Last fifty years of integer linear programming: A focus on recent practical advances

Mixed-integer linear programming (MILP) has become a cornerstone of operations research. This is driven by the enhanced efficiency of modern solvers, which can today find globally optimal solutions within seconds for problems that were out of reach a decade ago. The versatility of these solvers allo...

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Published in:European journal of operational research Vol. 324; no. 3; pp. 707 - 731
Main Authors: Clautiaux, François, Ljubić, Ivana
Format: Journal Article
Language:English
Published: Elsevier B.V 01.08.2025
Elsevier
Subjects:
Benders decomposition
Branch-and-cut
Combinatorial optimization
Computer Science
Dantzig–Wolfe decomposition
Mathematics
Mixed-integer linear programming
Benders decomposition
Combinatorial optimization
Dantzig–Wolfe decomposition
Branch-and-cut
Mixed-integer linear programming
Combinatorial Optimization
Dantzig-Wolfe Decomposition
Mixed-Integer Linear Programming
Branch-and-Cut
Benders Decomposition
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Abstract Mixed-integer linear programming (MILP) has become a cornerstone of operations research. This is driven by the enhanced efficiency of modern solvers, which can today find globally optimal solutions within seconds for problems that were out of reach a decade ago. The versatility of these solvers allowed successful applications in many areas, such as transportation, logistics, supply chain management, revenue management, finance, telecommunications, and manufacturing. Despite the impressive success already obtained, many challenges remain, and MILP is still a very active field. This article provides an overview of the most significant results achieved in advancing the MILP solution methods. Given the immense literature on this topic, we made deliberate choices to focus on computational aspects and recent practical performance improvements, emphasizing research that reports computational experiments. We organize our survey into three main parts, dedicated to branch-and-cut methods, Dantzig–Wolfe decomposition, and Benders decomposition. The paper concludes by highlighting ongoing challenges and future opportunities in MILP research. •We survey recent advances in developing exact solution methods for MILPs.•We focus on computational aspects and recent practical performance improvements.•We discuss design of modern branch-and-cut and branch-and-cut-and-price algorithms.•Major recent developments in Dantzig–Wolfe and Benders decomposition are provided.•Current trends and future challenges are addressed.
AbstractList Mixed-integer linear programming (MILP) has become a cornerstone of operations research. This is driven by the enhanced efficiency of modern solvers, which can today find globally optimal solutions within seconds for problems that were out of reach a decade ago. The versatility of these solvers allowed successful applications in many areas, such as transportation, logistics, supply chain management, revenue management, finance, telecommunications, and manufacturing. Despite the impressive success already obtained, many challenges remain, and MILP is still a very active field. This article provides an overview of the most significant results achieved in advancing the MILP solution methods. Given the immense literature on this topic, we made deliberate choices to focus on computational aspects and recent practical performance improvements, emphasizing research that reports computational experiments. We organize our survey into three main parts, dedicated to branch-and-cut methods, Dantzig–Wolfe decomposition, and Benders decomposition. The paper concludes by highlighting ongoing challenges and future opportunities in MILP research. •We survey recent advances in developing exact solution methods for MILPs.•We focus on computational aspects and recent practical performance improvements.•We discuss design of modern branch-and-cut and branch-and-cut-and-price algorithms.•Major recent developments in Dantzig–Wolfe and Benders decomposition are provided.•Current trends and future challenges are addressed.
Mixed-integer linear programming (MILP) has become a cornerstone of operations research. This is driven by the enhanced efficiency of modern solvers, which can today find globally optimal solutions within seconds for problems that were out of reach a decade ago. The versatility of these solvers allowed successful applications in many areas, such as transportation, logistics, supply chain management, revenue management, finance, telecommunications, and manufacturing. Despite the impressive success already obtained, many challenges remain, and MILP is still a very active field.This article provides an overview of the most significant results achieved in advancing the MILP solution methods. Given the immense literature on this topic, we made deliberate choices to focus on computational aspects and recent practical performance improvements, emphasizing research that reports computational experiments. We organize our survey into three main parts, dedicated to branch-and-cut methods, Dantzig-Wolfe decomposition, and Benders decomposition. The paper concludes by highlighting ongoing challenges and future opportunities in MILP research.
Author Clautiaux, François
Ljubić, Ivana
Author_xml – sequence: 1
  givenname: François
  orcidid: 0000-0002-9171-8012
  surname: Clautiaux
  fullname: Clautiaux, François
  organization: Université de Bordeaux, Institut de Mathématiques de Bordeaux, CNRS, Inria, France
– sequence: 2
  givenname: Ivana
  orcidid: 0000-0002-4834-6284
  surname: Ljubić
  fullname: Ljubić, Ivana
  email: ivana.ljubic@essec.edu
  organization: ESSEC Business School, Cergy-Pontoise, France
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Issue 3
Keywords Benders decomposition
Combinatorial optimization
Dantzig–Wolfe decomposition
Branch-and-cut
Mixed-integer linear programming
Combinatorial Optimization
Dantzig-Wolfe Decomposition
Mixed-Integer Linear Programming
Branch-and-Cut
Benders Decomposition
Language English
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Snippet Mixed-integer linear programming (MILP) has become a cornerstone of operations research. This is driven by the enhanced efficiency of modern solvers, which can...
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SubjectTerms Benders decomposition
Branch-and-cut
Combinatorial optimization
Computer Science
Dantzig–Wolfe decomposition
Mathematics
Mixed-integer linear programming
Title Last fifty years of integer linear programming: A focus on recent practical advances
URI https://dx.doi.org/10.1016/j.ejor.2024.11.018
https://inria.hal.science/hal-04776866
Volume 324
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