A deep learning guided memetic framework for graph coloring problems

A Memetic Algorithm with Adaptive Operator Selection for Graph Coloring

“…When we look at the frequencies of the local search operators selected by AHEAD, we see that TabuCol is selected most often in comparison with PartialCol, which is no surprise, as TabuCol is already better on its own for a greater number of instances. However, when it comes to crossovers, we observe a balanced choice between the three GPX variants, with a bias toward the more conservative crossover GPX-9 for geometric graphs (e.g., DSJR500.5) and sparse graphs (e.g., wap instances), for which local optima are very distant in the search space, while the GPX crossover is more often preferred for random and dense graphs (e.g., DSJC1000.9), for which there is often larger backbones of solutions shared by the high-quality solutions (as shown in [10]).…”

“…The architecture of the AHEAD framework, illustrated in Figure 1, extends the state-of-the-art HEAD framework [21] by introducing an operator selector. In particular, its simplicity with only two individuals in the population facilitates the parent matching and population updating phases compared to other memetic algorithms in the literature [7,18,24,10]. AHEAD takes as input a graph G = (V, E), and an integer value k for the kcol or a weight function w for the WVCP, a set of local search operators O l , a set of crossover operators O x , and a high-level selection strategy π θ characterized by a parameter vector θ.…”

“…This strategy is among the most elitist, as it gives more chances to the best strategy applied in previous iterations. -NN (Neural Network) uses the recommendations of a deep set neural network architecture [10,13,32]. This neural network g θ takes as input a coloring S as a set of k binary vectors v j of size n, S = {v 1 , .…”

“…HEAD also uses the GPX crossover and an improved TabuCol algorithm. This algorithm HEAD is currently one of the most efficient solvers for the k-col. For the WVCP, to our knowledge, there is only one memetic algorithm in the literature, DLMCOL [10], which uses a large population (more than 20,000) and parallel GPU-based local searches, combined with a neural network-guided crossover selection.…”

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“…Lü and Hao introduced a memetic algorithm (MACOL) to address GCP [5]. Goudet et al proposed a memetic framework guided by deep learning for graph coloring problems and implemented it on GPU devices to solve the classical vertex k-coloring problem and the weighted vertex coloring problem [6]. In a related study, Marappan et al concentrated on developing a new Particle Swarm Optimization (PSO) model that minimizes the search space and number of generations required.…”