Theoretical Properties of Two ACO Approaches for the Traveling Salesman Problem

Ant colony optimization (ACO) has been widely used for different combinatorial optimization problems. In this paper, we investigate ACO algorithms with respect to their runtime behavior for the traveling salesperson problem (TSP). We present a new construction graph and show that it has a stronger local property than one commonly used for constructing solutions of the TSP. Our rigorous runtime analyses for two ACO algorithms, based on these two construction procedures, show that they achieve a good approximation in expected polynomial time on random instances. Furthermore, we point out in which situations our algorithms get trapped in local optima and show where the use of the right amount of heuristic information is provably beneficial