Almost Symmetric

Integer Programs

Exploiting almost symmetries to faster solve interger programs

Almost symmetries can be exploited to reduce the size of optimization problems, potentially leading to huge speedups when solving those.

Almost Symmetric Integer Programs.

The objective of this collaborative research award is to develop techniques that exploit almost symmetry in integer programming. In the past decade, the exploitation of regular symmetries has led to a dramatic decrease in computation time for many classes of integer programming problems. Unfortunately, many of these problems, perhaps due to measurement or modeling error, are only close to being symmetric; minuscule differences in coefficients can hide exact symmetries. These almost symmetries are permutations that can become exact symmetries when the problem instance is modified slightly. This project seeks to expand the concept of symmetry to include almost symmetries and will develop a framework to treat almost symmetries as if they are actual symmetries. This will significantly broaden the class of optimization problem that can benefit from symmetry-exploiting techniques, resulting in improved computational times for a wider class of problems. This project will develop software that identifies almost symmetries and used to identify the prevalence of almost symmetries and assess how the existence of almost symmetries affect the difficulty of an integer programming instance. Algorithms designed to exploit almost symmetries will be developed and tested.