A graph-based neural approach to linear sum assignment problems

Linear assignment problems are well-known combinatorial optimization problems involving domains such as logistics, robotics, and telecommunications. In general, obtaining an optimal solution to such problems is computationally infeasible even in small settings, so heuristic algorithms are often used to find near-optimal solutions. In order to attain the right assignment permutation, this study investigates a general-purpose learning strategy that uses a bipartite graph to describe the problem structure and a Message Passing Graph Neural Network (GNN) model to learn the correct mapping. Comparing the proposed structure with two existing DNN solutions, simulation results show that the proposed approach significantly improves classification accuracy, proving to be very efficient in terms of processing time and memory requirements, due to its inherent parameter sharing capability. Among the many practical uses that require solving allocation problems in everyday scenarios, we decided to apply the proposed approach to address the scheduling of electric smart meters access within an electricity distribution smart grid infrastructure, since near-real-time energy monitoring is a key element of the green transition that has become increasingly important in recent times. The results obtained show that the proposed graph-based solver, although sub-optimal, exhibits the highest scalability, compared with other state-of-the-art heuristic approaches. To foster the reproducibility of the results, we made the code available at https://github.com/aircarlo/GNN\_LSAP.