A theoretical framework for runtime analysis of ant colony optimization

Ant colony optimization (ACO) is one of the most famous bio-inspired algorithms. Its theoretical research contains convergence proof and runtime analysis. The convergence of ACO has been proved since several years ago, but there are less results of runtime analysis of ACO algorithm except for some special and simple cases. The present paper proposes a theoretical framework of a class of ACO algorithms. The ACO algorithm is modeled as an absorbing Markov chain. Afterward its convergence can be analyzed based on the model, and the runtime of ACO algorithm is evaluated with the convergence time which reflects how many iteration times ACO algorithms spend in converging to the optimal solution. Moreover, the runtime analysis result is advanced as an estimation method, which is used to study a binary ACO algorithm as a case study.