Bees Resolve a Complex Mathematical Problem Daily

The ‘Traveling Salesman Problem’ is a mathematical puzzle on which researchers have been working for decades. In a new study, it was demonstrated that bumblebees resolve it every single day.

The TSP is heavily used in theoretical compute science and in operations research, and is classified as a NP-hard problem.

In its original formulation, the solver is given a list of cities, and their pairwise distances, and is then tasked with finding the shortest possible distance that will allow them to visit each of the cities exactly once.

The number of possible combinations is staggering, which is why the TSP is such a difficult problem. But that does not deter the common bumblebee from resolving it every single day as it visits flowers.

The small insects always select the shortest possible route between flowers, even if the flowers are discovered in various orders, AlphaGalileo reports.

According to researchers at the Royal Holloway, the University of London and Queen Mary, University of London, these are the first animals found to be capable of resolving the problem.

“Foraging bees solve traveling salesman problems every day. They visit flowers at multiple locations and, because bees use lots of energy to fly, they find a route which keeps flying to a minimum,” explains Dr Nigel Raine.

The expert, who holds an appointment at the Royal Holloway School of Biological Sciences, says that it's amazing the creatures are capable of doing this using a brain only the size of a grain.

In a series of simulations, the investigators used a computer to control artificial flowers, all while keeping track of the routes the bumblebees flew while traveling between their targets.

Even when the flowers were changing locations, the insects chose the shortest routes between their targets after they discovered where all the flowers were.

“Despite their tiny brains bees are capable of extraordinary feats of behavior. We need to understand how they can solve the Traveling Salesman Problem without a computer. What short-cuts do they use?” Raine says.

The new investigation could have significant implications for agriculture, because bee pollination patterns are critically important for next year's crops.

Additional details of the investigation are scheduled to be published in this week's issue of the esteemed scientific journal The American Naturalist.