ANT COLONY optimization (ACO) is part of a larger field of research termed ant algorithms or swarm intelligence that deals with algorithmic approaches that are inspired by the behavior of ant colonies and other social insects [1]–[3],[5]. Of particular interest are the collective activities of members of a colony, such as foraging, brood care, or nest building, which utilize mechanisms of self-organization, stigmergic communication [5],[13], and task partitioning. Ant algorithms have been proposed as a novel computational model that replaces the traditional emphasis on control, preprogramming, and centralization with designs featuring autonomy, emergence, and distributed functioning. These designs are proving flexible and robust, they are able to adapt quickly to changing environments, and they continue functioning when individual elements fail. A particularly successful research direction in ant algorithms, ACO [6],[7],[9],[10], is dedicated to their application to discrete optimization problems. ACO is inspired by the foraging behavior of real ants, which use pheromone trails to mark their paths to food sources. In ACO, the discrete optimization problem considered is mapped onto a graph called a construction graph in such a way that feasible solutions to the original problem correspond to paths on the construction graph. Then, artificial ants can generate feasible solutions by moving on the construction graph. In practice, colonies of artificial ants search for good solutions for several iterations. Every (artificial) ant of a given iteration builds a solution incrementally by taking several probabilistic decisions. The artificial ants that find a good solution mark their paths on the construction graph by putting some amount of pheromone on the edges of the path they followed. The ants in the next iteration are attracted by the pheromones, ie, their decision probabilities are biased by the pheromones: in this way, they will have a higher probability of building paths that are similar to paths that correspond to good solutions. ACO has been applied successfully to a large number of difficult combinatorial optimization problems including traveling salesman problems, quadratic assignment problems, and scheduling problems, as well as to dynamic routing problems in telecommunication networks. Unfortunately, it is difficult to analyze ACO algorithms theoretically, the main reason being that they are based on sequences of random decisions (taken by a colony of artificial ants) that are usually not independent and whose probability distribution changes from iteration to iteration. Accordingly, most of the ongoing research in ACO