Theoretical challenges towards cutting-plane selection

TL;DR

This paper reviews the theoretical challenges in selecting effective cutting-planes for integer programming, highlighting gaps in understanding and proposing new research directions for principled cut selection methods.

Contribution

It provides a comprehensive review of cutting-plane classes, theoretical insights, and explores initial theoretical foundations for cut selection strategies.

Findings

Different classes of cutting-planes and their relative strengths

Identification of key issues in cut selection

Proposed new directions for theoretical research in cut selection

Abstract

While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to be added to the LP relaxation at a given node of the branch-and-bound tree. In this paper we review the different classes of cutting-planes available, known theoretical results about their relative strength, important issues pertaining to cut selection, and discuss some possible new directions to be pursued in order to accomplish cutting-plane selection in a more principled manner. Finally, we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection.