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**The ant colony optimization metaheuristic: algorithms, applications, and advances.**
*(English)*
Zbl 1102.90378

Glover, Fred (ed.) et al., Handbook of metaheuristics. Boston, MA: Kluwer Academic Publishers (ISBN 1-4020-7263-5/hbk). Int. Ser. Oper. Res. Manag. Sci. 57, 251-285 (2003).

Summary: The field of ACO algorithms is very lively, as testified, for example, by the successful biannual workshop (ANTS – From Ant Colonies to Artificial Ants: A Series of International Workshops on Ant Algorithms; http://iridia.ulb.ac.be/ ants/) where researchers meet to discuss the properties of ACO and other ant algorithms, both theoretically and experimentally.

From the theory side, the most interesting ongoing work concern the study of the relationship between ACO algorithms and other well-known stochastic optimization techniques. For example, it has been shown that, when interpreting ACO algorithms as methods for searching in the space of pheromones (i.e., artificial ants are seen as procedures to update pheromone trails so to increase the probability of generating very good solutions to the combinatorial optimization problem), then AS can be interpreted as an approximate form of stochastic gradient descent (a well- known algorithm which has been extensively used in machine learning) in the space of pheromones. Similarly, it has been shown that there are strong connections between ACO algorithms and the Cross-Entropy method.

From the experimental side, most of the current research is in the direction of increasing the number of problems that are successfully solved by ACO algorithms, including real-word, industrial applications [39]. Currently, the great majority of problems attacked by ACO are static and well- defined combinatorial optimization problems, that is, problems for which all the necessary information is available and does not change during problem solution. For this kind of problems ACO algorithms must compete with very well established algorithms, often specialized for the given problem. Also, very often the role played by local search is extremely important to obtain good results. Although rather successful on these problems, we believe that ACO algorithms will really show their greatest advantage when they are systematically applied to “ill-structured” problems for which it is not clear how to apply local search, or to highly dynamic domains with only local information available. A first step in this direction has already been made with the application to telecommunications networks routing, but much further research will be necessary. The reader interested in learning more about ACO is referred to the book “Ant Colony Optimization”; by the same authors.

For the entire collection see [Zbl 1058.90002].

From the theory side, the most interesting ongoing work concern the study of the relationship between ACO algorithms and other well-known stochastic optimization techniques. For example, it has been shown that, when interpreting ACO algorithms as methods for searching in the space of pheromones (i.e., artificial ants are seen as procedures to update pheromone trails so to increase the probability of generating very good solutions to the combinatorial optimization problem), then AS can be interpreted as an approximate form of stochastic gradient descent (a well- known algorithm which has been extensively used in machine learning) in the space of pheromones. Similarly, it has been shown that there are strong connections between ACO algorithms and the Cross-Entropy method.

From the experimental side, most of the current research is in the direction of increasing the number of problems that are successfully solved by ACO algorithms, including real-word, industrial applications [39]. Currently, the great majority of problems attacked by ACO are static and well- defined combinatorial optimization problems, that is, problems for which all the necessary information is available and does not change during problem solution. For this kind of problems ACO algorithms must compete with very well established algorithms, often specialized for the given problem. Also, very often the role played by local search is extremely important to obtain good results. Although rather successful on these problems, we believe that ACO algorithms will really show their greatest advantage when they are systematically applied to “ill-structured” problems for which it is not clear how to apply local search, or to highly dynamic domains with only local information available. A first step in this direction has already been made with the application to telecommunications networks routing, but much further research will be necessary. The reader interested in learning more about ACO is referred to the book “Ant Colony Optimization”; by the same authors.

For the entire collection see [Zbl 1058.90002].