Multi-Objective Optimization

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Overview

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

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

Apr 12, 2026

Reinforcement Learning-Guided NSGA-II Enhanced with Gray Relational Coefficient for Multi-Objective Optimization: Application to NASDAQ Portfolio Optimization

In modern financial markets, decision-makers increasingly rely on quantitative methods to navigate complex trade-offs among multiple, often conflicting objectives. This paper addresses constrained multi-objective optimization (MOO) with an application to portfolio optimization for minimizing risk and maximizing return. To address existing gaps, we propose a novel reinforcement learning (RL)-guided non-dominated sorting genetic algorithm II (NSGA-II) enhanced with gray relational coefficients (GRC), termed RL-NSGA-II-GRC, which combines an RL agent controller and GRC-based selection to improve convergence and diversity of Pareto fronts. The agent adapts evolutionary parameters online using metrics of hypervolume, feasibility, and diversity, while the GRC tournament operator ranks parents via a unified score considering dominance rank, crowding distance, and proximity to ideal reference. We evaluate the framework on the Kursawe and CONSTR benchmarks and a NASDAQ portfolio application. On the benchmarks, RL-NSGA-II-GRC achieves convergence improvements of about 5.8% and 4.4% over NSGA-II, while preserving well-distributed non-dominated solutions. In the portfolio application, it produces a smooth, densely populated efficient frontier supporting identification of the maximum Sharpe ratio portfolio (annualized Sharpe =1.92) and utility-optimal portfolios for different risk-aversion levels. The main contributions are three-fold: 1) we propose an RL-NSGA-II-GRC method integrating an RL agent into the evolutionary framework to adaptively control parameters via generational feedback; 2) we design a GRC-enhanced binary tournament operator providing a comprehensive indicator to guide the search toward the Pareto front; 3) we demonstrate, on benchmark MOO and a NASDAQ case study, that the method delivers improved convergence and well-populated frontiers supporting actionable insights.

Zhiyuan Wang, Qinxu Ding, Ding Ding +4

School of Business, Singapore University of Social Sciences, Singapore 599494, Singapore

Multi-Objective Evolutionary OptimizationMulti-Objective OptimizationPortfolio Optimization
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Apr 10, 2026

Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?

Many-objective optimisation, a subset of multi-objective optimisation, involves optimisation problems with more than three objectives. As the number of objectives increases, the number of solutions needed to adequately represent the entire Pareto front typically grows substantially. This makes it challenging, if not infeasible, to design a search algorithm capable of effectively exploring the entire Pareto front. This difficulty is particularly acute in the Bayesian optimisation paradigm, where sample efficiency is critical and only a limited number of solutions (often a few hundred) are evaluated. Moreover, after the optimisation process, the decision-maker eventually selects just one solution for deployment, regardless of how many high-quality, diverse solutions are available. In light of this, we argue an idea that under a very limited evaluation budget, it may be more useful to focus on finding a single solution of the highest possible quality for the decision-maker, rather than aiming to approximate the entire Pareto front as existing many-/multi-objective Bayesian optimisation methods typically do. Bearing this idea in mind, this paper proposes a single point-based multi-objective search framework (SPMO) that aims to improve the quality of solutions along a direction that leads to a good tradeoff between objectives. Within SPMO, we present a simple acquisition function, called expected single-point improvement (ESPI), working under both noiseless and noisy scenarios. We show that ESPI can be optimised effectively with gradient-based methods via the sample average approximation (SAA) approach and theoretically prove its convergence guarantees under the SAA. We also empirically demonstrate that the proposed SPMO is computationally tractable and outperforms state-of-the-arts on a wide range of benchmark and real-world problems.

Chao Jiang, Jingyu Huang, Miqing Li

School of Computer Science, University of Birmingham · School of Mathematics, University of Birmingham

Multi-Objective OptimizationBayesian Optimization
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Apr 9, 2026

Robust Multi-Objective Optimization for Bicycle Rebalancing in Shared Mobility Systems

Dock-based bike-sharing systems exhibit spatial imbalances between bicycle supply and user demand, often addressed through overnight truck-based rebalancing. This work studies static overnight rebalancing under demand uncertainty modeled as a tri-objective optimization problem. The objectives minimize total travel distance, expected unmet demand, and a robustness-oriented unmet demand measure over high-demand scenarios. Route plans are evaluated via a recourse simulation that enforces truck loads and station capacity constraints across multiple demand realizations. The robustness objective supports selecting plans that reduce peak-demand service degradation. Trade-off solutions are approximated with Non-dominated Sorting Genetic Algorithm II using a permutation--partition encoding and domain-specific relocation operators, including a biased best-improvement move for station relocation. Experiments on the real Barcelona Bicing system with 460 stations show well-distributed Pareto sets and substantial contributions to the reference non-dominated set. Greedy constructive baselines mainly yield extreme solutions and are often dominated.

