DistrictNet: Decision-aware learning for geographical districting

TL;DR

DistrictNet is a novel graph neural network-based approach that efficiently produces high-quality geographical districting solutions by integrating combinatorial optimization, significantly reducing costs in real-world applications.

Contribution

It introduces a decision-aware learning framework combining graph neural networks with a combinatorial optimization layer for efficient districting.

Findings

Outperforms existing methods in real-world city scenarios

Reduces operational costs significantly

Generates solutions in a few minutes

Abstract

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.