Complex mathematical problem solved by bees

Oct 25, 2010

(PhysOrg.com) -- Bumblebees can find the solution to a complex mathematical problem which keeps computers busy for days.

Scientists at Queen Mary, University of London and Royal Holloway, University of London have discovered that 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.

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. However, bees solve it without computer assistance using a brain the size of grass seed.

Professor Lars Chittka from Queen Mary's School of Biological and Chemical Sciences said: "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. Studying how bee brains solve such challenging tasks might allow us to identify the minimal required for complex problem solving."

The team used computer controlled artificial flowers to test whether bees would follow a route defined by the order in which they discovered the flowers or if they would find the shortest route. After exploring the location of the flowers, bees quickly learned to fly the shortest route.

As well as enhancing our understanding of how bees move around the landscape pollinating crops and wild , this research, which is due to be published in The American Naturalist this week, has other applications. Our lifestyle relies on networks such as traffic on the roads, information flow on the web and business supply chains. By understanding how bees can solve their problem with such a tiny brain we can improve our management of these everyday networks without needing lots of computer time.

Co-author and Queen Mary colleague, Dr. Mathieu Lihoreau adds: "There is a common perception that smaller brains constrain animals to be simple reflex machines. But our work with bees shows advanced cognitive capacities with very limited neuron numbers. There is an urgent need to understand the neuronal hardware underpinning animal intelligence, and relatively simple nervous systems such as those of insects make this mystery more tractable."

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User comments : 23

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jdbertron
2.6 / 5 (17) Oct 25, 2010
This is so ridiculously hyped it's shameful.
First there's no link to the article.
Second, there's no mention of the size of the TSP that was solved.
Third, it's ludicrous to declare that the problem was solved since any decent size problem would likely take years to confirm anyway. Most likely, the problems that were solved were of minimal size, in which the paths would not exhibit local minima or the number of combinations would be so small, it would be hard to declare the sequence as distinct from random.
Either way, this is hype, especially without a decent abstract or link to the paper.
DavidMerchant
4.6 / 5 (7) Oct 25, 2010
@jdbertron - there is a link, to where the full article will appear. I suggest we wait for the full article to come out this week before calling it ludicrous. What we've read is only a second-hand, overly-brief summary. Read the primary text first, then critique. Otherwise it is a presumptuous and unfair critique.
rah
1 / 5 (1) Oct 25, 2010
How did the scientists know when and if the bee's were 100% focused on their mission, versus just taking time to smell the roses along the path? If you were a bee wouldn't you take time to just enjoy their beauty, especially because the flowers appear much more colorful and vivid to a bee?
Mario3k
5 / 5 (1) Oct 25, 2010
Please someone from physorg tell me if it was single bees that solved it or if it was a group of bees together that solved it. The collective intelligence of bees is a very interesting phenomenon. See Howard Bloom's book Global Brain for more details.
MIBO
4.9 / 5 (7) Oct 25, 2010
Surely you're all missing the point.
This just proves that travelling salesmen have small brains, that's why they drive BMW's.
Quantum_Conundrum
2 / 5 (4) Oct 25, 2010
While in common usage, "Complex" and "Complicated" are often enterchangeable, in mathematics they have specific, different meanings.

"Complex" problems are often easy to solve through some form of recursion. In studying fractals, for example, the complexity is a measure of the degree of recursion to which an algorithm is run. A true fractal is infinitely complex, but in nature there is a limit to complexity, whereby many "natural" fractals have a complexity of say, 3 or 4 levels of recursion.

"Complicated" are the ones that are difficult to solve.

Bees having compound eyes probably allows them to map spaces in their brains very efficiently, and then recursively solve for the shortest path in space through a very simple "instinctive" algorithm.
Quantum_Conundrum
2 / 5 (4) Oct 25, 2010
As an example:

A network of servers at a data center is highly complex.

Whereas the space shuttle is not complex, but rather complicated, even though it is often incorrectly claimed to be the most complex machine ever made, because this is the "common" usage of "complex".
Serkan_Halisdemir
2 / 5 (12) Oct 25, 2010
"And your Lord taught the honey bee to build its cells in hills, on trees, and in (men's) habitations; Then to eat of all the produce (of the earth), and find with skill the spacious paths of its Lord... verily in this is a Sign for those who give thought.
(Surat an-Nahl (The Chapter of The Bee), Quran 16:68-69)
Kedas
1 / 5 (1) Oct 25, 2010
If you would let a neural network learn a lot of different situations wouldn't you have the same effect.

I'm pretty sure the fly will choose the wrong path if the numbers of flowers are not what the fly is used to.
jjoensuu
2.3 / 5 (4) Oct 25, 2010
well they better find out what they can about bees while we still have bees around...considering that they are dying off...

...and this most likely because of factors caused by humankind...such as perhaps cell phone network radiation...

After all honey bees have been around for "millions" of years, right...so they should have "evolved" protection against all naturally existing pathogens. If this would not have happened they would have died out long ago...
Husky
not rated yet Oct 25, 2010
individual or swarm intelligence could make a huge difference, for instance ants use pheromones to mark semi randomly discovered paths to food and hence create self reinforcing collective topological neural networks, we would have to see the full article to weigh its value.
Vaughn
5 / 5 (5) Oct 25, 2010
I think we may be missing the point here - I see this as an investigation into how to do much (bee behavior) with so little (number of neurons)... The value here is in gaining some insight into nature's minimalist circuit design strategies.
PinkElephant
4.2 / 5 (5) Oct 25, 2010
How did the scientists know when and if the bee's were 100% focused on their mission, versus just taking time to smell the roses along the path?
I think rah may have inadvertently stumbled on a potential answer.

