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Do Ants Use Ant Colony Optimization?

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Shortest Path Solvers. From Software to Wetware

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 32))

Abstract

Ant Colony Optimization (ACO) is a widespread optimization technique used to solve complex problems in a broad range of fields, including engineering, software development and logistics. It was inspired by the behaviour of ants which can collectively select the shorter of two paths leading to a food source. They are able to do so even without any single ant comparing the lengths of the two paths. Ants, like other eusocial insects, have no central authority to coordinate the sophisticated and complex work of their colony members. Coordination is achieved through self-organization, principles of which inspired the development of ACO algorithms. Here we discuss both the similarities and the considerable differences between the behaviour of real ant colonies and techniques used by ACO. We also describe some of the latest findings in ant research and how they may contribute to new ACO algorithms.

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Notes

  1. 1.

    Nondeterministic polynomial means that an algorithm may be constructed which selects the different instances of the problem randomly (nondeterministic), constructs a solution for each instance and tests in polynomial time whether the solution solves the problem. A NP-problem is complete if any other NP-problem can be reduced to it in polynomial time. Polynomial time means that the time an algorithm needs to find a solution for a problem is no more than a polynomial function of the problem size. Although the test for each instance can be performed in polynomial time, there are no algorithms known that are able to solve a NP-complete problem in polynomial time. The reason is that the number of possible solutions grow much faster than the number of problem instances (from [57]).

  2. 2.

    Eusocial means that individuals of different generations live together, cooperate in caring for the juveniles and only a subset of individuals reproduce (reproductive division of labor). The best known eusocial animals are ants, bees, wasps and termites, but rare examples of eusocial mammals (naked mole rats) and crustaceans exist. Eusociality is rare in the animal kingdom and only 2% of all insect species are eusocial. However, eusocial insects make up more than half of the biomass of all insects [36].

  3. 3.

    Argentine ants (Linepithema humile) have spread from Argentina to become invasive to many ecosystems around the world. Unlike many other ant species, they show no or very little aggression towards members of other Argentine ant colonies, and they frequently share food, brood and workers between neighbouring colonies, which are often connected by trail systems. Since there is no clear distinction between the colonies, it is believed that they form large supercolonies which may spread over more than 3000 km [62]. Argentine ants have very poor vision, so are highly depend on pheromones [2]. They form extensive pheromone trails between their nest and their food sources and between the nests of different colonies [4, 37]. The ants deposit pheromone both on their way to and from the food [4] with up to four times more pheromone when returning to the nest [4]. This likely provides information about food quality similar to other ants, such as Lasius niger [6]. Very little is known about the absolute pheromone amounts the ants deposit on their trail [13, 58] and we are only able to measure relative pheromone concentrations by an indirect method based on the movements of their gaster when depositing pheromone [4].

  4. 4.

    To test this, we extended the simulations of the shortest path experiments described in Fig. 2a (DCF with k = 20 and b = 2) by adding further virtual bridges arranged in line. In this way, we simulated different path length to the food, as in a labyrinth. We counted the number of ants taking the short or the long sections. While in the original setting with one bridge, 75% of the ants selected the short sections, this ratio dropped to 64% if three bridges were present, 62% if five bridges were present, and 57% with ten bridges. This demonstrates that the majority of ants still chose the short sections but the effect size drops the more paths are available, and that there was a considerable percentage of virtual ants that took the long sections (von Thienen unpublished data).

  5. 5.

    The model settings were similar to those described in Fig. 6 with the exception, that U-turns were incorporated as described by Beckers [5]. The U-turn settings were such that in average half of the ants made a U-turn while travelling a distance equal to the long path if no pheromone was present. The probability to take a U-turn decreased with the pheromone concentration according to the formula given by Beckers [5] with P0 giving the U-turn-probability in the absence of pheromone set to 0.5, α set to 0.1 and C giving the pheromone concentration. The histogram of the short path selection was similar to that of the simulations without U-turns as shown in Fig. 6 from left to right: 29%–9%–7%–6%–49%.

  6. 6.

    The simulation settings were the same as described in Fig. 6 except that the paths were of equal length and led to two different food sources of different quality and that the returning ants deposited four times more pheromone on the right side with higher food quality than on the left side with lower food quality. L. humile and L. niger deposited pheromone in both directions with the exception that L. niger did not deposit pheromone on its first move to the food. For both ant species, we found a clear preference of the richer food source with following histogram similar to Fig. 6 from left to right:

    • DCF-L. humile: 11%–10%–8%–8%–63%—DCF-L. niger: 0%–0%–0%–100%–0%.

    • PF-L. humile: 1%–12%–17%–14%–56%—PF-L. niger: 0%–0%–0%–100%–0%.

    • Results are similar if pheromone is deposited only in one direction from food to nest.

    • ([57], unpublished data).

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Acknowledgements

We would like to thank Gabriele Valentini and Tanya Latty for comments on earlier versions of this chapter. TC was funded by the Deutsche Forschungsgemeinschaft (grant number CZ 237/1-1)

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  1. Animal Comparative Economics Lab, Institute of Zoology, University of Regensburg, Regensburg, Germany

    Wolfhard von Thienen & Tomer J. Czaczkes

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    Andrew Adamatzky

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von Thienen, W., Czaczkes, T.J. (2018). Do Ants Use Ant Colony Optimization?. In: Adamatzky, A. (eds) Shortest Path Solvers. From Software to Wetware. Emergence, Complexity and Computation, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-319-77510-4_10

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