A Surrogate-Assisted Evolutionary Framework With Regions of Interests-Based Data Selection for Expensive Constrained Optimization
Abstract
Optimization problems whose evaluations of the objective and constraints involve costly numerical simulations or physical experiments are referred to as expensive constrained optimization (ECO) problems. Such problems can be solved by evolutionary algorithms (EAs) in conjunction with computationally cheap surrogates that separately approximate the expensive objective and constraint functions. During the process of the ECO, the interested regions of surrogate models for the objective and constraints usually have a small overlap only. Specifically, the surrogate model for the objective function should focus on the prediction accuracy in the promising region, while the models for constraint functions should concentrate on the accuracy at the boundary of the feasible region. However, most existing methods neglect such differences and train those different models using the same training data, barely resulting in satisfactory performance. Therefore, we propose a general framework for solving expensive optimization problems with inequality constraints. In the proposed framework, the objective and constraints are separately trained with two different sets of training data to enhance the prediction accuracy and reliability in the interested regions. A novel infill sampling criterion is tailored to decide whether potentially better or more uncertain solutions should be sampled. Moreover, a new strategy, termed search intensity adjustment, is designed for adjusting the number of search generations on new surrogate models. We attempt to embed three competitive constrained EAs into our framework to verify its generality. The experimental results obtained on numerous benchmark functions from CEC2006, CEC2010, and CEC2017 have demonstrated the superiority of our approach over three state-of-the-art surrogate-assisted EAs.
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MoE models can significantly enhance efficiency by deploying model parallelism across multiple specialized expert modules, enabling transformer-based modules for dynamic token routing and scaling to trillions of parameters, reducing memory footprint and computational costs.
“MoE models can significantly enhance efficiency by deploying model parallelism across multiple specialized expert modules, which enables these models to leverage transformer-based modules for dynamic token routing, and to scale to trillions of parameters, thereby reducing both memory footprint and computational costs [94], [98].”
From From Google Gemini to OpenAI Q* (Q-Star): A Survey on Reshaping the Generative Artificial Intelligence (AI) Research Landscape (2025) · cites this paper as [98]
Cites
Derrac, J., García, S., Molina, D., & Herrera, F. (2011) · Swarm and Evolutionary Computation · doi:10.1016/j.swevo.2011.02.002 · Cited by 5,562 · see citing works
Empirical Model Building and Response Surfaces
Freeny, A. E., Box, G. E. P., & Draper, N. R. (1988) · Technometrics · doi:10.2307/1270169 · Cited by 5,238 · see citing works
An efficient constraint handling method for genetic algorithms
Deb, K. (2000) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/s0045-7825(99)00389-8 · Cited by 3,916 · see citing works
Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks
Broomhead, D. S., & Lowe, D. G. (1988) · Complex Systems · Cited by 3,429 · see citing works
McKay, M. D., Beckman, R. J., & Conover, W. J. (2000) · Technometrics · doi:10.1080/00401706.2000.10485979 · Cited by 2,882 · see citing works
Stochastic ranking for constrained evolutionary optimization
Rúnarsson, T. P., & Yao, X. (2000) · IEEE Transactions on Evolutionary Computation · doi:10.1109/4235.873238 · Cited by 1,816 · see citing works
Surrogate-assisted evolutionary computation: Recent advances and future challenges
Jin, Y. (2011) · Swarm and Evolutionary Computation · doi:10.1016/j.swevo.2011.05.001 · Cited by 1,547 · see citing works
Self-citationDifferential Evolution With Composite Trial Vector Generation Strategies and Control Parameters
Wang, Y., Cai, Z., & Zhang, Q. (2011) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2010.2087271 · Cited by 1,435 · see citing works
Constraint-handling in nature-inspired numerical optimization: Past, present and future
Mezura‐Montes, E., & Coello, C. A. C. (2011) · Swarm and Evolutionary Computation · doi:10.1016/j.swevo.2011.10.001 · Cited by 1,133 · see citing works
Expensive Multiobjective Optimization by MOEA/D With Gaussian Process Model
Zhang, Q., Liu, W., Tsang, E. P. K., & Virginas, B. (2009) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2009.2033671 · Cited by 748 · see citing works
Data-Driven Evolutionary Optimization: An Overview and Case Studies
Jin, Y., Wang, H., Chugh, T., Guo, D., & Miettinen, K. (2018) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2018.2869001 · Cited by 696 · see citing works
Self-citationChugh, T., Jin, Y., Miettinen, K., et al. (2016) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2016.2622301 · Cited by 636 · see citing works
Self-citationUsing Class Imbalance Learning for Software Defect Prediction
Wang, S., & Yao, X. (2013) · IEEE Transactions on Reliability · doi:10.1109/tr.2013.2259203 · Cited by 568 · see citing works
Mallipeddi, R., & Suganthan, P. N. (2010) · Cited by 524 · see citing works
A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization
Cai, Z., & Wang, Y. (2006) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2006.872344 · Cited by 400 · see citing works
Self-adaptive fitness formulation for constrained optimization
Farmani, R., & Wright, J. A. (2003) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2003.817236 · Cited by 366 · see citing works
