Intro
Preface
Organization
Contents
Efficiently Approximating High-Dimensional Pareto Frontiers for Tree-Structured Networks Using Expansion and Compression
1 Introduction
2 Problem Formulation
3 The Expansion Method
4 The Compression Method
5 Experiments
5.1 Experimental Setup
5.2 Evaluation Method
5.3 Experimental Results
5.4 Ablation Study
6 Conclusion
References
Objective-Based Counterfactual Explanations for Linear Discrete Optimization
1 Introduction
2 Background
2.1 Counterfactual Explanations

2.2 Nearest Counterfactual Explanations
2.3 Inverse Combinatorial Optimization
3 Problem Definition
3.1 Existence of an Explanation
4 The NCXplain Algorithm
5 Experimental Method
5.1 Forward Problems
5.2 NCEMILP Instances
5.3 Computational Details
6 Experimental Results
7 Limitations and Future Work
8 Related Work
9 Conclusion
References
Column Elimination for Capacitated Vehicle Routing Problems
1 Introduction
2 Column Formulation for CVRP
3 Decision Diagram Formulation for CVRP
3.1 From Dynamic Programming to Decision Diagrams

3.2 Dynamic Programming for Route Relaxations
3.3 Exact and Relaxed Decision Diagrams
3.4 Constrained Network Flow Formulation
4 Column Elimination Procedure
5 Lagrangian Relaxation
6 Cutting Planes
7 Reduced Cost-Based Arc Fixing
8 Experimental Results
9 Conclusion
References
Cutting Plane Selection with Analytic Centers and Multiregression
1 Introduction
2 Related Work
3 Contributions and Methodology
3.1 Analytic Center-Based Methods
3.2 Multiple LP Solutions
3.3 Properties and Limitations of the Distance Measures
3.4 Multi-output Regression

4 Experiments
4.1 Root Node Results
4.2 Branch and Bound Generalisation
4.3 Regression Model Results
5 Conclusion
References
Handling Symmetries in Mixed-Integer Semidefinite Programs
1 Introduction
2 Computing Symmetries
3 Symmetry Detection
4 Computational Results
References
A Mixed-Integer Linear Programming Reduction of Disjoint Bilinear Programs via Symbolic Variable Elimination
1 Introduction
2 Reducing a DBLP to a MILP: A Worked Example
3 Symbolic Calculus with Case Representation
3.1 Case Representation
3.2 Basic Case Operators

4 Symbolic Reduction of a DBLP to a MILP
4.1 Symbolic Minimization of Linear Piecewise Linear Functions
4.2 Symbolic Minimization of Disjointly Linear Piecewise Bilinear Functions
5 Empirical Analysis
6 Conclusion and Future Work
References
Local Branching Relaxation Heuristics for Integer Linear Programs
1 Introduction
2 Background
2.1 ILP and Its LP Relaxation
2.2 LNS for ILP Solving
2.3 LB Heuristic
3 Related Work
3.1 LNS for ILPs
3.2 LNS-Based Primal Heuristics in BnB
3.3 LNS for Other COPs
4 The Local Branching Relaxation Heuristic