One of the most famous mathematical problems is the traveling salesman problem: Given a set of cities, how do you determine the shortest route that visits each of the cities exactly once? Of course, you can simply go through all possible routes, but this approach is feasible only for a very limited number of cities. There are more clever ways to solve the problem, but the time needed to find a solution always increases exponentially with the number of cities. In other words, there is no known efficient way to solve the traveling salesman problem.
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It is quite cool, therefore, that bees appear to be able to solve the traveling salesman problem, as reported by Lihoreau, Chittka and Raine in a forthcoming paper in The American Naturalist. The authors made an artificial flower-arrangement. Recordings of the flight paths showed that the bees chose the most efficient route to visit all flowers. Quite a feat for such a tiny-brained animal!
I haven't read the entire paper (which is due in December, for now there is only a summary on the website of The American Naturalist), but I do wonder about a few things. One of the characteristics of the traveling salesman problem is that there are a finite number of connections and you're allowed to visit each city only once. In contrast, the bees can fly however they like and I would assume that they don't care if they have to fly over a flower that they have already visited, although they will probably not land again. (I'm not sure whether this makes the problem any easier, though.) In addition, I assume that the number of flowers was not that large, so it would be overstated to claim that the bees have solved a problem that computers can't, since the traveling salesman problem becomes truly problematic only with thousands of cities/ flowers. Nevertheless, I think the study demonstrates very nicely that even “simple” animals are extremley efficient when it comes to dealing with problems that are relevant to them!
Lihoreau, M., Chittka, L., Raine., N.E. (in press). Travel optimization by foraging bumblebees through readjustments of traplines after discovery of new feeding locations. The American Naturalist.