Multi-Objective Optimization

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The field studies problems where improving one objective—such as accuracy, cost, safety, energy use, or fairness—can worsen another, and represents the alternatives as a Pareto frontier. Common approaches include evolutionary algorithms such as NSGA-II, Bayesian optimization for expensive evaluations, gradient-based methods for learning systems, and reinforcement-learning or generative methods for sequential and design tasks. Researchers also develop preference elicitation and constraint-handling methods so people can select useful trade-offs without always computing an entire frontier. A central tension is balancing broad, reliable coverage of feasible trade-offs against evaluation cost, while scalarization, objective scaling, and changing preferences can all affect which solutions are found.

Latest papers

270 papers40 papers in the last four weeks, up 48% on the four weeks before. 0.2% of all new papers.

May 8, 2026

Optimal Recourse Summaries via Bi-Objective Decision Tree Learning

Actionable Recourse provides individuals with actions they can take to change an unfavorable classifier outcome. While useful at the instance level, it is ill-suited for global auditing and bias detection, since aggregating local actions is costly and often inconsistent. Recourse Summaries address this limitation by partitioning the population and assigning one shared action per subgroup, enabling comparison across subgroups. Designing summaries involves a fundamental trade-off between recourse effectiveness and recourse cost, which existing methods do not adequately address. We introduce Summaries of Optimal and Global Actionable Recourse (SOGAR), which formulates recourse summary learning as an optimal decision tree learning problem and finds the Pareto front -- the complete set of solutions where improving one objective necessarily worsens the other. SOGAR enables post-hoc selection of the desired trade-off without retraining. Using shallow axis-parallel decision trees and sparse leaf actions, SOGAR produces stable, low-cost, and effective recourse summaries that outperform existing approaches across effectiveness and cost metrics.

Ioannis Chatzis, Jason Liartis, Athanasios Voulodimos +1

Artificial Intelligence and Learning Systems Laboratory

Algorithmic Auditing Decision Tree Learning Counterfactual Reasoning Multi-Objective Optimization Algorithmic Recourse

May 8, 2026

From Feasible to Practical: Pareto-Optimal Synthesis Planning

Current computer-aided synthesis planning (CASP) methods often treat retrosynthesis as solved once a single feasible route is identified, focusing primarily on convergence or shortest-path metrics. This view is misaligned with real-world practice, where chemists must balance competing objectives such as cost, sustainability, toxicity, and overall yield. To address this, we formulate synthesis planning as a multi-objective search problem and introduce MORetro*, an algorithm that generates a Pareto front of synthesis routes to explicitly capture trade-offs among user-defined criteria. MORetro* uses weighted scalarization and BO-informed sampling to efficiently navigate the combinatorial search space and prioritize promising trade-offs. Building on multi-objective A*-search, we provide optimality guarantees showing that, for a fixed single-step model, MORetro* recovers the true Pareto front under admissibility. Across multiple retrosynthesis benchmarks, MORetro* produces diverse, high-quality Pareto fronts, uncovering solutions overlooked by single-objective approaches and better aligning CASP outputs with industrial decision-making.

Friedrich Hastedt, Dongda Zhang, Antonio del Rio Chanona

Department of Chemical Engineering, Imperial College London, UK · Department of Chemical Engineering, University of Manchester, UK

Multi-Objective Optimization Pareto Optimization Retrosynthesis

May 7, 2026

Bridging the Last Mile of Circuit Design: PostEDA-Bench, a Hierarchical Benchmark for PPA Convergence and DRC Fixing

LLM-based agents are increasingly applied to the "last mile" of Electronic Design Automation (EDA): repairing residual sign-off Design Rule Check (DRC) violations and converging Power-Performance-Area (PPA) targets after tool runs. Existing EDA-LLM benchmarks, however, omit DRC fixing entirely and rely on flat hierarchies tied to a single toolchain. We introduce PostEDA-Bench, a hierarchical benchmark with 145 tasks across DRC-Essential, DRC-Reasoning, PPA-Mono, and PPA-Multi, supported by EDA toolchains with machine-checkable evaluation. Across eight commercial and open-source LLMs under multiple agent scaffolds, we find that agents handle synthetic DRC-Essential and single-objective PPA-Mono reasonably well but degrade sharply on the more practical DRC-Reasoning, where the best success rate is 36.66%, and PPA-Multi, where the best success rate is 20.00%; vision augmentation consistently enhances DRC-Bench; and trade-off reasoning, rather than knob knowledge, is the dominant PPA-Multi bottleneck.

