2018/09/07 by Marcelo Prates, Prates, Marcelo O. R., Pedro H. C. Avelar +7 · 3 citations
Computer Science · #Advanced Graph Neural Networks #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Metaheuristic Optimization Algorithms Research #Neural and Evolutionary Computing (cs.NE)
paper · pdf · doi:10.48550/arxiv.1809.02721
openalex publication_date 2018/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Graph Neural Networks (GNN) are a promising technique for bridging\ndifferential programming and combinatorial domains. GNNs employ trainable\nmodules which can be assembled in different configurations that reflect the\nrelational structure of each problem instance. In this paper, we show that GNNs\ncan learn to solve, with very little supervision, the decision variant of the\nTraveling Salesperson Problem (TSP), a highly relevant \NP-Complete\nproblem. Our model is trained to function as an effective message-passing\nalgorithm in which edges (embedded with their weights) communicate with\nvertices for a number of iterations after which the model is asked to decide\nwhether a route with cost <C exists. We show that such a network can be\ntrained with sets of dual examples: given the optimal tour cost C*, we\nproduce one decision instance with target cost x % smaller and one with\ntarget cost x % larger than C*. We were able to obtain 80 % accuracy\ntraining with -2 %,+2 % deviations, and the same trained model can generalize\nfor more relaxed deviations with increasing performance. We also show that the\nmodel is capable of generalizing for larger problem sizes. Finally, we provide\na method for predicting the optimal route cost within 2 % deviation from the\nground truth. In summary, our work shows that Graph Neural Networks are\npowerful enough to solve \NP-Complete problems which combine\nsymbolic and numeric data.\n