Multi-Objective Optimization

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21 papers in the last four weeks, up 320% on the four weeks before. 0.2% of all new papers.

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Latest papers 171

Apr 21, 2026cs.IR

Think Before Writing: Feature-Level Multi-Objective Optimization for Generative Citation Visibility

Generative answer engines expose content through selective citation rather than ranked retrieval, fundamentally altering how visibility is determined. This shift calls for new optimization methods beyond traditional search engine optimization. Existing generative engine optimization (GEO) approaches primarily rely on token-level text rewriting, offering limited interpretability and weak control over the trade-off between citation visibility and content quality. We propose FeatGEO, a feature-level, multi-objective optimization framework that abstracts webpages into interpretable structural, content, and linguistic properties. Instead of directly editing text, FeatGEO optimizes over this feature space and uses a language model to realize feature configurations into natural language, decoupling high-level optimization from surface-level generation. Experiments on GEO-Bench across three generative engines demonstrate that FeatGEO consistently improves citation visibility while maintaining or improving content quality, substantially outperforming token-level baselines. Further analyses show that citation behavior is more strongly influenced by document-level content properties than by isolated lexical edits, and that the learned feature configurations generalize across language models of different scales.

Zikang Liu, Peilan Xu

School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China.

Generative Engine Optimization Multi-Objective Optimization

Apr 20, 2026cs.LG

Barrier-enforced multi-objective optimization for direct point and sharp interval forecasting

This paper proposes a multi-step probabilistic forecasting framework using a single neural-network based model to generate simultaneous point and interval forecasts. Our approach ensures non-crossing prediction intervals (PIs) through a model structure design that strictly satisfy a target coverage probability (PICP) while maximizing sharpness. Unlike existing methods that rely on manual weight tuning for scalarized loss functions, we treat point and PI forecasting as a multi-objective optimization problem, utilizing multi-gradient descent to adaptively select optimal weights. Key innovations include a new PI loss function based on an extended log-barrier with an adaptive hyperparameter to guarantee the coverage, a hybrid architecture featuring a shared temporal model with horizon-specific submodels, and a training strategy. The proposed loss is scale-independent and universally applicable; combined with our training algorithm, the framework eliminates trial-and-error hyperparameter tuning for balancing multiple objectives. Validated by an intra-day solar irradiance forecasting application, results demonstrate that our proposed loss consistently outperforms those in current literature by achieving target coverage with the narrowest PI widths. Furthermore, when compared against LSTM encoder-decoder and Transformer architectures--including those augmented with Chronos foundation models--our method remains highly competitive and can be seamlessly adapted to any deep learning structure.

Worachit Amnuaypongsa, Yotsapat Suparanonrat, Pana Wanitchollakit +1

Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand · Department of Computer Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, Thailand

Multi-Objective Optimization Probabilistic Time Series Forecasting Regression Prediction Intervals

Apr 20, 2026math.OC

The Magnitude of Dominated Sets: A Pareto Compliant Indicator Grounded in Metric Geometry

We investigate \emph{magnitude} as a new unary and strictly Pareto-compliant quality indicator for finite approximation sets to the Pareto front in multiobjective optimization. Magnitude originates in enriched category theory and metric geometry, where it is a notion of size or point content for compact metric spaces and a generalization of cardinality. For dominated regions in the

\ell_1

box setting, magnitude is close to hypervolume but not identical: it contains the top-dimensional hypervolume term together with positive lower-dimensional projection and boundary contributions. This paper gives a first theoretical study of magnitude as an indicator. We consider multiobjective maximization with a common anchor point. For dominated sets generated by finite approximation sets, we derive an all-dimensional projection formula, prove weak and strict set monotonicity on finite unions of anchored boxes, and thereby obtain weak and strict Pareto compliance. Unlike hypervolume, magnitude assigns positive value to boundary points sharing one or more coordinates with the anchor point, even when their top-dimensional hypervolume contribution vanishes. We then formulate projected set-gradient methods and compare hypervolume and magnitude on biobjective and three-dimensional simplex examples. Numerically, magnitude favors boundary-including populations and, for suitable cardinalities, complete Das--Dennis grids, whereas hypervolume prefers more interior-filling configurations. Computationally, magnitude reduces to hypervolume on coordinate projections; for fixed dimension this yields the same asymptotic complexity up to a factor

2^d-1

, and in dimensions two and three

Θ(n\log n)

time. These results identify magnitude as a mathematically natural and computationally viable alternative to hypervolume for finite Pareto front approximations.

