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

TL;DR

This paper presents a new best-known solution for the G63 Max-Cut problem in the G-set benchmark, achieved through an advanced GPU-accelerated Population Annealing Monte Carlo method with adaptive and non-local moves.

Contribution

The paper introduces a novel GPU-accelerated Population Annealing Monte Carlo approach with adaptive control and non-local moves for solving large Max-Cut instances.

Findings

Achieved a Max-Cut value of 27,047 for G63, surpassing previous solutions.

Demonstrated the effectiveness of adaptive stochastic control and non-local moves.

Showed significant acceleration using GPU computing.

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.