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.
Decision-making is posing an increasingly formidable challenge to investors because of the growing number of alternatives available in financial markets. A hot area of research over the past few decades has been portfolio optimization that seeks to determine how much an investor…
In multi-objective combinatorial optimization, unsupported non-dominated points typically outnumber supported points and are often significantly more challenging to compute. Recent studies show that extreme supported non-dominated points provide high-quality representations of th…
The continuous integral R2 indicator is a Pareto-compliant refinement of the classical finite-weight-vector R2 indicator, used in performance assessment, bounded archiving for a-posteriori multi-objective optimization, and skyline selection in databases. This work introduces a bi…
Classical space-filling designs often fail to provide reliable statistical results for Exploratory Landscape Analysis (ELA) when only limited evaluation budgets are available, as commonly occurs in high-dimensional problems or other resource-constrained settings, resulting in noi…
This paper presents a unified geometric, mathematical, and computational framework for the generation of the $complete$ admissible Pareto frontier. Several existing methods are structurally unable to capture the complete admissible Pareto frontier. These include widely used metho…
Soft metamaterials provide a promising platform for robotics, biomedical devices, and flexible electronics. The localized mechanical responses by nonuniform excitation are ubiquitous in soft materials, yet their controlled transmission across assemblies remains largely overlooked…