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Handbook of Metaheuristics pp 311–351Cite as

Ant Colony Optimization: Overview and Recent Advances

Part of the International Series in Operations Research & Management Science book series (ISOR,volume 272)

Abstract

Ant Colony Optimization (ACO) is a metaheuristic that is inspired by the pheromone trail laying and following behavior of some ant species. Artificial ants in ACO are stochastic solution construction procedures that build candidate solutions for the problem instance under concern by exploiting (artificial) pheromone information that is adapted based on the ants’ search experience and possibly available heuristic information. Since the proposal of Ant System, the first ACO algorithm, many significant research results have been obtained. These contributions focused on the development of high performing algorithmic variants, the development of a generic algorithmic framework for ACO algorithm, successful applications of ACO algorithms to a wide range of computationally hard problems, and the theoretical understanding of important properties of ACO algorithms. This chapter reviews these developments and gives an overview of recent research trends in ACO.

Keywords

  • Pheromone Trail
  • Heuristic Information
  • Solution Construction
  • Approximate Nondeterministic Tree Search (ANTS)
  • Single Machine Total Weighted Tardiness Problem (SMTWTP)

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 10.1
Fig. 10.2
Fig. 10.3
Fig. 10.4
Fig. 10.5

Notes

  1. 1.

    Other approximate methods are also conceivable. For example, when stopping exact methods, like Branch and Bound, before completion [11, 104] (e.g., using some given time bound, or when some guarantee on solution quality is obtained through the use of lower and upper bounds), we can convert exact algorithms into approximate ones.

  2. 2.

    The adaptation to maximization problems is straightforward.

  3. 3.

    Static problems are those whose topology and costs do not change while they are being solved. This is the case, for example, for the classic TSP, in which city locations and intercity distances do not change during the algorithm’s run-time. In contrast, in dynamic problems the topology and costs can change while solutions are built. An example of such a problem is routing in telecommunications networks [52], in which traffic patterns change all the time.

  4. 4.

    The experiment described was originally executed using a laboratory colony of Argentine ants (Iridomyrmex humilis). It is known that these ants deposit pheromone both when leaving and when returning to the nest [89].

  5. 5.

    In the ACO literature, this is often called differential path length effect.

  6. 6.

    A process like this, in which a decision taken at time t increases the probability of making the same decision at time T > t is said to be an autocatalytic process. Autocatalytic processes exploit positive feedback.

  7. 7.

    Note that, when applied to symmetric TSPs, the edges are considered to be bidirectional and edges (i, j) and (j, i) are both updated. This is different for the ATSP, where edges are directed; in this case, an ant crossing edge (i, j) will update only this edge and not edge (j, i).

  8. 8.

    ACS was an offspring of Ant-Q [82], an algorithm intended to create a link between reinforcement learning [179] and Ant Colony Optimization. Computational experiments have shown that some aspects of Ant-Q, in particular the pheromone update rule, could be strongly simplified without affecting performance. It is for this reason that Ant-Q was abandoned in favor of the simpler and equally good ACS.

  9. 9.

    The maximum time for the largest instances was 20 min on a 450 MHz Pentium III PC with 256 MB RAM. Programs were written in C++ and the PC was run under Red Hat Linux 6.1.

  10. 10.

    There have been several proposals of ant-inspired algorithms for continuous optimization [17, 73, 142]. However, these differ strongly from the underlying ideas of ACO (for example, they use direct communication among ants) and therefore cannot be considered as algorithms falling into the framework of the ACO metaheuristic.

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Acknowledgements

This work was supported by the COMEX project, P7/36, within the Interuniversity Attraction Poles Programme of the Belgian Science Policy Office. Marco Dorigo and Thomas Stützle acknowledge support from the Belgian F.R.S.-FNRS, of which they are Research Directors.

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  1. IRIDIA, Université Libre de Bruxelles (ULB), Brussels, Belgium

    Marco Dorigo & Thomas Stützle

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  1. Marco Dorigo
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  2. Thomas Stützle
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  1. Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Montreal, QC, Canada

    Michel Gendreau

  2. Département d’informatique et de recherche opérationnelle, Université de Montréal, Montreal, QC, Canada

    Jean-Yves Potvin

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Dorigo, M., Stützle, T. (2019). Ant Colony Optimization: Overview and Recent Advances. In: Gendreau, M., Potvin, JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-319-91086-4_10

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