Pengju Liu, Nuo Xu, Jinwei Tang +2

University of Minnesota

Automated Program Repair Electronic Design Automation LLM Agent Evaluation AI Agent Benchmarks Multi-Objective Optimization

May 7, 2026

Multi-Objective Multi-Agent Bandits: From Learning Efficiency to Fairness Optimization

We study multi-objective multi-agent multi-armed bandits (MO-MA-MAB) under stochastic rewards, where agents observe heterogeneous reward vectors and communicate over time-varying graphs. We formulate this emerging problem setting to address efficient learning, measured by Pareto regret, and incorporate fair learning as an additional goal, captured via social welfare. To measure efficiency, we formulate Pareto regret and develop Pareto UCB1 Gossip, whose novel exploration radius explicitly separates statistical uncertainty in Pareto-based inference from consensus error. To express the fairness constraint, we formulate a Nash Social Welfare objective over preference-scalarized rewards and propose Simulated NSW UCB Gossip, which integrates preference-based reward simulation, gossip-based utility estimation, and UCB-style exploration. We prove that Pareto UCB1 Gossip achieves

\mathcal{O}(\log T)

regret and an instance-independent rate of

\mathcal{O}(\sqrt{T})

, while Simulated NSW UCB Gossip achieves an instance-independent regret bound of

\mathcal{O}(T^{3/4})

. This separation reveals the cost of imposing the fairness constraint to our efficiency objective: fairness limits information aggregation and slows convergence. Experiments show that our methods consistently outperform baselines, improving performance by approximately

100\%

and

50\%

in the efficiency and fairness settings, respectively.

John Wang, Mengfan Xu

University of Massachusetts Amherst

Multi-Armed Bandits Multi-Agent System Optimization Multi-Agent Bandits Algorithmic Fairness Multi-Objective Optimization Social Welfare Maximization

May 7, 2026

MARBLE: Multi-Aspect Reward Balance for Diffusion RL

Reinforcement learning fine-tuning has become the dominant approach for aligning diffusion models with human preferences. However, assessing images is intrinsically a multi-dimensional task, and multiple evaluation criteria need to be optimized simultaneously. Existing practice deal with multiple rewards by training one specialist model per reward, optimizing a weighted-sum reward

R(x)=\sum_k w_k R_k(x)

, or sequentially fine-tuning with a hand-crafted stage schedule. These approaches either fail to produce a unified model that can be jointly trained on all rewards or necessitates heavy manually tuned sequential training. We find that the failure stems from using a naive weighted-sum reward aggregation. This approach suffers from a sample-level mismatch because most rollouts are specialist samples, highly informative for certain reward dimensions but irrelevant for others; consequently, weighted summation dilutes their supervision. To address this issue, we propose MARBLE (Multi-Aspect Reward BaLancE), a gradient-space optimization framework that maintains independent advantage estimators for each reward, computes per-reward policy gradients, and harmonizes them into a single update direction without manually-tuned reward weighting, by solving a Quadratic Programming problem. We further propose an amortized formulation that exploits the affine structure of the loss used in DiffusionNFT, to reduce the per-step cost from K+1 backward passes to near single-reward baseline cost, together with EMA smoothing on the balancing coefficients to stabilize updates against transient single-batch fluctuations. On SD3.5 Medium with five rewards, MARBLE improves all five reward dimensions simultaneously, turns the worst-aligned reward's gradient cosine from negative under weighted summation in 80% of mini-batches to consistently positive, and runs at 0.97X the training speed of baseline training.

Canyu Zhao, Hao Chen, Yunze Tong +3

Zhejiang University · Work done during an internship at HiThink. · HiThink +1

Multi-Objective Reinforcement Learning Diffusion Model Alignment Gradient Interference RL for Diffusion Models Multi-Objective Optimization Reward Design for RL

May 7, 2026

From Dual Tracking to Clipping: Provably Faster Distributionally Robust Multi-Objective Optimization

Multi-objective optimization (MOO) has received growing attention in applications that require learning under multiple criteria. However, most existing MOO formulations do not explicitly account for distributional shifts in the data. We introduce distributionally robust multi-objective optimization (DR-MOO), which minimizes multiple objectives under their respective worst-case distributions. We propose Pareto-type solution concepts for DR-MOO and develop multi-gradient descent algorithms (MGDA) with provable guarantees. Leveraging a Lagrangian dual reformulation, we first design a double-loop MGDA that uses an inner loop to estimate dual variables and achieves a total sample complexity

