Combinatorial Optimization

Ask about this topic

Overview

Combinatorial optimization studies how to choose the best arrangement, assignment, route, or schedule when decisions are discrete and constraints interact. Exact methods such as integer programming, constraint programming, SAT, dynamic programming, and branch-and-bound can certify optimality, while approximation algorithms and metaheuristics trade guarantees for speed on larger instances. Learning methods—including graph neural networks, reinforcement learning, and language-model-guided heuristic design—are increasingly paired with classical search to propose solutions, warm-start solvers, or select algorithms. A central challenge is making these methods scale and generalize without sacrificing feasibility, solution quality, or the guarantees that exact and approximation methods provide.

Latest papers

CardsList

386 papers47 papers in the last four weeks, up 47% on the four weeks before. 0.3% of all new papers.

  1. Generating Hadamard matrices with transformers

    Apr 13, 2026Geordie Williamson, Oded Yacobi, Paul Zinn-JustinCombinatorial OptimizationNeural Combinatorial Optimization

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

    Apr 13, 2026Ishara Hewa Pathiranage, Aneta NeumannCombinatorial OptimizationConstrained Optimization

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

  3. Graph-RHO: Critical-path-aware Heterogeneous Graph Network for Long-Horizon Flexible Job-Shop Scheduling

    Apr 11, 2026Yujie Li, Jiuniu Wang, Mugen Peng +2Flexible Job Shop SchedulingJob Shop Scheduling

    Beijing University of Posts and Telecommunications Beijing, China · City University of Hong Kong Hong Kong, China · Chinese Academy of Sciences Beijing, China

  4. Validated Intent Compilation for Constrained Routing in LEO Mega-Constellations

    Apr 8, 2026Yuanhang LiIntent-Based NetworkingLEO Satellite Networks

  5. Block-Bench: A Framework for Controllable and Transparent Discrete Optimization Benchmarking

    Apr 8, 2026Furong Ye, Frank Neumann, Thomas Bäck +1Benchmark DesignSynthetic Benchmark Generation

    LIACS, Leiden University, Leiden, the Netherlands · Optimisation and Logistics, School of Computer Science and Information Technology, Adelaide University, Adelaide, Australia

  6. A First Guess Is Rarely the Final Answer: Learned Local Search That Generalizes to Larger Routing Problems

    Apr 8, 2026Andoni Irazusta GarmendiaTraveling Salesperson ProblemNeural Combinatorial Optimization

    University of the Basque Country (UPV/EHU)

  7. The Traveling Thief Problem with Time Windows: Benchmarks and Heuristics

    Apr 8, 2026Helen Yuliana Angmalisang, Frank NeumannCombinatorial Optimization

    Optimisation and Logistics School of Computer Science and Information Technology Adelaide University Adelaide, SA 5000

  8. Cayley Graph Optimization for Scalable Multi-Agent Communication Topologies

    Apr 7, 2026Jingkai Luo, Yulin ShaoCommunication Topology OptimizationMulti-Agent Communication Topology

    Department of Electrical and Computer Engineering, The University of Hong Kong, Hong Kong, China

  9. Inventory of the 12 007 Low-Dimensional Pseudo-Boolean Landscapes Invariant to Rank, Translation, and Rotation

    Apr 7, 2026Arnaud Liefooghe, Sébastien VerelFitness Landscape AnalysisCombinatorial Optimization

    LISIC · Univ. Littoral Côte d’Opale, UR 4491, LISIC, F-62100 Calais, France

  10. TransGP: Task-Conditioned Transformer-Guided Genetic Programming for Multitask Dynamic Flexible Job Shop Scheduling

    Apr 4, 2026Meng Xu, Jiao Liu, Hua Yu +1Job Shop SchedulingAutomated Heuristic Design

  11. Breaking Validity-Induced Boundaries to Expand Algorithm Search Space: A Two-Stage AST-Based Operator for LLM-Driven Automated Heuristic Evolution

    Apr 3, 2026Sun Shengming, Shi JialongAutomated Heuristic DesignLarge Language Model-Guided Optimization

    School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

  12. How to measure the optimality of word or gesture order with respect to the principle of swap distance minimization

    Apr 2, 2026Ramon Ferrer-i-CanchoCombinatorial Optimization

    Quantitative, Mathematical and Computational Linguistics Research Group (LQMC), Departament de Ciències de la Computació, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, Jordi Girona Salgado 1-3, 08034 Barcelona, Catalonia, Spain

  13. When does learning pay off? A study on DRL-based dynamic algorithm configuration for carbon-aware scheduling

    Apr 2, 2026Andrea Mencaroni, Robbert Reijnen, Yingqian Zhang +1RL ControlLearning to Optimize

    Department of Industrial Systems Engineering and Product Design, Ghent University, Ghent, Belgium · Industrial Systems Engineering (ISyE), Flanders Make, Kortrijk, Belgium · Eindhoven Artificial Intelligence Systems Institute, Eindhoven University of Technology, The Netherlands +1

  14. Solving the Two-dimensional single stock size Cutting Stock Problem with SAT and MaxSAT

    Apr 2, 2026Tuyen Van Kieu, Chi Linh Hoang, Khanh Van ToBoolean SatisfiabilityCombinatorial Optimization

    VNU University of Engineering and Technology, Hanoi, Vietnam

  15. A Graph Neural Network Approach for Solving the Ranked Assignment Problem in Multi-Object Tracking

    Apr 2, 2026Robin Dehler, Martin Herrmann, Jan Strohbeck +1Data AssociationMulti-Object Tracking

    The authors are with the Institute of Measurement, Control and Microtechnology, Ulm University, D-89081 Ulm, Germany.

