Augmentation approaches for Mixed Integer Programming

TL;DR

This paper investigates the structure of feasible sets in mixed integer linear programs and introduces a finite test set for augmentation algorithms, enhancing solution methods for MIPs.

Contribution

It derives and characterizes a computable, finite test set for MIPs, enabling more effective augmentation algorithms.

Findings

Finite test set for MIPs is computable and characterizable.

The test set improves augmentation algorithms for solving MIPs.

Examples illustrate the relationship between the test set and existing approaches.

Abstract

This paper analyses the feasible sets structure of general mixed integer linear programs (MIPs) and its relationship with the existence of a finite cardinality test set which can be applied in augmentation algorithms. We derive and characterize a computable, finite test set for MIPs which can be embedded in a finite augmentation algorithm. Several examples illustrate the structure of this set and its relationship with previous approaches in the literature.