Chugh, T., Sindhya, K., Hakanen, J., & Miettinen, K. (2017) · Soft Computing · doi:10.1007/s00500-017-2965-0 · Cited by 310 · see citing works
A Kriging-Assisted Two-Archive Evolutionary Algorithm for Expensive Many-Objective Optimization
Song, Z., Wang, H., He, C., et al. (2021) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2021.3073648 · Cited by 270 · see citing works
Self-citationRegis, R. G. (2013) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2013.2262111 · Cited by 269 · see citing works
Data-Driven Surrogate-Assisted Multiobjective Evolutionary Optimization of a Trauma System
Wang, H., Jin, Y., & Jansen, J. O. (2016) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2016.2555315 · Cited by 262 · see citing works
Self-citationGuo, D., Jin, Y., Ding, J., & Chai, T. (2018) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2018.2794503 · Cited by 250 · see citing works
Self-citationWang, Y., Wang, B.-C., Li, H., & Yen, G. G. (2015) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2015.2493239 · Cited by 236 · see citing works
An insight into imbalanced Big Data classification: outcomes and challenges
Fernández, A., del Río, S., Chawla, N. V., & Herrera, F. (2017) · Complex & Intelligent Systems · doi:10.1007/s40747-017-0037-9 · Cited by 231 · see citing works
Composite Differential Evolution for Constrained Evolutionary Optimization
Wang, B.-C., Li, H., Li, J., & Wang, Y. (2018) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2018.2807785 · Cited by 218 · see citing works
Wang, H., & Jin, Y. (2018) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2018.2869674 · Cited by 218 · see citing works
Self-citationWang, Y., Yin, D.-Q., Yang, S., et al. (2018) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2018.2809430 · Cited by 185 · see citing works
Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization
Wang, B.-C., Li, H., Zhang, Q., et al. (2018) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2018.2876335 · Cited by 150 · see citing works
Multiple Penalties and Multiple Local Surrogates for Expensive Constrained Optimization
Li, G., & Zhang, Q. (2021) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2021.3066606 · Cited by 95 · see citing works
Yang, Z., Qiu, H., Gao, L., Cai, X., Jiang, C., & Chen, L. (2019) · Information Sciences · doi:10.1016/j.ins.2019.08.054 · Cited by 78 · see citing works
Dong, H., Wang, P., Fu, C., & Song, B. (2020) · Information Sciences · doi:10.1016/j.ins.2020.09.073 · Cited by 69 · see citing works
Fitness Approximation In Evolutionary Computation - a Survey.
Jin, Y., & Sendhoff, B. (2002) · Surrey Research Insight Open Access (The University of Surrey) · doi:10.1007/s00500-003-0328-5 · Cited by 57 · see citing works
Self-citationSong, Z., Wang, H., & Xu, H. (2021) · Memetic Computing · doi:10.1007/s12293-021-00351-8 · Cited by 55 · see citing works
Self-citationExpensive Optimization via Surrogate-Assisted and Model-Free Evolutionary Optimization
Li, G., Wang, Z., & Gong, M. (2022) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2022.3219080 · Cited by 55 · see citing works
Liu, Q., Cheng, R., Jin, Y., et al. (2022) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2022.3163129 · Cited by 47 · see citing works
Self-citationε -Constrained Differential Evolution Using an Adaptive ε -Level Control Method
Zhang, C., Qin, A. K., Shen, W., et al. (2020) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2020.3010120 · Cited by 38 · see citing works
Wei, F.-F., Chen, W., & Zhang, J. (2023) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2023.3259947 · Cited by 35 · see citing works
Yang, Z., Qiu, H., Gao, L., Xu, D., & Liu, Y. (2022) · Information Sciences · doi:10.1016/j.ins.2022.11.021 · Cited by 32 · see citing works
Liu, Y., Yang, Z., Xu, D., et al. (2022) · Information Sciences · doi:10.1016/j.ins.2022.11.167 · Cited by 29 · see citing works
Expensive Multiobjective Optimization Based on Information Transfer Surrogate
Luo, J., Dong, Y., Zhu, Z., et al. (2022) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2022.3205010 · Cited by 28 · see citing works
Jiao, R., Xue, B., & Zhang, M. (2021) · IEEE Transactions on Evolutionary Computation · doi:10.1109/tevc.2021.3120980 · Cited by 21 · see citing works
Zeng, Y., Cheng, Y., & Liu, J. (2022) · Information Sciences · doi:10.1016/j.ins.2022.07.162 · Cited by 18 · see citing works
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“Innovative approaches, from constrained optimization [84], [85], [86], [87], [88], to different types of reward modeling [89], [90], [91], [92], aim to embed human preferences within AI systems.”
Background
- Authors
- Song, Z., Wang, H., & Jin, Y.
- Affiliations
- Xidian University (CN)
- Bielefeld University (DE)
- Venue
- IEEE Transactions on Systems Man and Cybernetics Systems
- Published
- 2023-10
- Volume
- 53
- Issue
- 10
- Pages
- 6268-6280
- ISSN
- 2168-2216 (ISSN-L)
- 2168-2232
- OpenAlex
- W4380607290
- Cited by
- 38
- References
- 41
- Citations by year
- 2026: 12 · 2025: 17 · 2024: 6 · 2023: 3
- FWCI
- 5.42
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Systems Man and Cybernetics Systems (publishedVersion)
- PUB – Publications at Bielefeld University (Bielefeld University) (submittedVersion)
- Funders
- National Natural Science Foundation of China (61976165)
- Alexander von Humboldt Professorship for Artificial Intelligence
- German Federal Ministry of Education and Research
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Multi-Objective Optimization Algorithms
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Physical Sciences › Computer Science › Artificial Intelligence › Evolutionary Algorithms and Applications
- Keywords
- surrogate-assisted evolutionary algorithms, surrogate models, data selection, inequality constraints
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