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Many modern machine learning applications, such as multi-task learning, require finding optimal model parameters to trade-off multiple objective functions that may conflict with each other. The notion of the Pareto set allows us to focus on…

Optimization and Control · Mathematics 2022-09-05 Mao Ye , Qiang Liu

In single-objective optimization, it is well known that evolutionary algorithms also without further adjustments can tolerate a certain amount of noise in the evaluation of the objective function. In contrast, this question is not at all…

Neural and Evolutionary Computing · Computer Science 2023-08-25 Matthieu Dinot , Benjamin Doerr , Ulysse Hennebelle , Sebastian Will

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

Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…

Optimization and Control · Mathematics 2019-06-24 Stefan Banholzer , Bennet Gebken , Michael Dellnitz , Sebastian Peitz , Stefan Volkwein

Multi-Objective Evolutionary Algorithms (MOEAs) have been proved efficient to deal with Multi-objective Optimization Problems (MOPs). Until now tens of MOEAs have been proposed. The unified mode would provide a more systematic approach to…

Neural and Evolutionary Computing · Computer Science 2011-02-01 Bojin Zheng , Yuanxiang Li

In this study, we propose a novel multi-objective Bayesian optimization (MOBO) method to efficiently identify the Pareto front (PF) defined by risk measures for black-box functions under the presence of input uncertainty (IU). Existing BO…

Machine Learning · Statistics 2023-11-27 Yu Inatsu , Shion Takeno , Hiroyuki Hanada , Kazuki Iwata , Ichiro Takeuchi

Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains…

Machine Learning · Computer Science 2025-10-27 Lam Ngo , Huong Ha , Jeffrey Chan , Hongyu Zhang

The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then…

Machine Learning · Statistics 2024-06-24 Ben Tu , Nikolas Kantas , Robert M. Lee , Behrang Shafei

Multi-objective reinforcement learning (MORL) provides an effective solution for decision-making problems involving conflicting objectives. However, achieving high-quality approximations to the Pareto policy set remains challenging,…

Artificial Intelligence · Computer Science 2026-03-23 Tianmeng Hu , Biao Luo

Recent advancements in image customization exhibit a wide range of application prospects due to stronger customization capabilities. However, since we humans are more sensitive to faces, a significant challenge remains in preserving…

Computer Vision and Pattern Recognition · Computer Science 2025-09-09 Yufeng Cheng , Wenxu Wu , Shaojin Wu , Mengqi Huang , Fei Ding , Qian He

We introduce a nonmonotone extension of the Front Descent framework for multiobjective optimization. The method uses novel nonmonotone line searches that allow temporary increases in some objective functions. To our knowledge, this is the…

Optimization and Control · Mathematics 2025-09-03 Pierluigi Mansueto

For regular Pareto Fronts (PFs), such as those that are smooth, continuous, and uniformly distributed, using fixed weight vectors is sufficient for multi-objective optimization approaches using decomposition. However, when encountering…

Neural and Evolutionary Computing · Computer Science 2025-11-18 Xiaojing Han , Yuanxin Li

In the domain of multi-objective optimization, evolutionary algorithms are distinguished by their capability to generate a diverse population of solutions that navigate the trade-offs inherent among competing objectives. This has catalyzed…

Neural and Evolutionary Computing · Computer Science 2025-01-07 Yuxin Ma , Zherui Zhang , Ran Cheng , Yaochu Jin , Kay Chen Tan

Multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set, each independently mapping to the same Pareto-Front. Prevalent multi-objective evolutionary algorithms are not purely designed…

Neural and Evolutionary Computing · Computer Science 2021-02-04 Monalisa Pal , Sanghamitra Bandyopadhyay

In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…

Data Structures and Algorithms · Computer Science 2020-10-22 Heiko Röglin

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

Multi-objective preference alignment of large language models (LLMs) is critical for developing AI systems that are more configurable, personalizable, helpful, and safe. However, optimizing model outputs to satisfy diverse objectives with…

Computation and Language · Computer Science 2025-03-04 Raghav Gupta , Ryan Sullivan , Yunxuan Li , Samrat Phatale , Abhinav Rastogi

Offline optimization aims to maximize a black-box objective function with a static dataset and has wide applications. In addition to the objective function being black-box and expensive to evaluate, numerous complex real-world problems…

Machine Learning · Computer Science 2024-06-07 Ke Xue , Rong-Xi Tan , Xiaobin Huang , Chao Qian

In this paper, an evolutionary many-objective optimization algorithm based on corner solution search (MaOEA-CS) was proposed. MaOEA-CS implicitly contains two phases: the exploitative search for the most important boundary optimal solutions…

Artificial Intelligence · Computer Science 2018-06-11 Xinye Cai , Haoran Sun , Chunyang Zhu , Zhenyu Li , Qingfu Zhang

In multi-objective optimization, the set of optimal trade-offs -- the Pareto front -- often contains regions that are extremely steep or flat. The Pareto optimal points in these regions are typically of limited interest for decision-making,…

Optimization and Control · Mathematics 2026-02-26 Markus Herrmann-Wicklmayr , Kathrin Flaßkamp