Diego Daniel Pedroza-Perez, Gabriel Luque, Sergio Nesmachnow +1

ITIS Software, University of Malaga, Spain · Universidad de la República, Uruguay

Multi-Objective OptimizationRobust OptimizationVehicle RoutingMulti-Objective Evolutionary Optimization
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Apr 9, 2026

Exploration of Pareto-preserving Search Space Transformations in Multi-objective Test Functions

Benchmark problems are an important tool for gaining understanding of optimization algorithms. Since algorithms often aim to perform well on benchmarks, biases in benchmark design provide misleading insights. In single-objective optimization, for example, many problems used to have their optimum in the center of the search domain. To remedy these issues, search space transformations have been widely adopted by benchmark suites, preventing algorithms from exploiting unintended structure. In multi-objective optimization, problem design has focused primarily on the objective space structure. While this focus addresses important aspects of the multi-objective nature of the problems, the search space structures of these problems have received comparatively limited attention. In this work, we re-emphasize the importance of transformations in the search space, and address the challenges inherent in adding transformations to boundary constraints problems without impacting the structure of the objective space. We utilized two parameterized, bijective transformations to create different instantiations of popular benchmark problems, and show how these changes impact the performance of various multi-objective optimization algorithms. In addition to the search space transformations, we show that such parameterized transformations can also be applied to the objective space, and compare their respective performance impacts.

Diederick Vermetten, Jeroen Rook

Sorbonne Université, CNRS, LIP6, Paris, France · Paderborn University, Paderborn, Germany

Multi-Objective OptimizationSynthetic Benchmark Generation
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Apr 8, 2026

Auto-Configured Networks for Multi-Scale Multi-Output Time-Series Forecasting

Industrial forecasting often involves multi-source asynchronous signals and multi-output targets, while deployment requires explicit trade-offs between prediction error and model complexity. Current practices typically fix alignment strategies or network designs, making it difficult to systematically co-design preprocessing, architecture, and hyperparameters in budget-limited training-based evaluations. To address this issue, we propose an auto-configuration framework that outputs a deployable Pareto set of forecasting models balancing error and complexity. At the model level, a Multi-Scale Bi-Branch Convolutional Neural Network (MS--BCNN) is developed, where short- and long-kernel branches capture local fluctuations and long-term trends, respectively, for multi-output regression. At the search level, we unify alignment operators, architectural choices, and training hyperparameters into a hierarchical-conditional mixed configuration space, and apply Player-based Hybrid Multi-Objective Evolutionary Algorithm (PHMOEA) to approximate the error--complexity Pareto frontier within a limited computational budget. Experiments on hierarchical synthetic benchmarks and a real-world sintering dataset demonstrate that our framework outperforms competitive baselines under the same budget and offers flexible deployment choices.

Yumeng Zha, Shengxiang Yang, Xianpeng Wang

National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University, Shenyang, China · Innovative Artificial Intelligence Cluster, Digital Future Institute, De Montfort University, Leicester, U.K. · Key Laboratory of Data Analytics and Optimization for Smart Industry (Northeastern University), Ministry of Education, Shenyang, China

Time Series ForecastingMultivariate Time Series ForecastingAutomated Machine LearningMultiscale Time-Series ModelingMulti-Objective Optimization
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Apr 7, 2026

Multi-objective Evolutionary Merging Enables Efficient Reasoning Models

Reasoning models achieve strong performance on complex problems by leveraging long chains of thought, but this deliberate reasoning incurs substantial inference-time cost. The Long-to-Short (L2S) reasoning problem seeks to preserve accuracy while reducing generated tokens. Yet, current training-free model merging approaches rely on brittle, fixed-hyperparameter arithmetic methods that force suboptimal compromises. We introduce Evo-L2S, a multi-objective evolutionary model merging framework that explicitly optimizes accuracy and output length to recover a Pareto front of merged models. To make this search computationally tractable, we propose an entropy-based subset sampling technique that substantially reduces fitness-estimation overhead. Across six mathematical reasoning benchmarks, Evo-L2S reduces reasoning length by over 50% at the 1.5B and 7B scales while preserving or improving problem-solving accuracy; at 14B, the steeper Pareto front reveals that attainable compression depends on the intrinsic compressibility of the reasoning model. Overall, Evo-L2S shows that reasoning models can be made substantially more concise while preserving strong problem-solving performance.

Mario Iacobelli, Adrian Robert Minut, Tommaso Mencattini +4

Independent Researcher · Sapienza University of Rome · EPFL +2

Efficient Language Model ReasoningLanguage Model MergingLarge Reasoning ModelsMulti-Objective Optimization
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Apr 7, 2026

Beyond Compromise: Pareto-Lenient Consensus for Efficient Multi-Preference LLM Alignment

Transcending the single-preference paradigm, aligning LLMs with diverse human values is pivotal for robust deployment. Contemporary Multi-Objective Preference Alignment (MPA) approaches predominantly rely on static linear scalarization or rigid gradient projection to navigate these trade-offs. However, by enforcing strict conflict avoidance or simultaneous descent, these paradigms often prematurely converge to local stationary points. While mathematically stable, these points represent a conservative compromise where the model sacrifices potential global Pareto improvements to avoid transient local trade-offs. To break this deadlock, we propose Pareto-Lenient Consensus (PLC), a game-theoretic framework that reimagines alignment as a dynamic negotiation process. Unlike rigid approaches, PLC introduces consensus-driven lenient gradient rectification, which dynamically tolerates local degradation provided there is a sufficient dominant coalition surplus, thereby empowering the optimization trajectory to escape local suboptimal equilibrium and explore the distal Pareto-optimal frontier. Theoretical analysis validates PLC can facilitate stalemate escape and asymptotically converge to a Pareto consensus equilibrium. Moreover, extensive experiments show that PLC surpasses baselines in both fixed-preference alignment and global Pareto frontier quality. This work highlights the potential of negotiation-driven alignment as a promising avenue for MPA. Our codes are available at https://anonymous.4open.science/r/aaa-6BB8.

