Comparing Scalar Objective Functions for Multi-Criteria Engineering Optimization
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A utility-based analysis of equilibria in multi-objective normal form games
In multi-objective multi-agent systems (MOMAS), agents explicitly consider the possible tradeoffs between conflicting objective functions. We argue that compromises between competing objectives in MOMAS should be analyse…
FormMulti-Weight Ranking for Multi-Criteria Decision Making
Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it abs…
Decision MakingMulti-Objective Multi-Agent Decision Making: A Utility-based Analysis and Survey
The majority of multi-agent system (MAS) implementations aim to optimise agents' policies with respect to a single objective, despite the fact that many real-world problem domains are inherently multi-objective in nature…
Decision MakingEvolutionary Many-Objective Optimization Based on Adversarial Decomposition
The decomposition-based method has been recognized as a major approach for multi-objective optimization. It decomposes a multi-objective optimization problem into several single-objective optimization subproblems, each o…
What Makes an Effective Scalarising Function for Multi-Objective Bayesian Optimisation?
Performing multi-objective Bayesian optimisation by scalarising the objectives avoids the computation of expensive multi-dimensional integral-based acquisition functions, instead of allowing one-dimensional standard acqu…
Bayesian Optimisation