Districting is a complex combinatorial problem that consists in partitioning a geographical area into small districts.

Leveraging this flexibility, we implement 47 novel MCBO algorithms and benchmark them against seven existing MCBO solvers and five standard black-box optimization algorithms on ten tasks, conducting over 4000 experiments.

To this end, we first establish a new class of GNNs that can solve a strictly wider variety of problems than existing GNNs. Then, we bridge the gap between GNN theory and the theory of distributed local algorithms.

There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused onobtaining high-quality solutions, scalability tobillion-sized graphs has not been adequately addressed.

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems.

Yet, despite recent progress, CO problems still pose a significant challenge to neural networks. Successful models often rely on supervision, either in the form of labeled instances [45, 62, 35] or of expert demonstrations [27]. This success comes with drawbacks: obtaining labels for hard problem instances can be computationally infeasible [86],and direct supervision can lead topoor generalization[36].