Comparing Scalar Objective Functions for Multi-Criteria Engineering Optimization

• URL: http://arxiv.org/abs/2606.28541v1
• Date: Fri, 26 Jun 2026 18:51:16 GMT
• Title: Comparing Scalar Objective Functions for Multi-Criteria Engineering Optimization
• Abstract summary: This paper compares four formulations for normalized bi-criteria minimization: weighted sums, achievement scalarizing functions, desirability functions, and a fuzzy-logic-based formulation.<n>Two analytically defined Pareto fronts, one convex and one concave, isolate the effect of the objective formulation from numerical behavior.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Preference Data Selection for Mitigating the Alignment Tax in Large Language Models [52.18310687523229]
  BALIGN is a balanced data selection strategy that mitigates catastrophic forgetting while optimizing alignment efficacy.<n>By aggregating three key data-centric features into a unified composite risk score, BALIGN systematically filters out high-risk preference samples.<n>Experiments on standard human preference datasets demonstrate that BALIGN strongly preserves foundational capabilities without compromising alignment gains.
  arXiv  Detail & Related papers  (2026-08-25T07:58:42Z)
• Selective Ensemble Based on Preference-Directed Multi-Objective Bandits [90.75513823660775]
  We formalize a sequential decision problem under partially specified linear preferences.<n>We then propose a preference-directed upper confidence bound (PrefUCB) algorithm.<n> Experiments on large pre-trained model selective ensemble tasks and online asset allocation under institutional mandates validate our method.
  arXiv  Detail & Related papers  (2026-06-20T07:52:46Z)
• Differential Voting: Loss Functions For Axiomatically Diverse Aggregation of Heterogeneous Preferences [6.3240435869587515]
  Reinforcement learning from human feedback can be viewed as a form of voting, where the aggregation mechanism is defined by the loss function.<n>We introduce Differential Voting, a framework that constructs instance-wise, differentiable loss functions whose population-level optima provably correspond to classical voting rules.<n>Our analysis shows how design choices in loss geometry-such as margin sensitivity and boundary concentration-directly translate into normative aggregation behavior.
  arXiv  Detail & Related papers  (2026-01-25T03:59:51Z)
• From Coefficients to Directions: Rethinking Model Merging with Directional Alignment [66.99062575537555]
  We introduce a unified geometric framework, emphMerging with Directional Alignment (method), which aligns directional structures consistently in both the parameter and feature spaces.<n>Our analysis shows that directional alignment improves structural coherence, and extensive experiments across benchmarks, model scales, and task configurations further validate the effectiveness of our approach.
  arXiv  Detail & Related papers  (2025-11-29T08:40:58Z)
• Beyond Coordinates: Meta-Equivariance in Statistical Inference [0.0]
  Optimal statistical decisions should transcend the language used to describe them.<n>How do we guarantee that the choice of coordinates does not subtly dictate the solution?<n>We first analyse the optimal combination of twoally normal estimators under a strictly convex trace-AMSE risk.
  arXiv  Detail & Related papers  (2025-04-14T19:40:39Z)
• An incremental preference elicitation-based approach to learning potentially non-monotonic preferences in multi-criteria sorting [53.36437745983783]
  We first construct a max-margin optimization-based model to model potentially non-monotonic preferences. We devise information amount measurement methods and question selection strategies to pinpoint the most informative alternative in each iteration. Two incremental preference elicitation-based algorithms are developed to learn potentially non-monotonic preferences.
  arXiv  Detail & Related papers  (2024-09-04T14:36:20Z)
• Projection-Free Variance Reduction Methods for Stochastic Constrained Multi-Level Compositional Optimization [34.628967272528044]
  This paper investigates projection-free algorithms for constrained multi-level optimization functions. By using a stage-wise adaptation, we obtain complexities for convex and strongly convex functions.
  arXiv  Detail & Related papers  (2024-06-06T06:56:56Z)
• Controllable Preference Optimization: Toward Controllable Multi-Objective Alignment [103.12563033438715]
  Alignment in artificial intelligence pursues consistency between model responses and human preferences as well as values. Existing alignment techniques are mostly unidirectional, leading to suboptimal trade-offs and poor flexibility over various objectives. We introduce controllable preference optimization (CPO), which explicitly specifies preference scores for different objectives.
  arXiv  Detail & Related papers  (2024-02-29T12:12:30Z)
• Smoothing the Edges: Smooth Optimization for Sparse Regularization using Hadamard Overparametrization [10.009748368458409]
  We present a framework for smooth optimization of explicitly regularized objectives for (structured) sparsity. Our method enables fully differentiable approximation-free optimization and is thus compatible with the ubiquitous gradient descent paradigm in deep learning.
  arXiv  Detail & Related papers  (2023-07-07T13:06:12Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• A sampling criterion for constrained Bayesian optimization with uncertainties [0.0]
  We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. To tackle such problems, we propose a new Bayesian optimization method. It applies to the situation where the uncertainty comes from some of the inputs, so that it becomes possible to define an acquisition criterion in the joint controlled-uncontrolled input space.
  arXiv  Detail & Related papers  (2021-03-09T20:35:56Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.