classifyNDSetExtreme: Find extreme points of a nondominated set of points

In relund/gMOIP: Tools for 2D and 3D Plots of Single and Multi-Objective Linear/Integer Programming Models

Find extreme points of a nondominated set of points

Description

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

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)
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

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")
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

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)

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$z3)+2)))
plotHull3D(pts[, 1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
pts <- classifyNDSetExtreme(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()
pts

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$z3)+2)))
plotHull3D(pts[, 1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
pts <- classifyNDSetExtreme(pts[,1:3])
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[is.na(pts$cls),1:3], argsPlot3d = list(col = "yellow"))  # unclassified
finalize3D()
pts

relund/gMOIP documentation built on Oct. 28, 2024, 11:04 p.m.