GENETIC ALGORITHM WITH FITNESS PENALIZED FOR SELECTION OF VARIABLES IN LOGISTIC REGRESSION: AN APPLICATION TO THE DIAGNOSIS OF BREAST CANCER

This paper proposes a Genetic Algorithm for variable selection in logistic regression, applied to breast cancer diagnosis with 569 patients and 30 morphological variables — over one billion possible subsets, making exhaustive search infeasible. Three approaches are compared: Complete Model, Bidirectional Stepwise and Genetic Algorithm with binary chromosome. The main methodological contribution is the evolution of the fitness function, which goes beyond the sole use of the AIC metric by incorporating a multicollinearity penalty based on the log-scale mean VIF. The Genetic Algorithm outperformed Stepwise in model fit (AIC 19.2 points lower), discrimination (AUC=0.9898) and clinical sensitivity (98.41%). Ten independent initializations confirmed robustness, revealed two competing local optima and identified four variables present in all runs. An a posteriori importance and interaction analysis, based on chromosome gene flipping and extended to preserve the interaction sign, distinguished redundant from synergistic pairs and exposed limitations of the VIF penalty.