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）的神经网络。尽管PtrNet能够为复杂COPs实例提供实时前向推理，但其结果质量往往不尽人意。可能的原因之一是这一问题根源在于传统PtrNet训练方法（包括监督学习和强化学习）中广泛使用的梯度下降法缺乏全局搜索能力。为提升PtrNet性能，本文深入探究了采用进化算法（EAs）训练PtrNet的优势——进化算法因不易陷入局部最优而广受认可。基于旅行商问题（TSP）的大量实证研究表明，经进化算法训练的PtrNet在不同问题规模上均能持续获得显著优于八种前沿方法的推理结果。与基于梯度下降的PtrNet训练方法相比，在相同计算时间内，进化算法能将解的质量提升高达30.21%。凭借这一优势，本文首次实现了在1000维TSP上通过同维度训练PtrNet并报告求解结果，这有力表明扩展训练实例规模对于提升PtrNet求解高维COPs的性能具有重要意义。