“No Free Lunch” Theorem

The “No Free Lunch” Theorem is the idea that every problem cannot be solved by a single model. This would imply that multiple models must be used/built for different particular problems. In the case of computational complexity, the “No Free Lunch” theorem states for all algorithms solving all problems that the average output would be the same. This means that for any one algorithm there is no short cut to solving all problems. Opting to choose this approach would mean that the most effective solutions would be the ones that use the appropriate models that suit the problems they were designed for.

Using different programming languages to achieve particular tasks would be an example of this theorem. For example, using C++ to create a webpage is not nearly as effective as using HTML.

For the case of machine learning, swarm intelligence would not be the best model for every problem of this type as it has limitations. An example would be when looking at well defined problems, like business planning and management. Swarm intelligence, however, can still be used for different applications, like routing physical paths, to create a very good solutions.

Using routing physical paths as an example, slime mould can be observed to show that it is very good for this particular problem. If placed in a suitable environment, the mould will start to spread across the surface and in order for it to communicate with itself it has to create paths. If it is possible to create an algorithm to simulate how slime mould can create these paths, that would be extremely useful when creating network links (like train connections or roads).

Slime mould networking
Slime Mould Networking. (Credit: http://www.priceonomics.comĀ [https://pix-media.s3.amazonaws.com/blog/966/img_3323.jpg])
If, however, the slime mould path creating algorithm were to be used for sorting large structures of data, it would not be a very effective method to achieve the task. This shows that another algorithm or model would be needed and helps show that the idea of “No Free Lunch”.

Sources

  1. No Free Lunch – chemicalstatistician.wordpress.com
  2. No Free Lunch – Wikipedia
  3. Natural Computing – Lecture Slides
  4. Slime Mould – Scientific American
  5. Slime Mould – Priceonomics
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