Mixed-Integer QP

QP: Quadratic Programming

Mixed-integer quadratic programming studies optimization problems that combine continuous variables, quadratic objectives or constraints, and discrete choices such as whether to select an action or visit a location. It is useful in settings like path planning, autonomous control, retrieval, and supply-chain decisions, where choices interact with costs, resources, or safety requirements. Common approaches include solver-based formulations and relaxations, model-predictive control, and machine-learning-guided heuristics that predict useful decisions before optimization. A central challenge is balancing solution quality and optimality guarantees with the runtime needed for large, nonlinear, or frequently changing problems.

Latest papers

12 papers1 paper in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization
Sep 28, 2026Feijie Wu, Hugo Barbalho, Konstantina Mellou +5Automated Algorithm Discovery Automated Heuristic Design
Purdue University · Microsoft Research
Probabilistic Linear Explanations
Sep 16, 2026Frederic Koriche, Jean-Marie Lagniez, Chi TranExplainable Artificial Intelligence Mixed-Integer QP
Computer science Research Institute of Lens (CRIL), UMR CNRS 8188, University of Artois, Rue Jean Souvraz SP 18, Lens, F-62307, France
M $^3$ P-R1: Reinforcement Learning for Large Language Model Guided Multi-Modal Motion Planning via MIP Code Generation
Sep 16, 2026Xingpeng Sun, Zherong Pan, Kai Cheng +3Constrained Motion Planning Large Language Model-Based Robot Planning
Purdue University United States · LightSpeed Studios United States
Multi-Agent Planning with Spatio-Temporal and Topological Constraints using STL-GO
Jul 29, 2026Sheryl Paul, Vidisha Kudalkar, Anand Balakrishnan +3Constrained Motion Planning Combinatorial Optimization
University of Southern California, Los Angeles, CA, USA · University of Texas at Austin, Austin, TX, USA · ETH Zurich, Zurich, Switzerland +1
Safe Overtaking for Autonomous Racing Using Hierarchical Optimization and Learning-Based Control
Jul 15, 2026Hassan Jardali, Kai Yin, Lantao LiuNonlinear MPC Control Barrier Functions
Luddy School of Informatics, Computing, and Engineering, Indiana University · Machine Learning Science, Expedia Group, Austin, TX 78758 USA
Generative Robust Optimisation
Jun 21, 2026Yuhui Yin, Vassilis M. CharitopoulosRobust Optimization Mixed-Integer QP
Department of Chemical Engineering, Sargent Centre for Process Systems Engineering, UCL (University College London), Torrington Place, London WC1E 7JE, UK
Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programs
Jun 19, 2026El Mehdi Er Raqabi, Pascal Van HentenryckLearning to Optimize Combinatorial Optimization
Department of Operations and Decision Systems, Université Laval, Québec, Canada · H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA
Skill-Constrained Model Predictive Control for Resilient Manufacturing Supply Chains
Jun 15, 2026Carlos Eduardo SanojaManufacturing Model Predictive Control
Quanta Labs, LLC · Professor, FCEA, Universidad Monte´avila · Edificio Lomas del Sol, Calle Humboldt, Lomas del Sol, Caracas, Venezuela
Optimal Pattern Detection Tree for Symbolic Rule-Based Classification
May 14, 2026Young-Chae Hong, Yangho ChenRule-Based Classification Interpretable ML
Amazon Seattle, USA
ML-Guided Primal Heuristics for Mixed Binary Quadratic Programs
Apr 24, 2026Weimin Huang, Natalie M. Isenberg, Ján Drgoňa +2Combinatorial Optimization Mixed-Integer QP
University of Southern California, USA · Pacific Northwest National Laboratory, USA · Johns Hopkins University, USA
Principled and Scalable Diversity-Aware Retrieval via Cardinality-Constrained Binary Quadratic Programming
Apr 2, 2026Qiheng Lu, Nicholas D. SidiropoulosFrank-Wolfe Algorithms Constrained Optimization
University of Virginia Charlottesville, VA 22904, USA
LIPP: Load-Aware Informative Path Planning with Physical Sampling
Mar 6, 2026Hojune Kim, Guangyao Shi, Gaurav S. SukhatmeInformative Path Planning Constrained Optimization
School of Electrical and Computer Engineering University of Southern California Los Angeles, California · School of Computer Science University of Southern California Los Angeles, California

Sep 28, 2026J/K move · Enter open · S save

HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization

Feijie Wu, Hugo Barbalho, Konstantina Mellou, Marco Molinaro+4

Purdue University · Microsoft Research

Automated Algorithm Discovery Automated Heuristic Design Evolutionary Optimization Combinatorial Optimization Mixed-Integer QP

Open paper AskPDF arXiv

Recent advances in agentic heuristic design use AI agents and execution feedback to automate algorithm discovery for challenging optimization problems. In many practical settings, high-quality solutions must be obtained under strict runtime constraints, motivating hybrid approaches that combine problem-specific heuristics with powerful mathematical programming solvers. However, existing approaches typically improve heuristic components within predefined procedures or tune solver configurations in isolation. This limits holistic adaptation of where to allocate computation, how to leverage solvers, and how to refine the overall algorithmic structure. To address these limitations, we propose HeurEvo, an automated plan--code--component co-evolution framework that jointly evolves the high-level algorithmic structures, their implementations, and a shared pool of reusable components. A planner determines which algorithmic components to use, how to combine them, and how to allocate runtime across stages, a coder realizes the resulting plan as executable code, while a component evolver updates the shared component pool. Within an island-based evolutionary framework, plans and implementations co-evolve with feedback from an interpreter agent that analyzes execution results and identifies opportunities for improvement. Across diverse combinatorial optimization benchmarks and challenging MIPLIB instances, HeurEvo finds high-quality solutions within tight runtime budgets, often matching or surpassing state-of-the-art optimization solvers given hours or days of computation. On several nonlinear geometry problems such as hexagon packing, it also improves upon the best previously reported results. These results highlight the value of jointly searching over algorithmic structure and implementation for agentic heuristic design.