Michael T. M. Emmerich

Faculty of Information Technology, University of Jyväskylä, Finland

Multi-Objective Optimization Pareto Optimization

Apr 20, 2026cs.NE

On Scalability of Multi-Objective Evolutionary Algorithms on Combinatorial Optimisation Problems

Scalability of evolutionary algorithms refers to assessing how their performance changes as problem size increases. In the area of multi-objective optimisation, research on the scalability of multi-objective evolutionary algorithms (MOEAs) has predominantly focussed on continuous problems. However, multi-objective combinatorial optimisation problems (MOCOPs) differ from continuous ones. Their discrete and rigid structure often brings rugged landscape, numerous local optimal solutions and disjoint global optimal regions. This leads to different behaviour of MOEAs. For example, SEMO, a simple MOEA without mating selection and diversity maintenance mechanisms, has been shown to be highly competitive, and in many cases to outperform more sophisticated MOEAs on MOCOPs. Yet, it remains unclear whether such findings hold for large-scale cases. In this paper, we conduct an empirical investigation into the scalability of MOEAs on combinatorial problems, with problem size from 50 to 5,000. Our results show that SEMO experiences a decline in convergence speed as dimensionality increases, compared to other MOEAs such as NSGA-II, SMS-EMOA and MOEA/D. We further demonstrate that the absence of crossover is a major contributor to SEMO's underperformance in large-scale problems, and that incorporating crossover into SEMO can substantially accelerate convergence in general, despite being detrimental in spreading solutions over the Pareto front.

Menghao Tang, Zimin Liang, Miqing Li

University of Birmingham Birmingham, United Kingdom

Evolutionary Optimization Multi-Objective Evolutionary Optimization Combinatorial Optimization Multi-Objective Optimization Genetic Algorithms

Apr 19, 2026cs.LG

RosettaSearch: Multi-Objective Inference-Time Search for Protein Sequence Design

We introduce RosettaSearch, an inference-time multi-objective optimization approach for backbone conditioned protein sequence design. We use large language models (LLMs) as a generative optimizer within a search algorithm capable of controlled exploration and exploitation, using rewards computed from RosettaFold3, a structure prediction model, under a strict computational budget. In a large-scale evaluation, we apply RosettaSearch to 400 suboptimal sequences generated by LigandMPNN (a state-of-the-art model trained for protein sequence design), recovering high-fidelity designs that LigandMPNN's single-pass decoding fails to produce. RosettaSearch's designs show improvements in structural fidelity metrics ranging between 18% to 68%, translating to a 2.5x improvement in design success rate. We observe that these gains in success rate are robust when RosettaSearch-designed sequences are evaluated with an independent structure prediction oracle (Chai-1) and generalize across two distinct LLM families (o4-mini and Gemini-3), with performance scaling consistently with reasoning capability. We further demonstrate that RosettaSearch improves the sequence fidelity of ProteinMPNN designs for de novo backbones from the Dayhoff atlas, showing that the approach generalizes beyond native protein structures to computationally generated backbones. We also demonstrate a multi-modal extension of RosettaSearch with vision-language models, where images of predicted protein structures are used as feedback to incorporate structural context to guide protein sequence generation. To our knowledge, this is the first large-scale demonstration that LLMs can serve as effective generative optimizers for backbone-conditioned protein sequence design, yielding systematic gains without any model retraining.

