A tri-objective approach to support vector machines with cost-based feature selection

Support Vector Machines (SVMs) are among the most widely used algorithms for classification tasks due to their strong predictive performance. Feature selection is crucial in high-dimensional datasets to reduce computational costs, particularly when acquiring features involves additional expenses. In such cases, the problem must consider not only classifier performance but also the cost associated with selected features. This work investigates the effects and benefits of adding a third objective—cost minimisation—to the two classical SVM objectives when feature cost information is available. To this end, we propose an SVM model that extends the classical objectives by incorporating the minimisation of classifier cost. This results in a tri-objective formulation, increasing the complexity of an already challenging optimisation problem, and we show that solving certain real-world instances exactly is computationally infeasible. We then adapt the best existing metaheuristic developed for the bi-objective version to simultaneously handle all three objectives. The computational study demonstrates the strong performance of this approach, effectively identifying solutions that balance high classification accuracy with reduced cost. The applicability of the method is illustrated through a real-world case study in the healthcare context.