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Bees Beat Machines At 'Traveling Salesman' Problem 394

Posted by CmdrTaco
from the they're-in-my-mouth dept.
eldavojohn writes "Recent research on bumble bees has proven that the tiny bee is better than computers at the traveling salesman problem. As bees visit flowers to collect nectar and pollen they discover other flowers en route in the wrong order. But they still manage to quickly learn and fly the optimally shortest path between flowers. Such a problem is NP-Hard and keeps our best machines thinking for days searching for a solution but researchers are quite interested how such a tiny insect can figure it out on the fly — especially given how important this problem is to networks and transportation. A testament to the power of even the smallest batch of neurons or simply evidence our algorithms need work?"
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Bees Beat Machines At 'Traveling Salesman' Problem

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  • great... (Score:5, Funny)

    by MagicMerlin (576324) on Monday October 25, 2010 @11:36AM (#34012906)
    now you get a faster computer that makes honey!
  • Bees have a guide (Score:2, Interesting)

    by Anonymous Coward

    After the genetic vector is put in, all the bees have to do is keep track of the sun. What amazes me though is how they look at another bee and visualize it traveling to a set patch of flowers, by looking at its dance.

  • Wait, whut? (Score:3, Funny)

    by MyLongNickName (822545) on Monday October 25, 2010 @11:39AM (#34012960) Journal

    quite interested how such a tiny insect can figure it out on the fly

    I thought we were talking about bees? I am so confused...

  • Hah! They may be on top now, but thanks to CCD [wikipedia.org] we won't have to be #2 for long. Goooooooooo humans!

  • by Anonymous Coward on Monday October 25, 2010 @11:40AM (#34012974)

    Simulated annealing [wikipedia.org].

    Yours In Akademgorodok,
    Kilgore Trout.

  • Heuristic (Score:4, Insightful)

    by Sonny Yatsen (603655) * on Monday October 25, 2010 @11:40AM (#34012988) Journal

    Is it possible that the honey bees aren't really solving the Traveling Salesmen problem at all, but rather employ some sort of unknown heuristic that leads to solutions that's close enough to optimal for it to look like that they've solved it? Maybe that's what we should be looking at rather than pondering if bees somehow have some sort of superior calculating ability over a supercomputer.

    After all, when we're playing a game of baseball (right, right, I know, this is slashdot), and a ball is coming towards us, we aren't calculating in our heads the velocity, air resistance and other variables involved in catching the ball. We just reach out our arms and our brain makes its best guess based on some sort of heuristic or something to make the catch.

    • Re: (Score:2, Insightful)

      by Anonymous Coward

      your just playing word games... if i've developed a method of figuring out how to catch a ball without using newtonian physics, I've still solved the problem.

      • Re: (Score:2, Informative)

        by thePig (964303)

        Indeed - especially considering the fact that one of the major class of solutions based on simulated annealing is actually a heuristics based solution. It really doesnt matter how you solve it at all - any way is welcome - as long as it reaches close to the optimal solution.

      • Re: (Score:3, Interesting)

        by Anonymous Coward

        Nope. You've solved one small set of problems, which is related to the bigger problem. Does your method work for just balls? What about anvils? Churches? Very small rocks? How about when thrown through water, or over a hill? Can it be applied to every situation where Newtonian physics works?

        The travelling salesman problem is a very specific definition of a problem. Solving it for one specific set (a given graph, size, or even geometry) does not solve the whole problem. Similarly, I know of no non-euclidean

      • by Dunbal (464142) *

        I've still solved the problem.

              For yourself. However you are unable to break that problem down into tokens that can be taught to someone else or, say, programmed into a robot. Therefore although you might be good at catching a ball as an individual, you haven't solved the problem that those less adept than you face when put in the same situation.