\mathcal{O}(ε^{-8})

for reaching an

ε

-Pareto-stationary point. To further improve convergence, we combine large-batch sampling with gradient clipping to accommodate generalized smoothness and control bias in stochastic preference updates, eliminating the need for double sampling. This yields a single-loop double-clip MGDA with substantially improved sample complexity

\mathcal{O}(ε^{-4})

. Our theory applies to nonconvex problems without requiring uniformly bounded gradients of the dual objectives. Experiments demonstrate that our methods are competitive with state-of-the-art MGDA baselines.

Yufeng Yang, Fangning Zhuo, Ziyi Chen +2

Texas A&M University · A*STAR · University of Maryland

Gradient Clipping Gradient Descent Nonconvex Stochastic Optimization Distributionally Robust Optimization Robust Optimization Multi-Objective Optimization

May 5, 2026

QUIVER: Cost-Aware Adaptive Preference Querying in Surrogate-Assisted Evolutionary Multi-Objective Optimization

Interactive multi-objective optimization systems face a budget allocation dilemma: one can spend resources on expensive objective evaluations or on eliciting decision-maker preferences that identify the relevant region of the Pareto set. Moreover, preference elicitation itself spans modalities with different information content and cognitive burden, ranging from cheap, noisy pairwise preference statements (PS) to richer but costlier indifference adjustments (IA). We study cost-aware optimization under an unknown scalarization and introduce QUIVER (Query-Informed Value Estimation for Regret), a surrogate-assisted evolutionary multi-objective optimizer that adaptively chooses between objective evaluations and heterogeneous preference queries. At each step, QUIVER selects the next action by maximizing the expected decision-quality improvement per unit total cost. Across DTLZ and WFG benchmarks under synthetic decision-maker models, QUIVER achieves the lowest final utility regret on challenging WFG problems (utility regret of 2.14 on WFG4, 2.82 on WFG9: a 25% improvement over baselines), outperforming all single-modality baselines. We analyze how the optimal mix of PS and IA adapts to problem difficulty: on easy problems (DTLZ2), QUIVER selects 80% PS queries; on hard problems (WFG9), it shifts to 35% IA queries. This adaptive modality selection demonstrates cost-aware preference learning in action.

Florian A. D. Burnat

University of Warwick Warwick Business School Coventry, England, UK

Surrogate-Assisted Optimization Multi-Objective Evolutionary Optimization Multi-Objective Optimization Preference Learning Preference Elicitation

May 5, 2026

Contextual Multi-Objective Optimization: Rethinking Objectives in Frontier AI Systems

Frontier AI systems perform best in settings with clear, stable, and verifiable objectives, such as code generation, mathematical reasoning, games, and unit-test-driven tasks. They remain less reliable in open-ended settings, including scientific assistance, long-horizon agents, high-stakes advice, personalization, and tool use, where the relevant objective is ambiguous, context-dependent, delayed, or only partially observable. We argue that many such failures are not merely failures of scale or capability, but failures of objective selection: the system optimizes a locally visible signal while missing which objectives should govern the interaction. We formulate this problem as contextual multi-objective optimization. In this setting, systems must consider multiple, context-dependent objectives, such as helpfulness, truthfulness, safety, privacy, calibration, non-manipulation, user preference, reversibility, and stakeholder impact, while determining which objectives are active, which are soft preferences, and which must function as hard or quasi-hard constraints. These examples are not intended as an exhaustive taxonomy: different domains and deployment settings may activate different objective dimensions and different conflict-resolution procedures. Our framework models AI behavior as a context-dependent choice rule over candidate actions, objective estimates, active constraints, stakeholders, uncertainty, and conflict-resolution procedures. We outline an implementation pathway based on decomposed objective representations, context-to-objective routing, hierarchical constraints, deliberative policy reasoning, controlled personalization, tool-use control, diagnostic evaluation, auditing, and post-deployment revision.

