Performance report of heuristic algorithm that cracked the largest Gset Ising problems (G81 cut=14060)

TL;DR

This paper introduces Cosm, a heuristic algorithm that significantly improves speed and solution quality on large Gset Ising problems, achieving near-optimal solutions on previously unsolved instances.

Contribution

The paper presents Cosm, a novel heuristic that outperforms existing methods in speed and accuracy on large Gset Ising problems, including the largest instances.

Findings

Cosm reaches 99.9% of best solution quality rapidly.

Cosm attains new best cuts on G72, G77, and G81 instances.

Solutions provided can be independently validated.

Abstract

For the past 25 years, the Gset benchmark problems have challenged all manner of Ising and Max-Cut solvers. The largest of these problems have remained unsolved by any heuristic algorithm. In this report we provide data showing dramatically better speed and accuracy on these large sparse problems. Our newly discovered heuristic algorithm called Cosm reaches high (99.9% of best) solution quality orders of magnitude faster than the previous best heuristic solver results. Additionally, when afforded enough steps Cosm attains higher cuts than ever previously reported, specifically on instances G72 (cut=7008), G77 (cut=9940), and the 20,000-variable G81 (cut=14060). This report includes solution bitstrings so that the cuts can be independently validated. Remarkably, the new best solutions appear to be optimal. We believe the results are an early hint of disruptive opportunities for unconventional, hardware-centric approaches to algorithm discovery.