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I recently watched this video on youtube. It featured someone explaining how he used genetic algorithms to improve the efficiency of wind mill turbines by finding the optimal shape for the blades. Eventually, the narrator found a non-trivial shape for the blades that seemed to be more efficient than windmills that have blades with a "standard" shape.

He did, however, use the wrong viscosity for the substance in which the wind mills are situated. Therefore the preliminary questions are:

  • Would the shape of the new blades be the same if the same procedure would be carried out in a substance with the correct viscosity? Would the blades still be more efficient than the "standard" blades?

Now to the real question(s). The narrator in the video carries out this genetic algorithm procedure with two-dimensional wind turbine blades.

  • I was wondering, though, if a similar procedure could also be carried out in a tree-dimensional environment? I guess it would be more complicated, and perhaps would require more computing power/time, but if it can be used to enhance the efficiency of wind turbine blades, it would be a good idea to do so, right? Has this already been done? Why or why not?

Last question:

  • if the genetic algorithm would indeed create novel, more efficient wind turbine blades, would that mean that some company would actually pick up on the idea and start producing them? Or would the novel shape be too complicated and therefore too expensive to produce, rendering the design useless from a financial perspective?

Thanks a lot in advance!

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    $\begingroup$ This question might be better suited for Computational Science. $\endgroup$ – Jeffε Aug 28 '12 at 2:12
  • $\begingroup$ @JɛffE thank you, I was not aware of that website's existence. $\endgroup$ – Max Muller Aug 28 '12 at 12:44
  • $\begingroup$ almost surely the viscosity was a critical parameter that would affect the final solution. absolutely a 3d simulation is possible, but fluid dynamics is extremely compute intensive, ie it would require a supercomputer probably. it would help if you cite the video. did they use simulation to measure the fitness function? its not clear what you mean by 2d turbine blades. was the simulation in the video 3d fluid dynamics over 2d blades? or maybe it was a crude ~2d fluid dynamics simulation. yes GAs are a wonder of software engr/TCS and yes, defn being used to design commerical products. $\endgroup$ – vzn Aug 29 '12 at 16:16
  • $\begingroup$ @vzn you can view the video by clicking on the highlighted word "this" in the first sentence of the question. $\endgroup$ – Max Muller Sep 1 '12 at 20:02
  • $\begingroup$ oops! saw the video. nice scientific work/summary that highlights many of the remarkable aspects of GAs including optimums that dont turn out to be real based on "artefacts" of the fitness fn etc., incomprehensible designs, etc.. anyway MM-- know of some cool refs/work/applications on GAs, would like to see more here, & think this question works as "reference-request" and "application-of-theory" but unfortunately its apparently not a popular subj here on TCS.se & my refs in mind are not restricted to your specific question. however havent seen it addressed much on other stackexchanges either. $\endgroup$ – vzn Sep 2 '12 at 19:48
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Short answer, yes you could build a GA that worked on a 3D model of a turbine with the correct viscosity, and (probably) yes, it would still find good designs. Exactly what those designs would be is somewhat unpredictable -- they might be very conventional blade arrangements or they might be completely novel and weird.

However, that's also true of many other search algorithms. GAs are, at heart, just one of a class of hundreds of stochastic search algorithms. All you need for a GA to work is three things: (1) a way of describing what a possible solution looks like, (2) a way of trying to combine good solutions to get more good solutions, and (3) a way of determining when one solution is better than another. The former can be as simple as just a vector of numbers ([number of blades, distance between blades, angle of attack, ...]) or may be arbitrarily complex, allowing for each blade to have an independent length and position, etc. For number three, you need a model that tells you how good a turbine is. This is where you need to get the viscosity of air correct, embed the right equations governing the electrical outputs, etc.

That just leaves the genetic operators -- how do you take good designs and produce more or better ones? Again, this can be very complex, but it can also be quite simple. For instance, you have a design with three blades, each five meters long. OK, make a small random change to that. Try blades that are 5.2 meters long. If the model tells you this is better, keep it. If not, throw it away and keep the original five meter blades. It's in this stage where domain knowledge is often invaluable. Having someone who can say, "the number of blades is really important -- taking a good five blade design and removing a blade isn't going to work unless you also change lots of other aspects of the design" allows you to simply say, "OK, my algorithm will avoid making that type of change in favor of making changes that are more likely to help.

Like I said, GAs are just search algorithms. They tend to often perform a "broader" search, which can sometimes make them more likely to find these off-the-wall solutions than some other methods. On the flip side, they typically take much longer to find good solutions than some other methods. That's also an approximation; sometimes a GA works great, sometimes it works very poorly. Understanding which cases will be which is one of the great unsolved problems for people working in optimization.

Finally, would companies adopt them if better designs were found? As you say, that's a more complex question. It isn't even just a matter of "too complicated". Suppose you find a 5% better turbine design that's completely feasible. You'll still likely have to redesign manufacturing equipment and processes, perhaps find new suppliers, etc. In the real world, "good enough" is often just that. However, there are numerous examples of real-world problems where methods like GAs or other random search methods have found solutions that were adopted. A lot of them are tucked behind corporate walls, but there have been notable successes in things like antenna design and aircraft design, as well as non engineering optimization problems like vehicle routing problems, scheduling problems, etc.

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