论文标题

TSP之外的神经组合优化:现有的体系结构不足图形结构

Neural combinatorial optimization beyond the TSP: Existing architectures under-represent graph structure

论文作者

Boffa, Matteo, Houidi, Zied Ben, Krolikowski, Jonatan, Rossi, Dario

论文摘要

近年来,人们见证了强化学习,再加上图神经网络(GNN)体系结构,可以学会解决硬组合优化问题:给定的原始输入数据和一个评估者来指导该过程,想法是自动学习能够返回可行和高质量输出的策略。最近的工作显示出令人鼓舞的结果,但后者主要是在旅行推销员问题(TSP)和类似的摘要变体(例如拆分运送车辆路由问题(SDVRP))中评估的。在本文中,我们分析了如何以及如何将最近的神经体系结构应用于实际重要性的图形问题。因此,我们着手系统地将这些体系结构“转移”到功率和频道分配问题(PCAP),该问题与无线网络中的无线电资源分配具有实际相关性。我们的实验结果表明,现有的架构(i)仍然无法捕获图形结构特征,(ii)不适合图形上的操作更改图形属性的问题。从积极的角度来看,我们表明,通过距离编码增加问题的结构表示是朝着学习多功能自动求解器的仍然雄心勃勃的目标的有希望的一步。

Recent years have witnessed the promise that reinforcement learning, coupled with Graph Neural Network (GNN) architectures, could learn to solve hard combinatorial optimization problems: given raw input data and an evaluator to guide the process, the idea is to automatically learn a policy able to return feasible and high-quality outputs. Recent work have shown promising results but the latter were mainly evaluated on the travelling salesman problem (TSP) and similar abstract variants such as Split Delivery Vehicle Routing Problem (SDVRP). In this paper, we analyze how and whether recent neural architectures can be applied to graph problems of practical importance. We thus set out to systematically "transfer" these architectures to the Power and Channel Allocation Problem (PCAP), which has practical relevance for, e.g., radio resource allocation in wireless networks. Our experimental results suggest that existing architectures (i) are still incapable of capturing graph structural features and (ii) are not suitable for problems where the actions on the graph change the graph attributes. On a positive note, we show that augmenting the structural representation of problems with Distance Encoding is a promising step towards the still-ambitious goal of learning multi-purpose autonomous solvers.

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