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A deep learning guided memetic framework for graph coloring problems

Given an undirected graph $G=(V,E)$ with a set of vertices $V$ and a set of edges $E$, a graph coloring problem involves finding a partition of the vertices into different independent sets. In this paper we present a new framework that combines a deep neural network with the best tools of classical metaheuristics for graph coloring. The proposed method is evaluated on two popular graph coloring problems (vertex coloring and weighted coloring). Computational experiments on well-known benchmark graphs show that the proposed approach is able to obtain highly competitive results for both problems. A study of the contribution of deep learning in the method highlights that it is possible to learn relevant patterns useful to obtain better solutions to graph coloring problems.