Meghana Kshirsagar, Allen Nie, Ching-An Cheng +5

AI for Good, Microsoft Redmond · Google DeepMind · Google Research +3

Inference-Time Search Large Language Model-Guided Optimization Molecular Generation Protein Design Multi-Objective Optimization

Apr 17, 2026cs.LG

Multi-Objective Bayesian Optimization via Adaptive \varepsilon-Constraints Decomposition

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling

\varepsilon

-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in

\varepsilon

-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.

Yaohong Yang, Sammie Katt, Samuel Kaski

Department of Computer Science, Aalto University, Espoo, Finland · ELLIS Institute Finland · Department of Computer Science, University of Manchester, Manchester, United Kingdom

Bayesian Optimization Multi-Objective Optimization

Apr 17, 2026cs.AR

HYPERHEURIST: A Simulated Annealing-Based Control Framework for LLM-Driven Code Generation in Optimized Hardware Design

Large Language Models (LLMs) have shown promising progress for generating Register Transfer Level (RTL) hardware designs, largely because they can rapidly propose alternative architectural realizations. However, single-shot LLM generation struggles to consistently produce designs that are both functionally correct and power-efficient. This paper proposes HYPERHEURIST, a simulated annealing-based control framework that treats LLM-generated RTL as intermediate candidates rather than final designs. The suggested system not only focuses on functionality correctness but also on Power-Performance-Area (PPA) optimization. In the first phase, RTL candidates are filtered through compilation, structural checks, and simulation to identify functionally valid designs. PPA optimization is restricted to RTL designs that have already passed compilation and simulation. Evaluated across eight RTL benchmarks, this staged approach yields more stable and repeatable optimization behavior than single-pass LLM-generated RTL.

Shiva Ahir, Prajna Bhat, Alex Doboli

Department of ECE

Large Language Model-Guided Optimization Code Generation Multi-Objective Optimization LLM Code Generation

Apr 16, 2026cs.CV

VisPCO: Visual Token Pruning Configuration Optimization via Budget-Aware Pareto-Frontier Learning for Vision-Language Models

Visual token pruning methods effectively mitigate the quadratic computational growth caused by processing high-resolution images and video frames in vision-language models (VLMs). However, existing approaches rely on predefined pruning configurations without determining whether they achieve computation-performance optimality. In this work, we introduce , a novel framework that formulates visual token pruning as a Pareto configuration optimization problem to automatically identify optimal configurations. Our approach employs continuous relaxation and straight-through estimators to enable gradient-based search, solved via the Augmented Lagrangian method. Extensive experiments across 8 visual benchmarks demonstrate that effectively approximates the empirical Pareto frontier obtained through grid search and generalizes well across various pruning methods and VLM architectures. Furthermore, through learnable kernel functions, we investigate layer-wise pruning patterns and reveal that multi-step progressive pruning captures VLMs' hierarchical compression structure, achieving superior accuracy-efficiency trade-offs compared to single-layer approaches.

Huawei Ji, Yuanhao Sun, Yuan Jin +4

Shanghai Jiao Tong University, Shanghai, China · University of Edinburgh, Edinburgh, UK

Vision-Language Models Efficient VLM Inference Multi-Objective Optimization Visual Token Pruning

Apr 6, 2026cs.AI

MMORF: A Multi-agent Framework for Designing Multi-objective Retrosynthesis Planning Systems

Multi-objective retrosynthesis planning is a critical chemistry task requiring dynamic balancing of quality, safety, and cost objectives. Language model-based multi-agent systems (MAS) offer a promising approach for this task: leveraging interactions of specialized agents to incorporate multiple objectives into retrosynthesis planning. We present MMORF, a framework for constructing MAS for multi-objective retrosynthesis planning. MMORF features modular agentic components, which can be flexibly combined and configured into different systems, enabling principled evaluation and comparison of different system designs. Using MMORF, we construct two representative MAS: MASIL and RFAS. On a newly curated benchmark consisting of 218 multi-objective retrosynthesis planning tasks, MASIL achieves strong safety and cost metrics on soft-constraint tasks, frequently Pareto-dominating baseline routes, while RFAS achieves a 48.6% success rate on hard-constraint tasks, outperforming state-of-the-art baselines. Together, these results show the effectiveness of MMORF as a foundational framework for exploring MAS for multi-objective retrosynthesis planning. Code and data are available at https://github.com/ninglab/MMORF.

