Learning Pseudo-Backdoors for Mixed Integer Programs

by   Aaron Ferber, et al.

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. Learning-based approaches have seen success in the area of solving combinatorial optimization problems by being able to flexibly leverage common structures in a given distribution of problems. Our approach takes inspiration from the concept of strong backdoors, which corresponds to a small set of variables such that only branching on these variables yields an optimal integral solution and a proof of optimality. Our notion of pseudo-backdoors corresponds to a small set of variables such that only branching on them leads to faster solve time (which can be solver dependent). A key advantage of pseudo-backdoors over strong backdoors is that they are much amenable to data-driven identification or prediction. Our proposed method learns to estimate the solver performance of a proposed pseudo-backdoor, using a labeled dataset collected on a set of training MIP instances. This model can then be used to identify high-quality pseudo-backdoors on new MIP instances from the same distribution. We evaluate our method on the generalized independent set problems and find that our approach can efficiently identify high-quality pseudo-backdoors. In addition, we compare our learned approach against Gurobi, a state-of-the-art MIP solver, demonstrating that our method can be used to improve solver performance.


page 1

page 2

page 3


Optimal Solution Predictions for Mixed Integer Programs

Mixed Integer Programming (MIP) is one of the most widely used modeling ...

Solving Mixed Integer Programs Using Neural Networks

Mixed Integer Programming (MIP) solvers rely on an array of sophisticate...

Generating Hard Instances for Robust Combinatorial Optimization

While research in robust optimization has attracted considerable interes...

Learning Optimal Temperature Region for Solving Mixed Integer Functional DCOPs

Distributed Constraint Optimization Problems (DCOPs) are an important fr...

Online Mixed-Integer Optimization in Milliseconds

We propose a method to solve online mixed-integer optimization (MIO) pro...

A hybrid optimization approach for employee rostering: Use cases at Swissgrid and lessons learned

Employee rostering is a process of assigning available employees to open...

ReDUCE: Reformulation of Mixed Integer Programs using Data from Unsupervised Clusters for Learning Efficient Strategies

Mixed integer convex and nonlinear programs, MICP and MINLP, are express...