Efficient Few-Step Solution Generation via Discrete Flow Matching for Combinatorial Optimization

Abstract Combinatorial optimization problems (COPs) are fundamental to many real-world applications where efficiently producing high-quality solutions is critical. Recent advances in diffusion-based non-autoregressive models have reformulated solving COPs as a generative process, achieving promising results. However, almost all of these methods still suffer from accumulated errors and high inference costs due to the multi-step stochastic denoising process. To address these issues, we propose EFLOCO, an efficient discrete flow matching method for solving COPs, learning structured and deterministic solution trajectories. EFLOCO replaces noise-driven updates with smooth and guided transitions, thereby improves inference stability and quality. Furthermore, we introduce an adaptive time-step scheduler that makes more efforts in critical transition regions, yielding strong performance under few-step constraints. Experiments on standard Traveling Salesman Problems (TSPs) and Asymmetric TSPs (ATSPs) show that our method consistently outperforms both learning-based and heuristic baselines in terms of solution quality and inference speed.