Multi-objective Clustering Algorithm Applied to the MathE Categorization Problem

This work explores bio-inspired strategies and clustering techniques to propose an automatic clustering algorithm, named Multi-objective Clustering Algorithm (MCA). This algorithm uses a set of measure combinations to define the optimal number of clusters and the partitioning of the elements, minimizing an intra-clustering measure and maximizing an inter-clustering one. The MathE platform is an educational tool whose main objective is to assist students facing challenges in Mathematics at higher education level. Based on previous studies, the opinions of lecturers and students diverge regarding the difficulty level of the questions available on the platform. Therefore, this research aims to explore and develop a new clustering method for question categorization, taking into account the opinions of both lecturers and students about the difficulty levels of the questions. The Multi-objective Clustering Algorithm (MCA) is proposed to group the questions into clusters representing the difficulty level of the platform’s questions. Compared with the k-means algorithm, the MCA results exhibit outstanding performance. Through a combination of multi-objective clustering measures, the MCA successfully achieved a set of optimal solutions (Hybrid Pareto front). This method empowers the decision-maker, enabling them to choose the most appropriate solution based on additional insights beyond the model.