Analyzing bi-objective optimization Pareto fronts using square shape slope index and NSGA-II: A multi-criteria decision-making approach

Abstract

This paper introduces the Square Shape Slope Index (SSSI), a novel post-optimization multi-criteria decision-making (MCDM) approach for analyzing Pareto fronts generated from bi-objective optimization problems. SSSI leverages multiple Utopia and Nadir points—guided by a user-defined priority scale—to form a dynamic square region around particular segments of the Pareto front. Within this region, slope-based evaluations are used to rank solutions based on user preferences and criteria. The method’s effectiveness is demonstrated through empirical tests on diverse benchmark functions and real-world scenarios, such as energy distribution and portfolio optimization, each encompassing various shapes and patterns of the Pareto front. In addition, SSSI is compared against established decision-making approaches both geometrically and analytically using different aggregation methods. To account for the stochastic nature of evolutionary algorithms, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) is employed to generate Pareto fronts for each test function. Results confirm the robustness and adaptability of SSSI, offering a clear and flexible framework for balancing conflicting objectives in multi-objective decision-making contexts.