Pointer Network (PtrNet) is a specific neural network for solving Combinatorial Optimization Problems (COPs). While PtrNets offer real-time feed-forward inference for complex COPs instances, its quality of the results tends to be less satisfactory. One possible reason is that such issue suffers from the lack of global search ability of the gradient descent, which is frequently employed in traditional PtrNet training methods including both supervised learning and reinforcement learning. To improve the performance of PtrNet, this paper delves deeply into the advantages of training PtrNet with Evolutionary Algorithms (EAs), which have been widely acknowledged for not easily getting trapped by local optima. Extensive empirical studies based on the Travelling Salesman Problem (TSP) have been conducted. Results demonstrate that PtrNet trained with EA can consistently perform much better inference results than eight state-of-the-art methods on various problem scales. Compared with gradient descent based PtrNet training methods, EA achieves up to 30.21\% improvement in quality of the solution with the same computational time. With this advantage, this paper is able to at the first time report the results of solving 1000-dimensional TSPs by training a PtrNet on the same dimensionality, which strongly suggests that scaling up the training instances is in need to improve the performance of PtrNet on solving higher-dimensional COPs.

翻译：指针网络（PtrNet）是一种专门用于求解组合优化问题（COPs）的特定神经网络。尽管PtrNet能够为复杂COPs实例提供实时前馈推理，但其求解结果的质量往往不尽如人意。造成这一问题的可能原因之一是传统PtrNet训练方法（包括监督学习和强化学习）中常用的梯度下降法缺乏全局搜索能力。为提升PtrNet性能，本文深入探讨了采用进化算法（EA）训练PtrNet的优势——EA因其不易陷入局部最优的广泛共识而备受推崇。基于旅行商问题（TSP）的大量实证研究表明：在不同规模的问题上，经EA训练的PtrNet始终能产生比八种前沿方法更优的推理结果。相较于基于梯度下降的PtrNet训练方法，EA在相同计算时间内可实现高达30.21%的解质量提升。凭借这一优势，本文首次实现了通过训练1000维TSP同维度的PtrNet求解该问题，这强烈表明：扩大训练实例规模是提升PtrNet求解高维COPs性能的必要途径。