Hybrid Multiobjective Framework for Boolean Satisfiability Optimization With Application to Financial Risk Prediction

Financial distress prediction demands models that balance complex pattern recognition with interpretable decision logic. This study reframes the prediction task as a Boolean satisfiability (SAT) problem and introduces a hybrid neurosymbolic framework, Hopfield neural network (HNN)–RANkSATRA, that integrates HNNs with metaheuristic optimization to overcome the local minima limitations of conventional HNNs. Two hybrid architectures are developed: hybrid dragonfly–Hopfield algorithm (HNN–RANkSAT–HAD) and hybrid evolution strategy–Hopfield algorithm (HNN–RANkSAT–HES), both employing the RANkSATRA method for reverse logic mining from financial data. In computational simulations on synthetic RANkSAT benchmarks, HNN–RANkSAT–HDA consistently outperformed both the baseline HNN–RANkSAT and the HES variant, achieving superior global minima ratio (Zm = 0.90), convergence speed (10.8 iterations), energy minimization (0.10), and model calibration (log-loss = 0.34). The baseline model demonstrated a scalability constraint, plateauing in performance beyond 70 neurons. Applied to three real-world financial distress datasets, the German Credit dataset (GCSD), the Polish Companies dataset (PCDS), and the Taiwanese Bankruptcy dataset (TDS), the framework demonstrated robust predictive utility. HNN–RANkSAT–HDA achieved the highest median testing accuracy (0.941), F1-score (0.938), and AUC (0.934), while also showing the best probabilistic calibration, evidenced by the lowest average log-loss (0.315). Nonparametric statistical tests (Friedman and Wilcoxon signed-rank) confirmed a significant performance hierarchy: HNN–RANkSAT–HDA > HNN–RANkSAT–HES > HNN–RANkSAT (p