About

Willem-Jan Van Hoeve is the Carnegie Bosch Professor of Operations Research at the Tepper School of Business. His role involves research and teaching in the field of operations research, with a focus on the intersection of business, technology, and analytics. As a faculty member at Carnegie Mellon University, he contributes to the academic community through his expertise in operations research, supporting the school's strategic vision to lead in artificial intelligence, economic prosperity, and entrepreneurial pursuits.

Research topics

• Computer Science
• Artificial Intelligence
• Mathematics
• Algorithm
• Theoretical computer science
• Mathematical optimization
• Geometry

Selected publications

• Inverse Optimization Without Inverse Optimization: Direct Solution Prediction with Transformer Models

  Open MIND · 2026-02-05

  preprint

  We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and incorporates the known components, such as hard constraints, via a constraint reasoning module, yielding a constrained learning scheme. The trained model generates new solutions that are structurally similar to past solutions and are guaranteed to respect the known constraints. We apply our approach to three combinatorial optimization problems with unknown components: the knapsack problem with an unknown reward function, the bipartite matching problem with an unknown objective function, and the single-machine scheduling problem with release times and unknown precedence constraints, with the objective of minimizing average completion time. We demonstrate that transformer models have remarkably strong performance and often produce near-optimal solutions in a fraction of a second. They can be particularly effective in the presence of more complex underlying objective functions and unknown implicit constraints compared to an LSTM-based alternative and inverse optimization.

  DOI

• Inverse Optimization Without Inverse Optimization: Direct Solution Prediction with Transformer Models

  arXiv (Cornell University) · 2026-02-05

  articleOpen access

  We present an end-to-end framework for generating solutions to combinatorial optimization problems with unknown components using transformer-based sequence-to-sequence neural networks. Our framework learns directly from past solutions and incorporates the known components, such as hard constraints, via a constraint reasoning module, yielding a constrained learning scheme. The trained model generates new solutions that are structurally similar to past solutions and are guaranteed to respect the known constraints. We apply our approach to three combinatorial optimization problems with unknown components: the knapsack problem with an unknown reward function, the bipartite matching problem with an unknown objective function, and the single-machine scheduling problem with release times and unknown precedence constraints, with the objective of minimizing average completion time. We demonstrate that transformer models have remarkably strong performance and often produce near-optimal solutions in a fraction of a second. They can be particularly effective in the presence of more complex underlying objective functions and unknown implicit constraints compared to an LSTM-based alternative and inverse optimization.

  PublisherOA PDF

• Dantzig-Wolfe and Arc-Flow Reformulations: A Systematic Comparison

  arXiv (Cornell University) · 2026-02-26

  articleOpen access

  Dantzig-Wolfe reformulation is a widely used technique for obtaining stronger relaxations in the context of branch-and-bound methods for solving integer optimization problems. Arc-Flow reformulations are a lesser known technique related to dynamic programming that has experienced a resurgence as result of the recent popularization of decision diagrams as a tool for solving integer programs. Although these two reformulation techniques arose independently, the recently proposed solution paradigm known as column elimination has revealed that they are in fact closely connected. Building on a unified formulation and notation, this study clarifies the theoretical connections and computational trade-offs between these two reformulations. We first revisit the known fact that the LP relaxations of these two reformulations yield the same dual bound. We then dig deeper, establishing conditions under which valid inequalities in the original, Dantzig-Wolfe, or Arc-Flow spaces can be translated across reformulations without loss of strength, and reinterpreting iterative strengthening methods, such as decremental state-space relaxation and column elimination, through the lens of cutting planes. To assess the potential impact of these insights empirically, we benchmark both reformulations under identical conditions on the vehicle routing problem with time windows using state-of-the-art column- and cut-generation techniques. The results identify clear contrasts: the Arc-Flow reformulation benefits from faster convergence and performs best when subproblems are highly relaxed or low-dimensional, whereas the Dantzig-Wolfe reformulation is more efficient when the master problem remains compact. Overall, our study provides a unified perspective and practical guidelines for choosing between Dantzig-Wolfe and Arc-Flow reformulations in large-scale integer optimization.

  PublisherOA PDF

• Dantzig-Wolfe and Arc-Flow Reformulations: A Systematic Comparison

  Open MIND · 2026-02-26

  preprint

  Dantzig-Wolfe reformulation is a widely used technique for obtaining stronger relaxations in the context of branch-and-bound methods for solving integer optimization problems. Arc-Flow reformulations are a lesser known technique related to dynamic programming that has experienced a resurgence as result of the recent popularization of decision diagrams as a tool for solving integer programs. Although these two reformulation techniques arose independently, the recently proposed solution paradigm known as column elimination has revealed that they are in fact closely connected. Building on a unified formulation and notation, this study clarifies the theoretical connections and computational trade-offs between these two reformulations. We first revisit the known fact that the LP relaxations of these two reformulations yield the same dual bound. We then dig deeper, establishing conditions under which valid inequalities in the original, Dantzig-Wolfe, or Arc-Flow spaces can be translated across reformulations without loss of strength, and reinterpreting iterative strengthening methods, such as decremental state-space relaxation and column elimination, through the lens of cutting planes. To assess the potential impact of these insights empirically, we benchmark both reformulations under identical conditions on the vehicle routing problem with time windows using state-of-the-art column- and cut-generation techniques. The results identify clear contrasts: the Arc-Flow reformulation benefits from faster convergence and performs best when subproblems are highly relaxed or low-dimensional, whereas the Dantzig-Wolfe reformulation is more efficient when the master problem remains compact. Overall, our study provides a unified perspective and practical guidelines for choosing between Dantzig-Wolfe and Arc-Flow reformulations in large-scale integer optimization.

