🤖 AI Summary
This study addresses the challenge of selecting a single solution from the Pareto front in multi-objective engineering optimization through scalarization, noting that different scalarizing functions exhibit significant differences in attainability, preference articulation, and coverage of non-supported solutions. The authors systematically compare four normalized scalarization approaches—weighted sum, achievement scalarizing function, desirability function, and fuzzy logic—on both convex and concave Pareto fronts, evaluating their performance via analytical control experiments in terms of attainable regions, selection density, sensitivity, and parameter interpretability. The findings reveal structural limitations of the weighted sum method on concave fronts, while the other three methods effectively cover non-supported regions. Notably, the desirability function introduces nonlinear preference mapping, and the fuzzy approach enables reference-dependent and non-separable modeling of engineering preferences, offering new insights for scalarization under complex preference structures.
📝 Abstract
Scalar objective functions are required when a multi-criteria optimization problem must yield a single preferred design rather than only a Pareto set. The choice of scalarization influences which compromise is selected, how preference parameters are interpreted, and whether non-supported Pareto regions can be reached. This paper compares four formulations for normalized bi-criteria minimization: weighted sums, achievement scalarizing functions, desirability functions, and a fuzzy-logic-based formulation. Two analytically defined Pareto fronts, one convex and one concave, isolate the effect of the objective formulation from numerical optimizer behavior. The comparison focuses on reachable Pareto regions, parameter-induced selection density, compensation between criteria, sensitivity, and interpretability. Results show that weighted sums are simple but structurally limited on concave fronts, while achievement, desirability, and fuzzy formulations reach interior non-supported regions through different mechanisms. Desirability functions introduce nonlinear single-criterion preference mappings, whereas fuzzy rules express nonseparable and reference-dependent engineering preferences.