A Pareto front-based approach for constructing composite index of sustainability without weights: A comparative study of implementations

A composite index based on selected indicators is a widely used tool for guiding, monitoring, and evaluating a society's level of sustainability. However, determining the weight of each indicator is typically a methodologically problematic and highly controversial process. This paper proposes a weightless strategy for constructing composite sustainability indices based on the mathematical optimization concept of Pareto fronts. The core idea is to model each indicator as an individual objective and explore Pareto fronts within the resulting multi-objective solution space. In practice, a total of 24 typical implementations of the strategy were realized to represent four categories with varying parameter settings, i.e., straightforward/hierarchical implementations with/without avoiding basic indicator accuracy issues. Comparative experiments demonstrated that a hierarchical approach utilizing the goodness of variance fit-based (GVF = 0.80) natural breaks to nullify accuracy problems is the most effective implementation. To demonstrate its usefulness, the strategy implemented using this approach was applied to analyze the world's sustainability by revising the well-known sustainable society index. This study provides a novel paradigm of composite sustainability indices and represents the first assessment of world sustainability using multiple criteria (indicators) without weights.