Today, a colleague of mine sent me a link to a news article entitled Tiny Brained Bees Solve a Complex Mathematical Problem, which appeared on the Queen Mary, University of London web site and on the Guardian web site. Here’s what it says:

Scientists at Queen Mary, University of London and Royal Holloway, University of London have discovered that bees learn to fly the shortest possible route between flowers even if they discover the flowers in a different order. Bees are effectively solving the Travelling Salesman Problem, and these are the first animals found to do this.

I think this is actually pretty cool, and I had no idea that bees were capable of this kind of “optimization”. However, the article contains a couple of incorrect statements that are really vexing:

**Incorrect Statement 1:** “The Travelling Salesman must find the shortest route that allows him to visit all locations on his route. Computers solve it by comparing the length of all possible routes and choosing the shortest.”

If that were true, we wouldn’t be able to solve the TSP’s with thousands of cities that we can solve today. OR is about being much smarter than simply enumerating all the possible solutions to a problem.

**Incorrect Statement 2:** “In nature, bees have to link hundreds of flowers in a way that minimises travel distance, and then reliably find their way home – not a trivial feat if you have a brain the size of a pinhead! Indeed such travelling salesmen problems keep supercomputers busy for days.”

Wrong again! According to published results (e.g. see here), many 1000-city TSP’s can now be solved in a matter of minutes on a standard desktop computer.

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The article is not that bad, as far as scientific journalism goes nowadays.

With respect to the first incorrect statement, it’s interesting to note that the TSP is an NP-hard problem, and thus scales exponentially, just as complete enumeration. Certainly solving times don’t increase as fast as with CE for even a modestly smart algorithm, but one can argue that in the limit of large problems, it’s all the same.

Now, I have not read the paper in question, but I have a hard time believing that bees “solve” the TSP, as in finding the optimal route, rather than a good one. Many systems in nature use various heuristic procedures to find good solutions for interesting problems, but they are not optimal solutions by any measure.

Still, it would be interesting to understand the bees’ heuristic as a basis for new algorithms.

Joao. Thank you for the comment. Indeed, in the limit we cannot expect the current state-of-the-art to scale well, but the way it’s stated in the article is misleading to say the least. I also agree with you that the bees most likely do not solve the TSP. Indeed, it’s remarkable that they can coordinate to the point of finding a good solution and I’d love to understand how they do that.

There are indeed some unnecessary ‘hype’ and inaccuracies presented in this article, as it is common for news to overstate results and ignore the scientific method behind them. It reminded me of the P != NP question some months ago. However, we must also acknowledge how it is tough for people outside the field to grasp these concepts. Translating OR to a more comprehensible language is still a great challenge, so I am happy to see more optimization news in popular websites recently. (And believe me: explaining to a girl how waiters in a restaurant can improve their service times using TSP-related models is still a terrible ice breaker!)

I have checked this paper about the bees. As far as I understood, their experiment consisted of only 4 flowers (“cities”), which were added in sequence to observe how bees would change their routes after discovering new flowers. Clearly, you cannot state that they solve general TSP models. Nevertheless, it is quite interesting to learn how they adapt their routes (what kind of learning is involved?) and how they keep exploring other alternatives (search diversification?). Hopefully they will do more research in this direction.

The link of the paper is:

http://www.journals.uchicago.edu/doi/abs/10.1086/657042?journalCode=an

(Title: “Travel Optimization by Foraging Bumblebees through Readjustments of Traplines after Discovery of New Feeding Locations”)

André: I completely agree that it’s great to see OR in the news. I just think that it’s a journalist’s job to check their facts before publishing something. It would have been easy to fix the mistakes in that article without going into technicalities. Thanks for the pointer to the paper! I’m curious now about your TSP ice breaker story :-) You have to tell me all about it. Let’s try to catch up at INFORMS!