Jie Zhou, Qin Chen, Liang He

School of Computer Science and Technology, East China Normal University, Shanghai

AI Alignment AI Safety Multi-Objective Optimization

May 5, 2026

Exact and Evolutionary Algorithms for Sequential Multi-Objective Transmission Topology Planning

We study day-ahead transmission topology control for high-voltage grid operation under

N-1

security constraints. The operational task is to select, over a 24-hour horizon, a sequence of substation topologies obtained via busbar-coupler switching to relieve line overloads while limiting switching effort and topological complexity. We formulate this task as a sequential multi-objective optimization problem with four objectives used in TSO decision making: worst-case

N-1

line loading, maximum topological depth, number of topology changes, and time spent outside the reference topology. We propose an exact block algorithm that exploits the temporal structure of topology plans: consecutive hours with the same topology are represented as blocks, enabling enumeration of the complete Pareto front over the admissible set of topologies under fixed operational bounds on depth and switching. We also develop a tailored NSGA-III-based evolutionary heuristic and evaluate it against the exact front. Using real operational data from the Dutch high-voltage transmission grid operated by TenneT, the block algorithm computes the exact front for a highly congested day in under three minutes after topology-level load-flow preprocessing. The exact front reveals low-switching plans with no DC

N-1

thermal overloads that the tested evolutionary search fails to find. The proposed method, therefore, provides both a practical day-ahead decision-support tool for transmission operators and a benchmark for heuristic and learning-based topology-control methods.

Job Groeneveld, Miguel Muñoz, Jan Viebahn +1

TenneT TSO B.V., Arnhem, The Netherlands · Artelys, Paris, France · Department of Mathematics, Vrije Universiteit Amsterdam, The Netherlands

Multi-Objective Evolutionary Optimization Combinatorial Optimization Multi-Objective Optimization Power Systems

May 3, 2026

CoAction: Cross-task Correlation-aware Pareto Set Learning

Pareto set learning (PSL) is an emerging paradigm in multi-objective optimization that trains neural networks to map preference vectors to Pareto optimal solutions. However, existing PSL methods primarily focus on solving a single multi-objective optimization problem at a time. This limitation not only increases computational costs in multi-objective multitask optimization scenarios by requiring a separate model for each task, but also fails to exploit the inter-task correlations across tasks. To address this, we propose a Cross-tAsk correlation-aware Pareto Set Learning (CoAction) framework, which leverages task-aware transformer to handle multiple tasks simultaneously. Specifically, by assigning task-specific embedding vectors to individual tasks, the model effectively distinguishes between tasks while facilitating knowledge sharing among them. We utilize a Transformer encoder as the backbone architecture to leverage its self-attention mechanism for capturing complex task dependencies. The proposed approach is evaluated on comprehensive multitask test suites covering both benchmark problems and real-world applications, demonstrating effectiveness and competitive performance in Hypervolume, Range, and Sparsity.

Xinyue Chen, Yingxuan Liang, Yiqin Huang +3

Guangdong University of Technology, Guangzhou, China · Xiamen University, Xiamen, China

Multi-Task Learning Multi-Task Optimization Multi-Objective Optimization Pareto Optimization

May 1, 2026

Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmark

The co-optimization of geometry and physical parameters remains challenging in transient multiphysics systems involving moving boundaries, nonlinear material response, phase transitions, and competing objectives. Existing methods often optimize geometry and physical variables separately, rely on simplified steady-state physics, or require offline data generation and reduced design spaces. Here, we present an end-to-end differentiable co-optimization framework that couples an implicit neural representation of geometry with a JAX-compiled Eulerian multiphysics solver. Geometry is represented as a signed distance field using Fourier-feature-encoded spatial coordinates, while boundary conditions, initial conditions, process controls, and material parameters are optimized within the same differentiable loop. Continuous relaxations represent non-smooth physical transitions while preserving compatibility with reverse-mode automatic differentiation and backpropagation through time. We demonstrate the framework using a transient hamburger-cooking benchmark, selected as an interpretable multiphysics problem rather than a culinary optimization exercise. The benchmark combines conductive and convective heat transfer, latent energy effects, moisture and fat transport, shrinkage-induced geometry evolution, evolving contact boundary conditions, flipping-induced boundary-condition changes, and competing quality objectives. Results show that geometry-only optimization modifies shape to relieve thermal bottlenecks, while joint co-optimization distributes the design response across geometry, material state, process variables, and boundary conditions through gradients propagated over the full transient rollout.

