Neural Inf. Process. Syst., 9, 155-161 (1996) |
| [4] | Chen, S.; Cowan, C. F.N.; Grant, P. M., Orthogonal least squares learning algorithm for radial basis function networks, IEEE Trans. Neural Network, 2, 2, 302-309 (1991) |
| [5] | Williams, C.; Rasmussen, C., Gaussian processes for regression, Adv. Neural Inf. Process. Syst., 8, 514-520 (1995) |
| [6] | Qian, J. C.; Cheng, Y. S.; Zhang, J. L.; Liu, J.; Zhan, D. W., A parallel constrained efficient global optimization algorithm for expensive constrained optimization problems, Eng. Optim., 53, 300-320 (2021) · Zbl 1523.90319 |
| [7] | R. Jovanovic, S. Kais, F.H. Alharbi, Cuckoo search inspired hybridization of the nelder-mead simplex algorithm applied to optimization of photovoltaic cells, arXiv preprint arXiv:1411.0217, (2014). |
| [8] | Jin, Y., Surrogate-assisted evolutionary computation: recent advances and future challenges, Swarm Evol. Comput., 1, 2, 61-70 (2011) |
| [9] | Yang, Z.; Qiu, H. B.; Gao, L.; Cai, X. W.; Jiang, C.; Chen, L. M., Surrogate-assisted classification-collaboration differential evolution for expensive constrained optimization problems, Inf. Sci., 508, 50-63 (2020) · Zbl 1456.90161 |
| [10] | Habib, A.; Singh, H. K.; Ray, T., A multiple surrogate assisted multi/many-objective multi-fidelity evolutionary algorithm, Inf. Sci., 502, 537-557 (2019) |
| [11] | Yang, Z.; Qiu, H. B.; Gao, L.; Cai, X. W.; Jiang, C.; Chen, L. M., A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems, Eng. Optim., 51, 549-566 (2019) |
| [12] | Bouhlel, M. A.; Bartoli, N.; Regis, R.; Otsmane, A.; Morlier, J., Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method (vol 50, pg 2038, 2018), Eng. Optim., 50 (2018), X-X · Zbl 1523.90279 |
| [13] | Wang, X. L.; Jin, Y. C.; Schmitt, S.; Olhofer, M., An adaptive Bayesian approach to surrogate-assisted evolutionary multi-objective optimization, Inf. Sci., 519, 317-331 (2020) · Zbl 1457.90150 |
| [14] | Cai, X. W.; Gao, L.; Li, X. Y., Efficient generalized surrogate-assisted evolutionary algorithm for high-dimensional expensive problems, IEEE Trans. Evol. Comput., 24, 365-379 (2020) |
| [15] | Chaiyotha, K.; Krityakierne, T., A comparative study of infill sampling criteria for computationally expensive constrained optimization problems, Symmetry-Basel, 12, 10, 1631 (2020) |
| [16] | Couckuyt, I.; Deschrijver, D.; Dhaene, T., Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization, J. Global Optim., 60, 575-594 (2014) · Zbl 1303.90093 |
| [17] | Cox, D. D.; John, S., A statistical method for global optimization, ([Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics (1992), IEEE), 1241-1246 |
| [18] | Jones, D. R.; Schonlau, M.; Welch, W. J., Efficient global optimization of expensive black-box functions, J. Global Optim., 13, 455-492 (1998) · Zbl 0917.90270 |
| [19] | Liu, B.; Koziel, S.; Zhang, Q., A multi-fidelity surrogate-model-assisted evolutionary algorithm for computationally expensive optimization problems, J. Comput. Sci., 12, 28-37 (2016) |
| [20] | Knowles, J., ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems, IEEE Trans. Evol. Comput., 10, 50-66 (2006) |
| [21] | Villemonteix, J.; Vazquez, E.; Walter, E., An informational approach to the global optimization of expensive-to-evaluate functions, J. Global Optim., 44, 509 (2009) · Zbl 1180.90253 |
| [22] | Luo, C. T.; Zhang, S. L.; Wang, C.; Jiang, Z. L., A metamodel-assisted evolutionary algorithm for expensive optimization, J. Comput. Appl. Math., 236, 759-764 (2011) · Zbl 1269.65056 |
| [23] | Chugh, T.; Jin, Y. C.; Miettinen, K.; Hakanen, J.; Sindhya, K., A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization, IEEE Trans. Evol. Comput., 22, 129-142 (2018) |
| [24] | Kort, B. W.; Bertsekas, D. P., A new penalty function method for constrained minimization, (Proceedings of the 1972 IEEE Conference on Decision and Control and 11th Symposium on Adaptive Processes (1972)), 162-166 |
| [25] | Deb, K., An efficient constraint handling method for genetic algorithms, Comput. Methods Appl. Mech. Eng., 186, 311-338 (2000) · Zbl 1028.90533 |
| [26] | Durantin, C.; Marzat, J.; Balesdent, M., Analysis of multi-objective Kriging-based methods for constrained global optimization, Comput. Optim. Appl., 63, 903-926 (2016) · Zbl 1343.90066 |