      • by rhsanborn (773855)
        I think the point of the GP is that you haven't really "solved the problem", but rather came up with a close approximation, whereas those super computers are solving the problem absolutely.
      • by smartr (1035324)
        You don't solve a NP-Hard or NP-Complete mathematical problem by using a heuristic. Good heuristics for the TSP have existed for quite some time, and I'm sure they're faster than bees. https://secure.wikimedia.org/wikipedia/en/wiki/Travelling_salesman_problem#Heuristic_and_approximation_algorithms [wikimedia.org] I feel it's really deceptive that they claim this problem takes a supercomputer to solve the problem in days, when they certainly haven't proven the bees always get the best solution (I think at best, we could dis
    • Re: (Score:3, Interesting)

      by Liquidrage (640463)
      That was pretty much my thought. Do the bees ever get it wrong or at least not perfect? Seems obvious they world. I'd imagine the power lies in "good enough" thinking vs "perfect" thinking. Kinda an analog vs digital approach. If bees are able to map out where they are and which flower is closest to them at the time and head to that one next, they won't always get the perfect route, but it'll be close enough and sometimes be the best route based on a few variables in the layout.
    • Different Spaces (Score:5, Insightful)

      by eldavojohn (898314) * <eldavojohn.gmail@com> on Monday October 25, 2010 @11:53AM (#34013220) Journal

      After all, when we're playing a game of baseball (right, right, I know, this is slashdot), and a ball is coming towards us, we aren't calculating in our heads the velocity, air resistance and other variables involved in catching the ball. We just reach out our arms and our brain makes its best guess based on some sort of heuristic or something to make the catch.

      I think the problem with your analogy that there are an unlimited number of dimensions and responses where you could put your arm out to make the catch (well, not unlimited if you consider Planck distances to be the smallest possible distance). But when we are talking about computerized flowers with nectar, you pretty much can only go to one of the flowers next. I think they used RFID to track the bees (or at least this researcher has written about doing that before)? So we can sit there and do a star search on all paths of the 50 flowers and find the shortest one to connect all of them in three dimensions in a particular order (we assume the flight paths are straight lines). The difference is not that we have so many fewer things to search than in the ball catching example but that you take a very finite deterministic path (i.e. 2, 34, 23, 6, 18, etc) and the bees seem to be able to find and learn this very quickly. According to the researcher:

      "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 neural circuitry required for complex problem solving."

      If this holds true for hundreds of flowers, I think we're talking about a serious search space with a definite path that is far more specific than the heuristics of moving your arm and hand around dynamically in space to collide with a ball. You could have tons of error when trying to catch a ball and still catch it. You (frequently) only have one optimal path in shortest distance problems. It's probably true these traveling salesman problems look obvious to a bee like catching a ball does to us but something particularly interesting is going on there if it is.

      Let's say it is an unknown heuristic. I'd wager the network folks would kill to know how that heuristic is so cheaply computed.

      • Good point, but what I meant by the baseball analogy isn't about the unrestrictedness or complexity of the problem so much as simply an example of a heuristic that we naturally have (although dependent on our personal levels of coordination). We're descended from tree-living ancestors who naturally developed the ability to judge an object's distances and movement (otherwise, our ancestors would've just fallen out of trees or failed to grab a branch as it jumps). Likewise, a mountain goat will be able to nat

      • Re: (Score:3, Insightful)

        by Americano (920576)

        I'd be interested to read the full paper... looks like it won't be published until this week.

        I have to wonder if it's simply local optimization that the bees are using - i.e., "Fly to a close flower not yet visited" - that starts looking like they're solving a much more complex problem? Are they visiting *every* flower on the "map"? Are they ever skipping some? Do they visit the flowers in exactly the same order, or is there variance from bee to bee (or between two trips from the same bee?)

        It seems to me

    • Not the TSP (Score:5, Interesting)

      by sco08y (615665) on Monday October 25, 2010 @11:59AM (#34013382)

      Is it possible that the honey bees aren't really solving the Traveling Salesmen problem at all, but rather employ some sort of unknown heuristic that leads to solutions that's close enough to optimal for it to look like that they've solved it?

      This article is fundamentally misstating the TSP. If it were the TSP, the bees wouldn't get to choose their route.

