Convergence
For some versions of the algorithm, it is possible to prove that it is convergent (i.e., it is able to find the global optimum in finite time). The first evidence of a convergence ant colony algorithm was made in 2000, the graph-based ant system algorithm, and then algorithms for ACS and MMAS. Like most metaheuristics, it is very difficult to estimate the theoretical speed of convergence. In 2004, Zlochin and his colleagues showed that COA-type algorithms could be assimilated methods of stochastic gradient descent, on the cross-entropy and estimation of distribution algorithm. They proposed these metaheuristics as a "research-based model".
Read more about this topic: Ant Colony Optimization Algorithms