| [27] | Jiao, R. W.; Zeng, S. Y.; Li, C. H., A feasible-ratio control technique for constrained optimization, Inf. Sci., 502, 201-217 (2019) · Zbl 1453.90165 |
| [28] | Akbari, H.; Kazerooni, A., KASRA: a Kriging-based Adaptive Space Reduction Algorithm for global optimization of computationally expensive black-box constrained problems, Appl. Soft Comput., 90 (2020) |
| [29] | Li, C. N.; Fang, H.; Gong, C. L., Expensive inequality constraints handling methods suitable for dynamic surrogate-based optimization, (2019 Ieee Congress on Evolutionary Computation (Cec) (2019)), 2010-2017 |
| [30] | Wang, Y.; Yin, D. Q.; Yang, S.; Sun, G., Global and local surrogate-assisted differential evolution for expensive constrained optimization problems with inequality constraints, IEEE Trans. Cybern., 49, 1642-1656 (2019) |
| [31] | Deb, K.; Datta, R., A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach, (IEEE Congress on Evolutionary Computation (2010), IEEE), 1-8 |
| [32] | Handoko, S. D.; Keong, K. C.; Soon, O. Y., Using classification for constrained memetic algorithm: a new paradigm, (2008 IEEE International Conference on Systems, Man and Cybernetics (2008), IEEE), 547-552 |
| [33] | Shi, R. H.; Liu, L.; Long, T.; Wu, Y. F.; Tang, Y. F., Filter-based adaptive Kriging method for black-box optimization problems with expensive objective and constraints, Comput. Methods Appl. Mech. Eng., 347, 782-805 (2019) · Zbl 1440.62299 |
| [34] | Jiao, R. W.; Zeng, S. Y.; Li, C. H.; Jiang, Y. H.; Jin, Y. C., A complete expected improvement criterion for Gaussian process assisted highly constrained expensive optimization, Inf. Sci., 471, 80-96 (2019) · Zbl 1441.90109 |
| [35] | Dong, H. C.; Song, B. W.; Dong, Z. M.; Wang, P., SCGOSR: Surrogate-based constrained global optimization using space reduction, Appl. Soft Comput., 65, 462-477 (2018) |
| [36] | Qian, J.; Yi, J.; Cheng, Y.; Liu, J.; Zhou, Q., A sequential constraints updating approach for Kriging surrogate model-assisted engineering optimization design problem, Eng. Comput.-Germany, 1-17 (2019) |
| [37] | Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., 6, 2, 182-197 (2002) |
| [38] | MacQueen, J., Some methods for classification and analysis of multivariate observations, (Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Oakland, CA, USA (1967)), 281-297 · Zbl 0214.46201 |
| [39] | Ester, M.; Kriegel, H.-P.; Sander, J.; Xu, X., A density-based algorithm for discovering clusters in large spatial databases with noise, (Kdd (1996)), 226-231 |
| [40] | McKay, M. D., Latin hypercube sampling as a tool in uncertainty analysis of computer models, (Proceedings of the 24th Conference on Winter Simulation (1992)), 557-564 |
| [41] | Yi, J. X.; Zhou, Q.; Cheng, Y. S.; Liu, J., Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion, Struct. Multidiscip. Optim., 62, 2517-2536 (2020) |
| [42] | While, L.; Hingston, P.; Barone, L.; Huband, S., A faster algorithm for calculating hypervolume, IEEE Trans. Evol. Comput., 10, 29-38 (2006) |
| [43] | Liang, J.; Runarsson, T. P.; Mezura-Montes, E.; Clerc, M.; Suganthan, P. N.; Coello, C. C.; Deb, K., Problem Definitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-parameter Optimization, J. Appl. Mech., 41, 2006, 8-31 (2006) |
| [44] | Garg, H., Solving structural engineering design optimization problems using an artificial bee colony algorithm, J. Ind. Manag. Optim., 10, 777-794 (2014) · Zbl 1292.90212 |
| [45] | Thanedar, P.; Vanderplaats, G., Survey of discrete variable optimization for structural design, J. Struct. Eng., 121, 301-306 (1995) |
| [46] | Zhang, M.; Luo, W.; Wang, X. F., Differential evolution with dynamic stochastic selection for constrained optimization, Inf. Sci., 178, 3043-3074 (2008) |
| [47] | M. Schonlau, Computer experiments and global optimization, (1997) |
| [48] | Hollander, M.; Wolfe, D. A.; Chicken, E., Nonparametric Statistical Methods (1999), John Wiley & Sons: John Wiley & Sons New York · Zbl 0997.62511 |
| [49] | Holm, S., A simple sequentially rejective multiple test procedure, Scand. J. Stat., 65-70 (1979) · Zbl 0402.62058 |
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