      As other bees come in and report their route taken and pollen collected, another bee will put bits of those routes together. (Which would be the surprisingly difficult part to me, since the bees are doing some pretty complicated vector algebra.) But a bee is going to have a budget of so much daylight and will attempt to maximize the amount of nectar it collects in that time, given the bits of routes collected by other bees and its own scouting. But it's not given a list of points it has to hit, it picks its list from a larger list of points. That's fundamentally different from the TSP, even solving it by heuristic.

    • Re:Heuristic (Score:5, Interesting)

      by Dutch Gun (899105) on Monday October 25, 2010 @12:07PM (#34013480)

      After all, when we're playing a game of baseball (right, right, I know, this is slashdot), and a ball is coming towards us, we aren't calculating in our heads the velocity, air resistance and other variables involved in catching the ball. We just reach out our arms and our brain makes its best guess based on some sort of heuristic or something to make the catch.

      You should read "On Intelligence" if you're at all interested in that subject. Jeff Hawkins (Palm inventor) proposes a fascinating theory of the inner workings of the brain.

    • Re:Heuristic (Score:4, Informative)

      by IICV (652597) on Monday October 25, 2010 @12:12PM (#34013566)

      That's pretty much what I was going to post. The bees almost certainly aren't solving the Traveling Salesman problem, they're getting good enough approximations of a solution. Our computers don't chug for days trying to figure out the answer to TSPs, they chug for a couple of seconds and produce a close-to-optimal solution.

      And the thing is, not all instances of the TSP are necessarily NP-Hard (for instance: if there was only one road between each city + 1 extra road between the first and last cities, the optimal solution is obvious), and the cases of it found in practical applications are generally far easier to handle than the cases found in more esoteric theoretical constructs (for instance: if you move east, you move closer to all the flowers in the east; this is not necessarily true in the general TSP). Most real instances of the TSP can be handled well enough with simple, quick greedy algorithms; they won't necessarily give you the best answer, but it'll be pretty close.

    • The travelling salesman problem is the problem of finding the shortest route between a set of points. It doesn't matter HOW you solve it. You could time all possible journey's, you could do a sorting routine or god knows what. But if you solve it, you solved it.

      That is what the bee does. And maybe if we can learn HOW the bee does that, we might learn something from it. It might be a smarter way of solving things. Or maybe Bees have an additional variable from an unknown input that helps solve it.

      And as fo

      • Re: (Score:3, Insightful)

        by gnasher719 (869701)

        The travelling salesman problem is the problem of finding the shortest route between a set of points. It doesn't matter HOW you solve it. You could time all possible journey's, you could do a sorting routine or god knows what. But if you solve it, you solved it.

        That is what the bee does. And maybe if we can learn HOW the bee does that, we might learn something from it. It might be a smarter way of solving things. Or maybe Bees have an additional variable from an unknown input that helps solve it.

        That's not what the bee does. That is what someone _claims_ the bee does. Big, big difference. I imagine they found that the bees visit flowers faster than in random order, or faster than the order in which they were told about the flowers. I think a simple algorithm like "always visit the nearest flower that wasn't visited yet" would probably impress these "scientists" no end.

        BTW. Bees shouldn't even try to solve the travelling salesman problem. Assume a single flower very far away - the best solution m

    • Re: (Score:3, Funny)

      by Syberz (1170343)

      [...] our brain makes its best guess based on some sort of heuristic or something to make the catch.

      Maybe your brain, but not mine. Mine generally makes me miss the ball by 3 feet or get hit in the nads. Maybe my brain works like old Intel processors?

  • I doubt it (Score:3, Insightful)

    by MozeeToby (1163751) on Monday October 25, 2010 @11:41AM (#34013000)

    First and foremost, how many nodes are we talking about here? I highly doubt that the bees are keeping track of hundreds of feeding spots from one trip out to the next but the article doesn't say.

    The second problem is this "Computers solve it by comparing the length of all possible routes and choosing the shortest." Who on earth would try to solve the traveling salesman this way? Yeah, a brute force solution will get you the guaranteed best path, but the performance is horrible. There's lots and lots of shortcuts that can save a huge amount of time, things as simple as eliminating crossed paths can make a big difference. You can even use techniques like genetic engineering successfully on such a problem (though you might not reach the absolute best path that way).

