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Line 5: − It was used for the first time in 1969 as a pure optimization algorithm making the regions of acceptability smaller and smaller. Since 1970 it has been used for both ordinary optimization and manufacturing yield maximization.+ + + + + + + + + + + +
Gaussian adaptation (view source)
Revision as of 15:19, February 20, 2008
, 15:19, February 20, 2008no edit summary
The theorem is valid for all regions of acceptability and all Gaussian distributions. It may be used by cyclic repetition of random variation and selection (like the natural evolution). In every cycle a sufficiently large number of Gaussian distributed points are sampled and tested for membership in the region of acceptability. The centre of gravity of the Gaussian is then moved to the centre of gravity of the approved points. Thus, the process converges to a state of equilibrium fulfilling the theorem. A solution is always approximate because the centre of gravity is always determined for a limited number of points.
The theorem is valid for all regions of acceptability and all Gaussian distributions. It may be used by cyclic repetition of random variation and selection (like the natural evolution). In every cycle a sufficiently large number of Gaussian distributed points are sampled and tested for membership in the region of acceptability. The centre of gravity of the Gaussian is then moved to the centre of gravity of the approved points. Thus, the process converges to a state of equilibrium fulfilling the theorem. A solution is always approximate because the centre of gravity is always determined for a limited number of points.
== History ==
Gaussian adaptation was used for the first time in 1969 as a pure optimization algorithm making the regions of acceptability smaller and smaller. Since 1970 it has been used for both ordinary optimization and manufacturing yield maximization.
In 1972 Gaussian adaptation was tested on a complex technical system. The model of the system included 450 components (each of which had a parameter value) of which 130 were adjustable. Some early tests seemed promising. But then a joker said: “In this project nothing should be left to chance”. This, of course, was a good intention as long as all the stops were pulled out. But there was also a hidden meaning: The algorithm worked at random, and it should therefore not be used in this project.
After one year of hard work with deterministic methods - available at that time - a passable system was found, but because parameter values of components vary in the manufacturing process, only 5% of the manufactured systems were able to meet all requirements according to the specifications.
Those responsible for the project got nervous and caught at a straw; the random algorithm. After two months with the random algorithm, 95% of the systems were acceptable, and the system could now be manufactured and sold at a good profit. The example showed that random algorithms may create an enormous amount of information that is hardly available by other means.
This example was never published, but Kjellström & Taxén, 1981, showed an example with 76 parameters, which is also a large number in this context.
== Gaussian adaptation as a model of evolution ==
== Gaussian adaptation as a model of evolution ==