An improved mode-pursing sampling method that balances global exploration and local exploitation based on kriging. (English) Zbl 1523.62045
Summary: Mode-pursing sampling (MPS) is an efficient approach for solving expensive optimization problems. However, MPS does not actively seek sample points while considering the error information of the surrogate model. Hence, an improved MPS based on kriging (IMSK) is proposed in this article. This method employs the probability improvement function as a probabilistic distribution function and obtains multiple sampling points with a certain probability from a candidate set composed of the exploitation-exploration trade-off points in each iteration. In addition, two acceleration strategies are proposed to speed up the sequential optimization process. Several typical benchmark functions and an engineering problem are applied to test the performance of IMSK and compare it to that of different versions of MPS. The results show that IMSK can provide good optimized solutions at the same or lower computing costs. These properties may make IMSK suitable for addressing actual engineering optimization problems.
MSC:
| 62D05 | Sampling theory, sample surveys |
| 62G08 | Nonparametric regression and quantile regression |
| 90C56 | Derivative-free methods and methods using generalized derivatives |
| 90C90 | Applications of mathematical programming |
References:
| [1] | Akbari, H.; Kazerooni, A., KASRA: A Kriging-Based Adaptive Space Reduction Algorithm for Global Optimization of Computationally Expensive Black-Box Constrained Problems, Applied Soft Computing, 90, 106154 (2020) |
| [2] | Cai, X.; Qiu, H.; Gao, L., A Multi-point Sampling Method Based on Kriging for Global Optimization, Structural and Multidisciplinary Optimization, 56, 71-88 (2017) |
| [3] | Dong, H.; Li, J.; Wang, P.; Song, B.; Yu, X., Surrogate-Guided Multi-objective Optimization (SGMOO) Using an Efficient Online Sampling Strategy, Knowledge-Based Systems, 220, 106919 (2021) |
| [4] | Dong, H.; Song, B.; Dong, Z.; Wang, P., SCGOSR: Surrogate-Based Constrained Global Optimization Using Space Reduction, Applied Soft Computing, 65, 462-477 (2018) |
| [5] | Dong, H.; Song, B.; Wang, P.; Dong, Z., Hybrid Surrogate-Based Optimization Using Space Reduction (HSOSR) for Expensive Black-Box Functions, Applied Soft Computing, 64, 641-655 (2018) |
| [6] | Dong, H.; Wang, P.; Chen, W.; Song, B., SGOP: Surrogate-Assisted Global Optimization Using a Pareto-Based Sampling Strategy, Applied Soft Computing, 106, 107380 (2021) |
| [7] | Dong, H.; Wang, P.; Yu, X.; Song, B., Surrogate-Assisted Teaching-Learning-Based Optimization for High-Dimensional and Computationally Expensive Problems, Applied Soft Computing, 99, 106934 (2021) |
| [8] | Duan, X.; Wang, G.; Kang, X.; Niu, Q.; Naterer, G.; Peng, Q., Performance Study of Mode-Pursuing Sampling Method, Engineering Optimization, 41, 1, 1-21 (2009) |
| [9] | Feng, Z.; Zhang, Q. B.; Zhang, Q. F., A Multiobjective Optimization Based Framework to Balance the Global Exploration and Local Exploitation in Expensive Optimization, Journal of Global Optimization, 61, 4, 677-694 (2015) · Zbl 1323.90045 |
| [10] | García-García, J.; García-Ródenas, R.; Codina, E., A Surrogate-Based Cooperative Optimization Framework for Computationally Expensive Black-Box Problems, Optimization and Engineering, 21, 1053-1093 (2020) · Zbl 1457.90152 |
| [11] | He, Y.; Sun, J.; Song, P.; Wang, X., Dual Kriging Assisted Efficient Global Optimization of Expensive Problems with Evaluation Failures, Aerospace Science and Technology, 105, 106006 (2020) · doi:10.1016/j.ast.2020.106006 |
| [12] | Hong, L.; Li, H.; Peng, K.; Xiao, H., A Novel Kriging Based Active Learning Method for Structural Reliability Analysis, Journal of Mechanical Science and Technology, 34, 4, 1545-1556 (2020) |
| [13] | Jakobsson, S.; Patriksso, M.; Rudholm, J.; Wojciechowski, A., A Method for Simulation Based Optimization Using Radial Basis Functions, Engineering Optimization, 11, 4, 501-532 (2010) · Zbl 1243.65068 |
| [14] | Jie, H.; Wu, Y.; Ding, J., An Adaptive Metamodel-Based Global Optimization Algorithm for Black-Box Type Problems, Engineering Optimization, 47, 11, 1459-1480 (2015) |
| [15] | Jones, Donald R., A Taxonomy of Global Optimization Methods Based on Response Surfaces, Journal of Global Optimization, 21, 4, 345-383 (2001) · Zbl 1172.90492 |
| [16] | Jones, D.; Schonlau, M.; Welch, W., Efficient Global Optimization of Expensive Black-Box Functions, Journal of Global Optimization, 13, 4, 455-492 (1998) · Zbl 0917.90270 |
