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：组合优化问题广泛存在，但由于其离散性而本质上具有挑战性。现有方法的主要局限在于每次迭代只能访问解空间的一小部分，导致搜索全局最优的效率受限。为攻克这一难题，我们突破传统扩大求解器搜索范围的思路，转而聚焦于通过热扩散使信息主动向求解器传播。通过保持最优解不变的同时变换目标函数，热扩散促进了信息从远距离区域向求解器的流动，提供了更高效的导航。利用热扩散，我们提出了一种求解通用组合优化问题的框架。所提方法在一系列最具挑战性和最广泛遇到的组合优化问题上展现了优越性能。与近期利用热力学推动生成式人工智能的进展相呼应，我们的研究进一步揭示了其在推进组合优化方面的巨大潜力。