New Best-Known Max-Cut Solution for the G63 Instance in the G-Set Benchmark

TL;DR

This work addresses improving the Max-Cut value on the G63 instance from the G-set benchmark, a large-scale and historically challenging graph. It introduces Population Annealing Monte Carlo (PAMC) augmented with adaptive stochasticity and periodic non-local moves, implemented on GPU hardware. The method achieves a new best-known cut value of 27,047, surpassing the previous 27,045 and demonstrating the continued potential of advanced population-based Monte Carlo techniques for large COPs. The result underscores ongoing progress in solver design for the G-set and highlights the role of hardware acceleration in pushing state-of-the-art performance.

Abstract

For over two decades, the G-set benchmark has remained a cornerstone challenge for combinatorial optimization solvers. Remarkably, it continues to yield new best-known solutions even to the present day. Here, we report a new best-known Max-Cut of 27,047 for the 7000-node G63 instance-one of the two instances in the benchmark with the largest number of edges. This result is achieved using an optimized Population Annealing Monte Carlo framework, augmented with adaptive control of stochasticity and the periodic introduction of non-local moves, and accelerated on a GPU platform.