Solving Graph Coloring Problem Using Ant Colony Optimization, Simulated Annealing and Quantum Annealing—A Comparative Study

Abstract

AbstractGraph coloring’s paramount significance drives various advancements in developing state-of-the-art algorithms to resolve both empirical and practical problems in computer science. However, no single algorithm is robust enough to produce optimal solutions for all widely recognized benchmark instances. Meta-heuristic algorithms (MHA) and evolutionary algorithms (EA) make prudent and optimal solutions for most of the cases of graph coloring problems (GCP). Moreover, these algorithms can offer optimal solutions heuristically in contrast to conventional wearisome approaches. This paper presents a comparative study in solving GCP to find the chromatic number based on three MHAs, namely ant colony optimization (ACO), simulated annealing (SA), and quantum annealing (QA), in a single framework, with favorable outturns. The final result proves QA outperforms the performances of SA and ACO, but it takes more time than ACO and SA for large graph instances.KeywordsKinetic energyMeta-statePheromone intensityThermal gradientQuantum fluctuations