  DOI

• A single-level reformulation of binary bilevel programs using decision diagrams

  Mathematical Programming · 2025-12-16

  articleOpen accessSenior author

  Abstract Binary bilevel programs are notoriously difficult to solve due to the absence of strong and efficiently computable relaxations. In this work, we introduce a novel single-level reformulation of these programs by leveraging a network flow-based representation of the follower’s value function, utilizing decision diagrams and linear programming duality. This approach enables the development of scalable relaxations by applying it to a restricted solution set, which in turn provides dual bounds. We obtain an exact method by iteratively solving and strengthening the relaxation. We further extend the reformulation to address the pessimistic version of the original bilevel problem. We experimentally compare our method with state-of-the-art bilevel programming solvers, demonstrating competitive performance. Specifically, on the BOBILib benchmark set our approach provides new or improved bounds for six instances and closes two open instances for the first time. We also show experimentally that the decision diagram reformulation can be particularly effective when it can leverage the combinatorial structure of the follower’s problem.

  PublisherOA PDFDOI

• CODD: A Decision Diagram-Based Solver for Combinatorial Optimization

  Frontiers in artificial intelligence and applications · 2024-10-16

  book-chapterOpen accessSenior author

  We introduce CODD, a system for solving combinatorial optimization problems using decision diagram technology. Problems are represented as state-based dynamic programming models using the CODD language specification. The model specification is used to automatically compile relaxed and restricted decision diagrams that are embedded inside a branch-and-bound search process. We introduce abstractions that allow us to generically implement the solver components while maintaining overall execution efficiency. We demonstrate the functionality of CODD on a variety of combinatorial optimization problems and compare its performance to other state-based solvers as well as integer programming and constraint programming solvers. CODD provides competitive results and can outperform the other solvers, sometimes by orders of magnitude.

  PublisherOA PDFDOI

• An Introduction to Decision Diagrams for Optimization

  2024-10-01 · 2 citations

  book-chapter1st authorCorresponding

  TutORials in Operations Research is a collection of tutorials published annually and designed for students, faculty, and practitioners. The series provides in-depth instruction on significant operations research topics and methods. INFORMS has published the series, founded by Harvey J. Greenberg, since 2005.

  PublisherDOI

• Dual Bounds from Decision Diagram-Based Route Relaxations: An Application to Truck-Drone Routing

  Transportation Science · 2023-12-20 · 9 citations

  articleSenior author

  For vehicle routing problems, strong dual bounds on the optimal value are needed to develop scalable exact algorithms as well as to evaluate the performance of heuristics. In this work, we propose an iterative algorithm to compute dual bounds motivated by connections between decision diagrams and dynamic programming models used for pricing in branch-and-cut-and-price algorithms. We apply techniques from the decision diagram literature to generate and strengthen novel route relaxations for obtaining dual bounds without using column generation. Our approach is generic and can be applied to various vehicle routing problems in which corresponding dynamic programming models are available. We apply our framework to the traveling salesman with drone problem and show that it produces dual bounds competitive to those from the state of the art. Applied to larger problem instances in which the state-of-the-art approach does not scale, our method outperforms other bounding techniques from the literature. Funding: This work was supported by the National Science Foundation [Grant 1918102] and the Office of Naval Research [Grants N00014-18-1-2129 and N00014-21-1-2240]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2021.0170 .

  PublisherDOI

• Optimization Bounds from Decision Diagrams in Haddock

  Lecture notes in computer science · 2023-01-01

  book-chapterSenior author
  PublisherDOI

• Constraint Programming

  Encyclopedia of Optimization · 2023-01-01 · 4 citations

  book-chapterSenior authorCorresponding
  PublisherDOI

Recent grants

• FMitF: Collaborative Research: Track I: Embedding Constraint Reasoning in Machine Learning for Better Prediction and Decision-making

  NSF · $343k · 2019–2024

Frequent coauthors

• Andre A. Ciré

  University of Toronto

  52 shared

• David Bergman

  University of Connecticut

  35 shared

• John Hooker

  Carnegie Mellon University

  22 shared

• J. N. Hooker

  16 shared

• Ashish Sabharwal

  11 shared

• Amin Hosseininasab

  University of Florida

  8 shared

• Carla P. Gomes

  7 shared

• Louis-Martin Rousseau

  6 shared

Education

• Ph.D., Operations Research

  Carnegie Mellon University

  1998

• M.S., Operations Research

  Carnegie Mellon University

  1994

• B.S., Mathematics and Computer Science

  Delft University of Technology

  1991