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With gMOIP you can make plots of the criterion space for
tri-objective models (linear programming (LP), integer linear
programming (ILP), or mixed integer linear programming (MILP)). This
vignette gives examples on how to make plots of the criterion space.
First we load the package:
The criterion space can be plotted for tri-objective models. An example with many unsupported:
view <- matrix( c(0.333316594362259, 0.938472270965576, -0.0903875231742859, 0, 0.83994072675705, -0.339126199483871, -0.423665106296539, 0, -0.428250730037689, 0.0652943551540375, -0.901297807693481, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
set.seed(1234)
pts <- genNDSet(3, 20, argsSphere = list(below = FALSE), dubND = FALSE)
pts <- classifyNDSet(pts[,1:3])
head(pts)
#> z1 z2 z3 se sne us cls
#> 1 48 87 17 TRUE FALSE FALSE se
#> 2 14 59 83 TRUE FALSE FALSE se
#> 3 70 75 12 TRUE FALSE FALSE se
#> 4 98 36 55 FALSE FALSE TRUE us
#> 5 91 40 24 TRUE FALSE FALSE se
#> 6 34 93 31 TRUE FALSE FALSE se
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)))
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[!pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[!pts$us,1:3], argsPlot3d = list(col = "blue"))
plotCones3D(pts[,1:3], rectangle = TRUE, argsPolygon3d = list(alpha = 1, color = "cornflowerblue"))
plotHull3D(pts[,1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.25, color = "red"), useRGLBBox = TRUE)
finalize3D(argsAxes3d = list(edges = "bbox"))Example with many supported:
loadView(v = view)
pts <- genNDSet(3, 10, argsSphere = list(below = TRUE), dubND = FALSE)
pts <- classifyNDSet(pts[,1:3])
ini3D(argsPlot3d = list(xlim = c(min(pts[,1])-2,max(pts[,1])+2),
ylim = c(min(pts[,2])-2,max(pts[,2])+2),
zlim = c(min(pts[,3])-2,max(pts[,3])+2)))
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[!pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[!pts$us,1:3], argsPlot3d = list(col = "blue"))
plotCones3D(pts[,1:3], rectangle = TRUE, argsPolygon3d = list(alpha = 1, color = "cornflowerblue"))
plotHull3D(pts[,1:3], addRays = TRUE, argsPolygon3d = list(alpha = 0.25, color = "red"), useRGLBBox = TRUE)
finalize3D(argsAxes3d = list(edges = "bbox"))Non-dominated points can be classified using
classifyNDSet:
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)
open3d()
#> null
#> 32
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 <- classifyNDSet(pts[,1:3])
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 FALSE TRUE us
#> 5 0.25 0.5 0.25 FALSE TRUE FALSE sne
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[!pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[!pts$us,1:3], argsPlot3d = list(col = "blue"))
plotCones3D(pts[,1:3], rectangle = TRUE, argsPolygon3d = list(alpha = 1))
finalize3D()
rglwidget(reuse = F)
pts <- genNDSet(3,20, dubND = FALSE)[,1:3]
open3d()
#> null
#> 35
ini3D(argsPlot3d = list(xlim = c(0,max(pts$z1)+2),
ylim = c(0,max(pts$z2)+2),
zlim = c(0,max(pts$z3)+2)))
plotHull3D(pts, addRays = TRUE, argsPolygon3d = list(alpha = 0.5))
pts <- classifyNDSet(pts[,1:3])
pts
#> z1 z2 z3 se sne us cls
#> 1 3 62 45 TRUE FALSE FALSE se
#> 2 76 40 9 FALSE FALSE TRUE us
#> 3 23 45 10 TRUE FALSE FALSE se
#> 4 29 66 9 FALSE FALSE TRUE us
#> 5 22 11 60 TRUE FALSE FALSE se
#> 6 46 12 20 TRUE FALSE FALSE se
#> 7 49 2 39 TRUE FALSE FALSE se
#> 8 9 27 64 TRUE FALSE FALSE se
#> 9 32 10 29 TRUE FALSE FALSE se
#> 10 8 39 29 TRUE FALSE FALSE se
#> 11 37 5 36 TRUE FALSE FALSE se
#> 12 45 2 61 TRUE FALSE FALSE se
#> 13 19 30 18 TRUE FALSE FALSE se
#> 14 30 7 38 TRUE FALSE FALSE se
#> 15 11 33 26 TRUE FALSE FALSE se
#> 16 46 2 43 TRUE FALSE FALSE se
#> 17 12 21 39 TRUE FALSE FALSE se
#> 18 45 21 11 TRUE FALSE FALSE se
#> 19 21 26 20 TRUE FALSE FALSE se
#> 20 31 43 5 TRUE FALSE FALSE se
plotPoints3D(pts[pts$se,1:3], argsPlot3d = list(col = "red"))
plotPoints3D(pts[!pts$sne,1:3], argsPlot3d = list(col = "black"))
plotPoints3D(pts[!pts$us,1:3], argsPlot3d = list(col = "blue"))
finalize3D()
rglwidget(reuse = F)
The classification is done using the qhull algorithm
that find the convex hull of the points including the rays. If a vertex
then if must be supported extreme. Next we use the inHull
algorithm to find out if the remaining are on the border or not
(supported non-extreme and unsupported).
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.