  • by eln (21727) on Monday October 25, 2010 @11:42AM (#34013024) Homepage
    We need to expend more effort to recruit bees into computer science. Too many bees are wasting their lives solving these problems on the fly for a little nectar when they could be solving these problems in exchange for tenure at our nation's finest universities.
  • Shortcuts (Score:5, Interesting)

    by Imagix (695350) on Monday October 25, 2010 @11:42AM (#34013026)
    Was the Travelling Salesman presented with the completely connected graph the way the bees were? The bee isn't constrained to fly along predefined paths between nodes, the travelling salesman is.
    • Re:Shortcuts (Score:5, Insightful)

      by MozeeToby (1163751) on Monday October 25, 2010 @11:49AM (#34013144)

      Which makes the problem more difficult, not less. The way it is usually presented in CS the distance between the nodes is the minimum cost path, the bees would also have to 'calculate' that in addition to solving for the correct order. Think about it this way, imagine trying to solve the traveling salesman path between 100 cities, but you can take any route you want between cities. You could take all the back roads, the freeway, you could hop on a train or an airplane, you could kayak down the river between two cities. It doesn't make the problem any easier, in fact it adds a ton more variables to the mix, effectively increasing the number of routes that would need to be checked using a brute force solution.

  • Well... (Score:5, Funny)

    by Kufat (563166) <kufat&kufat,net> on Monday October 25, 2010 @11:44AM (#34013068) Homepage

    Does this mean that B >= NP?

  • Entomoengineering? (Score:5, Interesting)

    by schmidt349 (690948) on Monday October 25, 2010 @11:45AM (#34013082)

    We have a lot yet to learn from our six-legged colleagues, from the sound of it. Recently some work was done on optimizing machine vision using an algorithm derived from the way the house fly's vision works. [uwyo.edu] The termite's wood-digesting gut is a prime object of study for those seeking to manufacture fuel from biomass efficiently and cleanly. An insect virus (the baculovirus) is the new hotness for gene transduction in mammalian cells because it can't actually cause disease.

    I think this might be the next step in bioengineering. We've been grabbing genes out of various organisms and sticking them in bacteria to produce useful biomolecules like insulin and factor VIII. Maybe the insect is our next stop.

  • Oh, really? (Score:4, Interesting)

    by SoapBox17 (1020345) on Monday October 25, 2010 @11:47AM (#34013124) Homepage
    First TFS and TFA both make reference to problems which "keep super computers busy for days." That's pretty misleading since the bees are only dealing with "a few hundred" flowers. At brute force that would take your cell phone maybe a couple minutes to solve.

    But really no details are given. Do the bees still travel to all of the flowers? I'd imagine they might just decide to skip one or two if they don't fall close enough to the path to be worth it. They don't say what they did (probably nothing) to validate that the bees actually found the shortest path. Did the "graph" that they gave the bees include a section where a greedy algorithm would fail? What is more likely is the bees haven't solved it, but found a decent approximation.

    I think this is what you get when you let bee researchers write math/computer science articles.
    • Re:Oh, really? (Score:5, Insightful)

      by gumbi west (610122) on Monday October 25, 2010 @12:18PM (#34013688) Journal

      100 flowers=100! possibilities. Using brute force on a 1 GHz processor and computing one solution per cycle (quite optimistic), it would take you 3 times 10 to the 141 years to complete. Even if your cellphone had a helaflop [slashdot.org] processor, it would still take longer than the age of the universe to compute this way.

  • hierarchical models (Score:2, Informative)

    by allawalla (1030240)
    I imagine that the hierarchical models proposed by Scott Graham would be a pretty good candidate. If you break the TSP problem into a series of sub-problems of increasing complexity you get pretty good accuracy with reduced computations. Basically instead of trying to figure out how to move through all the towns in the US you first plan a route through all the states. You could probably derive a few simple heuristics that would give you that sort of behavior from a swarm...
  • They leave a trail of hormones, the shortest paths get more travelers, over time, it becomes obvious which path to use, it has the strongest scent.
    • by Sarten-X (1102295)

      Like ants with wings!