Renxuan Tan, Rongpeng Li, Zhifeng Zhao +1

College of Information Science and Electronic Engineering, Zhejiang University · Zhejiang Lab, Hangzhou, China · Macau University of Science and Technology, Macau, China

Preference AlignmentMulti-Objective Language Model AlignmentPareto OptimizationMulti-Objective Optimization
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Apr 6, 2026

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 SystemsMulti-Agent PlanningMulti-Objective Optimization
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Apr 6, 2026

Efficient Multi-Objective Planning with Weighted Maximization Using Large Neighbourhood Search

Autonomous navigation often requires the simultaneous optimization of multiple objectives. The most common approach scalarizes these into a single cost function using a weighted sum, but this method is unable to find all possible trade-offs and can therefore miss critical solutions. An alternative, the weighted maximum of objectives, can find all Pareto-optimal solutions, including those in non-convex regions of the trade-off space that weighted sum methods cannot find. However, the increased computational complexity of finding weighted maximum solutions in the discrete domain has limited its practical use. To address this challenge, we propose a novel search algorithm based on the Large Neighbourhood Search framework that efficiently solves the weighted maximum planning problem. Through extensive simulations, we demonstrate that our algorithm achieves comparable solution quality to existing weighted maximum planners with a runtime improvement of 1-2 orders of magnitude, making it a viable option for autonomous navigation.

Krishna Kalavadia, Shamak Dutta, Yash Vardhan Pant +1

Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Canada

Multi-Objective Motion PlanningMulti-Objective OptimizationLarge Neighborhood Search
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Apr 6, 2026

Ranking Constraints via Topological Dual-Directional Search in Evolutionary Multi-Objective Optimization

Existing evolutionary algorithms for Constrained Multi-objective Optimization Problems (CMOPs) typically treat all constraints uniformly, overlooking their distinct geometric relationships with the true Constrained Pareto Front (CPF). In reality, constraints play different roles: some directly shape the final CPF, some create infeasible obstacles, while others are irrelevant. To exploit this insight, we propose a novel algorithm named RCCMO, which sequentially performs unconstrained exploration, single-constraint exploitation, and full-constraint refinement. The core innovation of RCCMO lies in a constraint prioritization method derived from these geometric insights, seamlessly coupled with a unique dual-directional search mechanism. Specifically, RCCMO first prioritizes constraints that constitute the final CPF, approaching them from the evolutionary direction (optimizing objectives) to locate the CPF directly shaped by single-constraint boundaries. Subsequently, for constraints that merely hinder the population's progress, RCCMO searches from the anti-evolutionary direction (targeting the infeasible boundaries where hindering constraints intersect with the CPF) to effectively discover how these constraints obstruct and form the final CPF. Meanwhile, irrelevant constraints are intentionally bypassed. Furthermore, a series of specialized mechanisms are proposed to accelerate the algorithm's execution, reduce heuristic misjudgments, and dynamically adjust search directions in real time. Extensive experiments on 5 benchmark test suites and 29 real-world CMOPs demonstrate that RCCMO significantly outperforms seven state-of-the-art algorithms.

Ruiqing Sun, Dawei Feng, Sheng Qi +6

National Key Laboratory of Parallel and Distributed Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410000, P.R. China · College of System Engineering, National University of Defense Technology, Changsha 410000, P.R. China · College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, P.R. China +1

Multi-Objective Evolutionary OptimizationEvolutionary OptimizationMulti-Objective Optimization
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Apr 5, 2026

PATHFINDER: Multi-objective discovery in structural and spectral spaces

Automated decision-making is becoming key for automated characterization including electron and scanning probe microscopies and nano indentation. Most machine learning driven workflows optimize a single predefined objective and tend to converge prematurely on familiar responses, overlooking rare but scientifically important states. More broadly, the challenge is not only where to measure next, but how to coordinate exploration across structural, spectral, and measurement spaces under finite experimental budgets while balancing target-driven optimization with novelty discovery. Here we introduce PATHFINDER, a framework for autonomous microscopy that combines novelty driven exploration with optimization, helping the system discover more diverse and useful representations across structural, spectral, and measurement spaces. By combining latent space representations of local structure, surrogate modeling of functional response, and Pareto-based acquisition, the framework selects measurements that balance novelty discovery in feature and object space and are informative and experimentally actionable. Benchmarked on pre acquired STEM EELS data and realized experimentally in scanning probe microscopy of ferroelectric materials, this approach expands the accessible structure property landscape and avoids collapse onto a single apparent optimum. These results point to a new mode of autonomous microscopy that is not only optimization-driven, but also discovery-oriented, broad in its search, and responsive to human guidance.

