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Bees Beat Machines At 'Traveling Salesman' Problem
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?"
now you get a faster computer that makes honey!
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.
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...
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Hah! They may be on top now, but thanks to CCD we won't have to be #2 for long. Goooooooooo humans!
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Simply evidence that our algorithms need work. God has worked out these issues long before we even thought of them. (:
"There is a way that seems right to a man, but its end is the way of death." Proverbs 16:25 (NKJV)
Simulated annealing.
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Kilgore Trout.
Anyone can look smart when they're cribbing notes from flies.
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.
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I took a class with one of the inventors of particle swarm optimization (PSO) at Purdue. He claimed that PSO could could finish the traveling salesman problem faster than more traditional algorithms. The problem is that PSO is so random (as it attempts to emulate flocking behavior) that you really can't prove that it's faster. Similarly, you really couldn't formally prove that a bee is faster besides just doing empirical testing.
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).
Actually I worked this problem years ago, despite having not found a solution, I was able to determine the problem is fundamentally far simpler than traveling salesman as the nodes are distributed on a sheet with simple calculations.
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.
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.
Maybe P=NP and the solution is easy?
Does this mean that B >= NP?
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. 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.
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.
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.
Presumably, bees take advantage of the triangle equality. In this case, they are solving an easier problem, one for which computer scientists already have very fast approximation schemes.
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.
My work here is dung.
What this really shows is how efficient society would be if we sterilized all workers.
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.
It was at least an interesting read.
In the number 8 bee... Yaritza Burgos!
Gentlemen, we have a race
For justice, we must go to Don Corleone
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.
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.
MMO Quests are like orgasms:
You may solo them, I prefer them in a group.
I suppose we finally have the proof that Bee = NBee.... /ducks algorithm analysis text
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.
stuff |
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.
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 for your brain just GUESSING? Jezus, do you know how FUCKING difficult GUESSING is? Been trying to get computers to make a best guess for ages. It is advanced computer science.
Calculating the path of a ball in flight is actually pretty easy. All I need is a couple of accurate measurements of its position in time and space. Trivial stuff. But GUESSING from in complete and missing data were a ball is going to be AND being right most of the time or at least have moved an appendage in time so that when more accurate data is available I already got the appendage in roughly the right area? THAT is NOT easy. And yet our brain and the brains of many an animal does it. And does it VERY fast indeed. Throw a bouncy ball at a cat and watch it chase it (or in the case of my cat decide in a pico second that "you threw it, you catch it" is the wisest course of action and fall asleep), control a body and CATCH it. Meanwhile we marvel at a robot because it managed to stand upright...
Now if a machine could duplicate the brains method for catching a ball, that would be very handy indeed. Because SOMEHOW our brain does do it. And yes, this DOES include wind velocity correction. We are aware of the wind and we correct for it. Thanks to our brain. It doesn't matter that we don't use a laser ranger finder or dopler radar, that is just details. It is the logic that can use incomplete, unreliable data that results in accurate results that scientists are interested. It would allow for computers to keep functioning even when sensor data goes missing. An essential for computers/robots to come out of the production halls and into our daily lives. If a spell checker could guess as accurately what I meant to write as YOU can read over my mis spellings and lousy grammer, Clippy would be a lot more usefull.
MMO Quests are like orgasms:
You may solo them, I prefer them in a group.
Kinda reminds me of the Geek shopping team. If you want perfect you'll never get close enough to pull the trigger but shoot for close enough and you're off to the races.
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 will shred my adversaries. Pull their eyes out just enough to turn them towards their mewing, mutilated faces. Illyria
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.
``Tension, apprehension & dissension have begun!'' - Duffy Wyg&, in Alfred Bester's _The Demolished Man_
an ordinary honey bee only visits 5 flowers over the course of a day? Its probably on the order of hundreds, usually one ever 50-120 seconds, when not spending time in the hive.
I want it!
Hello Man.
I am Bee #32653. Do you want better flowers for your mate?
Click here!
