Optimization

Note

In-depth information about the theoretical underlying and the calculation methods will be described in a book chapter releasing in the near future.

To find the Optimal Experimental Design that corresponds to the maximum objective function (Fisher criterion) different algorithms can be used. Some of the suggested global optimization algorithms used in the current package are:

1. Differential Evolution

   Stochastic global optimization developed by Storn and Price (1996) [1]. Creating new candidate solutions by combining existing ones to achieve the best solution.

2. Basin-hopping

   Combination of the Monte-Carlo and local optimization introduced by David Wales and Jonathan Doye [2]

3. Brute force

   Calculating the objective function value at each point of a multidimensional grid.

[1]

Rainer Storn and Kenneth Price. Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces. Journal of Global Optimization, 4(11):341–359, 1997. doi:10.1023/A:1008202821328.

[2]

David J. Wales and Jonathan P. K. Doye. Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms. The Journal of Physical Chemistry A, 101(28):5111–5116, July 1997. doi:10.1021/jp970984n.