Frazier N. Baker, Trieu Nguyen, Reza Averly +4

Department of Computer Science and Engineering, The Ohio State University · Department of Mathematics and Statistics, University of South Florida · Division of Medicinal Chemistry and Pharmacognosy, The Ohio State University +2

Multi-Agent LLM Systems Multi-Agent Planning Multi-Objective Optimization

Mar 22, 2026cs.LG

Joint Surrogate Learning of Objectives, Constraints, and Sensitivities for Efficient Multi-objective Optimization of Neural Dynamical Systems

Gaussian process surrogates dominate constrained multi-objective optimization because they are effective in data-scarce regimes, but their cubic scaling in training samples limits their ability to capture shared structure between objectives and constraints as problems grow in dimensionality. We show that deterministic neural network surrogates, equipped with feature tokenization and adaptive output normalization, match or exceed Gaussian process accuracy, while scaling to high-dimensional output spaces and training on all data including infeasible samples. Jointly training a single Feature Tokenizer Transformer to predict objectives, constraint satisfaction, and parameter sensitivities yields a unified gradient that simultaneously improves objective values, steers toward feasibility, and identifies the most influential parameters: a coherent search signal that disjoint per-output models cannot provide. We validate this on biophysical neural optimization problems of increasing complexity. In the hardest regime, with wide, uninformed parameter bounds where random sampling finds zero feasible solutions, descending the surrogate's learned constraint gradient steers the search into the feasible region and recovers near-optimal solutions where standard surrogate optimization and constrained Bayesian optimization find none.

Frithjof Gressmann, Ivan Georgiev Raikov, Seung Hyun Kim +3

Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign, Urbana, IL · The Grainer College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL · Department of Neurosurgery, Stanford University, Stanford, CA +3

Neural Surrogate Modeling Surrogate-Assisted Optimization Multi-Objective Optimization Sensitivity Analysis

Feb 8, 2026cs.RO

Multi-Agent Route Planning as a QUBO Problem

Multi-Agent Route Planning considers selecting vehicles, each associated with a single predefined route, such that route-level coverage utility is maximized while redundant spatial overlaps are limited. This paper gives a formal problem definition, proves NP-hardness by reduction from the Weighted Set Packing problem, and derives a Quadratic Unconstrained Binary Optimization formulation whose coefficients directly encode route utility rewards and pairwise overlap penalties. A single penalty parameter

λ

controls the coverage--overlap trade-off. We distinguish between a soft regime, which supports multi-objective exploration, and a hard regime, in which the penalty is strong enough to effectively enforce near-disjoint routes. We describe a practical pipeline for generating city instances, constructing candidate routes, building the QUBO matrix, and solving it with a binary quadratic programming baseline (Gurobi), simulated annealing, and D-Wave hybrid quantum annealing. Experiments on Barcelona instances with up to

10{,}000

vehicles reveal a clear coverage--overlap knee and show that Pareto-optimal solutions are mainly obtained under the hard-penalty regime, while D-Wave hybrid solvers and Gurobi achieve very similar objective values on matching configurations with only minor runtime differences as problem size grows.

Renáta Rusnáková, Martin Chovanec, Juraj Gazda

Department of Computers and Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice

