A deep learning guided memetic framework for graph coloring problems

Abstract

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 which combines a deep neural network with the best tools of "classical" metaheuristics for graph coloring. The proposed algorithm is evaluated on the weighted graph coloring problem and computational results show that the proposed approach allows to obtain new upper bounds for medium and large graphs. A study of the contribution of deep learning in the algorithm highlights that it is possible to learn relevant patterns useful to obtain better solutions to this problem.

Conflict Optimization for Binary CSP Applied to Minimum Partition into Plane Subgraphs and Graph Coloring

“…We notice that the conflict optimizer works extremely poorly on random graphs, but it is fast and appears to perform well on geometric graphs (r250.5, r1000.1c, r1000.5, dsjr500.1c and dsjr500.5), matching the best-known results [11]. Interestingly, these geometric graphs are not intersection graphs as in the CG:SHOP challenge, but are generated based on a distance threshold.…”

On Monte Carlo Tree Search for Weighted Vertex Coloring

“…A variant of the GCP called the Weighted Vertex Coloring Problem (WVCP) has recently attracted a lot of interest in the literature [9,16,20,22]. In this problem, each vertex of the graph has a weight and the objective is to find a legal solution such that the sum of the weights of the heaviest vertex of each color group is minimized.…”

“…The second category of existing heuristics for the WVCP relies on the populationbased memetic framework that combines local search with crossovers. A recent algorithm [9] of this category uses a deep neural network to learn an invariant by color permutation regression model, useful to select the most promising crossovers at each generation.…”

On Monte Carlo Tree Search for Weighted Vertex Coloring

“…A variant of the GCP called the Weighted Vertex Coloring Problem (WVCP) has recently attracted much interest in the literature [3][4][5][6]. In this problem, each vertex of the graph has a weight and the objective is to find a legal solution such that the sum of the weights of the heaviest vertex of each color group is minimized.…”

“…The second category of existing heuristics for the WVCP relies on the population-based memetic framework that combines local search with crossovers. A recent algorithm [3] of this category uses a deep neural network to learn an invariant by color permutation regression model, useful to select the most promising crossovers at each generation.…”