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Find extreme points of a nondominated set of points

Source: R/ndset.R
classifyNDSetExtreme.Rd

Find extreme points of a nondominated set of points

Usage

classifyNDSetExtreme(pts, direction = 1)

Arguments

pts

A set of non-dominated points. It is assumed that ncol(pts) equals the number of objectives ($p$).

direction

Ray direction. If i'th entry is positive, consider the i'th column of the pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of the pts minus a value greater than on equal zero (maximize objective $i$).

Value

The classification is extreme (se), supported non-extreme (sne) and unsupported us nondominated points. Return the ND set with classification columns se (true/false), sne (true/false), us (true/false) and cls (se, sne or us).

Note

It is assumed that pts are nondominated. This algorithm is faster than classifyNDSet(), since only check for extreme points.

See also

classifyNDSet()

Examples

# \donttest{
pts <- matrix(c(0,0,1, 0,1,0, 1,0,0, 0.5,0.2,0.5, 0.25,0.5,0.25), ncol = 3, byrow = TRUE)
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+2),
  ylim = c(min(pts[,2])-2,max(pts[,2])+2),
  zlim = c(min(pts[,3])-2,max(pts[,3])+2)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5), useRGLBBox = TRUE)
#> Warning: edge not found:1 2
#> Warning: edge not found:1 2
pts <- classifyNDSetExtreme(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))  # extreme
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()


pts
#>     z1  z2   z3    se   sne    us  cls
#> 1 0.00 0.0 1.00  TRUE FALSE FALSE   se
#> 2 0.00 1.0 0.00  TRUE FALSE FALSE   se
#> 3 1.00 0.0 0.00  TRUE FALSE FALSE   se
#> 4 0.50 0.2 0.50 FALSE    NA    NA <NA>
#> 5 0.25 0.5 0.25 FALSE    NA    NA <NA>

pts <- matrix(c(0,0,1, 0,1,0, 1,0,0, 0.2,0.1,0.1, 0.1,0.45,0.45), ncol = 3, byrow = TRUE)
di <- -1 # maximize
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-1,max(pts[,1])+1),
  ylim = c(min(pts[,2])-1,max(pts[,2])+1),
  zlim = c(min(pts[,3])-1,max(pts[,3])+1)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5), direction = di,
           addText = "coord")
#> Warning: edge not found:1 2
#> Warning: edge not found:1 2
pts <- classifyNDSetExtreme(pts[,1:3], direction = di)
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()


pts
#>    z1   z2   z3    se   sne    us  cls
#> 1 0.0 0.00 1.00  TRUE FALSE FALSE   se
#> 2 0.0 1.00 0.00  TRUE FALSE FALSE   se
#> 3 1.0 0.00 0.00  TRUE FALSE FALSE   se
#> 4 0.2 0.10 0.10 FALSE    NA    NA <NA>
#> 5 0.1 0.45 0.45 FALSE    NA    NA <NA>

pts <- matrix(c(0,0,1, 0,0,1, 0,1,0, 0.5,0.2,0.5, 1,0,0, 0.5,0.2,0.5, 0.25,0.5,0.25), ncol = 3,
              byrow = TRUE)
classifyNDSetExtreme(pts)
#>     z1  z2   z3    se   sne    us  cls
#> 1 0.00 0.0 1.00  TRUE FALSE FALSE   se
#> 2 0.00 1.0 0.00  TRUE FALSE FALSE   se
#> 3 0.50 0.2 0.50 FALSE    NA    NA <NA>
#> 4 1.00 0.0 0.00  TRUE FALSE FALSE   se
#> 5 0.25 0.5 0.25 FALSE    NA    NA <NA>
#> 6 6.00 0.0 1.00 FALSE    NA    NA <NA>
#> 7 6.00 1.0 0.00 FALSE    NA    NA <NA>

pts <- genNDSet(3,15)[,1:3]
ini3D(argsPlot3d = list(xlim = c(0,max(pts$z1)+2),
  ylim = c(0,max(pts$z2)+2),
  zlim = c(0,max(pts$z3)+2)))
plotHull3D(pts[, 1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
#> Warning: edge not found:1 2
#> Warning: edge not found:1 2
pts <- classifyNDSetExtreme(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()


pts
#>    z1 z2 z3    se   sne    us  cls
#> 1  19 15 36  TRUE FALSE FALSE   se
#> 2  13 21 37  TRUE FALSE FALSE   se
#> 3  24 75 17 FALSE    NA    NA <NA>
#> 4  29 57  7  TRUE FALSE FALSE   se
#> 5  43  2 47  TRUE FALSE FALSE   se
#> 6  46 52  1  TRUE FALSE FALSE   se
#> 7  20 13 40  TRUE FALSE FALSE   se
#> 8  62  8 28  TRUE FALSE FALSE   se
#> 9   6 31 61  TRUE FALSE FALSE   se
#> 10 14 17 45  TRUE FALSE FALSE   se
#> 11  4 69 51  TRUE FALSE FALSE   se
#> 12 14 58 18  TRUE FALSE FALSE   se
#> 13 65 47  3 FALSE    NA    NA <NA>
#> 14 68 24 12  TRUE FALSE FALSE   se
#> 15  5 48 32  TRUE FALSE FALSE   se

pts <- genNDSet(3, 15, keepDom = FALSE, argsSphere = list(below = FALSE, factor = 10))[,1:3]
ini3D(argsPlot3d = list(xlim = c(0,max(pts$z1)+2),
  ylim = c(0,max(pts$z2)+2),
  zlim = c(0,max(pts$z3)+2)))
plotHull3D(pts[, 1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
#> Warning: edge not found:1 2
#> Warning: edge not found:1 2
pts <- classifyNDSetExtreme(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()


pts
#>    z1 z2 z3    se   sne    us  cls
#> 1  14 65 80  TRUE FALSE FALSE   se
#> 2  19 55 89 FALSE    NA    NA <NA>
#> 3  20 77 79 FALSE    NA    NA <NA>
#> 4  95 28 51 FALSE    NA    NA <NA>
#> 5  79 67 13  TRUE FALSE FALSE   se
#> 6  55 86 16 FALSE    NA    NA <NA>
#> 7  87 54 18  TRUE FALSE FALSE   se
#> 8  91 21 53  TRUE FALSE FALSE   se
#> 9  37 34 95  TRUE FALSE FALSE   se
#> 10 48 90 21  TRUE FALSE FALSE   se
#> 11 60 80 12  TRUE FALSE FALSE   se
#> 12 23 45 91  TRUE FALSE FALSE   se
#> 13 23 91 47  TRUE FALSE FALSE   se
#> 14 29 87 75 FALSE    NA    NA <NA>
#> 15 48 26 93  TRUE FALSE FALSE   se
# }