Related papers: Cutting Planes for Binarized Network Flow Problems
While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
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…
We study an incremental network design problem, where in each time period of the planning horizon an arc can be added to the network and a maximum flow problem is solved, and where the objective is to maximize the cumulative flow over the…
Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims…
Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better…
Mixed Integer Linear Programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and requires expert formulation. Current deep learning approaches for MILP focus on…
We analyze different ways of constructing binary extended formulations of mixed-integer problems with bounded integer variables and compare their relative strength with respect to split cuts. We show that among all binary extended…
In this paper, we propose two exact distributed algorithms to solve mixed integer linear programming (MILP) problems with multiple agents where data privacy is important for the agents. A key challenge is that, because of the non-convex…
We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions.…
By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP 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…
Mixed integer predictive control deals with optimizing integer and real control variables over a receding horizon. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this…
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
We study cyclic binary strings with bounds on the lengths of the intervals of consecutive ones and zeros. This is motivated by scheduling problems where such binary strings can be used to represent the state (on/off) of a machine. In this…
Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or…