Monday, October 25, 2010

Here we go again! Bees and TSP

First the original story today doing the rounds on the Internet on bees solving a TSP while traversing a sequence of flowers for nectar. Their approach resembles the ant-colony / swarm-optimization approach, and while this 'bee story' is truly astounding, the author further states the computers have to explore every possible path to select the best and that takes days. Obviously, they did not hear about Operations Research, and the fantastic work done on inventing efficient algorithms for solving gigantic and difficult TSP problems to provable (near-) global optimality in quick time. The fantastic book on TSP by Dr. Applegate, Dr. Bixby, et al. gives us a fascinating blow-by-blow account of the work on this topic from the TSP past to the present. You can even try out their Concorde solver. The state-of-the-art is truly amazing and based on decades of breakthrough ideas.

Yet, article after article that seem to come out every couple of years assumes that if a problem is NP-Hard, then it is almost "impossible to solve efficiently in practice" and enumeration is the only way. Nope. A pure application of software programming and hardware strategies certainly does not work or scale. OR leads the way.

An incredible amount of success in OR practice has come via successfully tackling precisely such large-scale and ultra-complex NP-Hard problems. Large-scale TSP-structured problems have been routinely solved in Supply-chain planning, vehicle routing, aircraft routing, etc. Not only are problems solved well and quickly, but we also know how well and how much improvement is still possible. These small optimality gaps matter. A TSP solution that is 1% closer to optimality may save a company another million dollars.

Heuristics of unknown quality based on bees and ants are nice, but they don't really tell you if there is another solution that could your save your company another 10%. And if you were to change your input parameters, it may return an entirely different solution that makes such approaches largely unpractical for use within products. And adding a constraint the prohibits certain paths may well make such approaches useless. This Tab has discussed the practical problems with using such heuristics in previous posts here, and you will find more in Dr. Trick's OR Blog when TSP was "solved" last year by creatures with even smaller brains, i.e. bacteria :-)

There's even TSP art. Check this out as well. Let's give O.R. and humans some credit please!

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