Multi-Objective Optimization

Feb 6, 2026cs.CL

Uncovering Cross-Objective Interference in Multi-Objective Alignment

We study a persistent failure mode in multi-objective alignment for large language models (LLMs), in which scalarized training improves only some objectives while the others degrade. We formalize this phenomenon as cross-objective interference and, to our knowledge, conduct the first systematic study of scalarization algorithms for multi-objective LLM alignment. The study shows that interference is pervasive across algorithms yet strongly model-dependent. To understand how interference arises, we derive a local covariance law stating that an objective improves or degrades at first order according to the sign of the covariance between its reward and the scalarized score. We extend this law to the clipped surrogate objectives of modern reinforcement fine-tuning and show that it still holds under mild conditions. Building on this law, we propose COVariance-floor Enforced Reweighting (COVER), a one-sided controller that raises an objective's weight only when the covariance between its reward and the clipped advantage weight falls below a target. Through extensive experiments, we find that COVER can mitigate cross-objective interference while matching linear scalarization when objectives already co-improve. Finally, to explain why interference is model-dependent, we complement the local covariance law with a global convergence analysis. This analysis gives sufficient conditions for the non-convex scalarized objective to satisfy the Polyak--Łojasiewicz condition and relates interference to model geometry.

Yining Lu, Meng Jiang

University of Notre Dame

Adaptive Loss Weighting Multi-Objective Language Model Alignment Multi-Objective Optimization

Feb 5, 2026cs.NE

Variable Search Stepsize for Randomized Local Search in Multi-Objective Combinatorial Optimization

Over the past two decades, research in evolutionary multi-objective optimization has predominantly focused on continuous domains, with comparatively limited attention given to multi-objective combinatorial optimization problems (MOCOPs). Combinatorial problems differ significantly from continuous ones in terms of problem structure and landscape. Recent studies have shown that on MOCOPs multi-objective evolutionary algorithms (MOEAs) can even be outperformed by simple randomised local search. Starting with a randomly sampled solution in search space, randomised local search iteratively draws a random solution (from an archive) to perform local variation within its neighbourhood. However, in most existing methods, the local variation relies on a fixed neighbourhood, which limits exploration and makes the search easy to get trapped in local optima. In this paper, we present a simple yet effective local search method, called variable stepsize randomized local search (VS-RLS), which adjusts the stepsize during the search. VS-RLS transitions gradually from a broad, exploratory search in the early phases to a more focused, fine-grained search as the search progresses. We demonstrate the effectiveness and generalizability of VS-RLS through extensive evaluations against local search and MOEAs methods on diverse MOCOPs.

Xuepeng Ren, Maocai Wang, Guangming Dai +4

School of Computer, China University of Geosciences, Engineering Research Center of Natural Resource Information Management and Digital Twin Engineering Software, Ministry of Education, and Hubei Key Laboratory of Intelligent Geo-Information Processing, Wuhan 430074, China · School of Computer, Science and Informatics, De Montfort University, Leicester LE1 9BH, U.K. · School of Computer Science, University of Birmingham, Birmingham B15 2TT, U.K. +1

Metaheuristic Optimization Multi-Objective Optimization

Jan 30, 2026cs.NE

Fairness-Aware Performance Evaluation for Multi-Party Multi-Objective Optimization

In multiparty multiobjective optimization problems, solution sets are usually evaluated using classical performance metrics, aggregated across DMs. However, such mean-based evaluations may be unfair by favoring certain parties, as they assume identical geometric approximation quality to each party's PF carries comparable evaluative significance. Moreover, prevailing notions of MPMOP optimal solutions are restricted to strictly common Pareto optimal solutions, representing a narrow form of cooperation in multiparty decision making scenarios. These limitations obscure whether a solution set reflects balanced relative gains or meaningful consensus among heterogeneous DMs. To address these issues, this paper develops a fairness-aware performance evaluation framework grounded in a generalized notion of consensus solutions. From a cooperative game-theoretic perspective, we formalize four axioms that a fairness-aware evaluation function for MPMOPs should satisfy. By introducing a concession rate vector to quantify acceptable compromises by individual DMs, we generalize the classical definition of MPMOP optimal solutions and embed classical performance metrics into a Nash-product-based evaluation framework, which is theoretically shown to satisfy all axioms. To support empirical validation, we further construct benchmark problems that extend existing MPMOP suites by incorporating consensus-deficient negotiation structures. Experimental results demonstrate that the proposed evaluation framework is able to distinguish algorithmic performance in a manner consistent with consensus-aware fairness considerations. Specifically, algorithms converging toward strictly common solutions are assigned higher evaluation scores when such solutions exist, whereas in the absence of strictly common solutions, algorithms that effectively cover the commonly acceptable region are more favorably evaluated.

