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：组合优化问题因其离散本质而普遍存在且极具挑战性。现有方法的主要局限性在于每次迭代仅能访问解空间的一小部分，导致全局最优搜索效率有限。为突破这一瓶颈，我们摒弃了传统扩大求解器搜索范围的努力，转而聚焦于通过热扩散使信息主动传播至求解器。通过在不改变目标函数最优值的前提下变换其形态，热扩散促进了远端区域信息向求解器的流动，从而提供更高效的导航路径。基于热扩散机制，我们提出了一套适用于通用组合优化问题的求解框架。该方法在最具挑战性且广泛存在的一系列组合优化问题中展现了优越性能。与近期利用热力学推动生成式人工智能的进展相呼应，本研究进一步揭示了热扩散在推动组合优化发展方面的巨大潜力。