A full process algebraic representation of Ant Colony Optimization
Maria Garcia, Natalia Lopez, Ismael Rodriguez
TL;DR
This work presents PA$^2$CO, a probabilistic process algebra tailored to fully specify parallel Ant Colony Optimization algorithms with both functional and concurrent behavior. It formalizes three core ACO variants Ant System, MAX-MIN Ant System, and Ant Colony System under two parallelization granularities, providing detailed state, transformation, and operational rules for each. The approach yields a suite of precise, unambiguous models that cover fine-grained and coarse-grained implementations, including variants with free ants and occasional inter-copy communication. The resulting framework supports systematic analysis, potential standardization of parallel ACO methods, and serves as a foundation for extending formal methods to other swarm intelligence algorithms.
Abstract
We present a process algebra capable of specifying parallelized Ant Colony Optimization algorithms in full detail: PA$^2$CO. After explaining the basis of three different ACO algorithms (Ant System, MAX-MIN Ant System, and Ant Colony System), we formally define PA$^2$CO and use it for representing several types of implementations with different parallel schemes. In particular fine-grained and coarse-grained specifications, each one taking advantage of parallel executions at different levels of system granularity, are formalized.