MmSimplex: Maxmin Simplex Design

In simplexdesign: Simplex Design for Stochastic Simulations and Agent Based Models

Description

Constructs a Maximin space-filling design on a k-dimensional simplex.

Usage

MmSimplex(k,N,l,cords = 1, randst = 1, phival = 50, tol = 0.0001)

Arguments

k	Number of factors in the design
N	Number of experimental runs
l	Number of levels for the search grid
cords	Number of coordinates to exchange simultaneously using an exchange algorithm
randst	Number of random starts to the design
phival	Value of p in the PhiP criterion
tol	Tolerance of the optimization, the value for which an improvement smaller than this ends the optimization

Details

This function applies a coordinate-exchange algorithm to optimize the Maximin distance criterion for a simplex. A maximin design maximizes the minimum interpoint distance and is one commonly used space-filling criterion. We do not optimize this criterion directly, but rather optimizes

φ_p = ( ∑∑ d_{ij}^{-p})^{1/p}

This is done for optimization purposes since it is a smoother criteria.

Value

D1

The optimal design among the random starts standardized to [0,1]

phival

The phiP value of the design

phistore

A vector of phiP values from each random start

References

• Johnson, M. E., L. M. Moore, and D. Ylvisaker (1990). Minimax and maximin distance designs. Journal of statistical planning and inference 26 (2). 131-148.

• Meyer, R. K., and C.J. Nachtsheim (1995). The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 37 (1). 60-69.

Examples

## Generate Design
time1 <- Sys.time()
D1 <- MmSimplex(5,40,10,cords = 1,randst = 2,phival = 50)
Sys.time() - time1

##View best design scaled to [0,1]^5
D1[[1]]

##View PhiP criterion for best design among 2 random starts
D1[[2]]

simplexdesign documentation built on March 16, 2020, 5:06 p.m.