Solving Combinatorial Optimization Problems with Graph Neural Networks and Genetic Algorithms: Application to Road Networks

This study takes the road closure problem as a case of combinatorial optimization and proposes a hybrid method that combines a Graph Neural Network (GNN) with a Ge-netic Algorithm (GA). The proposed approach uses the GNN to predict a clo-sure-potential score for each road (edge), and biases the GA’s initial solution genera-tion and mutation operations accordingly. In a virtual road network environment, the hybrid method reduced average travel time by approximately 3% compared to using GA alone. These results suggest that combining learning-based heuristics with evolu-tionary search can be an efficient and practically viable approach to solving combina-torial optimization problems.