Description Details labsimplex functions Author(s) References

The `labsimplex`

package implements the simplex
optimization algorithms firstly proposed by Spendley et al. (1962)
<doi:10.1080/00401706.1962.10490033> and later modified by Nelder
and Mead (1965) <doi:10.1093/comjnl/7.4.308> for laboratory and
manufacturing processes. The package also provides tools for
graphical representation of the simplexes and some example response
surfaces that are useful for illustrating the optimization process.

A simplex is a geometric element defined as the simpler polytope possible
in an *n*-dimensional space. If the space has *n* dimensions,
the simplexes there will have *n+1* corners called vertexes.
The simplexes in two and three-dimensional spaces are the well-known
triangle and tetrahedron, respectively.

In the simplex optimization algorithms, the experimental variables are
represented by the dimensions in the abstract space. Each vertex in the
simplex represents an experiment, then the coordinates of the vertex
represent the values for the variables in that experimental setting. The
experiments must be performed and a response must be assigned to each
vertex. In the optimization process, one of the vertexes is discarded in
favor of a new one that must be evaluated. In the first simplex, the vertex
with the worst response is discarded. The second worst vertex in this
simplex is discarded in the following simplex and the procedure is repeated
until the optimum is reached or a response good enough is obtained. The
process of discarding a vertex and generating a new one is known as a
movement of the simplex.

In this document, the words vertex and experiment are used
interchangeably. The same applies to dimensions and experimental
variables.

`labsimplex`

functionsThis package uses list objects of class `'smplx'`

to store the
simplex information, including all the coordinates of the
vertexes and their responses.

The `labsimplex`

functions can generate a new `'smplx'`

class
object, assing responses to the vertices to generate the next one and to
visualize different spatial representations of the *n*-dimensional
simplex in 2D or 3D projections. Detailed information can be found by
typing `vignette('labsimplex')`

.

Cristhian Paredes, craparedesca@unal.edu.co

Jesús Ágreda, jagreda@unal.edu.co

Nelder, J. A., and R. Mead. 1965. “A Simplex Method for Function Minimization.” The Computer Journal 7 (4): 308–13.

Spendley, W., G. R. Hext, and F. R0. Himsworth. 1962. “Sequential Application of Simplex Designs in Optimization and Evolutionary Operation.” Technometrics 4 (4): 441–61.

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