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The canonical traveling salesman problem usually is states that all cities must be visited. The bee is not under this constraint. This changes the problem from a do-or-fail NP hard problem to a more simple approximate optimization problem. The latter have many many many many many good solution paths in computers. Perhaps the newest and best approach that resembles the bee's agent based learning approach is called Probability Collectives (google it). You'll want to learn it since it works well on parallel computers, distributed computing, and most of all on systems composed on many dumb subunits on a sparsely connected network with no central command and control (think mobile devices).
Some drink at the fountain of knowledge. Others just gargle.
must be isomorphic to genetic algorithm problem solving, which can also solve the traveling salesman problem quickly, if slightly imperfectly. I'm guessing the same imperfections will show up in the bee's solution to this problem.
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No "I for one welcome our new insect overlords"? Who are you and what have you done with Slashdot?
Hoist Number One and Number Six.
(A) Bee algorithms - worked out by God (done)
(B) Human (bigger than bees but afraid of them - worked out by God (done)
(A) + (B) = Dead Bee (and order in my universe)
L'esperienza de questa dolce vita (The experience of this sweet life) - Dante Alighieri, The Divine Comedy
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. 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.)
Nostalgia's not what it used to be.
A bee will never beat me at Ticket to Ride, the ultimate traveling salesman problem game.
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There are two types of people in the world: Those who crave closure
We need a better algorithm.
"The second problem is this "Computers solve it by comparing the length of all possible routes and choosing the shortest."
Well they can try, but this does not provide a closed solution since there are too many comparisons to evaluate for optimaliity. In the traveling salesman problem there is a very high rate of generation of subproblems in making any comparison as to which of any possible combination of nodes to discover the optimally correct solution. As one adds more nodes to the graph, the number of their combinations multiply at a faster rate than
does an iterative procedure in counting (compare) them. Consequently, the problem of choosing an optimal solution depends not only upon what one how one defines optimal, but also becomes non-polynomial bounded the as the number of potential additional nodes are considered increases the number of subproblems. Hence, the number of subproblems that must be solved in order to work out the potential optimal solution is enormous even for a few nodes. Get out to 1500 or so and you are talking about more potential combinations than electrons in the known universe. No supercomputer yet devised comes up with that solution in real time of where in space these electrons must be in order to move the least among their positions that won't take millions of years.
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.
Maybe they are able to quickly identify distinct groups of flowers on their first pass using their compound eyes, which by necessity would be tightly clustered. Then they just visit the groups in the most obvious order starting at the point they observe the last flower. They could compare 100 runs over the same flower bed and easily find groupings by overlaying the paths.
while [ 1 ]; do echo -n -e "\xe2\x95\xb$((($RANDOM&1)+1))"; done
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:
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.
If we had the answer to how bees can do this so much better than computers, we'd have the answer to making self-aware machines - I suspect it has much to do with not being able to effectively program biology, physics, chemistry and a few million years of evolution (the understanding of which we are still far from grasping ourselves) at the microcosmic scale. The bees are not thinking about this, or running a computation. (Have you seen their brains? Me neither. Probably only hobbyists and biologists have seen their brains. That's my point. They're awfully small, and not well suited to algorithms.) They're adapting to their environment in a way we don't -- and can't -- understand; in the same way a computer can't understand the reasons for the rules we program into it. It's too far outside of our frame of reference.
NP-Complete is a much tighter constraint on the computational complexity. Yeah, it's NP-H, but it's also NP-C. NP-Hard must sound harder... I dunno.
Imagine if you weren't allowed to use roads because a bus company complained about your driving 3 times. --skunkpussy
Probability Collectives are interesting because they are one of very few optimization alogorithms born from first principles considerations. For example, Simmulated annealing comes from Metropolis/hastings search and that was a brilliant breakthrough that allowed rapid exploration in a way that guarentees detailed balance. Parallel Tempering is the parallel extension of that first-principles argument. Most other search and optimization algorithms are born from either heurisitics expected to align with a search domain or considerations based on efficient algorithmic implementation (such as genetic algorithms). While one can go back and try to develop rigorous theories around expedients and heuristics, and there's a whole industry of that, in the end it's better I think to start from first principles.
Probability collectives starts with the assumption that that a team of agents will be making decision independently that affect the search path and that each agent is bounded rational. That is, each agent not only can't know everything, but can't be relied on to make optimal choices every time. You then discover what game theory says is the best way to search in this situation. You might visualize a set of airliners trying to negotiate landing times under conditions were some of them have been delayed and you have to reprogram flights in real time with incomplete knowledge.