Navid Zobeiry

Department of Materials Science and Engineering, University of Washington · William E. Boeing Department of Aeronautics & Astronautics, University of Washington, Seattle, WA 98195, USA

Differentiable Optimization Multi-Objective Optimization Multiphysics Simulation

Apr 27, 2026

Meta-Aligner: Bidirectional Preference-Policy Optimization for Multi-Objective LLMs Alignment

Multi-Objective Alignment aims to align Large Language Models (LLMs) with diverse and often conflicting human values by optimizing multiple objectives simultaneously. Existing methods predominantly rely on static preference weight construction strategies. However, rigidly aligning to fixed targets discards valuable intermediate information, as training responses inherently embody valid preference trade-offs even when deviating from the target. To address this limitation, we propose Meal, i.e., MEta ALigner, a bi-level meta-learning framework enabling bidirectional optimization between preferences and policy responses, generating instructive dynamic preferences for steadier training. Specifically, we introduce a preference-weight-net as a meta-learner to generate adaptive preference weights based on input prompts and update the preference weights as learnable parameters, while the LLM policy acts as a base-learner optimizing response generation conditioned on these preferences with rejection sampling strategy. Extensive empirical results demonstrate that our method achieves superior performance on several multi-objective benchmarks, validating the effectiveness of the dynamic bidirectional preference-policy optimization framework.

Wenzhe Xu, Biao Liu, Yiyang Sun +2

Meta-Learning Multi-Objective Language Model Alignment Preference Alignment Multi-Objective Optimization

Apr 26, 2026

MAEO: Multiobjective Animorphic Ensemble Optimization for Scalable Large-scale Engineering Applications

Multiobjective optimization remains challenging for many scientific and engineering problems due to the need to balance convergence, diversity, and computational efficiency across high-dimensional objective landscapes. This work presents the Multiobjective Animorphic Ensemble Optimization (MAEO) framework, a parallelizable ensemble strategy that unifies state-of-the-art evolutionary algorithms within an island-based architecture, overcoming the limitations of relying on a single optimizer, as implied by the No Free Lunch theorem. MAEO uses a parameter-free hypervolume indicator for island performance assessment and a strict Pareto-rank-based individual scoring formulation that incorporates crowding distance and nadir-point proximity to ensure consistent selection pressure within each front. The framework is initiated using four algorithms (NSGA-III, CTAEA, AGEMOEA2, SPEA2) and evaluated through extensive benchmarking on 12 DTLZ/ZDT functions under 36 dimensionality settings using Wilcoxon signed-rank tests with both hypervolume and inverse generational distance metrics. Results show that MAEO achieves balanced convergence-diversity performance, outperforming or matching some of the leading multiobjective optimization algorithms across different benchmark problems. To demonstrate practical applicability, MAEO is applied to the equilibrium-cycle optimization of a small modular nuclear reactor. Eight discrete design variables (and three objectives (levelized cost of electricity, peak soluble boron concentration, fuel cycle length) are optimized under two safety constraints. The algorithm carried out roughly 40000 evaluations using computer simulations. MAEO identifies core designs that lower both the levelized cost of electricity and the peak boron concentration, while preserving fuel cycle length and meeting all safety constraints.

Omer F. Erdem, Dean Price, Paul Seurin +1

Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109, United States · Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 60 Vassar St., Cambridge, MA 02139 · Idaho National Laboratory, Idaho Falls, ID 83415, United States +1

Evolutionary Optimization Multi-Objective Evolutionary Optimization Multi-Objective Optimization

Apr 25, 2026

CombiMOTS: Combinatorial Multi-Objective Tree Search for Dual-Target Molecule Generation

Dual-target molecule generation, which focuses on discovering compounds capable of interacting with two target proteins, has garnered significant attention due to its potential for improving therapeutic efficiency, safety and resistance mitigation. Existing approaches face two critical challenges. First, by simplifying the complex dual-target optimization problem to scalarized combinations of individual objectives, they fail to capture important trade-offs between target engagement and molecular properties. Second, they typically do not integrate synthetic planning into the generative process. This highlights a need for more appropriate objective function design and synthesis-aware methodologies tailored to the dual-target molecule generation task. In this work, we propose CombiMOTS, a Pareto Monte Carlo Tree Search (PMCTS) framework that generates dual-target molecules. CombiMOTS is designed to explore a synthesizable fragment space while employing vectorized optimization constraints to encapsulate target affinity and physicochemical properties. Extensive experiments on real-world databases demonstrate that CombiMOTS produces novel dual-target molecules with high docking scores, enhanced diversity, and balanced pharmacological characteristics, showcasing its potential as a powerful tool for dual-target drug discovery. The code and data is accessible through https://github.com/Tibogoss/CombiMOTS.

