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

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.