labsimplex: Simplex Optimization Algorithms for Laboratory and
Manufacturing ProcessesThe 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.
This 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').
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.
Nelder, J. A., and R. Mead. 1965. <U+201C>A Simplex Method for Function Minimization.<U+201D> The Computer Journal 7 (4): 308<U+2013>13.
Spendley, W., G. R. Hext, and F. R0. Himsworth. 1962. <U+201C>Sequential Application of Simplex Designs in Optimization and Evolutionary Operation.<U+201D> Technometrics 4 (4): 441<U+2013>61.