Open Access

ARTICLE

A Novel Variable-Fidelity Kriging Surrogate Model Based on Global Optimization for Black-Box Problems

Yi Guan¹, Pengpeng Zhi^2,3,*, Zhonglai Wang^1,4,*

1 School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China
2 Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou, 313000, China
3 Institute of Electronic and Information Engineering of University of Electronic Science and Technology of China in Guangdong, Dongguan, 523808, China
4 Institute of Electronics and Information Industry Technology of Kash, Kash, 844000, China

* Corresponding Authors: Pengpeng Zhi. Email: ; Zhonglai Wang. Email:

(This article belongs to the Special Issue: Data-Driven and Physics-Informed Machine Learning for Digital Twin, Surrogate Modeling, and Model Discovery, with An Emphasis on Industrial Applications)

Computer Modeling in Engineering & Sciences 2025, 144(3), 3343-3368. https://doi.org/10.32604/cmes.2025.069515

Received 25 June 2025; Accepted 25 August 2025; Issue published 30 September 2025

Abstract

Variable-fidelity (VF) surrogate models have received increasing attention in engineering design optimization as they can approximate expensive high-fidelity (HF) simulations with reduced computational power. A key challenge to building a VF model is devising an adaptive model updating strategy that jointly selects additional low-fidelity (LF) and/or HF samples. The additional samples must enhance the model accuracy while maximizing the computational efficiency. We propose ISMA-VFEEI, a global optimization framework that integrates an Improved Slime-Mould Algorithm (ISMA) and a Variable-Fidelity Expected Extension Improvement (VFEEI) learning function to construct a VF surrogate model efficiently. First, A cost-aware VFEEI function guides the adaptive LF/HF sampling by explicitly incorporating evaluation cost and existing sample proximity. Second, ISMA is employed to solve the resulting non-convex optimization problem and identify global optimal infill points for model enhancement. The efficacy of ISMA-VFEEI is demonstrated through six numerical benchmarks and one real-world engineering case study. The engineering case study of a high-speed railway Electric Multiple Unit (EMU), the optimization objective of a sanding device attained a minimum value of 1.546 using only 20 HF evaluations, outperforming all the compared methods.

---

Keywords

---