Zifan Zhao, Peilan Xu, Wenjian Luo

School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China · Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, Institute of Cyberspace Security, School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen 518055, China

Cooperative Game Theory Algorithmic Fairness Multi-Objective Optimization

Dec 30, 2025cs.NE

Decoupling Constraints from Two Directions for Evolutionary Constrained Multi-objective Optimization

Real-world constrained multi-objective optimization problems (CMOPs) commonly involve multiple constraints, and understanding and exploiting their coupling relationships is crucial for efficient optimization. Recent constraint-decoupling methods handle individual constraints separately, but they generally search only in the evolutionary direction to approximate single-constraint Pareto fronts (SCPFs). In this study, we show that part or all of the constrained Pareto front (CPF) may be unrelated to any SCPF and instead be shaped by the boundaries of infeasible regions. We refer to such a portion as the independent CPF (ICPF) and introduce the reverse CPF (RCPF) to characterize its associated informative infeasible boundaries. Based on these observations, we propose a bidirectional constraint-decoupling coevolutionary algorithm named DCF2D. DCF2D dynamically identifies the constraints obstructing the main population and activates constraint-specific auxiliary populations. These populations adaptively search in the evolutionary direction for the corresponding SCPFs or in the reverse evolutionary direction for the corresponding RCPFs. Its three-stage framework integrates unconstrained global exploration, event-driven bidirectional coevolution, and final convergence refinement. Experiments on 87 benchmark instances from seven test suites and 28 real-world engineering CMOPs demonstrate that DCF2D achieves the best overall performance among nine algorithms. Code available at: https://github.com/RuiqingS/DCF2D.

Ruiqing Sun, Dawei Feng, Xing Zhou +6

College of Computer Science and Technology, National University of Defense Technology, Changsha 410000, P.R. China · College of Intelligence Science and Technology, National University of Defense Technology, Changsha, 410000, P.R. China · State Key Laboratory of Complex & Critical Software Environment, College of Information and Communication, National University of Defense Technology, Wuhan 430019, P.R. China +1

Evolutionary Optimization Multi-Objective Evolutionary Optimization Constrained Optimization Multi-Objective Optimization

Dec 20, 2025cs.NE

Large-scale benchmarking of multi-objective soft-computing metaheuristics for redundancy allocation in repairable k-out-of-n systems

This paper presents a large-scale budget-aware benchmark of multi-objective soft-computing metaheuristics for a bi-objective redundancy allocation problem in repairable k-out-of-n systems. The problem combines cost minimization and steady-state availability maximization under weight constraints, with binary subsystem-level decisions determining both the number of redundant components and the redundancy strategy. Four strategies are considered: cold standby, warm standby, hot standby, and a mixed active-warm standby strategy. Subsystem availability is evaluated using continuous-time Markov chains, while the optimization task is treated as a constrained mixed-integer multi-objective problem. The study compares 65 metaheuristic algorithms from multiple algorithmic families under two initialization settings, with and without Scaled Binomial Initialization (SBI), across six case studies of increasing structural and dimensional complexity and four weight limits per case. Performance is assessed using hypervolume, budget-dependent convergence profiles, and non-parametric statistical comparisons. The results show that algorithm rankings are strongly budget-dependent, indicating that a single final-budget ranking can be misleading. SBI provides a substantial early advantage and can change the relative performance of competing methods, especially for larger instances. The best-performing algorithms vary across budget regimes: NNIA-SBI and CMOPSO-SBI are competitive under tight budgets, whereas NSGA-II+ARSBX-SBI performs robustly for medium and large budgets. From a system design perspective, Pareto-optimal solutions are dominated by hot standby and mixed redundancy strategies, while cold and warm standby rarely appear. The benchmark highlights the importance of initialization, computational budget, and problem complexity when selecting soft-computing optimizers for practical redundancy allocation.