Thibaud Southiratn, Bonil Koo, Yijingxiu Lu +1

Department of Computer Science and Engineering, Seoul National University, Seoul, Republic of Korea · Interdisciplinary Program in Bioinformatics, Seoul National University, Seoul, Republic of Korea · AIGENDRUG Co., Ltd., Seoul, Republic of Korea +1

Monte Carlo Tree Search Molecular Generation Multi-Objective Optimization Drug Discovery

Apr 23, 2026

Learning Coverage- and Power-Optimal Transmitter Placement from City Maps: A Comparative Study of Direct and Indirect Neural Approaches

Optimal wireless transmitter placement is a central task in radio-network planning, and exhaustive search becomes prohibitively expensive at scale. This paper studies the single-transmitter setting under a learned propagation model, enabling exhaustive per-pixel assessment at scale in a regime where measurement-based labeling is infeasible and ray-tracing-based labeling is computationally out of reach. We introduce a dataset of 167525 urban scenarios (RadioMapSeer-Deployment) with dual ground-truth labels for coverage-optimal and power-optimal transmitter locations. Benchmark analysis reveals an asymmetric coverage-power trade-off: coverage-optimal placement sacrifices 13.86% of received-power, whereas power-optimal placement sacrifices 5.50% of coverage; the best balanced placement lies at

\bar{d}=2.60

from the ideal point (100%,100%). We evaluate two learning formulations: indirect heatmap-based models predicting received-power radio maps, and direct score-map models predicting the objective landscape over feasible transmitter locations. Within the heatmap family, discriminative models deliver one-shot predictions 1350-2400

\times

faster than exhaustive search, while diffusion models additionally support multi-sample inference that improves single-objective performance and, by reusing the same sample pool under a balanced criterion, recovers strong balanced placements without explicit multi-objective training. Dual score-map strategies combining power and coverage score-maps match the exhaustive balanced optimum (

\bar{d}=2.60

) and remain close to it across smaller candidate budgets, at 14-22

\times

speedups including the cost of evaluating shortlisted candidates. Dual score-map methods are strongest overall, whereas heatmap formulations remain attractive for their physically meaningful intermediate maps and, in the diffusion setting, for inference-time search.

Çağkan Yapar

Wireless Communications Multi-Objective Optimization

Apr 22, 2026

Generative Discovery of Magnetic Insulators under Competing Physical Constraints

Discovering materials that must simultaneously satisfy multiple competing constraints remains a central challenge in computational materials design, particularly in data-scarce regimes where conventional data-driven approaches are least effective. Magnetic insulators represent a stringent example: the electronic conditions that favor magnetic order often also promote metallicity, while insulating behavior suppresses the interactions that stabilize magnetism. As a result, experimentally viable magnetic insulators are rare and difficult to identify through conventional screening. Here, we introduce MagMatLLM, a constraint-guided generative discovery framework that integrates language-model-based crystal generation with evolutionary selection, surrogate screening, and first-principles validation to target simultaneous stability, magnetism, and insulating behavior. Unlike stability-first approaches, the framework enforces functional constraints during generation and selection, steering the search toward sparsely populated regions of materials space defined by competing physical requirements. Using this workflow, we identify twelve previously unreported candidate magnetic insulators, including Tm

_4

Co

_2

Cr

_2

O

_{12}

and Cr

_4

Nb

_2

O

_{12}

. Of these, ten are dynamically stable by phonon analysis and exhibit finite band gaps and nonzero magnetic moments in spin-polarized density functional theory calculations. Beyond the specific compounds identified here, this work establishes a general constraint-guided paradigm for multi-objective materials discovery in sparse chemical spaces and provides a transferable strategy for the design of quantum materials under competing physical constraints.

