minimaxdesign (version 0.1.5)

minimax: Compute minimax designs using clustering on constrained design regions

Description

minimax computes minimax designs using the minimax clustering algorithm in Mak and Joseph (2018). Current design region options include the unit hypercube ("hypercube"), the unit simplex ("simplex"), the unit ball ("ball"), the inequality-constrained unit hypercube ("ineq"), and custom clustering points ("custom").

Usage

minimax(N,p,q=10,region="hypercube",ini=NA,const=NA,clust_pts=NA,
        params_pso=list(w=0.72,c1=1.49,c2=1.49),
        npart=5,nclust=1e5,neval=nclust,
        itmax_pso=50,itmax_pp=100,itmax_inn=1e4,jit=0.1/sqrt(N))

Arguments

N

Number of design points.

p

Dimension of design region.

q

Power parameter for approximating the minimax criterion (see paper for details). Larger values of q give a better approximation, but may cause numerical instability.

region

String for desired design region. Current options include "hypercube", "simplex", "ball", "ineq" and "custom".

ini

String for initial design. Current choices include NA (automatic choice), "sobol" (Sobol' sequence), and "ff" (fractional factorial).

const

Function for desired constraints (inequalities) on design space. See examples for implementation.

clust_pts

Custom clustering points (used only if region == "custom").

params_pso

Particle swarm optimization parameters (particle momentum (w), local-best velocity (c1) and global-best velocity (c2)).

npart

Number of particles for particle swarm optimization.

nclust,neval

Number of sample points for minimax clustering and post-processing.

itmax_pso,itmax_pp,itmax_inn

Maximum number of iterations for minimax clustering, post-processing and inner optimization.

jit

Jitter radius for post-processing.

Value

An N-by-p matrix for the minimax design.

Examples

# NOT RUN {
# }
# NOT RUN {
#20-point minimax design on the hypercube [0,1]^2
D <- minimax(N=20,p=2)
plot(NULL,xlim=c(0,1),ylim=c(0,1),xlab="x1",ylab="x2") #set up plot
polygon(c(0,0,1,1),c(0,1,1,0),col="gray") #design space
points(D,xlim=c(0,1),ylim=c(0,1),xlab="x1",ylab="x2",pch=16) #design points
mM <- mMdist(D)
mM$dist #minimax (fill) distance
lines(rbind(mM$far.pt,mM$far.despt),col="red",lty=2,lwd=2) #plot farthest point

#20-point minimax design on design space [0,1]^2 constrained by given inequalities
ineqs <- function(xx){ #user-defined inequalities
  bool.vec <- rep(TRUE,2)
  bool.vec[1] <- (xx[2]<=2-2*xx[1]) #inequality 1: x2 <= 2 - 2*x1
  bool.vec[2] <- (xx[1]>=xx[2]) #inequality 2: x1 >= x2
  return(all(bool.vec))
}
D <- minimax(N=20,p=2,region="ineq",const=ineqs)
plot(NULL,xlim=c(0,1),ylim=c(0,1),xlab="x1",ylab="x2") #set up plot
polygon(c(0,2/3,1),c(0,2/3,0),col="gray") #design space
points(D,pch=16) #design points
mM <- mMdist(D,region="custom",const=ineqs)
mM$dist #minimax (fill) distance
lines(rbind(mM$far.pt,mM$far.despt),col="red",lty=2,lwd=2) #plot farthest point

#20-point minimax design on custom clustering points
p <- 2
NN <- 10000
clust_pts <- matrix(runif(NN*p),nrow=NN,ncol=p)
D <- minimax(N=20,p=2,region="custom",clust_pts=clust_pts)
plot(NULL,xlim=c(0,1),ylim=c(0,1),xlab="x1",ylab="x2") #set up plot
points(clust_pts,xlim=c(0,1),ylim=c(0,1),col="gray",pch=4,cex=0.5) #clustering points
points(D,xlim=c(0,1),ylim=c(0,1),xlab="x1",ylab="x2",pch=16) #design points
mM <- mMdist(D,eval_pts=clust_pts)
mM$dist #minimax (fill) distance
lines(rbind(mM$far.pt,mM$far.despt),col="red",lty=2,lwd=2) #plot farthest point

# }