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We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…

Optimization and Control · Mathematics 2015-01-13 Bram L. Gorissen , Dick den Hertog

An important task in multi-objective optimization is generating the Pareto front -- the set of all Pareto-optimal compromises among multiple objective functions applied to the same set of variables. Since this task can be computationally…

Quantum Physics · Physics 2025-11-04 Andrew D. King

In this work, we propose a novel method to tackle the problem of multiobjective optimization under parameteric uncertainties, by considering the Conditional Pareto Sets and Conditional Pareto Fronts. Based on those quantities we can define…

Optimization and Control · Mathematics 2026-01-15 Victor Trappler , Céline Helbert , Rodolphe Le Riche

Multi-objective alignment from human feedback (MOAHF) in large language models (LLMs) is a challenging problem as human preferences are complex, multifaceted, and often conflicting. Recent works on MOAHF considered a-priori multi-objective…

Machine Learning · Computer Science 2024-12-10 Subhojyoti Mukherjee , Anusha Lalitha , Sailik Sengupta , Aniket Deshmukh , Branislav Kveton

Scalarisation functions are widely employed in MORL algorithms to enable intelligent decision-making. However, these functions often struggle to approximate the Pareto front accurately, rendering them unideal in complex, uncertain…

Machine Learning · Computer Science 2025-11-21 Muhammad Sa'ood Shah , Asad Jeewa

A common goal in evolutionary multi-objective optimization is to find suitable finite-size approximations of the Pareto front of a given multi-objective optimization problem. While many multi-objective evolutionary algorithms have proven to…

Neural and Evolutionary Computing · Computer Science 2024-09-26 Hao Wang , Angel E. Rodriguez-Fernandez , Lourdes Uribe , André Deutz , Oziel Cortés-Piña , Oliver Schütze

A new method to estimate the Pareto Front (PF) in bi-objective optimization problems is presented. Assuming a continuous PF, the approach, named ROBBO (RObust and Balanced Bi-objective Optimization), needs to sample at most a finite,…

Optimization and Control · Mathematics 2025-06-24 Roberto Boffadossi , Marco Leonesio , Lorenzo Fagiano

There is a well known intrinsic trade-off between the fairness of a representation and the performance of classifiers derived from the representation. Due to the complexity of optimisation algorithms in most modern representation learning…

Machine Learning · Statistics 2025-10-27 Mark Kozdoba , Binyamin Perets , Shie Mannor

Many real-world optimization problems such as engineering design can be eventually modeled as the corresponding multiobjective optimization problems (MOPs) which must be solved to obtain approximate Pareto optimal fronts. Multiobjective…

Neural and Evolutionary Computing · Computer Science 2021-11-12 Wang Chen , Jian Chen , Weitian Wu , Xinmin Yang , Hui Li

Federated learning has emerged as a promising, massively distributed way to train a joint deep model over large amounts of edge devices while keeping private user data strictly on device. In this work, motivated from ensuring fairness among…

Machine Learning · Computer Science 2023-01-25 Zeou Hu , Kiarash Shaloudegi , Guojun Zhang , Yaoliang Yu

any practical multiobjective optimization (MOO) problems include discrete decision variables and/or nonlinear model equations and exhibit disconnected or smooth but nonconvex Pareto surfaces. Scalarization methods, such as the weighted-sum…

Optimization and Control · Mathematics 2024-10-23 Ye Seol Lee , George Jackson , Amparo Galindo , Claire S. Adjiman

In one of our earlier works, we proposed to approximate Pareto fronts to multiobjective optimization problems by two-sided approximations, one from inside and another from outside of the feasible objective set, called, respectively, lower…

Optimization and Control · Mathematics 2018-04-24 Ignacy Kaliszewski , Janusz Miroforidis

Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives…

Optimization and Control · Mathematics 2023-02-01 C. Yalçın Kaya , Helmut Maurer

Choices in scientific research and management require balancing multiple, often competing objectives.Multiple-objective optimization (MOO) provides a unifying framework for solving multiple objective problems. Model selection is a critical…

Applications · Statistics 2018-10-26 Perry Williams , William Kendall , Mevin Hooten

Optimizing multiple, non-preferential objectives for mixed-variable, expensive black-box problems is important in many areas of engineering and science. The expensive, noisy, black-box nature of these problems makes them ideal candidates…

Machine Learning · Computer Science 2022-11-15 Haris Moazam Sheikh , Philip S. Marcus

Many practical applications of multi-objective optimization (MOO), including engineering design, autonomous systems, and machine learning, often yield complex Pareto frontiers (e.g., discontinuous, degenerate, or non-convex), which pose…

Machine Learning · Computer Science 2026-03-31 Phuong Mai Dinh , Van-Nam Huynh

The discovery of therapeutic molecules is fundamentally a multi-objective optimization problem. One formulation of the problem is to identify molecules that simultaneously exhibit strong binding affinity for a target protein, minimal…

Quantitative Methods · Quantitative Biology 2023-10-17 Jenna C. Fromer , David E. Graff , Connor W. Coley

We introduce Pareto-NRPA, a new Monte-Carlo algorithm designed for multi-objective optimization problems over discrete search spaces. Extending the Nested Rollout Policy Adaptation (NRPA) algorithm originally formulated for single-objective…

Artificial Intelligence · Computer Science 2025-11-04 Noé Lallouet , Tristan Cazenave , Cyrille Enderli

The issue of fairness in recommendation is becoming increasingly essential as Recommender Systems touch and influence more and more people in their daily lives. In fairness-aware recommendation, most of the existing algorithmic approaches…

Information Retrieval · Computer Science 2022-01-04 Yingqiang Ge , Xiaoting Zhao , Lucia Yu , Saurabh Paul , Diane Hu , Chu-Cheng Hsieh , Yongfeng Zhang

Bayesian optimization (BO) is a popular method to optimize expensive black-box functions. It efficiently tunes machine learning algorithms under the implicit assumption that hyperparameter evaluations cost approximately the same. In…

Machine Learning · Computer Science 2020-11-25 Gauthier Guinet , Valerio Perrone , Cédric Archambeau
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