Integrating K-means clustering with entropy-weighted TOPSIS for large-scale multi-criteria decision making

Multi-Criteria Decision Making (MCDM) methods like Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) consider all the alternatives at once, which can be computationally expensive and confusing as the problem size increases to hundreds or even thousands of alternatives, as is common in supplier selection, healthcare resource allocation, and renewable energy assessment problems. This paper introduces an entropy-weighted hierarchical clustering algorithm for implementing the TOPSIS method. The proposed approach first classifies alternatives into homogeneous clusters using the K-means algorithm and then calculates the weights of the objective criterion based on Shannon entropy. Next, TOPSIS is run within each cluster, and the representatives are selected. The framework is then tested using two different data sets, each characterized by its own size and nature: synthetic data, including 1,000 alternatives across 12 criteria, and the Global Renewable Energy and Indicators Dataset, containing 2,500 actual alternatives across 53 criteria. Quality of clustering is measured through four internal validity indices (Elbow, Silhouette, Davies-Bouldin, and Calinski-Harabasz), while the quality of ranking is tested against up to six standard MCDM techniques through Spearman and Kendall rank correlations; robustness is measured under weight perturbations ranging up to ± 20%, while scalability is measured on alternative samples of sizes from 100 to 2,500. For both data sets, the ranking procedure presented in this work returns the highest-ranked alternative but does not guarantee a global optimum, since only cluster representatives are considered in the algorithm's second phase. The presented ranking procedure agrees with at least one benchmark ranking for the small set of representative cluster objects. The chosen alternative is invariant to changes in the weight vector, but the algorithm's complexity increases with the number of alternatives.