In recent years, the application of Neural Combinatorial Optimization (NCO) techniques in Combinatorial Optimization (CO) has emerged as a popular and promising research direction. Currently, there are mainly two types of NCO, namely, the Constructive Neural Combinatorial Optimization (CNCO) and the Perturbative Neural Combinatorial Optimization (PNCO). The CNCO generally trains an encoder-decoder model via supervised learning to construct solutions from scratch. It exhibits high speed in construction process, however, it lacks the ability for sustained optimization due to the one-shot mapping, which bounds its potential for application. Instead, the PNCO generally trains neural network models via deep reinforcement learning (DRL) to intelligently select appropriate human-designed heuristics to improve existing solutions. It can achieve high-quality solutions but at the cost of high computational demand. To leverage the strengths of both approaches, we propose to hybrid the CNCO and PNCO by designing a hybrid framework comprising two stages, in which the CNCO is the first stage and the PNCO is the second. Specifically, in the first stage, we utilize the attention model to generate preliminary solutions for given CO instances. In the second stage, we employ DRL to intelligently select and combine appropriate algorithmic components from improvement pool, perturbation pool, and prediction pool to continuously optimize the obtained solutions. Experimental results on synthetic and real Capacitated Vehicle Routing Problems (CVRPs) and Traveling Salesman Problems(TSPs) demonstrate the effectiveness of the proposed hybrid framework with the assistance of automated algorithm design.

近年来，神经组合优化（NCO）技术在组合优化（CO）中的应用已成为一个流行且有前途的研究方向。目前，NCO主要有两种类型，即构造性神经组合优化（CNCO）和扰动神经组合优化（PNCO）。 CNCO 通常通过监督学习来训练编码器-解码器模型，以从头开始构建解决方案。它在构建过程中表现出较高的速度，但由于一次性映射而缺乏持续优化的能力，这限制了其应用潜力。相反，PNCO 通常通过深度强化学习 (DRL) 来训练神经网络模型，以智能地选择适当的人为设计的启发式方法来改进现有解决方案。它可以实现高质量的解决方案，但代价是高计算需求。为了利用这两种方法的优势，我们建议通过设计一个包含两个阶段的混合框架来混合 CNCO 和 PNCO，其中 CNCO 是第一阶段，PNCO 是第二阶段。具体来说，在第一阶段，我们利用注意力模型为给定的 CO 实例生成初步解决方案。在第二阶段，我们利用DRL从改进池、扰动池和预测池中智能地选择和组合合适的算法组件，以不断优化获得的解决方案。合成和真实的容量车辆路径问题（CVRP）和旅行商问题（TSP）的实验结果证明了所提出的混合框架在自动化算法设计的帮助下的有效性。