      Of course, the ant solution still isn't very fast, or reliable, and is usually far slower than algorithmic solutions. Nice try, though.

    • Re:Wild Guess (Score:4, Interesting)

      by smoothnorman (1670542) on Monday October 25, 2010 @12:16PM (#34013640)
      ...or even simpler, the scent of the flowers themselves. those antennae on the bees' heads aren't just for a sense of fashion. so to all you NP-mathematicians out there: suppose our traveling salesman had a means to follow a concentration gradient to the nearest sales point?
  • I read TFA and it seems more focused on the excitement that the bees can solve the TSP, but the researchers never seem to indicate how the bees are doing it, and given the nature of the problem, how do they know it really is the "optimum" solution. Based on my limited work with the TSP, the only algorithm that, for my purposes, has worked the best is Nearest Neighbor, which is also, I believe, the simplest but also most naive.

    Would be interesting to know what the bees' algorithm is.

  • by SmallFurryCreature (593017) on Monday October 25, 2010 @12:00PM (#34013396) Journal

    Gosh, that is one hell of a bee if it has the brain of a piece of corn... or is corn not a grass anymore? At least when you take some idiotic comparison, take one that has a non-changing size. Penny is okay because all pennies at least within a country tend to stay the same. But grass seeds?

    Next up is "brain the size of a pinhead". Oh okay, so there are many sizes of pin but at least we can assume some kind of standard. And that is FAR smaller then most grasses I know and see seeds of in Holland.

    Otherwise intresting stuff but I loathe this "make it easier" by obuscating the facts.

    Number of neurons in honey bee brain = 950,000 (from Menzel, R. and Giurfa, M., Cognitive architecture of a mini-brain: the honeybee, Trd. Cog. Sci., 5:62-71, 2001.)

    Now THAT is a fact. We? We got 100 billion. So, while a bee has a tiny brain compared to ours, it is HARDLY simple. And because it is far smaller and far more primitive it doesn't need as as much intelligence to deal with things it doesn't need to. Listening and producing speech is complex, but bees don't bother with that. Living for half a century and remembring everything is complex. But bees don't do that.

    This why computers can do math so fast despite being so stupid, because they only do math.

    How can the bee do route calculation with close to a million neurons? I have no idea but didn't research show that far fewer rat neurons could fly a plane? I think some people fastly underestimate the complexity of the brain even small ones. We already know that a neuron is far more then a simple transistor so 1 million super transistors would make for a hell of a complex computer. Suddenly it doesn't seem to odd that a bee can do computations far more complex because THAT is what it is designed to do. You could just as easily marvle at the fact that the bee with its tiny brain can fly, while I with my large brain can't. And no I don't just mean I don't have wings, I mean that if you put me in a helicopter you would have a horrible crash in seconds and that is in the passenger seat.

    Marvle at nature, learn from it but don't belittle it. It takes us year to program a robot to walk very very slowly. A deer learns it in minutes and this includes learning to control legs locked up in a womb for months. We can either accept that nature is amazing or we are very very poor programmers... as a developer, I choose to believe that nature is amazing.

  • by 192939495969798999 (58312) <info@@@devinmoore...com> on Monday October 25, 2010 @12:02PM (#34013432) Homepage Journal

    The computer isn't going to die if it doesn't get the right path, the bee might. Death is a remarkably strong motivator to be efficient.

  • The bees that didn't knew how to somewhat "solve" that are the dead ones.
  • Or just use Ant Colony Optimisation, which has been doing this for 18 years.