Qiulin Zeng, Tahiya Chowdhury, Md Shafayat Hossain

Department of Math, University of Southern California, Los Angeles, CA, 90007 · Department of Computer Science, Colby College, Waterville, ME, 04901 · Department of Materials Science and Engineering, University of California, Los Angeles, Los Angeles, CA 90095, United States +1

Materials Science Crystal Structure Generation Large Language Model-Guided Scientific Discovery Multi-Objective Optimization Computational Materials Science

Apr 22, 2026

MGDA-Decoupled: Geometry-Aware Multi-Objective Optimisation for DPO-based LLM Alignment

Aligning large language models (LLMs) to desirable human values requires balancing multiple, potentially conflicting objectives such as helpfulness, truthfulness, and harmlessness, which presents a multi-objective optimisation challenge. Most alignment pipelines rely on a fixed scalarisation of these objectives, which can introduce procedural unfairness by systematically under-weighting harder-to-optimise or minority objectives. To promote more equitable trade-offs, we introduce MGDA-Decoupled, a geometry-based multi-objective optimisation algorithm that finds a shared descent direction while explicitly accounting for each objective's convergence dynamics. In contrast to prior methods that depend on reinforcement learning (e.g., GAPO) or explicit reward models (e.g., MODPO), our approach operates entirely within the lightweight Direct Preference Optimisation (DPO) paradigm. Experiments on the UltraFeedback dataset show that geometry-aware methods -- and MGDA-Decoupled in particular -- achieve the highest win rates against golden responses, both overall and per objective.

Andor Vári-Kakas, Ji Won Park, Natasa Tagasovska

Prescient Design, CS CoE, Genentech | Roche

Direct Preference Optimization Gradient Descent Multi-Objective Language Model Alignment Multi-Objective Optimization

Apr 22, 2026

Lexicographic Minimum-Violation Motion Planning using Signal Temporal Logic

Motion planning for autonomous vehicles often requires satisfying multiple conditionally conflicting specifications. In situations where not all specifications can be met simultaneously, minimum-violation motion planning maintains system operation by minimizing violations of specifications in accordance with their priorities. Signal temporal logic (STL) provides a formal language for rigorously defining these specifications and enables the quantitative evaluation of their violations. However, a total ordering of specifications yields a lexicographic optimization problem, which is typically computationally expensive to solve using standard methods. We address this problem by transforming the multi-objective lexicographic optimization problem into a single-objective scalar optimization problem using non-uniform quantization and bit-shifting. Specifically, we extend a deterministic model predictive path integral (MPPI) solver to efficiently solve optimization problems without quadratic input cost. Additionally, a novel predicate-robustness measure that combines spatial and temporal violations is introduced. Our results show that the proposed method offers an interpretable and scalable solution for lexicographic STL minimum-violation motion planning within a single-objective solver framework.

Patrick Halder, Lothar Kiltz, Hannes Homburger +2

School of Computation, Information and Technology, Technical University of Munich, 85748 Garching, Germany · 2ZF Friedrichshafen AG, 88046 Friedrichshafen, Germany · Institute of System Dynamics, HTWG Konstanz, 78562 Konstanz, Germany

STL Motion Planning Motion Planning MPPI Control Autonomous Driving Planning Multi-Objective Optimization

Apr 21, 2026

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, 2026

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, 2026

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

We investigate 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, 2026

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, 2026

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, 2026

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, 2026

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, 2026

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 14, 2026

Skyline-First Traversal as a Control Mechanism for Multi-Criteria Graph Search

In multi-criteria graph traversal, paths are compared via Pareto dominance, an ordering that identifies which paths are non-dominated, but says nothing about which path to expand next or when the search may stop. As a result, existing approaches rely on external mechanisms-heuristics, scalarization, or population-based exploration while Pareto dominance remains confined to passive roles such as pruning or ranking. This paper shows that, under constrained cost models, finite cost grids, Markovian transitions, and a nonzero progress measure, Pareto geometry alone is sufficient to drive both scheduling and termination. We show that extracting exclusively from the first Pareto layer, the skyline, induces a deterministic descent in a discrete completion potential, ensuring monotone progress toward solution completion. In parallel, a vector lower-bound certificate provides a stopping condition that guarantees dominance coverage of all remaining traversals without requiring a predefined number of solutions. Our analysis establishes deterministic potential descent, certified termination via dominance coverage, a uniform bound on layer width induced by cost-grid geometry, and greedy cost-space dispersion within the skyline. The resulting framework operates without scalarization, heuristic guidance, or probabilistic models, and repositions Pareto dominance from a passive filter to a deterministic driver of search.

