The optimization methods described in this chapter attempt to minimize a objective function which is the root-sum-square of a diagram simulation result deviations from experimental data. There are several ways to do this and Optimization application supports some different methods for the minimization of the objective function.

Adaptive simulated annealing (ASA)

Adaptive simulated annealing (ASA) is a global optimization algorithm that relies on randomly importance-sampling the parameter space (Ingber, 1996).

The following options of the algorithm must be set.

Stochastic ranking evolution strategy (SRES)

The Evolution Strategy using Stochastic Ranking (Runarsson & Yao, 2000) is a (µ λ)-ES evolutionary optimization algorithm that uses stochastic ranking as the constraint handling technique. The stochastic ranking is based on the bubble-sort algorithm and is supported by the idea of dominance (Moles et al, 2003).

The following options of the algorithm must be set.

Global optimization using the DIRECT algorithm (GLBSOLVE)

A deterministic GO method (Holmström, 1999) is a version of the DIRECT algorithm (Jones et al, 1993; Jones et al, 2001). GLBSOLVE runs for a predefined number of iterations and consider the best function value found as the global optimum.

The following options of the algorithm must be set.

Quadratic Hill-climbing

The gradient method for minimizing a quadratic approximation to a general function on a suitably chosen spherical region (Goldfeld, 1965). The method requires no assumption about the concavity of the function to be minimized and automatically modifies the step size in the light of the success of the quadratic approximation to the function.

The following options of the algorithm must be set.