We investigate diffusion models to solve the Traveling Salesman Problem. Building on the recent DIFUSCO and T2TCO approaches, we propose IDEQ. IDEQ improves the quality of the solutions by leveraging the constrained structure of the state space of the TSP. Another key component of IDEQ consists in replacing the last stages of DIFUSCO curriculum learning by considering a uniform distribution over the Hamiltonian tours whose orbits by the 2-opt operator converge to the optimal solution as the training objective. Our experiments show that IDEQ improves the state of the art for such neural network based techniques on synthetic instances. More importantly, our experiments show that IDEQ performs very well on the instances of the TSPlib, a reference benchmark in the TSP community: it closely matches the performance of the best heuristics, LKH3, being even able to obtain better solutions than LKH3 on 2 instances of the TSPlib defined on 1577 and 3795 cities. IDEQ obtains 0.3% optimality gap on TSP instances made of 500 cities, and 0.5% on TSP instances with 1000 cities. This sets a new SOTA for neural based methods solving the TSP. Moreover, IDEQ exhibits a lower variance and better scales-up with the number of cities with regards to DIFUSCO and T2TCO.

翻译：我们研究利用扩散模型解决旅行商问题。基于最近的DIFUSCO和T2TCO方法，我们提出了IDEQ。IDEQ通过利用TSP状态空间的约束结构来提高解的质量。IDEQ的另一个关键组成部分在于，通过考虑以2-opt算子的轨道收敛到最优解的哈密顿回路上的均匀分布作为训练目标，取代了DIFUSCO课程学习的最后阶段。我们的实验表明，IDEQ在合成实例上改进了此类基于神经网络的技术的最先进水平。更重要的是，我们的实验表明，IDEQ在TSP社区参考基准测试集TSPlib的实例上表现非常出色：它与最佳启发式算法LKH3的性能非常接近，甚至能够在TSPlib中定义在1577和3795个城市的2个实例上获得比LKH3更好的解。IDEQ在由500个城市组成的TSP实例上获得了0.3%的最优性差距，在具有1000个城市的TSP实例上获得了0.5%的最优性差距。这为基于神经网络的TSP求解方法设定了新的最高水平。此外，与DIFUSCO和T2TCO相比，IDEQ表现出更低的方差，并且能更好地随城市数量扩展。