As the algorithm searches the bound on the rationallity is annealed towards perfect rationality since more information is learned.
The algorithm tends to very efficiently use past information (compared to a GA or simulated annealing) but the per-interation computation effort is higher. Thus it is best applied in cases where agents are distributed (no centralized optimizer) or where the cost of gathering data is high or where the agents have available computing time between samples. One example of it's use in dumb-ditributed systems was the control of wing flaps on UAVs. Many micro flaps were agents which, without a central processor, solve the problem of prevent turbulence instability. presently it has achieved the highest wing speed without turbulence of any method, even ones that try to solve detailed physics equations in a central flight computer.
Most research on this approach is still in academics of the basic theory. very little attention has been placed on efficient coding of the methods. There are no libraries for it available. This would make a great CS master's thesis project for someone or indeed many people since the theory at this point is large.
The travelling salesman problem is nice because the "best" answer is actually the worst answer, in that to arrive at it, you have to perform massive amounts of computation that's difficult to serialize. But bees most certainly do not do this! I'm going to guess that, like people, they automatically factor in the expected cost of computation and look for an answer that's "good enough" - not technically perfect, but an approximation thereof that's cheap to compute.
Look at it this way - you are more likely to go for a software solution that's a button-click or uses off-the-shelf or already available OSS simply because the computational overhead of writing your own webserver is generally considered too difficult, even though you would arrive at a more technically correct or optimum solution by going at it yourself.
Good software design consists of many "good enough" solutions that avoid unnecessary "Expensive" computation (Engineer's time) at the cost of "Cheap" computation. (CPU time) When we apply this idea to the algorithm, we can have similar results. Compare simple literal string matching algorithms to the Boyer-Moore search algorithm - dramatic improvements in performance by pruning the amount of necessary computation!
I have no problem with your religion until you decide it's reason to deprive others of the truth.
NP=B?
Except that flowers aren't inert. A bee is getting constant feedback to the "closest" flower, because it can see it (albeit in UV), and smell it. There is also reinforcing as bees communicate with each other. So many of you are IT guys - you know that its far easier to track agents and find optimal paths when each agent is sending out a signal that varies in amplitude/time and possible even leaving a gradient. In the traveling salesman problem, locations are essentially just that - non-interactive coordinates. Also the salesman doesn't have an army of other salesmen who will share information with him.
It's very interesting to see how bees work, but this definitely is NOT the classical traveling salesman problem. Same with slime moulds, their strategy is to follow chemical gradients, and then communicate WITH each other, reinforcing that path.
Entia non sunt multiplicanda praeter necessitatem.
No details are given, and the article contains the worrisome BS: “Computers solve it by comparing the length of all possible routes and choosing the shortest”. What size problem do bees solve? Less than, say, 10 flower groups? Do they get a good solution (which can be trivially done via computer or human inspection for even large N), but not always perfectly optimal solution ? How do bees do on 10^4 flowers or more where the traveling salesman problem’s Np completeness causes problems? The paywalled journal’s abstract describes experiments with a total of seven flower groups- sure didn’t induce me to pay $15 for the article.
The TSP is not only NP-hard, it's NP-complete. In case you didn't know, the "complete" in NP-complete means that the problem is formally equivalent to any other NP-complete problem and that if an efficient solution is found to one NP-complete problem then an efficient solution follows for all NP-complete problems. Thus, if the bees are really SOLVING the TSP, then we now have a means of solving all NP-complete problems, and we can replace our fancy supercomputers with bee hives. Somehow, I doubt it.
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.
The solution to the Traveling Salesman Problem has already been found--it's called a chastity belt.
Set your phasers on "funky"!
flowers == advertisements
Deleted
Why on Earth would someone worship an entity that feels the compunction to deceive them from the get-go?!
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
http://xkcd.com/399/ :)
I had thought the obligatory XKCD was this one.
~KingAlanI
the best algorithms a group of socially inept nerds locked up in flourescently lighted rooms could come up with can't compete with either millions of years of evolution and/or an omnipotent, omnipresent guy who may or may not be bearded...
