Parallel Graver Basis Extraction for Nonlinear Integer Optimization

TL;DR

This paper introduces a parallel heuristic for approximating the Graver basis in nonlinear integer programming, enabling efficient solution refinement by leveraging parallelizable methods to identify promising directions.

Contribution

It presents a novel massively parallel heuristic to approximate the Graver basis, improving the practicality of nonlinear integer optimization.

Findings

Achieves comparable performance to advanced solvers on benchmark instances.

Utilizes parallelizable first-order methods for nonconvex problem optimization.

Addresses computational bottleneck in accessing Graver basis directions.

Abstract

The augmentation scheme provides a nontraditional approach to nonlinear integer programming by iteratively refining incumbent solutions along objective-improving directions from the Graver basis. Its main computational bottleneck, however, lies in the practical difficulty of accessing such directions. To address this challenge, we develop a massively parallel heuristic for approximating Graver basis, extracting promising directions by optimizing nonconvex continuous problems using parallelizable first-order methods. Experiments on QPLIB and MINLPLib instances show that our method achieves comparable performance to advanced solvers.