Kamyar Barakati, Boris N. Slautin, Utkarsh Pratiush +2

Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, USA · Department of Materials Science and Engineering, Institute of Science Tokyo, Yokohama, Japan

Autonomous ExperimentationMulti-Objective OptimizationElectron MicroscopyNovelty Search
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Apr 4, 2026

RDEx-CMOP: Feasibility-Aware Indicator-Guided Differential Evolution for Fixed-Budget Constrained Multiobjective Optimization

Constrained multiobjective optimisation requires fast feasibility attainment together with stable convergence and diversity preservation under strict evaluation budgets. This report documents RDEx-CMOP, the differential evolution variant used in the IEEE CEC 2025 numerical optimisation competition (C06 special session) constrained multiobjective track. RDEx-CMOP integrates an ε-level feasibility schedule, a SPEA2-style indicator-driven fitness assignment, and a fitness-oriented current-to-pbest/1 mutation operator. We evaluate RDEx-CMOP on the official CEC 2025 CMOP benchmark using the median-target U-score framework and the released trace data. Experimental results show that RDEx-CMOP achieves the highest total score and the best overall average rank among all released comparison algorithms, with strong target-attainment behaviour and near-zero final violation on most problems.

Sichen Tao, Yifei Yang, Ruihan Zhao +3

Department of Engineering, University of Toyama, Toyama-shi 930-8555, Japan · Cyberscience Center, Tohoku University, Sendai-shi 980-8578, Japan · Faculty of Science and Technology, Hirosaki University, Hirosaki-shi 036-8560, Japan +5

Multi-Objective Evolutionary OptimizationMulti-Objective OptimizationDifferential Evolution
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Apr 4, 2026

Finding Sets of Pareto Sets in Real-World Scenarios -- A Multitask Multiobjective Perspective

Recently, evolutionary multitasking has been employed to generate a ``set of Pareto sets" (SOS) for machine learning models, addressing diverse task settings across heterogeneous environments. This involves creating a repository of compact, specialized solution models that are collectively tailored to each specific task setting and environment, enabling users to select the most suitable model based on particular specifications and preferences. In this paper, we further demonstrate the versatility and applicability of the SOS concept across diverse domains, focusing on three real-world problems: engineering design problems, inventory management problems, and hyperparameter optimization problems. Additionally, as evolutionary multitasking has proven effective in generating the SOS, we investigate the performance of current evolutionary multitasking methods on these real-world problems. Subsequently, we present visualizations of the generated SOS in both decision and objective spaces, complemented by the development of a measurement to gauge the similarity between different Pareto sets corresponding to diverse tasks. Finally, we show that by systematically examining the shifts in Pareto optimal designs across different task settings though the SOS solutions, users can gain deeper understandings on the dynamic interplay between design solutions and their performance in different settings or contexts.

Jiao Liu, Yew Soon Ong, Melvin Wong

College of Computing & Data Science, Nanyang Technological University, Singapore

Evolutionary Multitask OptimizationMulti-Objective OptimizationMulti-Task Optimization
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Apr 2, 2026

A Comprehensive Framework for Long-Term Resiliency Investment Planning under Extreme Weather Uncertainty for Electric Utilities

Electric utilities must make massive capital investments in the coming years to respond to explosive growth in demand, aging assets and rising threats from extreme weather. Utilities today already have rigorous frameworks for capital planning, and there are opportunities to extend this capability to solve multi-objective optimization problems in the face of uncertainty. This work presents a four-part framework that 1) incorporates extreme weather as a source of uncertainty, 2) leverages a digital twin of the grid, 3) uses Monte Carlo simulation to capture variability and 4) applies a multi-objective optimization method for finding the optimal investment portfolio. We use this framework to investigate whether grid-aware optimization methods outperform model-free approaches. We find that, in fact, given the computational complexity of model-based metaheuristic optimization methods, the simpler net present value ranking method was able to find more optimal portfolios with only limited knowledge of the grid.

Emma Benjaminson

Boston Consulting Group’s AI Science Institute, Pittsburgh, PA, USA

Power SystemsDecision-Making under UncertaintyMulti-Objective Optimization
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Apr 1, 2026

Approximating Pareto Frontiers in Stochastic Multi-Objective Optimization via Hashing and Randomization

Stochastic Multi-Objective Optimization (SMOO) is critical for decision-making trading off multiple potentially conflicting objectives in uncertain environments. SMOO aims at identifying the Pareto frontier, which contains all mutually non-dominating decisions. The problem is highly intractable due to the embedded probabilistic inference, such as computing the marginal, posterior probabilities, or expectations. Existing methods, such as scalarization, sample average approximation, and evolutionary algorithms, either offer arbitrarily loose approximations or may incur prohibitive computational costs. We propose XOR-SMOO, a novel algorithm that with probability 1−δ1-δ, obtains γγ-approximate Pareto frontiers (γ>1γ>1) for SMOO by querying an SAT oracle poly-log times in γγ and δδ. A γγ-approximate Pareto frontier is only below the true frontier by a fixed, multiplicative factor γγ. Thus, XOR-SMOO solves highly intractable SMOO problems (#P-hard) with only queries to SAT oracles while obtaining tight, constant factor approximation guarantees. Experiments on real-world road network strengthening and supply chain design problems demonstrate that XOR-SMOO outperforms several baselines in identifying Pareto frontiers that have higher objective values, better coverage of the optimal solutions, and the solutions found are more evenly distributed. Overall, XOR-SMOO significantly enhanced the practicality and reliability of SMOO solvers.

