Evolutionary Dynamics of Ant Colony Optimization

Swarm intelligence has been successfully applied in various domains, e.g., path planning, resource allocation and data mining. Despite its wide use, a theoretical framework in which the behavior of swarm intelligence can be formally understood is still lacking. This article starts by formally deriving the evolutionary dynamics of ant colony optimization, an important swarm intelligence algorithm. We then continue to formally link these to reinforcement learning. Specifically, we show that the attained evolutionary dynamics are equivalent to the dynamics of Q-learning. Both algorithms are equivalent to a dynamical system known as the replicator dynamics in the domain of evolutionary game theory. In conclusion, the process of improvement described by the replicator dynamics appears to be a fundamental principle which drives processes in swarm intelligence, evolution, and learning.