Mixed-Integer Linear Programming

Also known as MILP

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Overview

Mixed-integer linear programming combines continuous quantities with integer or binary choices to model problems such as scheduling, routing, resource allocation, and power-system operations. Exact solvers rely on branch-and-bound, cutting planes, presolve, and decomposition methods such as Benders decomposition to find solutions and certify their quality. Current work also uses machine learning to guide branching, warm-start solvers, and predict useful decisions, with learned guidance increasingly combined with rather than substituted for exact optimization. The central challenge is making large instances faster to solve without sacrificing feasibility, reliable performance across problem types, or certificates of solution quality.

Latest papers

CardsList

50 papers13 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

  1. Nominate-then-Adjudicate: LLM-Assisted One-Pass and Per-Instance MIP Solver Tuning

    Oct 21, 2026Yifan Zhao, Qianyang Zhao, Xinyu Guan +2Large Language Model-Guided OptimizationMixed-Integer Linear Programming

    Alibaba Group, Hangzhou, China

  2. Interpretable Cutting Plane Selection for Mixed-Integer Linear Programming Using Genetic Programming

    Oct 21, 2026Gwen maudet, Mathis Da Cunha, Grégoire DanoyMixed-Integer Linear ProgrammingInterpretable ML

    SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg · FSTM/DCS, SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg

  3. Evo-B&B: Behavior-Aware LLM-Guided Joint Evolution of Branching and Node Selection Policies for MILP

    Oct 16, 2026Jiayu Chen, Chentong Chen, Yuhan Liu +3Branch and BoundMixed-Integer Linear Programming

    School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China · School of Electronics and Information, Northwestern Polytechnical University, Xi’an, China

  4. Imperfect Is Perfect: Learned Column Prefilling for Branch-Price-and-Cut

    Oct 14, 2026Haoran Liu, Yu YangLearning to OptimizeMixed-Integer Linear Programming

    Department of Industrial Systems Engineering, University of Florida, Florida, United States

  5. Optimizing Sparse Boolean Rule Networks using Mixed Integer Linear Programming

    Oct 14, 2026Thomas Pammer, Johannes Fürnkranz, Markus SinnlBoolean Function LearningInterpretable ML

    Institute for Application-Oriented Knowledge Processing (FAW), Johannes Kepler University Linz, Austria · LIT AI Lab, Johannes Kepler University Linz, Austria · Institute of Business Analytics & Technology Transformation/JKU Business School, Johannes Kepler University Linz, Austria

  6. Sequence-Structured Decision Learning for Branch-and-Bound in Mixed-Integer Linear Programming

    Oct 10, 2026Tengfei Liu, Jinrun Liu, Bai Yan +2Branch and BoundMixed-Integer Linear Programming

    Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China · School of Computer Science and Technology, Dongguan University of Technology, Dongguan, China

  7. When Solvers Get Moody: Quantifying and Predicting Performance Variability in Mixed Integer Programming

    Oct 9, 2026Mourchid Adegbindin, Brenda Dietrich, Jamol Pender +1Mixed-Integer Linear Programming

    Cornell University

  8. ORDO: Operation-level Round-aware Dynamic Ordering for MIP Presolve

    Oct 8, 2026Zehuan Chen, Chunhe SongMixed-Integer Linear ProgrammingOperations Research

    Institute of Industrial Artificial Intelligence, CAS

  9. Outperformance Inverse Optimization: Learning Objective Functions that Outperform Agent Decisions

    Oct 7, 2026Akira KitaokaLearning to OptimizeMixed-Integer Linear Programming

  10. Reformulation-Contrastive Learning for Mixed Integer Programs

    Sep 30, 2026Ousema Bouaneni, Mathis Le Bail, Clément Elliker +2Contrastive LearningRepresentation Learning

    LIX (École Polytechnique, IP Paris, CNRS) · AMIAD (Agence Ministérielle pour l’IA de Défense)

  11. Autoresearch in Mixed-Integer Linear and Nonlinear Programming

    Sep 30, 2026Yuwei Gu, Yaoxin Wu, Tong Guo +2Automated Algorithm DiscoveryMixed-Integer Linear Programming

    Chengdu University of Information Technology · Eindhoven University of Technology · Nanyang University of Technology +2

  12. Teaching LLMs to Generate Challenging MILP Instances via Solver Feedback

    Sep 29, 2026Jitin Singla, Parikshit Pareek, Pratik Jawanpuria +1Mixed-Integer Linear ProgrammingLarge Language Model-Guided Optimization

    IIT Roorkee · IIT Bombay · IIT Delhi

  13. BiFE: Search-Efficient Discovery of CPU-Only Branching Policies via LLM-based Bi-Fidelity Evolution

    Sep 29, 2026Ce Zhang, Bin Zhang, Zhiwei Xu +5Multi-Fidelity OptimizationAutomated Algorithm Discovery

    Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · Shandong University

  14. Mixed-integer flow formulations for motion planning and decision-making of networked multi-agent systems

    Sep 21, 2026Angelo Caregnato-Neto, Paul-Louis Delacour, Raf Van de Plas +2Constrained Motion PlanningMixed-Integer Linear Programming

    Department of Computational Mechanics (DMC), School of Mechanical Engineering (FEM), State University of Campinas (UNICAMP), São Paulo, Brazil · Delft Center for Systems and Control, Delft University of Technology, Delft, Netherlands · Dept. of Biochemistry, Vanderbilt University, Nashville, TN, USA

  15. Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimization

    Aug 31, 2026Jessica D. Elrefaei, Kaixun Hua, Seungbae Kim +2Graph Neural NetworksValue Function Estimation

  16. SHSP: Structure-Aware Hierarchical Solution Prediction for Mixed-Integer Linear Programming

    Aug 26, 2026Zherong Zhang, Guanlin Li, Chengrui Gao +5Mixed-Integer Linear ProgrammingNeural Combinatorial Optimization

    State Key Laboratory of Novel Software Technology, Nanjing University · School of Artificial Intelligence, Nanjing University · State Key Laboratory of Technology and Equipment for Defense Against Power System Operational Risks, Nari Technology Co., Ltd.

