Related papers: Learning to Use Local Cuts
We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to…
In mixed-integer programming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-coded heuristics for cut plane…
Cutting planes are crucial in solving mixed integer linear programs (MILP) as they facilitate bound improvements on the optimal solution. Modern MILP solvers rely on a variety of separators to generate a diverse set of cutting planes by…
Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then…
Outer-approximation-based branch-and-bound is a common algorithmic framework for solving MINLPs (mixed-integer nonlinear programs) to global optimality, with branching variable selection critically influencing overall performance. In modern…
Cutting planes are essential for solving mixed-integer linear problems (MILPs), because they facilitate bound improvements on the optimal solution value. For selecting cuts, modern solvers rely on manually designed heuristics that are tuned…
Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational…
Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
A key ingredient in branch and bound (B&B) solvers for mixed-integer programming (MIP) is the selection of branching variables since poor or arbitrary selection can affect the size of the resulting search trees by orders of magnitude. A…
Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs…
Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of…
Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for…
Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), as they significantly tighten the dual bounds and improve the solving performance. A key problem for cuts is when to stop cuts generation, which…
Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter…
Mixed-integer programming (MIP) provides a powerful framework for optimization problems, with Branch-and-Cut (B&C) being the predominant algorithm in state-of-the-art solvers. The efficiency of B&C critically depends on heuristic policies…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their…
The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria,…