Mind, Body, World- Foundations of Cognitive Science, 2013a

salesman’s tour increases linearly, the computational effort for finding the shortest
route increases exponentially.
Because of its importance and difficulty, a number of different approaches
to solving the travelling salesman problem have been explored. These include a
variety of numerical optimization algorithms (Bellmore & Nemhauser, 1968). Some
other algorithms, such as simulated annealing, are derived from physical metaphors
(Kirkpatrick, Gelatt, & Vecchi, 1983). Still other approaches are biologically
inspired and include neural networks (Hopfield & Tank, 1985; Siqueira, Steiner,
& Scheer, 2007), genetic algorithms (Braun, 1991; Fogel, 1988), and molecular computers
built using DNA molecules (Lee et al., 2004).
Given the difficulty of the travelling salesman problem, it might seem foolish
to suppose that cognitively simple agents are capable of solving it. However, evidence
shows that a colony of ants is capable of solving a version of this problem,
which has inspired new algorithms for solving the travelling salesman problem
(Dorigo & Gambardella, 1997)!
One study of the Argentine ant Iridomyrmex humilis used a system of bridges
to link the colony’s nest to a food supply (Goss et al., 1989). The ants had to choose
between two different routes at two different locations in the network of bridges;
some of these routes were shorter than others. When food was initially discovered,
ants traversed all of the routes with equal likelihood. However, shortly afterwards, a
strong preference emerged: almost all of the ants chose the path that produced the
shortest journey between the nest and the food.
The ants’ solution to the travelling salesmen problem involved an interaction
between the world and a basic behaviour: as Iridomyrmex humilis moves, it deposits
a pheromone trail; the potency of this trail fades over time. An ant that by chance
chooses the shortest path will add to the pheromone trail at the decision points
sooner than will an ant that has taken a longer route. This means that as other ants
arrive at a decision point they will find a stronger pheromone trail in the shorter
direction, they will be more likely to choose this direction, and they will also add to
the pheromone signal.
Each ant that passes the choice point modifies the following ant’s probability of
choosing left or right by adding to the pheromone on the chosen path. This positive
feedback system, after initial fluctuation, rapidly leads to one branch being
‘selected.’ (Goss et al., 1989, p. 581)
The ability of ants to choose shortest routes does not require a great deal of individual
computational power. The solution to the travelling salesman problem emerges
from the actions of the ant colony as a whole.
The selection of the shortest branch is not the result of individual ants comparing
the different lengths of each branch, but is instead a collective and self-organizing
Elements of Embodied Cognitive Science 211