  16. Infeasibility Aware Large Language Models for Combinatorial Optimization

    Apr 1, 2026Yakun Wang, Min Chen, Zeguan Wu +3Combinatorial OptimizationLarge Language Model-Guided Optimization

    Lehigh University, Bethlehem, PA 18015, USA · Department of Computer Science, University of Pittsburgh, Pittsburgh, PA 15260, USA · Johnson & Johnson, New Brunswick, NJ 08933, USA

  17. Optimizing Donor Outreach for Blood Collection Sessions: A Scalable Decision Support Framework

    Mar 31, 2026André Carneiro, Pedro T. Monteiro, Rui HenriquesHealthcareSupply Chain Management

    INESC-ID and Técnico Universidade de Lisboa Portugal

  18. Reducing Complexity for Quantum Approaches in Train Load Optimization

    Mar 31, 2026Zhijie Tang, Albert Nieto-Morales, Arit Kumar BishwasCombinatorial OptimizationSupply Chain Management

    Commercial Technology and Innovation, Shanghai, China · Tech and Innovation, San Francisco, US

  19. Differentiable Initialization-Accelerated CPU-GPU Hybrid Combinatorial Scheduling

    Mar 30, 2026Mingju Liu, Jiaqi Yin, Alvaro Velasquez +1Combinatorial OptimizationInteger Linear Programming

    University of Maryland, College Park, Maryland, USA · University of Colorado, Boulder, Colorado, USA

  20. Transferable knowledge graphs with executable learned operators for algorithm design

    Mar 30, 2026Camilo Chacón Sartori, José H. García, Andrei Voicu Tomut +1Knowledge GraphsAutomated Algorithm Discovery

    Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193, Barcelona, Spain · Artificial Intelligence Research Institute (IIIA-CSIC), Bellaterra, Spain

  21. DSevolve: Enabling Real-Time Adaptive Scheduling on Dynamic Flexible Job Shop with LLM-Evolved Heuristic Portfolios

    Mar 29, 2026XinLei Zhou, Jin Huang, Jie Yang +2Flexible Job Shop SchedulingReal-Time Scheduling

    School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, PR China

  22. A gentle tutorial on Bock's algorithm for minimum directed spanning trees with a structured reformulation

    Mar 29, 2026Yuxi Wang, Jungyeul ParkCombinatorial OptimizationPrimal-Dual Optimization

    UBC, Canada · KAIST, South Korea

  23. Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization

    Mar 28, 2026Shaodi Feng, Zhuoyi Lin, Yaoxin Wu +4Combinatorial OptimizationNeural Combinatorial Optimization

    National Yang Ming Chiao Tung University · Institute for Infocomm Research (I2R), A*STAR · Eindhoven University of Technology Eindhoven +3

  24. On the Complexity of Optimal Graph Rewiring for Oversmoothing and Oversquashing in Graph Neural Networks

    Mar 27, 2026Mostafa Haghir ChehreghaniOver-Squashing in GNNsOver-Smoothing in GNNs

    Department of Computer Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

  25. Online Learning for Dynamic Constellation Topologies

    Mar 26, 2026João Norberto, Ricardo Ferreira, Cláudia SoaresCombinatorial OptimizationWireless Communications

    NOVA School of Science and Technology, Caparica, Portugal

  26. Scheduling with Time Dependent Utilities: Fairness and Efficiency

    Mar 26, 2026Gaia Nicosia, Andrea Pacifici, Ulrich PferschyFair Resource AllocationCombinatorial Optimization

    Dipartimento di Ingegneria Civile, Informatica e delle Tecnologie Aeronautiche, Università degli Studi “Roma Tre”, via della Vasca Navale 79, 00146 Rome, Italy · Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università degli Studi di Roma “Tor Vergata”, Via del Politecnico 1, 00133 Rome, Italy · Department of Operations and Information Systems, University of Graz, Universitaetsstrasse 15, 8010 Graz, Austria

  27. A Deep Reinforcement Learning (DRL)-Based Transformer Method for Solving the Open Shop Scheduling Problem

    Mar 25, 2026Faezeh Ardali, Mwembezi A. Nyelele, Gerald M. KnappCombinatorial OptimizationNeural Combinatorial Optimization

    Louisiana State University, Baton Rouge, LA, USA · University of Minnesota Duluth, Duluth, MN, USA

  28. Fleet-Level Battery-Health-Aware Scheduling for Autonomous Mobile Robots

    Mar 24, 2026Jiachen Li, Shihao Li, Jian Chu +2Multi-Robot Task AllocationMulti-Agent System Optimization

    University of Texas at Austin, Austin, TX 78712 USA

  29. cuGenOpt: A GPU-Accelerated General-Purpose Metaheuristic Framework for Combinatorial Optimization

    Mar 19, 2026Yuyang LiuMetaheuristic OptimizationCombinatorial Optimization

    Independent Researcher, Shenzhen, China

  30. Domain-Independent Dynamic Programming with Constraint Propagation

    Mar 17, 2026Imko Marijnissen, J. Christopher Beck, Emir Demirović +1Resource-Constrained Project SchedulingConstraint Propagation

    Delft University of Technology, The Netherlands · University of Toronto, Canada · National Institute of Informatics, Japan +1