# End-to-End Pareto Set Prediction with Graph Neural Networks for Multi-objective Facility Location

arXiv: https://arxiv.org/abs/2210.15220 · HTML: https://mlsanity.com/paper/2210.15220/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 20 of 20)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Edge-labeling Graph Neural Network for Few-shot Learning](https://mlsanity.com/paper/1905.01436/) (2019)
- [Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking](https://mlsanity.com/paper/2005.11081/) (2020)
- [Graph Neural Network Guided Local Search for the Traveling Salesperson Problem](https://mlsanity.com/paper/2110.05291/) (2021)
- [On Learning Paradigms for the Travelling Salesman Problem](https://mlsanity.com/paper/1910.07210/) (2019)
- [The Non-Uniform k-Center Problem](https://mlsanity.com/paper/1605.03692/) (2016)

## Built on by (most cited first, 3 of 3)

- [A Graph Neural Network with Negative Message Passing for Graph Coloring](https://mlsanity.com/paper/2301.11164/) (2023)
- [An Edge-Aware Graph Autoencoder Trained on Scale-Imbalanced Data for Traveling Salesman Problems](https://mlsanity.com/paper/2310.06543/) (2023)
- [LEO: Learning Efficient Orderings for Multiobjective Binary Decision Diagrams](https://mlsanity.com/paper/2307.03171/) (2023)

## Abstract (arXiv)

The facility location problems (FLPs) are a typical class of NP-hard combinatorial optimization problems, which are widely seen in the supply chain and logistics. Many mathematical and heuristic algorithms have been developed for optimizing the FLP. In addition to the transportation cost, there are usually multiple conflicting objectives in realistic applications. It is therefore desirable to design algorithms that find a set of Pareto solutions efficiently without enormous search cost. In this paper, we consider the multi-objective facility location problem (MO-FLP) that simultaneously minimizes the overall cost and maximizes the system reliability. We develop a learning-based approach to predicting the distribution probability of the entire Pareto set for a given problem. To this end, the MO-FLP is modeled as a bipartite graph optimization problem and two graph neural networks are constructed to learn the implicit graph representation on nodes and edges. The network outputs are then converted into the probability distribution of the Pareto set, from which a set of non-dominated solutions can be sampled non-autoregressively. Experimental results on MO-FLP instances of different scales show that the proposed approach achieves a comparable performance to a widely used multi-objective evolutionary algorithm in terms of the solution quality while significantly reducing the computational cost for search.