Darwin’s Crayons: Genetic Algorithms for Coloring a Dynamic Graph

We studied the relative performance of genetic algorithms on coloring a dynamic graph for di↵erent graph and algorithm conditions. Graph coloring is a well-studied NP-complete problem with a wide range of applications in scheduling and assignment problems, while dynamic graphs are a natural way to model a diverse range of dynamic systems, from register allocation to mobile ad-hoc networks. Coloring a dynamic graph can be used for the online scheduling of conflicting tasks, when the tasks are not known beforehand. As genetic algorithms (GAs) have been shown to be e↵ective for graph coloring and are adaptable to dynamic environments, they are an promising choice for the dynamic graph coloring problem. We examined graphs of di↵erent sizes, edge densities, structures, and change rates, using di↵erent amounts of evolution between changes in the graph. For these graphs, we compared the performance of three algorithms: DSATUR, a standard graph coloring algorithm, on each time-step of the graph, a GA with a single population adapting to the changing graph, and a GA with a new population at each time-step of the graph. Finally, we present the impact of variation in these factors on the relative performance of the three algorithms.