Jinzhao Li, Nan Jiang, Yexiang Xue

Department of Computer Science, Purdue University, 610 Purdue Mall, West Lafayette, 47907, IN, United States. · Department of Computer Science, University of Texas at El Paso, 500 W University Ave, El Paso, 79968, TX, United States.

Multi-Objective OptimizationPareto OptimizationApproximation Algorithms
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Apr 1, 2026

Preference Guided Iterated Pareto Referent Optimisation for Accessible Route Planning

We propose the Preference Guided Iterated Pareto Referent Optimisation (PG-IPRO) for urban route planning for people with different accessibility requirements and preferences. With this algorithm the user can interact with the system by giving feedback on a route, i.e., the user can say which objective should be further minimized, or conversely can be relaxed. This leads to intuitive user interaction, that is especially effective during early iterations compared to information-gain-based interaction. Furthermore, due to PG-IPRO's iterative nature, the full set of alternative, possibly optimal policies (the Pareto front), is never computed, leading to higher computational efficiency and shorter waiting times for users.

Paolo Speziali, Arno De Greef, Mehrdad Asadi +3

Vrije Universiteit Brussel Brussels, Belgium · Gemeente Amsterdam Amsterdam, Netherlands

Travel PlanningPareto OptimizationMulti-Objective Optimization
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Apr 1, 2026

A Decoupled Basis-Vector-Driven Generative Framework for Dynamic Multi-Objective Optimization

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

Yaoming Yang, Shuai Wang, Bingdong Li +2

Multi-Party Multi-Objective OptimizationMulti-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 30, 2026

Active Preference Learning over Latent Preference Archetypes for Many-Objective Bayesian Optimization

Preference-based many-objective Bayesian optimization typically assumes that all pairwise comparisons arise from a single latent utility function, despite real decision makers often exhibiting multiple latent preference archetypes across contexts. We propose an active preference learning framework for many-objective Bayesian optimization that infers latent preference archetypes from pairwise comparisons, enabling both the identification of the active trade-off strategy and the refinement of its associated preferences. Our framework represents preferences as a Dirichlet-process mixture of latent archetypes and introduces mixture-aware information-theoretic query strategies that separately target archetype identification and within-archetype refinement through a hybrid acquisition policy. Experiments on synthetic benchmarks and real-world chemical process design case-study consistently outperforms state-of-the-art preference-based Bayesian optimization methods while recovering interpretable latent preference structure beyond conventional single-utility models. The proposed mixture-aware diagnostics further quantify archetype recovery and preference calibration, providing insights that are not captured by optimization performance alone.

Manisha Dubey, Sebastiaan De Peuter, Wanrong Wang +1

Department of Computer Science, University of Manchester, UK · Centre for AI in Assistive Autonomy, University of Edinburgh, Scotland, UK · Department of Computer Science, Aalto University, Espoo, Finland +2

Active Preference LearningBayesian OptimizationPreference LearningMulti-Objective OptimizationPairwise Preference Learning
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Mar 29, 2026

A Novel Immune Algorithm for Multiparty Multiobjective Optimization

Traditional multiobjective optimization problems (MOPs) are insufficiently equipped for scenarios involving multiple decision makers (DMs), which are prevalent in many practical applications. These scenarios are categorized as multiparty multiobjective optimization problems (MPMOPs). For MPMOPs, the goal is to find a solution set that is as close to the Pareto front of each DM as much as possible. This poses challenges for evolutionary algorithms in terms of searching and selecting. To better solve MPMOPs, this paper proposes a novel approach called the multiparty immune algorithm (MPIA). The MPIA incorporates an inter-party guided crossover strategy based on the individual's non-dominated sorting ranks from different DM perspectives and an adaptive activation strategy based on the proposed multiparty cover metric (MCM). These strategies enable MPIA to activate suitable individuals for the next operations, maintain population diversity from different DM perspectives, and enhance the algorithm's search capability. To evaluate the performance of MPIA, we compare it with ordinary multiobjective evolutionary algorithms (MOEAs) and state-of-the-art multiparty multiobjective optimization evolutionary algorithms (MPMOEAs) by solving synthetic multiparty multiobjective problems and real-world biparty multiobjective unmanned aerial vehicle path planning (BPUAV-PP) problems involving multiple DMs. Experimental results demonstrate that MPIA outperforms other algorithms.

Kesheng Chen, Wenjian Luo, Qi Zhou +3

Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies, School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen 518055, China. · Peng Cheng Laboratory, Shenzhen 518000, China. · School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China. +1

Multi-Party Multi-Objective OptimizationMulti-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 27, 2026

Breaking Exponential Complexity in Games of Ordered Preference: A Tractable Reformulation

Games of ordered preference (GOOPs) model multi-player equilibrium problems in which each player maintains a distinct hierarchy of strictly prioritized objectives. Existing approaches solve GOOPs by deriving and enforcing the necessary optimality conditions that characterize lexicographically constrained Nash equilibria through a single-level reformulation. However, the number of primal and dual variables in the resulting KKT system grows exponentially with the number of preference levels, leading to severe scalability challenges. We derive a compact reformulation of these necessary conditions that preserves the essential primal stationarity structure across hierarchy levels, yielding a "reduced" KKT system whose size grows polynomially with both the number of players and the number of preference levels. The reduced system constitutes a relaxation of the complete KKT system, yet it remains a valid necessary condition for local GOOP equilibria. For GOOPs with quadratic objectives and linear constraints, we prove that the primal solution sets of the reduced and complete KKT systems coincide. More generally, for GOOPs with arbitrary (but smooth) nonlinear objectives and constraints, the reduced KKT conditions recover all local GOOP equilibria but may admit spurious non-equilibrium solutions. We introduce a second-order sufficient condition to certify when a candidate point corresponds to a local GOOP equilibrium. We also develop a primal-dual interior-point method for computing a local GOOP equilibrium with local quadratic convergence. The resulting framework enables scalable and efficient computation of GOOP equilibria beyond the tractable range of existing exponentially complex formulations.

