Scaleable neural combinatorial optimization and real world logistics application

Abstract

This research introduces novel algorithms designed to provide scalable constructive nerual solver to a wide range of combinatorial optimization (CO) problems. These problems, characterized by their NP-completeness and their relationship to the traveling salesman problem, present formidable computational hurdles when attempting to find efficient solutions. In recent years, constructive RL methods have demonstrated competitive performance in small-scale instances (fewer than 100 nodes) when compared to heuristic methods. Their effectiveness diminishes significantly as the problem size increases. because existing constructive methods lack the ability to scale effectively. To address this challenge, our research aims to incorporate inductive bias during both the training and testing phases. Our research encompasses two main topics, namely, Meta-SAGE and Equity-Transformer. Firstly, our approach harnesses pre-trained models to handle larger-scale problems during testing, utilizing two components: a scale meta-learner (SML) and scheduled adaptation with guided exploration (SAGE). Secondly, we delve into the min-max VRPs problem, which adds an additional layer of complexity and closely mirrors real-world logistical challenges. Here, we employ a deep reinforcement learning approach and customize a transformer-based neural architecture, presenting the "Equity-Transformer" as a dedicated solution for effectively tackling min-max VRPs.