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Info about the GRSM algorithm?

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I am doing a master thesis regarding structural optimization and I'm wondering if there are any proper information (in addition to the one in the help info) about how the GRSM algorithm in Hyperstudy works?


Things of interest that I'd like to know:

  1. The DOE it creates after each iteration
  2. The type of fit it does for its response surface
  3. The actual search algorithm on how it finds the optima on the current response surface and how it handles constraints.





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In addition of the information in the Help about usability and settings, we would like to share with you some suggestions and good practices you may want to use. A general suggestion in HyperStudy is to accept the default settings, which work optimally for most applications.

So, do run GRSM with 50 evaluations and then observe the system’s improvement:

  • If it is sufficient in your case (objective goals are already met or further improvement seems unlikely), then there is no reason to add more evaluations;
  • Otherwise, you can leverage in the existing 50 evaluations and ask GRSM to run for an additional set of evaluations. You can copy the first optimization and add the existing data as an Inclusion matrix; the included runs will be used to build the initial response surface and optimize on it. As a result, you can notice in the Iteration History tab that Iteration_1 provides the same optimum as the best solution from the 1st optimization. It is like you start the 2nd GRSM from the best solution of the 1st one.  This process could be repeated…

Another suggestion is to observe the Inputs vs Iterations. For instance, the plots below show that the bounds of the design space are reached and may be a better solution could be found by relaxing the bounds. If you want and can, do run a 2nd optimization with new bounds. And don’t forget that if you change your bounds to still use the previously run data as an inclusion.  The information from those points is still valid even if the optimization formulation has changed. This is why we sometimes refer to inclusion as recycling data – it is more than a restart!

Input Vs Iteration.png

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I have the same problem. Is not possible to know how the algorithm works in GRSM method? There are a lot of different algorithms, for instance:

  • Line-Search Approach
  • Trust Region Approach
  • Simplex Method
  • Newton’s Method
  • Quasi-Newton Methods
  • Conjugate Direction Methods
  • Levenberg–Marquardt Methods
  • Elimination Methods
  • Lagrangian Methods
  • Active Set Methods
  • Penalty and Barrier Function Methods
  • Sequential Quadratic Programming
  • Mixed Integer Programming

Many Thanks

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