A hierarchical metaheuristic framework for CPT-based soil liquefaction prediction with Kolmogorov–Arnold Network variants

Soil liquefaction is a critical geotechnical hazard that threatens the safety of civil infrastructure under seismic loading, necessitating robust and interpretable prediction models. This study proposes a hierarchical framework for CPT-based soil liquefaction prediction using meta-heuristic-optimized Kolmogorov–Arnold Network (KAN) variants. The framework follows a two-stage optimization strategy. First, six state-of-the-art meta-heuristic algorithms are statistically compared to identify the most effective optimization method. Second, the selected algorithm is employed to optimize six KAN variants, including FastKAN, EfficientKAN, FourierKAN, ChebyKAN, JacobiRKAN, and PadéRKAN. Statistical comparisons based on the Wilcoxon signed-rank test demonstrate that the Colony-Based Search algorithm (CSA) achieves lower objective-function values than the competing meta-heuristics (p<0.01) and is therefore adopted as the core optimization strategy. Performance evaluation reveals that the CSA-optimized ChebyKAN model achieves the highest predictive accuracy, with an F1 Score of 0.8875 ± 0.011 and an AUC of 0.9115 ± 0.013. Pairwise McNemar tests detected no statistically significant difference in classification decisions for any evaluated model pair (p>0.01). SHapley Additive exPlanations analysis identified qc, qc1N, and amax as the variables with the largest model-specific attributions, whereas d, c, and σv received lower attributions. A cost-sensitive error analysis further showed that ChebyKAN produced the lowest false-negative rate and the lowest asymmetric error cost under 5:1 and 10:1 false-negative-to-false-positive cost scenarios, supporting its conservative behaviour for safety-critical liquefaction screening. The results establish the proposed CSA–KAN framework as a reliable, high-accuracy, and interpretable solution for CPT-based soil liquefaction assessment in geotechnical engineering practice.