A thinking innovation strategy based Northern goshawk optimizer enhanced extreme learning machine for bankruptcy prediction problems.

Bankruptcy risk prediction, a core issue in financial risk management, plays a critical role in assessing corporate financial health and supporting decision-making for financial institutions. Traditional machine learning models often struggle with parameter optimization when handling high-dimensional, nonlinear financial data. In contrast, metaheuristic algorithms, owing to their global search capabilities, have emerged as effective tools to enhance model performance. This paper proposes a novel bankruptcy prediction model that integrates a Kernel Extreme Learning Machine (KELM) with an improved Northern goshawk Optimizer (TIS_NGO), which incorporates a Thought-Inspired Strategy (TIS). The enhancements to TIS_NGO include a divergence-based thought innovation mechanism, a prey-attacking strategy inspired by differential evolution, and a centroid opposition-based boundary control mechanism. Experimental evaluations on the CEC2017 and CEC2022 benchmark suites demonstrate that TIS_NGO outperforms the standard NGO as well as other well-known algorithms such as Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO) in terms of convergence speed and solution accuracy. The optimized KELM, with TIS_NGO-tuned penalty parameter [Formula: see text] and kernel parameter [Formula: see text], achieves high classification accuracy and robustness on the Wieslaw bankruptcy dataset. These results validate the effectiveness of combining improved metaheuristic algorithms with machine learning models for financial risk forecasting. Overall, the proposed method offers a promising approach to improving the accuracy and stability of bankruptcy prediction, thereby contributing a new technical pathway for early warning in the financial domain.