If all the "flowers" are emitting volatiles into the air, and the volatile 'haloes' of all the flowers overlap to create a kind of 3D scalar intensity field, then the bees might simply be navigating this field via olfaction, by taking advantage of the aroma gradients. In essence, this may be a case of the air in the lab solving the problem for the insect, via a kind of dynamic programming algorithm.

This would be possible if the air in the lab is relatively still. Which one would expect, as the researchers would fear that excessive air turbulence might affect the insects' flight patterns and/or make it harder for the insects to actually determine the location of each "flower" (particularly when trying to discover new "flowers".)
Quantum_Conundrum
1 / 5 (1) Oct 25, 2010
I think we may be missing the point here - I see this as an investigation into how to do much (bee behavior) with so little (number of neurons)... The value here is in gaining some insight into nature's minimalist circuit design strategies.


Perhaps it's because the bee is solving a specific instance of the problem, whereas in software or in mathematics we often try to solve the most abstracted, generalized form of a problem ahead of time, in hopes of cutting down on future solving of special cases as needed.

The bee is a flight organism, so it's brain is wired better (relative to size,) for 3-dimensional spacial recognition, while humans primarily think in "2-d plus six to ten feet of z-axis" for normal daily living.

Consider, the bee is doing up/down, left/right, front/back, headwind, tailwind, crosswind, updraft, downdraft, all while planning the actual course from location to location.
kasen
5 / 5 (1) Oct 26, 2010
The bees "learn" to fly the shortest route. Are we to understand it takes them a few tries? If that were the case, it may just be a probabilistic result. Some kind of natural Monte Carlo method.

then the bees might simply be navigating this field via olfaction


Not sure if that's how bees work, but the idea that the maths is done by the environment seems pretty valid to me. Constructal theory might have something to do with this.
barakn
not rated yet Oct 30, 2010
If all the "flowers" are emitting volatiles into the air, and the volatile 'haloes' of all the flowers overlap to create a kind of 3D scalar intensity field, then the bees might simply be navigating this field via olfaction,

It is well known that bees' primary sense for finding flowers is vision, not olfaction. Also the article itself mentioned that the bees found the flowers in one order but then changed the path they took on subsequent visits to minimize the distance. If they were relying on some sort of smell-space, it seems like they should be able to find the flowers and the shortest path the first time 'round. Finally, if the traveling salesman problem was easily solvable by sampling a scalar field, then it would be easy to model and solve in a computer, and it wouldn't be the famously intractable problem that it is.
PinkElephant
not rated yet Oct 31, 2010
It is well known that bees' primary sense for finding flowers is vision, not olfaction.
Who's to say they don't use olfaction as a crutch? Their brains ARE pretty tiny...
the bees found the flowers in one order but then changed the path
That's not conclusive either way.
If they were relying on some sort of smell-space, it seems like they should be able to find the flowers and the shortest path the first time 'round.
Not necessarily. At each nexus in the "smell space", there may be arbitrary decisions made that can be modulated by learning: e.g. do I take the left fork or the right fork in the road at this point?
it would be easy to model and solve in a computer
Not really: try to compute a scalar field; you'll quickly see that the complexity of that task is nontrivial. Moreover, the TSP is frequently specified as just a list of paired distances, with no information regarding the actual locations of the "cities" in space.
Titto
2.3 / 5 (3) Nov 01, 2010
Just shows....
And there are still idi@ts believing in evolution and this all just develops by it self then?
random
not rated yet Nov 01, 2010
"And your Lord taught the honey bee to build its cells in hills, on trees, and in (men's) habitations; Then to eat of all the produce (of the earth), and find with skill the spacious paths of its Lord... verily in this is a Sign for those who give thought.
(Surat an-Nahl (The Chapter of The Bee), Quran 16:68-69)


I'm an atheist but I like this. Very appropriate. I wonder if there's any quotes concerning the Traveling Salesman Problem.
Truth
5 / 5 (1) Nov 01, 2010
"And your Lord taught the honey bee to build its cells in hills, on trees, and in (men's) habitations; Then to eat of all the produce (of the earth), and find with skill the spacious paths of its Lord... verily in this is a Sign for those who give thought.
(Surat an-Nahl (The Chapter of The Bee), Quran 16:68-69)

What you may be forgetting is that it took billions of bees millions of years to get to that point. On the journey, untold quadrillions of bees that failed the test of nature fell by the wayside and died. Only the ones that had evolved along the most productive path remained and passed their genes on to their offspring. It's called evolution. You just seem to acknowledge the end product, not the very long process it took to get there.
Truth
not rated yet Nov 01, 2010
"And your Lord taught the honey bee to build its cells in hills, on trees, and in (men's) habitations; Then to eat of all the produce (of the earth), and find with skill the spacious paths of its Lord... verily in this is a Sign for those who give thought.
(Surat an-Nahl (The Chapter of The Bee), Quran 16:68-69)

If I wanted to go to a mosque, or a church, or a temple, to start mouthing off about science and evolution, and I asked the clergy to be allowed to do so, I would be in no uncertain terms stopped and chased out the door. But here you are mouthing off about religion on a science website, freely and vigorously, like so many other holier-than-thou's do everyday. So I ask you: which is the more enlightened and open-minded forum? Take a wild guess.
frajo
1 / 5 (1) Nov 02, 2010
If I wanted to go to a mosque, or a church, or a temple, to start mouthing off about science and evolution, and I asked the clergy to be allowed to do so, I would be in no uncertain terms stopped and chased out the door.
You are mistaken by unscientific induction. Your assumptions about mosques/churches/temples are right for some cases but not correkt for all cases. The RCC, for example, is backing the concept of evolution since at least 100 years.
subdeviant
not rated yet Nov 11, 2010
buzzin! how could it bee so simple?