A Mathematics-Inspired Metaheuristic Based on Secant-Method Updates for Robust Parameter Estimation in Cancer Research

Goal: Distinguish lung adenocarcinoma (LUAD) vs lung squamous cell carcinoma (LUSC) using transcriptomic profiles.Challenge: High-dimensional, heterogeneous data makes optimization difficult.Method: We propose the Secant Optimization Algorithm (SOA), a derivative-free optimizer inspired by the classical secant method, and use it to jointly select genes and tune XGBoost.Data: TCGA-LUAD, TCGA-LUSC; external validation on GEO GSE81089.Performance: Accuracy 0.9580; AUC 0.9879. Interpretability: SHAP highlights validated markers (DSG3, KRT5, SPRR2E), supported by protein interaction analysis.Take-home: SOA enables scalable and interpretable molecular subtyping and biomarker discovery.