Optimisation in a natural system: Argentine ants solve the Towers of Hanoi

Abstract

SUMMARYNatural systems are a source of inspiration for computer algorithms designed to solve optimisation problems. Yet most 'natureinspired' algorithms take only superficial inspiration from biology, and little is known about how real biological systems solve difficult problems. Moreover, ant algorithms, neural networks and similar methods are usually applied to static problems, whereas most biological systems have evolved to perform under dynamically changing conditions. We used the Towers of Hanoi puzzle to test whether Argentine ants can solve a potentially difficult optimisation problem. We also tested whether the ants can adapt to dynamic changes in the problem. We mapped all possible solutions to the Towers of Hanoi on a single graph and converted this into a maze for the ants to solve. We show that the ants are capable of solving the Towers of Hanoi, and are able to adapt when sections of the maze are blocked off and new sections installed. The presence of exploration pheromone increased the efficiency of the resulting network and increased the ants' ability to adapt to changing conditions. Contrary to previous studies, our study shows that mass-recruiting ant species such as the Argentine ant can forage effectively in a dynamic environment. Our results also suggest that novel optimisation algorithms can benefit from stronger biological mimicry.

Solving the Towers of Hanoi – how an amoeboid organism efficiently constructs transport networks

“…Using the Argentine ant Linepithema humile we previously showed that traillaying ants are efficient at solving the ToH, and are capable of adapting to the modified ToH maze (Reid et al, 2011). Argentine ants were better able to construct one or two shortest paths in the original ToH maze compared with the slime mould, and required a lower number of corrective moves.…”

“…We used a version of the maze from our study on Argentine ants (Reid et al, 2011), but scaled down to 135mm in length (Fig.1C), the standard Petri dish size used by Nakagaki et al (Nakagaki et al, 2000) in their labyrinth maze-solving experiments with P. polycephalum. We constructed the ToH using acetate on agar substrate.…”

“…Recently we examined how Argentine ants adapt their foraging network to solve a dynamic version of the Towers of Hanoi (ToH) problem, a wellknown shortest-path problem (Reid et al, 2011). In the ToH problem, N discs of different diameters are stacked upon one of three pegs in order of decreasing diameter from the base (see Fig.1B).…”

“…We used the same ToH setup used for ants (Reid et al, 2011) to investigate how the slime mould reconstructs a network when its initial solution is disturbed. This allows us to compare the properties of the networks built by our study organism to the properties of the most efficient network possible.…”

Argentine ants (Linepithema humile) use adaptable transportation networks to track changes in resource quality

“…Similar trail flexibility has been described when traillaying ants face an obstruction of sections of their trail. Reid et al (2011) found that Argentine ants (Linepithema humile) switched to alternative paths in a maze when their initial route was blocked. Laisus niger, another trail-laying ant, used one arm of a two-armed maze when ant densities were low and traffic was free flowing, but switched to using both maze arms when densities increased and trails become congested (Dussutour et al, 2004).…”