Mutation-Guided Differentiable Quadratic Combinatorial Optimization

2026-05-07

AI Summary

Gradient-based methods for large-scale combinatorial optimization often become trapped in local optima, particularly under non-massively-parallel settings where their performance is constrained. This work identifies the core bottleneck as optimization stagnation rather than limitations in model capacity or computational resources, and introduces a differentiable global reset algorithm incorporating a mutation mechanism. By synergistically combining local search strategies with a newly designed quadratic objective function for MaxCut within a relaxed QUBO framework, the proposed approach effectively escapes local optima. Experimental results demonstrate that the method significantly outperforms state-of-the-art heuristics, commercial integer programming solvers, and recent GPU-accelerated techniques on large-scale graphs, all without relying on extensive parallel initialization.

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.

Problem

• Quadratic Unconstrained Binary Optimization
• Maximum Independent Set
• Maximum Cut
• local maxima
• gradient-based optimization

Innovation

• mutation-guided optimization
• differentiable combinatorial optimization
• QUBO
• local maxima escape
• MaxCut