Mateusz Oszczypała, David Ibehej, Jakub Kudela

Military University of Technology, gen. Sylwestra Kaliskiego Street 2, 00-908 Warsaw, Poland. · Institute of Automation and Computer Science, Brno University of Technology, Brno, Czech Republic.

Benchmark Design Metaheuristic Optimization Multi-Objective Optimization

Nov 9, 2025math.OC

Feature weighting for data analysis via evolutionary simulation

We analyze an algorithm for assigning weights prior to scalarization in discrete multi-objective problems arising from data analysis. The algorithm evolves weights (interpreted as the relevance of features) by a replicator-type dynamic on the standard simplex, with update indices computed from a normalized data matrix. We prove that the resulting sequence converges globally to a unique interior equilibrium, yielding non-degenerate limiting weights.

Aris Daniilidis, Alberto Domínguez Corella, Philipp Wissgott

Institut für Stochastik und Wirtschaftsmathematik, Variational Analysis, Dynamics and Operations Research Unit E105-04, Technische Universität Wien, Wiedner Hauptstraße 8, 1040 Vienna, Austria · Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstraße 36, A-8010 Graz, Austria · danube.ai solutions gmbh, 1040 Vienna, Austria

Replicator Dynamics Importance Weighting Multi-Objective Optimization

Sep 26, 2025cs.LG

OFMU: Optimization-Driven Framework for Machine Unlearning

Large language models deployed in sensitive applications increasingly require the ability to unlearn specific knowledge, such as user requests, copyrighted materials, or outdated information, without retraining from scratch to ensure regulatory compliance, user privacy, and safety. This task, known as machine unlearning, aims to remove the influence of targeted data (forgetting) while maintaining performance on the remaining data (retention). A common approach is to formulate this as a multi-objective problem and reduce it to a single-objective problem via scalarization, where forgetting and retention losses are combined using a weighted sum. However, this often results in unstable training dynamics and degraded model utility due to conflicting gradient directions. To address these challenges, we propose OFMU, a penalty-based bi-level optimization framework that explicitly prioritizes forgetting while preserving retention through a hierarchical structure. Our method enforces forgetting via an inner maximization step that incorporates a similarity-aware penalty to decorrelate the gradients of the forget and retention objectives, and restores utility through an outer minimization step. To ensure scalability, we develop a two-loop algorithm with provable convergence guarantees under both convex and non-convex regimes. We further provide a rigorous theoretical analysis of convergence rates and show that our approach achieves better trade-offs between forgetting efficacy and model utility compared to prior methods. Extensive experiments across vision and language benchmarks demonstrate that OFMU consistently outperforms existing unlearning methods in both forgetting efficacy and retained utility.

Sadia Asif, Mohammad Mohammadi Amiri

Rensselaer Polytechnic Institute

Bilevel Optimization Machine Unlearning Multi-Objective Optimization LLM Unlearning

Jun 27, 2025cs.AI

Interactive Multi-Objective Probabilistic Preference Learning with Soft and Hard Bounds

High-stakes decision-making involves navigating multiple competing objectives with expensive evaluations. For instance, in brachytherapy, clinicians must balance maximizing tumor coverage (e.g., an aspirational target or soft bound of >95% coverage) against strict organ dose limits (e.g., a non-negotiable hard bound of <601cGy to the bladder). Selecting Pareto-optimal solutions that match implicit preferences is challenging, as exhaustive Pareto frontier exploration is computationally and cognitively prohibitive, necessitating interactive frameworks to guide users. While decision-makers (DMs) often possess domain knowledge to narrow the search via such soft-hard bounds, current methods often lack systematic approaches to iteratively refine these multi-faceted preference structures. Furthermore, DMs often require confidence that they have not overlooked superior alternatives, a paramount necessity in high-stakes scenarios. We present Active-MoSH, an interactive local-global framework designed for this process. Its local component integrates probabilistic preference learning with an active sampling strategy to adaptively refine Pareto subsets while minimizing cognitive burden. To bolster decision confidence, Active-MoSH's global component, C-MoSH, leverages multi-objective sensitivity analysis to identify potentially overlooked, high-value points beyond immediate feedback. We demonstrate Active-MoSH's performance benefits through diverse synthetic and real-world applications. A high-stakes case study with real cervical cancer brachytherapy treatment plans and an image selection user study further validate our hypotheses regarding the framework's ability to improve convergence, enhance DM confidence, and provide expressive preference articulation.