Dong Ho Lee, Jingqi Li, Lasse Peters +2

Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, TX 78712-1221 USA · Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712-1221 USA · Department of Mechanical Engineering, UC Berkeley, Berkeley, CA 94720-1740 USA +1

Nash Equilibrium ComputationMulti-Objective OptimizationConstrained Optimization
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Mar 27, 2026

Agents on a Tree: Pathwise Coordination for Multi-Objective Molecular Optimization

Multi-objective molecular optimization requires searching vast chemical spaces under conflicting objectives, where early design decisions strongly constrain downstream outcomes. Existing methods typically rely on a single policy or fixed scalarization, which limits their ability to represent diverse trade-offs and to explore multiple promising design trajectories. We propose ATOM, a multi-agent framework that formulates molecular optimization as a tree-structured search. Each node corresponds to an atomic operation and hosts an agent specialized for a particular objective or decision context. Agents coordinate along different paths of the tree rather than enforcing a global consensus, enabling the method to maintain and compare alternative molecular evolution trajectories. A global memory of past optimization behaviors further supports balanced exploration and exploitation across objectives. This tree-structured interaction enables reasoning over long-horizon dependencies inherent in molecular design. Experiments on challenging multi-objective benchmarks involving activity, synthesizability, and ADMET-related properties show that ATOM consistently achieves improved Pareto coverage and hypervolume over strong baselines. These results demonstrate the effectiveness of pathwise multi-agent coordination for molecular optimization. Code is available at https://anonymous.4open.science/r/ATOM-41CE.

Jia Zhang, Tengfei Ma, Tianle Li +3

College of Computer Science and Electronic Engineering, Hunan University · College of Information and Science, Hunan Normal University.

Molecular OptimizationMulti-Objective OptimizationMulti-Agent CoordinationTree Search
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Mar 27, 2026

Efficient Disruption of Criminal Networks through Multi-Objective Genetic Algorithms

Criminal networks, such as the Sicilian Mafia, pose substantial threats to public safety, national security, and economic stability. Outdated disruption methods with a focus on removing influential individuals or key players have proven ineffective due to the covertness of the network. Thus, researchers have been trying to apply Social Network Analysis (SNA) techniques, such as centrality-based measures, to identify key players. However, removing individuals with high centrality often proves to be inefficient, as it does not mimic the real-world scenarios that Law Enforcement Agencies (LEAs) face. For instance, the operational costs limit the LEAs from exploiting the results of the centrality-based methods. This study proposes a multi-objective optimisation framework like the Weighted Sum Genetic Algorithm (WS-GA) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to identify disruption strategies that balance two conflicting goals, maximising fragmentation and minimising operational cost which is captured by the spatial distance between nodes and the nearest LEA headquarters. The study utilises the "Montagna Operation" dataset for the experiments. The results demonstrate that although centrality-based approaches can fragment network effectively, they tend to incur higher operational costs. In contrast, the proposed algorithms achieve comparable disruption outcomes with significantly lower operational costs. The contribution of this work lies in incorporating operational costs in a form of spatial distance constraints into disruption strategy, which has been largely overlooked in prior studies. This research offers a scalable multi-objective capability that improves practical application of SNA in guiding LEAs in disrupting criminal networks more efficiently and strategically.

Yehezkiel Darmadi, Thanh Thi Nguyen, Campbell Wilson

Faculty of Information Technology, Monash University, Melbourne, Victoria, 3800, Australia · AiLECS Lab, Faculty of Information Technology, Monash University, Melbourne, Victoria, 3800, Australia

Multi-Objective OptimizationComputational Social ScienceMulti-Objective Evolutionary Optimization
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Mar 25, 2026

Bridging the Evaluation Gap: Standardized Benchmarks for Multi-Objective Search

Empirical evaluation in multi-objective search (MOS) has historically suffered from fragmentation, relying on heterogeneous problem instances with incompatible objective definitions that make cross-study comparisons difficult. This standardization gap is further exacerbated by the realization that DIMACS road networks, a historical default benchmark for the field, exhibit highly correlated objectives that fail to capture diverse Pareto-front structures. To address this, we introduce the first comprehensive, standardized benchmark suite for exact and approximate MOS. Our suite spans four structurally diverse domains: real-world road networks, structured synthetic graphs, game-based grid environments, and high-dimensional robotic motion-planning roadmaps. By providing fixed graph instances, standardized start-goal queries, reference exact Pareto-optimal solution sets, and a standardized approximate (ε\varepsilon-dominance) evaluation protocol, this suite captures a full spectrum of objective interactions: from strongly correlated to strictly independent. Ultimately, this benchmark provides a common foundation to ensure future MOS evaluations are robust, reproducible, and structurally comprehensive.

