The Efficient Planet

# What Willy Loman Could Learn From the Birds and Bees

## Animals solve a wildly complex mathematical problem that humans still struggle with.

It’s Saturday; you’ve got errands to run. Your spouse wants bread from the bakery, you need to pick up the dry cleaning, your kids need new shoes, and you’ve got a dentist appointment. None of this is any fun, so you might as well do it as quickly as possible by calculating the fastest and most efficient route that takes you to each stop.

It may seem like it should be a matter of simple math, but the solution to this so-called “traveling salesman” problem is surprisingly elusive. The issue was first identified in an 1832 brochure for actual traveling salesmen in Germany, but mathematicians only began seriously investigating it 100 years later, when Karl Menger and Hassler Whitney proposed the problem at Harvard and Princeton, respectively. (Which institution has a stronger claim to the genesis of the puzzle remains a point of debate for both Ivies.) Menger and Whitney both discovered that the number of possible routes between stops increases exponentially with each additional destination. In a typical model, for instance, three stops yield six routes, while eight stops yield 40,320. As the number of potential routes skyrockets, it becomes nearly impossible to account for the nuanced differences in distance between potential routes—differences that can add up after only a few stops. Computer scientists have recently proposed various algorithms to solve the problem, and one professor seems to have actually found a solution. His wildly complex computer program, however, is probably inapplicable to your weekend chores.

That’s where the bees come in.

Researchers at University of London have discovered that bees calculate the fastest route among the flowers with the most pollen and nectar. By setting up five artificial flowers in a pentagon shape and tracking each bee’s path, the researchers discovered that every bee optimized its route, visiting the highest-reward flowers in the shortest possible amount of time. It took only a brief moment of exploration of the fake flowers for the bees to calculate a perfect route, and each seemed to accomplish the feat independently—no groupthink or supercomputer required. The bees were especially keen when faced with the issue of short-term inconvenience for longer-term reward, going slightly out of their way to visit the higher-yield flowers even when it cost them a few seconds of travel time.