Edward Chen, Sang T. Truong, Natalie Dullerud +2

Department of Computer Science, Stanford University, Stanford, California, USA

Active Learning Multi-Criteria Decision Analysis Multi-Objective Optimization Preference Learning

Dec 11, 2024cs.LG

Variational Model Merging for Pareto Front Estimation in Multitask Finetuning

Pareto fronts are useful to find good task-mixing strategies for multitask finetuning, but they are also costly to compute. To reduce costs, recent works have used existing model merging methods to help train cheap surrogate models to estimate the Pareto fronts. However, no work has yet considered designing new model-merging methods to directly, and provably, improve the quality of Pareto fronts. Here, we fill this gap by proposing a new Bayesian approach called Variational Model Merging. In this approach, existing model-merging methods are obtained as special cases of "posterior-merging" when Gaussian posteriors are used and new model-merging strategies can be derived by using non-Gaussian posteriors. Our main theoretical result is to show that more flexible posteriors necessarily yield better estimates of Pareto fronts. For instance, a Pareto front estimate obtained by merging full-Gaussian posteriors is expected to be better than that obtained by using isotropic Gaussian posteriors. We validate the theory through extensive empirical results on vision and language transformers where better Gaussian families consistently yields better or comparable Pareto fronts. Our work is a rare instance where Bayesian ideas are used to improve Pareto analysis.

Hugo Monzón Maldonado, Nico Daheim, Thomas Möllenhoff +2

RIKEN Center for AI Project, Japan · Ubiquitous Knowledge Processing Lab (UKP Lab), Department of Computer Science, Technical University of Darmstadt and National Research Center for Applied Cybersecurity ATHENE, Germany · National Research Center for Applied Cybersecurity ATHENE, Germany

Bayesian Inference Multi-Task Learning Multi-Task Optimization Language Model Merging Variational Inference Multi-Objective Optimization

Jan 7, 2024math.OC

Multi-Objective Hyperparameter Search via Damped Gauss--Newton Optimization

We study hyperparameter optimization (HPO) from a numerical-optimization perspective and propose a multi-objective damped Newton--Gauss--Newton search method. Rather than perturbing each hyperparameter separately or treating model evaluations as independent trials, the method uses performance changes between successive full hyperparameter vectors to construct an iterative secant approximation of the local sensitivity matrix. Each iteration therefore requires only one new full-vector model evaluation while jointly updating all optimized hyperparameters. A Tikhonov-regularized Gauss--Newton system stabilizes the update when the number of hyperparameters exceeds the number of performance objectives. The search is initialized from readily available empirical/default settings of the underlying learner, without requiring a separate initialization search. We evaluate four-dimensional XGBoost HPO on three public classification datasets against exhaustive grid search, random search, and tree-structured Parzen estimator (TPE) optimization. On Breast Cancer Wisconsin, the proposed method matches the best validation accuracy of a 320-configuration grid search with slightly better log loss and ROC--AUC. Across three datasets and three seeds, predictive performance remains competitive with random search and TPE while using substantially fewer search iterations. A supplementary proprietary eight-dimensional threshold-optimization case study further demonstrates joint multi-parameter optimization under competing performance targets and reveals non-monotonic, oscillatory trajectories that motivate damping and best-iterate selection. Overall, the results establish iterative secant sensitivity as an evaluation-efficient local alternative to exhaustive HPO.

Qinwu Xu, Yifan Jiang

Gauss-Newton Optimization Second-Order Optimization Multi-Objective Optimization Hyperparameter Optimization