Related papers: Safe and Verified Gomory Mixed Integer Cuts in a R…
Many operations related optimization problems involve repeatedly solving similar mixed integer linear programming (MILP) instances with the same constraint matrix but differing objective coefficients and right-hand-side values. The goal of…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
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…
The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We…
For almost two decades, mixed integer programming (MIP) solvers have used graph-based conflict analysis to learn from local infeasibilities during branch-and-bound search. In this paper, we improve MIP conflict analysis by instead using…
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…
It is well known that reformulating the original problem can be crucial for the performance of mixed-integer programming (MIP) solvers. To ensure correctness, all transformations must preserve the fea sibility status and optimal 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…
We present a proof system for establishing the correctness of results produced by optimization algorithms, with a focus on mixed-integer programming (MIP). Our system generalizes the seminal work of Bogaerts, Gocht, McCreesh, and…
We present a version of GMI (Gomory mixed-integer) cuts in a way so that they are derived with respect to a "dual form" mixed-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex…
This paper presents the integration of constraint propagation and dual proof analysis in an exact, roundoff-error-free MIP solver. The authors employ safe rounding methods to ensure that all results remain provably correct, while…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. These solvers are the foremost method for solving discrete optimization problems…
Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
Sparse cutting-planes are often the ones used in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch-&-bound more efficiently. However, how well can we approximate the integer…
We present a depth-aware optimization framework for quantum circuit compilation that unifies provable optimality with scalable heuristics. For exact synthesis of a target unitary, we formulate a mixed-integer linear program (MILP) that…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
We propose a machine learning approach for quickly solving Mixed Integer Programs (MIP) by learning to prioritize a set of decision variables, which we call pseudo-backdoors, for branching that results in faster solution times.…