An Adversarial-robust Graph Representation Learning for Energy-aware Vehicle Routing Considering Privacy

The electrification of the transportation sector is increasingly recognized as a pivotal strategy for enhancing environmental sustainability, reducing greenhouse gas emissions, and improving overall energy utilization. In this context, the development of vehicle routing solutions that are not only energy-efficient but also resilient to adversarial threats, and mindful of privacy considerations has become important. This paper introduces an innovative Graphormer-based model that adeptly balances energy efficiency, task sequencing, and privacy protection. Unlike traditional approaches that either neglect adversarial threats or employ simplistic energy scheduling, our model uniquely integrates Graph Neural Networks and Transformers to enhance global graphical information embedding to infer adversarial data. Under privacy protection, the regions instead of the exact locations of tasks are given. A mathematical model for the energy-aware vehicle routing problem that incorporates privacy protection is introduced, alongside a refined Graphormer model enhanced by three novel encoding structures: centrality encoding, spatial encoding, and edge encoding architectures. Through comprehensive simulations, our model not only achieves near-optimal solutions rapidly, adapting swiftly to environmental changes and adversarial attacks but also significantly surpasses existing benchmarks in energy efficiency and privacy preservation.