LAPSE:2026.0449
Published Article
LAPSE:2026.0449
Machine Learning and Adaptive Sampling Powered Feasible Path Algorithm for Black-box Optimization
June 12, 2026
Abstract
Black-box optimization (BBO) deals with problems involving functions that are either unknown, imprecise, or costly to evaluate. Current BBO methods encounter multiple challenges, such as high computational demands from excessive function evaluations, difficulties in handling complex constraints, lack of theoretical convergence guarantees, and unstable performance due to significant variations in solution quality. This work presents a machine learning-powered feasible path (MLFP) framework for general BBO problems involving complex constraints. An adaptive sampling strategy is first proposed to explore optimal regions and pre-filter potentially infeasible points, thereby reducing the number of evaluations. Machine learning algorithms are utilized to build surrogates for black-box functions. The feasible path algorithm is integrated to accelerate theoretical convergence by updating only independent variables instead of all variables. Computational experiments demonstrate that MLFP can rapidly and robustly converge near the KKT point, even when training surrogates with small datasets. Compared to state-of-the-art BBO algorithms, MLFP stably delivers equivalent or superior solutions with fewer evaluations across benchmark examples.
Black-box optimization (BBO) deals with problems involving functions that are either unknown, imprecise, or costly to evaluate. Current BBO methods encounter multiple challenges, such as high computational demands from excessive function evaluations, difficulties in handling complex constraints, lack of theoretical convergence guarantees, and unstable performance due to significant variations in solution quality. This work presents a machine learning-powered feasible path (MLFP) framework for general BBO problems involving complex constraints. An adaptive sampling strategy is first proposed to explore optimal regions and pre-filter potentially infeasible points, thereby reducing the number of evaluations. Machine learning algorithms are utilized to build surrogates for black-box functions. The feasible path algorithm is integrated to accelerate theoretical convergence by updating only independent variables instead of all variables. Computational experiments demonstrate that MLFP can rapidly and robustly converge near the KKT point, even when training surrogates with small datasets. Compared to state-of-the-art BBO algorithms, MLFP stably delivers equivalent or superior solutions with fewer evaluations across benchmark examples.
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Keywords
Adaptive Sampling, Black-box, Feasible Path Algorithm, Machine Learning, Optimization, Surrogate Model
Subject
Suggested Citation
Zhang Z, Song X, Li J, Zeng Y, Nie Y, Zhu M, Lu D, Zhang Y, Xiao X, Li J. Machine Learning and Adaptive Sampling Powered Feasible Path Algorithm for Black-box Optimization. Systems and Control Transactions 5:1974-1985 (2026) https://doi.org/10.69997/sct.103112
Author Affiliations
Zhang Z: Chinese Academy of Science, Institute of Process Engineering, Beijing, China. University of Chinese Academy of Science, School of Chemical Engineering, Beijing, China
Song X: Chinese Academy of Science, Institute of Process Engineering, Beijing, China. University of Chinese Academy of Science, School of Chemical Engineering, Beijing, China
Li J: Chinese Academy of Science, Institute of Process Engineering, Beijing, China. University of Chinese Academy of Science, School of Chemical Engineering, Beijing, China
Zeng Y: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Nie Y: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Zhu M: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Lu D: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Zhang Y: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Xiao X: Chinese Academy of Science, Institute of Process Engineering, Beijing, China. China Institute for Innovation and Development Strategy, Work Committee on Carbon Neutral Intelligent Industry Innovation, Beijing, China
Li J: The University of Manchester, Department of Chemical Engineering, Manchester, United Kingdom. China Institute for Innovation and Development Strategy, Work Committee on Carbon Neutral Intelligent Industry Innovation, Beijing, China
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Song X: Chinese Academy of Science, Institute of Process Engineering, Beijing, China. University of Chinese Academy of Science, School of Chemical Engineering, Beijing, China
Li J: Chinese Academy of Science, Institute of Process Engineering, Beijing, China. University of Chinese Academy of Science, School of Chemical Engineering, Beijing, China
Zeng Y: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Nie Y: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Zhu M: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Lu D: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Zhang Y: Chinese Academy of Science, Institute of Process Engineering, Beijing, China
Xiao X: Chinese Academy of Science, Institute of Process Engineering, Beijing, China. China Institute for Innovation and Development Strategy, Work Committee on Carbon Neutral Intelligent Industry Innovation, Beijing, China
Li J: The University of Manchester, Department of Chemical Engineering, Manchester, United Kingdom. China Institute for Innovation and Development Strategy, Work Committee on Carbon Neutral Intelligent Industry Innovation, Beijing, China
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Journal Name
Systems and Control Transactions
Volume
5
First Page
1974
Last Page
1985
Year
2026
Publication Date
2026-06-12
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Original Submission
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PII: 1974-1985-110-SCT-5-2026, Publication Type: Journal Article
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LAPSE:2026.0449
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https://doi.org/10.69997/sct.103112
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Jun 12, 2026
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References Cited
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