Differentiable Projection-Guided Graph Neural Networks for Large-Scale Logistics Optimization for Sustainable Renewable Energy
Keywords:
Large-Scale-Logistics, Graph Neural Networks, Optimization, Renewable energy, DPG-GNNAbstract
Maximum Combinatorial optimization problems in large-scale logistics networks, such as vehicle routing and node assignment, remain challenging due to their NP-hard nature and the stringent feasibility requirements imposed by real-world constraints. Conventional neural approaches often rely on autoregressive decoders or heuristic search, which scale poorly and struggle to guarantee constraint satisfaction. We propose a Differentiable Projection-Guided Graph Neural Network (DPG-GNN) that reformulates the solver as a parallel fixed-point iteration scheme integrating learnable differentiable projection operators. The architecture first employs a sparse hierarchical message-passing encoder to process raw logistics graph data, computing node embedding via a cluster-aware attention mechanism that maintains nearly linear complexity on large graphs. These embedding initialize a continuous relaxation of the decision variables. The core technical novelty is an iterative refinement module that alternates between a line-graph message-passing step and a parallelized alternating direction method of multipliers (ADMM) that projects the candidate solution onto the intersection of constraint polytopes, including simplex projections for capacity limits and Sink horn iterations for assignment constraints. The entire unrolled refinement process is trained end-to-end using a differentiable proxy loss that combines cost minimization with quadratic constraint penalties. At inference, a deterministic rounding and greedy repair procedure produces feasible integer solutions. The DPG-GNN avoids the sequential bottlenecks of autoregressive methods and learns to produce low-cost, nearly feasible continuous solutions directly. This work therefore introduces a principled framework for integrating constraint satisfaction directly into the differentiable optimization pipeline, with significant implications for large-scale logistics planning where both solution quality and computational efficiency are critical.
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Copyright (c) 2026 Fredrick Kayusi, Bismark Agura Kayus, Suram Likhita Reddy (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
