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.

翻译：我们提出了一种能够详细描述并行化蚁群优化算法的过程代数：PA$^2$CO。在解释三种不同蚁群优化算法（蚁群系统、最大-最小蚁群系统和蚁群系统）的基础之后，我们正式定义了PA$^2$CO，并利用它来表示采用不同并行方案的多种实现类型。特别是细粒度和粗粒度两种规范，每种规范都在系统粒度的不同层面上利用并行执行，均得到了形式化描述。