Carbon-Aware Last-Mile Delivery Optimization using Sparrow search algorithm and graph neural network risk assessment

Abstract

With the advancement of global carbon neutrality strategies and explosive growth in e-commerce, urban last-mile delivery faces multiple challenges in balancing economic benefits, environmental impact, and risk management. Traditional optimization methods struggle to simultaneously address multi-objective trade-offs, network topological dependencies, and small-sample risk prediction problems. This study proposes a hybrid intelligent framework integrating an Improved Sparrow Search Algorithm (ISSA) with a Meta-Learning Graph Convolutional Network on Prototype Space (ML-GCNPS) for carbon-aware delivery optimization and risk assessment. ISSA-NSGA-III generates high-quality initial populations through Tent chaotic mapping, designs an adaptive periodic convergence factor to dynamically balance exploration and exploitation, and enhances global search capability by integrating Lévy flight with Elite Opposition-Based Learning (EOBL), achieving multi-objective collaborative optimization through embedding in the NSGA-III framework. ML-GCNPS designs a feature extraction network to extract discriminative features from multi-modal node data, explicitly models class centers through prototype space embedding to enhance small-sample generalization, constructs an adaptive Vertex-to-Edge (V2E) network to dynamically infer edge weights and capture risk propagation paths, and employs a two-layer graph convolutional architecture for sufficient information propagation. Experiments on the Kaggle Supply Chain Management dataset and Carbon Monitor risk dataset demonstrate that compared to standard SSA, ISSA-NSGA-III improves total cost, carbon emissions, and resource utilization by 14.0%, 14.2%, and 15.4%, respectively, with Pareto front quality improved by 28.5%. ML-GCNPS achieves an AUPRC of 0.850 (standard deviation 0.005) and a Macro Fl-Score of 0.850 (standard deviation 0.005) in 5-way 1-shot scenarios, reduces the False Negative Rate (FNR) to 0.080 (standard deviation 0.003), and achieves a Weighted Average Cost (WAC) of 45, significantly outperforming baseline methods such as ProtoNG and MAML-GNN (paired t-test, p less than 0.01 for AUPRC and FNR versus the second-best baseline GAT-FSL). Ablation experiments validate the necessity of the meta-learning framework, graph convolutional structure, V2E network, and prototype space embedding, while alternative design comparisons demonstrate the superiority of the technical choices. While the individual algorithmic components (Tent chaotic mapping, Lévy flight, EOBL, prototypical networks, and GCN) are established techniques, the principal contribution of this study líes in their systematic integration into a closed-loop optimization-assessment-feedback decision framework, where graph structure serves as an information bridge connecting delivery optimization with risk prediction. This study provides a teclmical solution for smart city logistics and offers theoretical basis and practica! guidance for sustainable delivery under carbon neutrality goals. All reported improvements over baseline methods are statistically significant across all evaluation metrics (paired t-test or Wilcoxon rank-sum test, p < 0.001

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