GPS-X Technical Reference

373 Optimizer
If after the reflection step the reflected vertex is worse than the second worst vertex on the
previous iteration, the polyhedron is contracted. The reflected vertex is contracted through the
centroid of the remaining p vertices if it is the new worst point. If the reflected vertex is the new
second worst point, the worst point is contracted through the centroid. The amount of contraction
is controlled by a contraction constant.
When a contraction step is unsuccessful, the polyhedron is shrunk by moving the vertices toward
the best point. The amount of shrinkage is controlled by a shrink constant.
At each step checks are made to ensure that the parameter bounds have not been violated. If they
have been, the new vertex is moved back inside the bounds.
When the optimizer termination criteria are satisfied, the optimizer runs one additional simulation
using the parameter values from the best point found during the iteration process. There is the
possibility of encountering a local minimum that is not the global minimum of the objective
function. This is a problem that is common to most optimization algorithms. As a result, it is
important to solve optimization problems (e.g. parameter estimation or process optimization
problems) from a number of different starting guesses to ensure that the optimizer has found the
global minimum.
If the user requests the printing of confidence limits or derivative information (See Summary of
the Optimizer Settings and Parameters section below) the optimizer conducts additional
simulations to generate numerical derivatives.
The constants that control the reflection, expansion, contraction, and shrinkage of the polyhedron
in the simplex method can be accessed by selecting
General Data > System > Parameters > Optimizer and then clicking on the More... button in the
Static sub-section. The resulting form is shown in Figure 14-1. You can change any of the
constant values if you wish. The parameter entitled scaled step size in initial guess is used to
control the initial perturbation size.
Figure 14-1 – Form Containing the Simplex Method Constants
GPS-X Technical Reference