  17. FLARE: Verifying MILP Reformulations with LLM-Based Theorem Proving

    Aug 25, 2026Henry Robbins, Connor Lawless, Madeleine Udell +1Mixed-Integer Linear ProgrammingFormal Verification

    Stanford University

  18. FormuEvo: LLM-Guided Evolution for Discovering Solver-Efficient Mixed-Integer Programming Formulations

    Aug 24, 2026Haofeng Yuan, Jianing Peng, Jieyi Bi +3Large Language Model-Guided OptimizationMixed-Integer Linear Programming

    Department of Automation, BNRist, Tsinghua University · College of Computing and Data Science, Nanyang Technological University · School of Computing and Information Systems, Singapore Management University

  19. Learning Early-to-Final Solution Consistency for MILP Acceleration

    Aug 20, 2026Guanlin Li, Chengrui Gao, Chenguang Wang +6Mixed-Integer Linear ProgrammingLearning to Optimize

    State Key Laboratory of Novel SoftwareTechnology, Nanjing University · School of Artificial Intelligence,Nanjing University · State Key Laboratory of Technology and Equipment for Defense Against Power System Operational Risks, Nari Technology Co., Ltd.

  20. Constrained Graph Diffusion for Mixed Integer Optimization

    Aug 13, 2026Vincenzo Di Vito, Yusuf Guven, Babak Badnava +3Mixed-Integer Linear ProgrammingConstrained Optimization

    University of Virginia · MIT · Los Alamos National Laboratory

  21. Input convex neural networks as surrogates in mathematical optimisation

    Aug 10, 2026Yu Liu, Jan Kronqvist, Fabricio OliveiraSurrogate-Assisted OptimizationMixed-Integer Linear Programming

    Department of Mathematics and Systems Analysis, School of Science, Aalto University, Espoo, Finland · Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden · DTU Management, Technical University of Denmark, Lyngby, Denmark

  22. Not All Problems Are Best Modeled as MILP: A DSL-Centric Framework for Flexible and Accurate Optimization Modeling

    Aug 7, 2026Shaofeng Zhang, Hongyuan Su, Qingwen Peng +4Mixed-Integer Linear ProgrammingLarge Language Model-Guided Optimization

    Southern University of Science and Technology, Shenzhen · Zhongguancun Academy, Beijing · Tsinghua University, Beijing +1

  23. A Weisfeiler-Leman Characterization of Global-Attention Graph Transformers for Mixed-Integer Linear Programs

    Jul 20, 2026Md Abrar Jahin, Craig A. Knoblock, Jay PujaraMixed-Integer Linear ProgrammingGNN Expressivity

    University of Southern California, Los Angeles, CA 90089, USA · USC Information Sciences Institute, Marina del Rey, CA 90292, USA

  24. Low-Latency Relay Selection in NR-V2X Vehicular Communications via Graph Isomorphism Networks with Edge Features

    Jul 15, 2026Giambattista Amati, Federica Mangiatordi, Emiliano Pallotti +3Mixed-Integer Linear ProgrammingLearning to Optimize

    Fondazione Ugo Bordoni (FUB) Rome, Italy · University of Rome Tor Vergata (UniRoma2) Rome, Italy

  25. LP Mining with LP2Graph: A Use Case for Railway Rescheduling

    Jul 13, 2026Jörn Maurischat, Nikola Bešinović, Michael FärberMixed-Integer Linear ProgrammingInteger Linear Programming

    aTU Dresden, Chair of Railway Operations,"Friedrich List" Faculty of Transport and Traffic Sciences, Dresden, 01069, Germany · bTU Dresden, ScaDS.AI Dresden/Leipzig, Chair of Scalable Software Architectures for Data Analytics, Dresden, 01069, Germany

  26. GraphBU: MILP Instance Generation with Graph-Native Block Units

    Jul 7, 2026Xiaolei Guo, Chenyu Zhou, Jianghao Lin +1Mixed-Integer Linear ProgrammingSynthetic Benchmark Generation

    Shanghai Jiao Tong University

  27. Solver-Verified Formulation Generation and Selection for Multi-Warehouse Inventory Allocation Using Large Language Models

    Jun 28, 2026Jintao Xu, Yingzheng Ma, Jiong Dong +4Integer Linear ProgrammingMixed-Integer Linear Programming

    Supply Chain Tech Team Y, JD.com

  28. GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs

    Jun 22, 2026Yidong Luo, Xuemin Chen, Chenguang Wang +3Surrogate-Assisted OptimizationMixed-Integer Linear Programming

    School of Data Science, The Chinese University of Hong Kong, Shenzhen · School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen · Noah’s Ark Lab, Huawei

  29. The Proxy Benders Decomposition

    Jun 5, 2026Changkun Guan, El Mehdi Er Raqabi, Mathieu Tanneau +1Surrogate-Assisted OptimizationMixed-Integer Linear Programming

    H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA · Department of Operations and Decision Systems, Université Laval, Quebec, Canada

  30. Solving Integer Linear Programming with Parallel Tempering

    May 28, 2026Kyuil Sim, Sanghyeok Choi, Jinkyoo ParkMarkov Chain Monte CarloMixed-Integer Linear Programming

    1KAIST · University of Edinburgh