*boggles*
whooda thunk it?
or "miada". In Spanish that would make it Bee Pee.
Here's a cool thing for ants, but most of you are probably already aware of it:
http://en.wikipedia.org/wiki/Ant_colony_optimization
Didn't read the article, but it's totally bunk. The two dimensional TSP is not NP complete (unless P=NP), it's actually in P. In order for the 2d TSP to be NP complete, you have to allow crossing paths and arbitrary values (not just the euclidean distance between the nodes) for the lengths of the edges.
http://fakescience.tumblr.com/post/1367356168/how-are-bees-organized shows how bees are organized to beat machines and anything else. [grin]
Ant(Dude) @ Quality Foraged Links (AQFL.net) & The Ant Farm (antfarm.ma.cx / antfarm.home.dhs.org).
thanks
All going to the same places and adding a few in between as they went...then meeting other salesman on the route and each exchange new locations....by the time all the salesman return to the home office all new data would be synced at the bar over stingers.
"A testament to the power of even the smallest batch of neurons or simply evidence our algorithms need work?" ...Or both?
I never understood why BeeOS didn't catch on, since it was clearly the most clever of the bunch. I guess their salesmen traveled efficiently, but not effectively.
As Alec Baldwin pointed out in Glengarry Glen Ross: A...B...C - Always Bee Closing!
I wonder if those bees just sniff their way into an optimal solution. A bee gathering pollen will probably lose some in flight. Even more so when 'fully loaded'. Those lost pollen would fan out in time. That would mean that from a certain point/ flower, a bee could find the direction of the best path to take by sniffing the direction where the most pollen come from. Doesn't take much computing power. So I guess my question would be: is the hypotheses tested with different weather conditions? Especially wind direction and force.
I think we will find that neurons behave more like a quantum computer and less like a finite state machine.
I for one wish to welcome our new bee overlords . . .
That's what you get when biologists write articles on computer science topics, a bunch of false claims.
1. Solving a TSP with a few hundred cities does not keep our computers busy "for days". Concorde, an implementation of what is probably the best optimal algorithm for the TSP can solve thousand-city problems in under three minutes. That's hardly "days" : http://www.tsp.gatech.edu/concorde/benchmarks/bench.html.
2. State-of-the-art algorithms for the TSP are intricate, but they obviously do not do anything like "computing the length of all possible paths and choosing the shortest". Indeed, the problem is NP-hard and an n-city TSP has (n-1)!/2 possible solutions, computing all of them would not keep our computers busy for days, but rather a bit longer.
3. I would be very surprised if the bees found the optimal solution every time. If they don't they use a heuristic. The best heuristic algorithms for the TSP can solve 1000-city problems to within a few percent of optimality in fractions of a second.
4. If the bees would have evolved an efficient (P) algorithm for the TSP, that would change our entire understanding of the field of computer science and computational complexity. That's not going to happen.
I doubt that bees are any good at playing Quake so I wonder if a dedicated massively parallel TSPU wouldn't do wonders for running time of the algorithm on silicon. Add fuzzy logic as I doubt bees are interested in the theoretically best path, only one that lets the hive survive.
A theoretical computation book had an example of a 100-city traveling salesman problem in the last pages of the book. I put the numbers into my PC-XT running at 10 MHz programmed for a day and found the exact same solution that was published in the book in just under a minute of CPU time. The authors of the book had spent an hour I believe on a CRAY to prove that my/their solution was indeed the best possible.
Some, if not most NP-Hard problems can be solved in reasonable time provided your problem size is small (e.g. a few tens of cities/flowers) or if you accept that your solution might be a few percent worse than the theoretical optimal solution.
My program simply did "hill climbing". It just used one solution and tested if it could improve on that one solution. This is effectively what the bees are doing as well. They take one solution (fly to that far flower), and if they stumble on a better solution (drain that other flower en route) they proceed to that one....
You've collected some blue-ish pale icky green chu-chu jelly.
The flowers that are close by have a stronger perfume. Ergo, bees can outwit the computerized travelling salesman problem. Bees do have noses, don't they?
Leslie Satenstein Montreal Quebec Canada