Hadar Peer, Carlos Hernandez, Sven Koenig +2

Technion – Israel Institute of Technology · Universidad San Sebastián · University of California, Irvine +1

Benchmark DesignMulti-Objective OptimizationMulti-Objective Motion Planning
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Mar 23, 2026

Training-Free Diffusion-Driven Modeling of Pareto Set Evolution for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization problems (DMOPs) feature time-varying objectives, which cause the Pareto optimal solution (POS) set to drift over time and make it difficult to maintain both convergence and diversity under limited response time. Many existing prediction-based dynamic multiobjective evolutionary algorithms (DMOEAs) either depend on learned models with nontrivial training cost or employ one-step population mapping, which may overlook the gradual nature of POS evolution. This paper proposes DD-DMOEA, a training-free diffusion-based dynamic response mechanism for DMOPs. The key idea is to treat the POS obtained in the previous environment as a "noisy" sample set and to guide its evolution toward the current POS through an analytically constructed multi-step denoising process. A knee-point-based auxiliary strategy is used to specify the target region in the new environment, and an explicit probability-density formulation is derived to compute the denoising update without neural training. To reduce the risk of misleading guidance caused by knee-point prediction errors, an uncertainty-aware scheme adaptively adjusts the guidance strength according to the historical prediction deviation. Experiments on the CEC2018 dynamic multiobjective benchmarks show that DD-DMOEA achieves competitive or better convergence-diversity performance and provides faster dynamic response than several state-of-the-art DMOEAs.

Jian Guan, Huolong Wu, Zhenzhong Wang +2

Institute of Artificial Intelligence, Xiamen University, Xiamen, 361005, China · Department of Artificial Intelligence, School of Informatics, Xiamen University; the Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education; and the Key Laboratory of Digital Protection and Intelligent Processing of Intangible Cultural Heritage of Fujian and Taiwan, Ministry of Culture and Tourism, Xiamen, 361005, China · Department of Artificial Intelligence, Sichuan University, Chengdu, 610065, China

Multi-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 23, 2026

Evolutionary Biparty Multiobjective UAV Path Planning: Problems and Empirical Comparisons

Unmanned aerial vehicles (UAVs) have been widely used in urban missions, and proper planning of UAV paths can improve mission efficiency while reducing the risk of potential third-party impact. Existing work has considered all efficiency and safety objectives for a single decision-maker (DM) and regarded this as a multiobjective optimization problem (MOP). However, there is usually not a single DM but two DMs, i.e., an efficiency DM and a safety DM, and the DMs are only concerned with their respective objectives. The final decision is made based on the solutions of both DMs. In this paper, for the first time, biparty multiobjective UAV path planning (BPMO-UAVPP) problems involving both efficiency and safety departments are modeled. The existing multiobjective immune algorithm with nondominated neighbor-based selection (NNIA), the hybrid evolutionary framework for the multiobjective immune algorithm (HEIA), and the adaptive immune-inspired multiobjective algorithm (AIMA) are modified for solving the BPMO-UAVPP problem, and then biparty multiobjective optimization algorithms, including the BPNNIA, BPHEIA, and BPAIMA, are proposed and comprehensively compared with traditional multiobjective evolutionary algorithms and typical multiparty multiobjective evolutionary algorithms (i.e., OptMPNDS and OptMPNDS2). The experimental results show that BPAIMA performs better than ordinary multiobjective evolutionary algorithms such as NSGA-II and multiparty multiobjective evolutionary algorithms such as OptMPNDS, OptMPNDS2, BPNNIA and BPHEIA.

Kesheng Chen, Wenjian Luo, Xin Lin +2

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

UAV Trajectory OptimizationMulti-Objective Motion PlanningMulti-Objective OptimizationMulti-Objective Evolutionary OptimizationMetaheuristic Optimization
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Mar 22, 2026

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 ModelingSurrogate-Assisted OptimizationMulti-Objective OptimizationSensitivity Analysis
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Mar 19, 2026

CAMO: A Conditional Neural Solver for the Multi-objective Multiple Traveling Salesman Problem

Robotic systems often require a team of robots to collectively visit multiple targets while optimizing competing objectives, such as total travel cost and makespan. This setting can be formulated as the Multi-Objective Multiple Traveling Salesman Problem (MOMTSP). Although learning-based methods have shown strong performance on the single-agent TSP and multi-objective TSP variants, they rarely address the combined challenges of multi-agent coordination and multi-objective trade-offs, which introduce dual sources of complexity. To bridge this gap, we propose CAMO, a conditional neural solver for MOMTSP that generalizes across varying numbers of targets, agents, and preference vectors, and yields high-quality approximations to the Pareto front (PF). Specifically, CAMO consists of a conditional encoder to fuse preferences into instance representations, enabling explicit control over multi-objective trade-offs, and a collaborative decoder that coordinates all agents by alternating agent selection and node selection to construct multi-agent tours autoregressively. To further improve generalization, we train CAMO with a REINFORCE-based objective over a mixed distribution of problem sizes. Extensive experiments show that CAMO outperforms both neural and conventional heuristics, achieving a closer approximation of PFs. In addition, ablation results validate the contributions of CAMO's key components, and real-world tests on a mobile robot platform demonstrate its practical applicability.

