🤖 AI Summary
This study addresses the lack of a systematic formal description for parallel implementations of ant colony optimization (ACO) algorithms. To this end, it proposes PA²CO, a dedicated process algebra that establishes, for the first time, a unified formal framework supporting both fine-grained and coarse-grained parallelism. This framework precisely captures the full lifecycle behavior of canonical ACO algorithms—including Ant System, MAX-MIN Ant System, and Ant Colony System—as well as their parallel variants. By enabling rigorous modeling of diverse parallel ACO structures, the work not only advances the formal understanding of these algorithms but also provides a solid theoretical foundation for verifying correctness, analyzing performance, and guiding efficient implementations.