5. Ant Colony Optimization Vittorio Maniezzo, Luca Maria Gambardella, Fabio de Luigi 5.1 Introduction Ant Colony Optimization (ACO) is a paradigm for designing metaheuristic algo- rithms for combinatorial optimization problems. The first algorithm which can be classified within this framework was presented in 1991 [21, 13] and, since then, many diverse variants of the basic principle have been reported in the literature. The essential trait of ACO algorithms is the combination of a priori information about the structure of a promising solution with a posteriori information about the structure of previously obtained good solutions. Metaheuristic algorithms are algorithms which, in order to escape from local optima, drive some basic heuristic: either a constructive heuristic starting from a null solution and adding elements to build a good complete one, or a local search heuristic starting from a complete solution and iteratively modifying some of its elements in order to achieve a better one. The metaheuristic part permits the low- level heuristic to obtain solutions better than those it could have achieved alone, even if iterated. Usually, the controlling mechanism is achieved either by con- straining or by randomizing the set of local neighbor solutions to consider in local search (as is the case of simulated annealing [46] or tabu search [33]), or by com- bining elements taken by different solutions (as is the case of evolution strategies [11] and genetic [40] or bionomic [56] algorithms). The characteristic of ACO algorithms is their explicit use of elements of previ- ous solutions. In fact, they drive a constructive low-level solution, as GRASP [30] does, but including it in a population framework and randomizing the construction in a Monte Carlo way. A Monte Carlo combination of different solution elements is suggested also by Genetic Algorithms [40], but in the case of ACO the probabil- ity distribution is explicitly defined by previously obtained solution components. The particular way of defining components and associated probabilities is prob- lem-specific, and can be designed in different ways, facing a trade-off between the specificity of the information used for the conditioning and the number of solu- tions which need to be constructed before effectively biasing the probability dis- This work was partially supported by the Future & Emerging Technologies unit of the European Commission through Project BISON (IST-2001-38923).