Coluna.jl: A Branch-Cut-and-Price Framework in Julia
Published Online:20 Aug 2026https://doi.org/10.1287/ijoc.2025.1130
References
- (2007) Constraint integer programming. Ph.D. thesis, Technische Universitat, Berlin.Google Scholar
- (2020) Presolve reductions in mixed integer programming. INFORMS J. Comput. 32(2):473–506.Link, Google Scholar
- (2021) Exploiting parallelism in the open-source Coluna.jl framework. Second Internat. Workshop Parallel Optim. Using Multi- Many-Core High Performance Comput. (POMCO 2020). Internat. Conf. High Performance Comput. Simulation 2021 (IEEE, Piscataway, NJ), 1–6.Google Scholar
- (2015) Automatic Dantzig–Wolfe reformulation of mixed integer programs. Math. Programming 149(1–2):391–424.Crossref, Google Scholar
- (2022) Frankwolfe.jl: A high-performance and flexible toolbox for Frank-Wolfe algorithms and conditional gradients. INFORMS J. Comput. 34(5):2611–2620.Link, Google Scholar
- (2024) The SCIP Optimization Suite 9.0. Preprint, submitted February 27, https://arxiv.org/abs/2402.17702.Google Scholar
- (2021) Automatic Dantzig‐Wolfe reformulation of mixed integer linear programs. Ph.D. thesis, Technical University of Denmark (DTU), Kongens Lyngby, Denmark.Google Scholar
- (2022) Solving natural conic formulations with Hypatia.jl. INFORMS J. Comput. 34(5):2686–2699.Link, Google Scholar
- (1961) The decomposition algorithm for linear programs. Econometrica 29(4):767–778.Crossref, Google Scholar
- (2021) Sddp.jl: A Julia package for stochastic dual dynamic programming. INFORMS J. Comput. 33(1):27–33.Link, Google Scholar
- FICO (2024) FICO Xpress Optimization Suite, version 9.1. Accessed December 23, 2024, https://www.fico.com/products/fico-xpress-optimization-suite.Google Scholar
- (2010) Decomposition methods for integer linear programming. Ph.D. thesis, Lehigh University, Bethlehem, PA.Google Scholar
- (2012) Computational experience with generic decomposition using the DIP framework. COR@L technical report 127-021, Lehigh University, Bethlehem, PA.Google Scholar
- (2010) Experiments with a generic Dantzig-Wolfe decomposition for integer programs. Festa P, ed. Experiment. Algorithms (SEA 2010) (Springer, Berlin), 239–252.Google Scholar
- (2023) BilevelJuMP.jl: Modeling and solving bilevel optimization problems in Julia. INFORMS J. Comput. 36(2):327–335.Link, Google Scholar
- (2022) Cardinal Optimizer (COPT) user guide. Accessed December 23, 2024, https://guide.coap.online/copt/en-doc.Google Scholar
- Google (2024) OR-Tools: Google’s operations research tools, version 9.7. Accessed December 23, 2024, https://developers.google.com/optimization.Google Scholar
- Gurobi Optimization, LLC (2025) Gurobi Optimizer reference manual. Accessed December 23, 2024, https://www.gurobi.com.Google Scholar
- (2018) Parallelizing the dual revised simplex method. Math. Programming Comput. 10(1):119–142.Crossref, Google Scholar
- IBM (2024) IBM ILOG CPLEX Optimization Studio, version 22.1. Accessed December 23, 2024, https://www.ibm.com/products/ilog-cplex-optimization-studio.Google Scholar
- (2008) Subset-row inequalities applied to the vehicle-routing problem with time windows. Oper. Res. 56(2):497–511.Link, Google Scholar
- (1998) Introduction to ABACUS—A branch-and-cut system. Oper. Res. Lett. 22(2–3):83–95.Crossref, Google Scholar
- (2009) Fundaments of branching heuristics. Biere A, van Maaren H, Walsh T, eds. Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185 (IOS Press, Amsterdam), 205–244.Crossref, Google Scholar
- (2017) An abstract model for branching and its application to mixed integer programming. Math. Programming 166(1):369–405.Crossref, Google Scholar
- (2022) MathOptInterface: A data structure for mathematical optimization problems. INFORMS J. Comput. 34(2):672–689.Link, Google Scholar
- Lubin M, Dowson O, Garcia JD, Huchette J, Legat B, Vielma JP (2023) JuMP 1.0: Recent improvements to a modeling language for mathematical optimization. Math. Programming Comput. 15(3):581–589.Crossref, Google Scholar
- (2012) Gnu linear programming kit, version 5.0. Accessed December 23, 2024, https://www.gnu.org/software/glpk/.Google Scholar
- (2017) Clean Architecture: A Craftsman’s Guide to Software Structure and Design, 1st ed. (Prentice Hall Press, Hoboken, NJ).Google Scholar
- (1997) Object-Oriented Software Construction, vol. 2 (Prentice Hall, Englewood Cliffs, NJ).Google Scholar
- (2017) Improved branch-cut-and-price for capacitated vehicle routing. Math. Programming Comput. 9(1):61–100.Crossref, Google Scholar
- (2018) Automation and combination of linear-programming based stabilization techniques in column generation. INFORMS J. Comput. 30(2):339–360.Link, Google Scholar
- (2003) Integer program reformulation for robust branch-and-cut-and-price algorithms. Math. Program Rio Conf. Honour Nelson Machulan, 56–61.Google Scholar
- (2004) COIN-OR branch-cut-price framework (BCP). Accessed December 23, 2024, https://github.com/coin-or/Bcp.Google Scholar
- (2021) BaPCod—A generic branch-and-price code. Accessed December 23, 2024, https://bapcod.math.u-bordeaux.fr.Google Scholar
- (2019) Primal heuristics for branch and price: The assets of diving methods. INFORMS J. Comput. 31(2):251–267.Link, Google Scholar
- (1991) Functional description of MINTO, a Mixed INTeger Optimizer. Technical report COC-91-03, Georgia Institute of Technology, Atlanta.Google Scholar
- (2005) Implementing mixed integer column generation. Desaulniers G, Desrosiers J, Solomon MM, eds. Column Generation (Springer, Boston), 331–358.Crossref, Google Scholar
- (2006) A generic view of Dantzig–Wolfe decomposition in mixed integer programming. Oper. Res. Lett. 34(3):296–306.Crossref, Google Scholar
- (2026) Coluna.jl: A branch-cut-and-price framework in Julia. Accessed December 23, 2024, https://doi.org/10.1287/ijoc.2025.1130.cd, https://github.com/INFORMSJoC/2025.1130.Google Scholar

