Combinatorial optimization problems are widespread but inherently challenging due to their discrete nature. The primary limitation of existing methods is that they can only access a small fraction of the solution space at each iteration, resulting in limited efficiency for searching the global optimal. To overcome this challenge, diverging from conventional efforts of expanding the solver's search scope, we focus on enabling information to actively propagate to the solver through heat diffusion. By transforming the target function while preserving its optima, heat diffusion facilitates information flow from distant regions to the solver, providing more efficient navigation. Utilizing heat diffusion, we propose a framework for solving general combinatorial optimization problems. The proposed methodology demonstrates superior performance across a range of the most challenging and widely encountered combinatorial optimizations. Echoing recent advancements in harnessing thermodynamics for generative artificial intelligence, our study further reveals its significant potential in advancing combinatorial optimization.

翻译：组合优化问题普遍存在，但由于其离散特性而具有内在挑战性。现有方法的主要局限在于每次迭代仅能访问解空间的极小部分，导致搜索全局最优解的效率受限。为克服这一挑战，不同于传统扩展求解器搜索范围的思路，我们聚焦于通过热扩散使信息主动传播至求解器。热扩散在保持目标函数最优解不变的前提下对其进行变换，促进了信息从遥远区域向求解器的流动，从而提供更高效的搜索导航。利用热扩散机制，我们提出了一个求解通用组合优化问题的框架。该方法在一系列最具挑战性且广泛存在的组合优化问题上展现出优越性能。呼应近期利用热力学推动生成式人工智能发展的进展，本研究进一步揭示了热扩散在推进组合优化领域的巨大潜力。