Graph Convolutional Branch and Bound

Abstract: This article demonstrates the effectiveness of employing a deep learning model in an optimization pipeline. Specifically, in a generic exact algorithm for a NP problem, multiple heuristic criteria are usually used to guide the search of the optimum within the set of all feasible solutions. In this context, neural networks can be leveraged to rapidly acquire valuable information, enabling the identification of a more expedient path in this vast space. So, after the explanation of the tackled traveling salesman problem, the implemented branch and bound for its classical resolution is described. This algorithm is then compared with its hybrid version termed "graph convolutional branch and bound" that integrates the previous branch and bound with a graph convolutional neural network. The empirical results obtained highlight the efficacy of this approach, leading to conclusive findings and suggesting potential directions for future research.