Nicolas Tacheny

Ni2 Innovation Lab, Liège, Belgium · University of Mons (UMONS), Belgium

Pareto Optimization Multi-Objective Optimization

Apr 14, 2026

Scaffold-Conditioned Preference Triplets for Controllable Molecular Optimization with Large Language Models

Molecular property optimization is central to drug discovery, yet many deep learning methods rely on black-box scoring and offer limited control over scaffold preservation, often producing unstable or biologically implausible edits. While large language models (LLMs) are promising molecular generators, optimization remains constrained by the lack of chemistry-grounded preference supervision and principled data curation. We introduce Scaffold-Conditioned Preference Triplets (SCPT), a pipeline that constructs similarity-constrained triplets

\langle\text{scaffold}, \text{better}, \text{worse}\rangle

via scaffold alignment and chemistry-driven filters for validity, synthesizability, and meaningful property gains. Using these preferences, we align a pretrained molecular LLM as a conditional editor, enabling property-improving edits that retain the scaffold. Across single- and multi-objective benchmarks, SCPT improves optimization success and property gains while maintaining higher scaffold similarity than competitive baselines. Compared with representative non-LLM molecular optimization methods, SCPT-trained LLMs are better suited to scaffold-constrained and multi-objective optimization. In addition, models trained on single-property and two-property supervision generalize effectively to three-property tasks, indicating promising extrapolative generalization under limited higher-order supervision. SCPT also provides controllable data-construction knobs that yield a predictable similarity-gain frontier, enabling systematic adaptation to diverse optimization regimes.

Yi Xiong, Liang Xiong, Xiaohong Ji +4

National Key Laboratory of Parallel and Distributed Processing College of Computer Science and Technology National University of DefenseTechnology · DP Technology

Molecular Optimization Large Language Model-Guided Optimization Multi-Objective Optimization Preference Learning

Apr 13, 2026

On the Use of Bi-Objective Evolutionary Algorithms for the Stochastic MKP under Dynamic Constraints

The multiple knapsack problem (MKP) generalizes the classical knapsack problem by assigning items to multiple knapsacks subject to capacity constraints. It is used to model many real-world resource allocation and scheduling problems. In practice, these optimization problems often involve stochastic and dynamic components. Evolutionary algorithms provide a flexible framework for addressing such problems under uncertainty and dynamic changes. In this paper, we investigate a stochastic and dynamic variant of MKP with chance constraints, where the item weights are modeled as independent normally distributed random variables and knapsack capacities change during the optimization process. We formulate the problem as a bi-objective optimization formulation that balances profit maximization and probabilistic capacity satisfaction at a given confidence level. We conduct an empirical comparison of four widely used multi-objective evolutionary algorithms (MOEAs), representing both decomposition- and dominance-based search paradigms. The algorithms are evaluated under varying uncertainty levels, confidence thresholds, and dynamic change settings. The results provide comparative insights into the behavior of decomposition-based and dominance-based MOEAs for stochastic MKP under dynamic constraints.

Ishara Hewa Pathiranage, Aneta Neumann

Machine Learning and Optimisation, School of Computer Science and Information Technology, Adelaide University, Adelaide, Australia

Combinatorial Optimization Constrained Optimization Multi-Objective Optimization Multi-Objective Evolutionary Optimization Chance-Constrained Optimization

Apr 12, 2026

Preference-Agile Multi-Objective Optimization for Real-time Vehicle Dispatching

Multi-objective optimization (MOO) has been widely studied in literature because of its versatility in human-centered decision making in real-life applications. Recently, demand for dynamic MOO is fast-emerging due to tough market dynamics that require real-time re-adjustments of priorities for different objectives. However, most existing studies focus either on deterministic MOO problems which are not practical, or non-sequential dynamic MOO decision problems that cannot deal with some real-life complexities. To address these challenges, a preference-agile multi-objective optimization (PAMOO) is proposed in this paper to permit users to dynamically adjust and interactively assign the preferences on the fly. To achieve this, a novel uniform model within a deep reinforcement learning (DRL) framework is proposed that can take as inputs users' dynamic preference vectors explicitly. Additionally, a calibration function is fitted to ensure high quality alignment between the preference vector inputs and the output DRL decision policy. Extensive experiments on challenging real-life vehicle dispatching problems at a container terminal showed that PAMOO obtains superior performance and generalization ability when compared with two most popular MOO methods. Our method presents the first dynamic MOO method for challenging \rev{dynamic sequential MOO decision problems

Jiahuan Jin, Wenhao Zhao, Rong Qu +4

School of Computer Science, University of Nottingham Ningbo China, Ningbo, China. · School of Computer Science, University of Nottingham, Nottingham, UK. · Department of Computer Science, City University of Hong Kong, Hong Kong

Multi-Party Multi-Objective Optimization Multi-Objective Optimization Reinforcement Learning