A recent trend in the mathematical optimization literature is to embed trained machine learning predictors into a larger optimization model. The m ost common application is for a practitioner to train a machine learning predictor as a sur rogate for a more complicated subsystem that cannot be directly embedded into an optimiza tion model, for example, because it does not have an algebraic form or because it is non -differentiable. L opez-Flores et al. (2024) provide a review of the field.

In the last years, many neural network-based approaches have been proposed to tackle combinatorial optimization problems such as routing problems. Many of these approaches are based on graph neural networks (GNNs) or related transformers, operating on the Euclidean coordinates representing the routing problems. However, GNNs are inherently not well suited to operate on dense graphs, such as in routing problems. Furthermore, models operating on Euclidean coordinates cannot be applied to non-Euclidean versions of routing problems that are often found in real-world settings. To overcome these limitations, we propose a novel GNN-related edge-based neural model called Graph Edge Attention Network (GREAT). We evaluate the performance of GREAT in the edge-classification task to predict optimal edges in the Traveling Salesman Problem (TSP). We can use such a trained GREAT model to produce sparse TSP graph instances, keeping only the edges GREAT finds promising. Compared to other, non-learningbased methods to sparsify TSP graphs, GREAT can produce very sparse graphs while keeping most of the optimal edges. Furthermore, we build a reinforcement learning-based GREAT framework which we apply to Euclidean and non-Euclidean asymmetric TSP. This framework achieves state-of-the-art results. Graph neural networks (GNNs) have emerged as a powerful tool for learning on graph-structured data such as molecules, social networks, or citation graphs Wu et al. (2020). In recent years, GNNs have also been applied in the setting of combinatorial optimization, especially routing problems Joshi et al. (2019); Hudson et al. (2021); Xin et al. (2021) since such problems can be interpreted as graph problems.

Dr. Rothberg has served in senior leadership positions in optimization software companies for more than twenty years. Prior to his role as Gurobi CEO, Dr. Rothberg held the Gurobi COO position since co-founding Gurobi in 2008, and prior to that he led the ILOG CPLEX team. Dr. Edward Rothberg has a BS in Mathematical and Computational Science from Stanford University, and an MS and PhD in Computer Science, also from Stanford University. Dr. Rothberg has published numerous papers in the fields of linear algebra, parallel computing, and mathematical programming. He is one of the world's leading experts in sparse Cholesky factorization and computational linear, integer, and quadratic programming.