P3DE: A novel integration of deep ensemble learning and parameter-less optimization for superior breast cancer biomarker discovery

Breast cancer is a leading public health concern that demands improved strategies for early diagnosis and prognosis. In this study, we propose P3DE, a novel computational framework that combines deep ensemble learning with the Parameter-less Population Pyramid (P3) metaheuristic for the identification of breast cancer biomarkers from gene expression data. P3DE integrates multiple autoencoders with diverse activation functions and dynamically computes ensemble weights based on reconstruction performance, enabling robust and adaptive feature selection without manual parameter tuning. Applied to the GSE42568 dataset, P3DE achieved outstanding classification performance (97.22% accuracy, 100% precision, 96.88% recall, 98.41% F1 and F2 scores, and 94.02% TMCC), outperforming conventional and state-of-the-art metaheuristic methods. Biological analysis revealed that the selected genes are enriched in key pathways and processes associated with breast cancer, such as peptide hormone response, membrane raft signaling, protein heterodimerization, and the PPAR signaling pathway. Notably, several identified genes (ALDH1A1, FGF2, TOP2A, EPCAM, CDH1) are linked to drugs, emphasizing their potential in targeted therapy. These results demonstrate the effectiveness of P3DE in uncovering biologically meaningful and clinically actionable biomarkers, highlighting the promise of hybrid, parameter-free computational models in precision oncology.