# Graph Coloring with Adaptive Evolutionary Algorithms

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## Abstract

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EAs). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping Genetic Algorithm (GGA) on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping (GA) and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity.

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