Fengxiaoxiao Li, Xiao Mao, Mingfeng Fan +4

National University of Singapore, Singapore. · China Unicom Shenzhen Branch, Shenzhen, China. · Central South University, Changsha, China.

Neural Combinatorial OptimizationMulti-Objective OptimizationMulti-Robot Coordination
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Mar 18, 2026

Stochastic set-valued optimization and its application to robust learning

In this paper, we develop a stochastic set-valued optimization (SVO) framework tailored for robust machine learning. In the SVO setting, each decision variable is mapped to a set of objective values, and optimality is defined via set relations. We focus on SVO problems with hyperbox sets, which can be reformulated as multi-objective optimization (MOO) problems with finitely many objectives and serve as a foundation for representing or approximating more general mapped sets. Two special cases of hyperbox-valued optimization (HVO) are interval-valued (IVO) and rectangle-valued (RVO) optimization. We construct stochastic IVO/RVO formulations that incorporate subquantiles and superquantiles into the objective functions of the MOO reformulations, providing a new characterization for subquantiles. These formulations provide interpretable trade-offs by capturing both lower- and upper-tail behaviors of loss distributions, thereby going beyond standard empirical risk minimization and classical robust models. To solve the resulting multi-objective problems, we adopt stochastic multi-gradient algorithms and select a Pareto knee solution. In numerical experiments, the proposed algorithms with this selection strategy exhibit improved robustness and reduced variability across test replications under distributional shift compared with empirical risk minimization, while maintaining competitive accuracy.

Tommaso Giovannelli, Jingfu Tan, Luis Nunes Vicente

Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH 45221, USA · Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA 18015-1582, USA

Stochastic OptimizationDistribution Shift RobustnessMulti-Objective Optimization
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Mar 17, 2026

Deep Reinforcement Learning-Assisted Automated Operator Portfolio for Constrained Multi-objective Optimization

Constrained multi-objective optimization problems (CMOPs) are of great significance in the context of practical applications, ranging from scientific to engineering domains. Most existing constrained multi-objective evolutionary algorithms (CMOEAs) usually employ fixed operators all the time, which exhibit poor versatility in handling various CMOPs. Therefore, some recent studies have focused on adaptively selecting the best operators for the current population states during the search process. The evolutionary algorithms proposed in these studies learn the value of each operator and recommend the operator with the highest value for the current population, resulting in only a single operator being recommended at each generation, which can potentially lead to local optima and inefficient utilization of function evaluations. To address the dilemma in operator adaptation, this paper proposes a reinforcement learning-based automated operator portfolio approach to learn an allocation scheme of operators at each generation. This approach considers the optimization-related and constraint-related features of the current population as states, the overall improvement in population convergence and diversity as rewards, and different operator portfolios as actions. By utilizing deep neural networks to establish a mapping model between the population states and the expected cumulative rewards, the proposed approach determines the optimal operator portfolio during the evolutionary process. By embedding the proposed approach into existing CMOEAs, a deep reinforcement learning-assisted automated operator portfolio based evolutionary algorithm for solving CMOPs, abbreviated as CMOEA-AOP, is developed. Empirical studies on 33 benchmark problems demonstrate that the proposed algorithm significantly enhances the performance of CMOEAs and exhibits more stable performance across different CMOPs.

Shuai Shao, Ye Tian, Shangshang Yang +1

the School of Computer Science and Technology, Anhui University, Hefei 230601, China

Multi-Objective OptimizationMulti-Objective Evolutionary Optimization
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Mar 14, 2026

MO-SAE:Multi-Objective Stacked Autoencoders Optimization for Edge Anomaly Detection

Stacked AutoEncoders (SAE) have been widely adopted in edge anomaly detection scenarios. However, the resource-intensive nature of SAE can pose significant challenges for edge devices, which are typically resource-constrained and must adapt rapidly to dynamic and changing conditions. Optimizing SAE to meet the heterogeneous demands of real-world deployment scenarios, including high performance under constrained storage, low power consumption, fast inference, and efficient model updates, remains a substantial challenge. To address this, we propose an integrated optimization framework that jointly considers these critical factors to achieve balanced and adaptive system-level optimization. Specifically, we formulate SAE optimization for edge anomaly detection as a multi-objective optimization problem and propose MO-SAE (Multi-Objective Stacked AutoEncoders). The multiple objectives are addressed by integrating model clipping, multi-branch exit design, and a matrix approximation technique. In addition, a multi-objective heuristic algorithm is employed to effectively balance the competing objectives in SAE optimization. Our results demonstrate that the proposed MO-SAE delivers substantial improvements over the original approach. On the x86 architecture, it reduces storage space and power consumption by at least 50%, improves runtime efficiency by no less than 28%, and achieves an 11.8% compression rate, all while maintaining application performance. Furthermore, MO-SAE runs efficiently on edge devices with ARM architecture. Experimental results show a 15% improvement in inference speed, facilitating efficient deployment in cloud-edge collaborative anomaly detection systems.

Lizhao Zhang, Shengsong Kong, Tao Guo +2

Faculty of computing, Harbin Institute of Technology, Harbin 150000, China.

AutoencodersEfficient Neural Network InferenceEnergy-Efficient MLAnomaly DetectionMulti-Objective Optimization
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