  • Don't we already know that babies can pick out shapes/voices/etc that take computers all sorts of processing power to figure out. Or how we are still trying to refine things like recognizing a face or depth or whatever, when people just 'know'. The brain is still amazing despite all the power computers now have, regardless of human or insect species.
  • I think computer algorithms fail to appreciate the cost-benefit of their suboptimal solutions, and need about 70 million years of evolution to get it right. It's probably also true that these vespids had another use for the algorithm before they evolved into co-adapted pollinators, possibly dating back another 100 million years or so. The earliest honeybees in amber, dating to the Cretaceous, are obviously honeybees, which makes their clade and its adaptations immensely old.
    • Re: (Score:3, Interesting)

      by grikdog (697841)
      Also, why assume that ganglia are the progenitors of such an unexpected result? In insects, as in shrimps and crabs, those densely packed ommatidia provide a ready made neural net suitable for extraordinary in-flight calculations, such as reaction times 10x greater then human reflexes in hunting dragonflies. Just because they're called "compound eyes" doesn't mean they function ONLY as "eyes."
  • by Stargoat (658863) * <stargoat@gmail.com> on Monday October 25, 2010 @12:25PM (#34013804) Journal

    No "I for one welcome our new insect overlords"? Who are you and what have you done with Slashdot?

  • by smellsofbikes (890263) on Monday October 25, 2010 @12:29PM (#34013888) Journal
    If you build a maze that has multiple routes through it, and two pieces of food in it, and drop a bunch of slime molds into the maze in various places, they will fairly rapidly coalesce into a single slime mold that extends through the maze on the shortest route between the two bits of food [abc.net.au]. Now, that's no traveling salesman problem -- but slime molds are single-celled animals, so they don't have *any* brains to do the calculations. They just rely on minimizing surface area and maximizing access to food. (And being able to stop being multiple organisms and start being a single organism, but that's an aside.)
  • Bullshit (Score:3, Insightful)

    by nedlohs (1335013) on Monday October 25, 2010 @12:50PM (#34014228)

    So they have proof that these bees solve the travelling salesman problem? Not just get a good approximation? Not just solve a slightly constrained version? Not just solve a slightly different problem? You know all the things that computers do just fine thank you very much, and aren't NP-hard.

    I notice the journal is a Naturalist one and the researchers aren't are bioligists and chemists not computer scientists.

    I have no difficulty believing bees have evolved (or been designed with if you must for those I don't feel like arguing with) a very efficient way of collecting pollen - it is after all fundamnental to their survival and reproduction. But that they happened to solve an NP-Hard problem that they have no need of solving (does an individual bee really visit *every* location on one trip? surely some imperfection would help in discovering new plants by having bees follow different paths?) - that seems a bit of a stretch.

  • Bogus claim (Score:5, Informative)

    by Animats (122034) on Monday October 25, 2010 @12:58PM (#34014348) Homepage

    Oh, this one again. I've seen this claim made for neural nets back in the 1980s, and for DNA computers in the 2000s. It's bogus.

    The guaranteed-optimum solution to the TSP is NP-hard. The "gets to the optimum 99% of the time and close to it all the time" solution is easy. It was developed at Bell Labs in the 1960s. Here it is:

    1. Link all the nodes in some arbitrary path.
    2. Pick two random links, and cut the path into three pieces by cutting those links.
    3. Try reassembling the three paths in all possible ways (there are 3*2*2*2*2/2 = 24 different paths) and measure the length of each. Pick the shortest.
    4. If the path length hasn't improved in some reasonable number of iterations, stop. Otherwise go back to step 2.

    This is a particularly efficient way to do it. I once coded this for a PC/AT, and it took less than a second for N=50. Almost any scheme which randomly breaks links and tries to improve the path will eventually converge on a near-optimum solution.

  • by sneakyimp (1161443) on Monday October 25, 2010 @01:58PM (#34015260)

    I'd be willing to bet it has something to do with the fact that you have an entire hive of bees each attempting to find the shortest path and then sharing their experience via that 'bee dance' thing (http://www.youtube.com/watch?v=-7ijI-g4jHg). Each bee is a thread with its own particular solution to the problem. Each bee's behavior contributes random heuristic alterations to the nectar-gathering path based on bee instincts evolved over millions of years. The bees periodically exchange solutions via the bee dance. It's a classic Genetic Algorithm.

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