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Generate a sample of nondominated points.

Source: R/ndset.R
genNDSet.Rd

Generate a sample of nondominated points.

Usage

genNDSet(
  p,
  n,
  range = c(1, 100),
  random = FALSE,
  sphere = TRUE,
  planes = FALSE,
  box = FALSE,
  keepDom = FALSE,
  crit = "min",
  dubND = FALSE,
  classify = FALSE,
  ...
)

Arguments

p

Dimension of the points.

n

Number nondominated points generated.

range

The range of the points in each dimension (a vector or matrix with p rows).

random

Random sampling.

sphere

Generate points on a sphere.

planes

Generate points between two planes.

box

Generate points in boxes.

keepDom

Keep dominated points also.

crit

Criteria used (a vector of min/max).

dubND

Should duplicated non-dominated points be considered as non-dominated.

classify

Non-dominated points are classified into supported extreme (se), supported non-extreme (sne) and unsupported (us)

...

Further arguments passed on to genSample.

Value

A data frame with p+1 columns (last one indicate if dominated or not).

Examples

# \donttest{
## Random
range <- matrix(c(1,100, 50, 100, 10, 50), ncol = 2, byrow = TRUE)
pts <- genNDSet(3, 5, range = range, random = TRUE, keepDom = TRUE)
head(pts)
#>   z1 z2 z3    nd
#> 1 73 51 34 FALSE
#> 2 72 98 41 FALSE
#> 3 21 89 16 FALSE
#> 4 66 94 49 FALSE
#> 5 41 86 47 FALSE
#> 6 13 63 38  TRUE
Rfast::colMinsMaxs(as.matrix(pts[, 1:3]))
#>     [,1] [,2] [,3]
#> min   13   51   11
#> max   73   98   49
ini3D(FALSE, argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+10),
  ylim = c(min(pts[,2])-2,max(pts[,2])+10),
  zlim = c(min(pts[,3])-2,max(pts[,3])+10)))
plotPoints3D(pts[,1:3])
plotPoints3D(pts[pts$nd,1:3], argsPlot3d = list(col = "red", size = 10))
plotCones3D(pts[pts$nd,1:3], argsPolygon3d = list(alpha = 1))
finalize3D()




## Between planes
range <- matrix(c(1,10000, 1,10000), ncol = 2, byrow = TRUE)
pts <- genNDSet(2, 50, range = range, planes = TRUE, classify = TRUE)
head(pts)
#>     z1   z2   nd    se   sne    us cls
#> 1 7169  986 TRUE FALSE FALSE  TRUE  us
#> 2 6736 1564 TRUE FALSE FALSE  TRUE  us
#> 3 1244 6964 TRUE FALSE FALSE  TRUE  us
#> 4 4311 3808 TRUE FALSE FALSE  TRUE  us
#> 5 1464 6621 TRUE FALSE FALSE  TRUE  us
#> 6   27 9405 TRUE  TRUE FALSE FALSE  se
Rfast::colMinsMaxs(as.matrix(pts[, 1:2]))
#>     [,1] [,2]
#> min   27    2
#> max 8229 9405
plot(pts[, 1:2])


range <- matrix(c(1,100, 50,100, 10, 50), ncol = 2, byrow = TRUE)
center <- rowMeans(range)
planeU <- c(rep(1, 3), -1.2*sum(rowMeans(range)))
planeL <- c(rep(1, 3), -0.8*sum(rowMeans(range)))
pts <- genNDSet(3, 50, range = range, planes = TRUE, keepDom = TRUE, classify = TRUE,
   argsPlanes = list(center = center, planeU = planeU, planeL = planeL))
head(pts)
#>   z1 z2 z3    nd    se   sne   us cls
#> 1 85 66 31 FALSE FALSE FALSE TRUE   d
#> 2 90 57 25 FALSE FALSE FALSE TRUE   d
#> 3 31 93 32 FALSE FALSE FALSE TRUE   d
#> 4 43 86 35 FALSE FALSE FALSE TRUE   d
#> 5 80 85 17 FALSE FALSE FALSE TRUE   d
#> 6 31 99 35 FALSE FALSE FALSE TRUE   d
Rfast::colMinsMaxs(as.matrix(pts[, 1:3]))
#>     [,1] [,2] [,3]
#> min    1   50   10
#> max  100  100   50
ini3D(FALSE, argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+10),
  ylim = c(min(pts[,2])-2,max(pts[,2])+10),
  zlim = c(min(pts[,3])-2,max(pts[,3])+10),
  box = TRUE, axes = TRUE))
plotPoints3D(pts[,1:3])
plotPoints3D(pts[pts$nd,1:3], argsPlot3d = list(col = "red", size = 10))
rgl::planes3d(planeL[1], planeL[2], planeL[3], planeL[4], alpha = 0.5)
rgl::planes3d(planeU[1], planeU[2], planeU[3], planeU[4], alpha = 0.5)


finalize3D()


## On a sphere
ini3D()
range <- c(1,100)
cent <- rep(range[1] + (range[2]-range[1])/2, 3)
pts <- genNDSet(3, 20, range = range, sphere = TRUE, keepDom = TRUE,
       argsSphere = list(center = cent))
rgl::spheres3d(cent, radius=49.5, color = "grey100", alpha=0.1)
plotPoints3D(pts)
plotPoints3D(pts[pts$nd,], argsPlot3d = list(col = "red", size = 10))
rgl::planes3d(cent[1],cent[2],cent[3],-sum(cent^2), alpha = 0.5, col = "red")


finalize3D()

ini3D()
cent <- c(100,100,100)
r <- 75
planeC <- c(cent+r/3)
planeC <- c(planeC, -sum(planeC^2))
pts <- genNDSet(3, 20, keepDom = TRUE,
  argsSphere = list(center = cent, radius = r, below = FALSE, plane = planeC, factor = 6))
rgl::spheres3d(cent, radius=r, color = "grey100", alpha=0.1)
plotPoints3D(pts)
plotPoints3D(pts[pts$nd,], argsPlot3d = list(col = "red", size = 10))
rgl::planes3d(planeC[1],planeC[2],planeC[3],planeC[4], alpha = 0.5, col = "red")


finalize3D()


# }