Learning Cuts via Enumeration Oracles

TL;DR

This paper introduces a novel method for learning cutting planes in integer programming by using an enumeration oracle within a Frank-Wolfe algorithm, demonstrated on the multidimensional knapsack problem.

Contribution

It presents a new generic approach to learn polyhedral facets via an enumeration oracle, bypassing traditional LP-based methods.

Findings

Effective in generating strong cutting planes

Applicable to multidimensional knapsack problem

Outperforms some existing methods

Abstract

Cutting-planes are one of the most important building blocks for solving large-scale integer programming (IP) problems to (near) optimality. The majority of cutting plane approaches rely on explicit rules to derive valid inequalities that can separate the target point from the feasible set. Local cuts, on the other hand, seek to directly derive the facets of the underlying polyhedron and use them as cutting planes. However, current approaches rely on solving Linear Programming (LP) problems in order to derive such a hyperplane. In this paper, we present a novel generic approach for learning the facets of the underlying polyhedron by accessing it implicitly via an enumeration oracle in a reduced dimension. This is achieved by embedding the oracle in a variant of the Frank-Wolfe algorithm which is capable of generating strong cutting planes, effectively turning the enumeration oracle into a separation oracle. We demonstrate the effectiveness of our approach with a case study targeting the multidimensional knapsack problem (MKP).