Mutation-Guided Differentiable Quadratic Combinatorial Optimization

TL;DR

This paper introduces mQO, a mutation-based differentiable global reset algorithm that significantly enhances gradient-based methods for large-scale quadratic combinatorial optimization problems, outperforming existing heuristics and solvers.

Contribution

The paper proposes a novel mutation-guided approach, mQO, which improves gradient-based optimization by escaping local maxima without heavy parallelization, advancing large-scale combinatorial problem solving.

Findings

mQO outperforms state-of-the-art heuristics on large graphs.

The approach reduces reliance on GPU parallelization.

It effectively escapes local maxima in non-convex QUBO problems.

Abstract

Recent studies suggest that gradient-based methods applied to relaxed box-constrained Quadratic Unconstrained Binary Optimization (QUBO) formulations can outperform classical heuristics in some large-scale regimes, often relying on heavy parallelization. However, these methods still underperform heuristics in other settings. In this work, we clarify this apparent discrepancy through a detailed analysis of the relaxed non-convex QUBO local maxima for both the Maximum Independent Set (MIS) and Maximum Cut (MaxCut) problems, and by introducing a new quadratic objective for MaxCut. Motivated by this analysis, we propose a mutation-based differentiable global reset algorithm, combined with local search to escape local maxima. We term our approach mQO, standing for mutation-based Quadratic combinatorial Optimization. The proposed strategy dramatically improves the performance of gradient-based solvers without heavy reliance on GPU parallelized initializations, indicating that stalling, rather than model capacity or compute, is the dominant bottleneck. As a result, on large-scale graphs, mQO achieves superior performance against state-of-the-art heuristics, commercial integer programming solvers, and recent GPU methods.