DistrictNet: Decision-aware learning for geographical districting
This addresses a major strategic decision in logistics that determines operating costs, offering a novel method for a domain-specific problem.
The paper tackles the intractable combinatorial problem of geographical districting in logistics by proposing a structured learning approach that integrates a combinatorial optimization layer into a graph neural network, achieving high-quality solutions in minutes and significantly reducing costs on real-world cities.
Districting is a complex combinatorial problem that consists in partitioning a geographical area into small districts. In logistics, it is a major strategic decision determining operating costs for several years. Solving districting problems using traditional methods is intractable even for small geographical areas and existing heuristics often provide sub-optimal results. We present a structured learning approach to find high-quality solutions to real-world districting problems in a few minutes. It is based on integrating a combinatorial optimization layer, the capacitated minimum spanning tree problem, into a graph neural network architecture. To train this pipeline in a decision-aware fashion, we show how to construct target solutions embedded in a suitable space and learn from target solutions. Experiments show that our approach outperforms existing methods as it can significantly reduce costs on real-world cities.