| [17] | Li, Y.; Shi, J.; Cen, H.; Shen, J.; Chao, Y., A Kriging Based Adaptive Global Optimization Method with Generalized Expected Improvement and Its Application in Numerical Simulation and Crop Evapotranspiration, Agricultural Water Management, 245, 106623 (2021) |
| [18] | Liu, H.; Ong, Y.; Cai, J., A Survey of Adaptive Sampling for Global Meta-modeling in Support of Simulation-Based Complex Engineering Design, Structural and Multidisciplinary Optimization, 57, 1, 393-416 (2018) |
| [19] | Maia, M.; Parente, E.; de Melo, A., Kriging-Based Optimization of Functionally Graded Structures, Structural and Multidisciplinary Optimization, 64, 4, 1887-1908 (2021) |
| [20] | Passos, A.; Luersen, M., Kriging-Based Multiobjective Optimization Using Sequential Reduction of the Entropy of the Predicted Pareto Front, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42, 10 (2020) |
| [21] | Picheny, V.; Wagner, T.; Ginsbourger, D., A Benchmark of Kriging-Based Infill Criteria for Noisy Optimization, Structural and Multidisciplinary Optimization, 48, 3, 607-626 (2013) |
| [22] | Qian, J.; Yi, J.; Zhang, J.; Cheng, Y.; Liu, J., An Entropy Weight-Based Lower Confidence Bounding Optimization Approach for Engineering Product Design, Applied Sciences-Basel, 10, 10, 3554 (2020) |
| [23] | Rezaveisi, M.; Sepehrnoori, K.; Johns, R., Tie-Simplex-Based Phase-Behavior Modeling in an IMPEC Reservoir Simulator, SPE Journal, 19, 2, 327-339 (2014) |
| [24] | Ribaud, M.; Blanchet-Scalliet, C.; Helbert, C.; Gillot, F., Robust Optimization: A Kriging-Based Multi-objective Optimization Approach, Reliability Engineering and System Safety, 200, 106913 (2020) |
| [25] | Sasena, M.; Papalambros, P.; Goovaerts, P., Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization, Engineering Optimization, 34, 3, 263-278 (2002) |
| [26] | Shi, R.; Liu, L.; Long, T.; Wu, Y.; Wang, G., Multi-fidelity Modeling and Adaptive Co-Kriging-Based Optimization for All-Electric Geostationary Orbit Satellite Systems, Journal of Mechanical Design, 142, 2, 021404 (2020) |
| [27] | Sobester, A.; Leary, S.; Keane, A., On the Design of Optimization Strategies Based on Global Response Surface Approximation Models, Journal of Global Optimization, 33, 31-59 (2005) · Zbl 1137.90743 |
| [28] | Tao, T.; Zhao, G.; Ren, S., An Efficient Kriging-Based Constrained Optimization Algorithm by Global and Local Sampling in Feasible Region, Journal of Mechanical Design, 142, 5 (2020) |
| [29] | Wang, Y.; Hao, P.; Guo, Z.; Liu, D.; Gao, Q., Reliability-Based Design Optimization of Complex Problems with Multiple Design Points via Narrowed Search Region, Journal of Mechanical Design, 142, 6, 061702 (2020) |
| [30] | Wang, L.; Shan, S.; Wang, G., Mode-Pursuing Sampling Method for Global Optimization on Expensive Black-Box Functions, Engineering Optimization, 36, 4, 419-438 (2004) |
| [31] | Wu, Y.; Long, T.; Shi, R.; Wang, G., Mode-Pursuing Sampling Method Using Discriminative Coordinate Perturbation for High-Dimensional Expensive Black-Box Optimization, Journal of Mechanical Design, 143, 041703 (2021) |
| [32] | Xia, B.; Liu, R.; He, Z.; Koh, C., A Single- and Multi-objective Optimization Algorithm for Electromagnetic Devices Assisted by Adaptive Kriging Based on Parallel Infilling Strategy, Journal of Electrical Engineering and Technology, 16, 1, 301-308 (2021) |
| [33] | Xing, J.; Luo, Y.; Gao, Z., A Global Optimization Strategy Based on Kriging Surrogate Model and Parallel Computing, Structural and Multidisciplinary Optimization, 62, 1, 405-417 (2020) |
| [34] | Zhan, D.; Qian, J.; Cheng, Y., Balancing Global and Local Search in Parallel Efficient Global Optimization Algorithms, Journal of Global Optimization, 67, 873-892 (2017) · Zbl 1369.90139 |
| [35] | Zhan, D.; Qian, J.; Cheng, Y., Pseudo Expected Improvement Criterion for Parallel EGO Algorithm, Journal of Global Optimization, 68, 641-662 (2017) · Zbl 1377.90069 |
| [36] | Zhang, Q.; Li, H., MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition, IEEE Transactions on Evolutionary Computation, 11, 712-731 (2007) |
| [37] | Zhang, X.; Wang, L.; Sorensen, J., AKOIS: An Adaptive Kriging Oriented Importance Sampling Method for Structural System Reliability Analysis, Structural Safety, 82, 101876 (2020) |
| [38] | Zhou, Y.; Haftka, R.; Cheng, G., Balancing Diversity and Performance in Global Optimization, Structural and Multidisciplinary Optimization, 54, 4, 1093-1105 (2016) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
