Skip to contents

Plotting polytopes in 3D - Example 3

Source: vignettes/polytope_3d_ex3.Rmd
polytope_3d_ex3.Rmd

With gMOIP you can make 3D plots of the polytope/feasible region/solution space of a linear programming (LP), integer linear programming (ILP) model, or mixed integer linear programming (MILP) model. This vignette gives examples on how to make plots given a model with three variables.

First we load the package:

We define the model:

A <- matrix( c(
   -1, 1, 0,
   1, 4, 0,
   2, 1, 0,
   3, -4, 0,
   0, 0, 4
), nc = 3, byrow = TRUE)
b <- c(5, 45, 27, 24, 10)
obj <- c(5, 45, 15)

We load the preferred view angle for the RGL window:

view <- matrix( c(0.976349174976349, -0.202332556247711, 0.0761845782399178, 0, 0.0903248339891434,
                  0.701892614364624, 0.706531345844269, 0, -0.196427255868912, -0.682940244674683,
                  0.703568696975708, 0, 0, 0, 0, 1), nc = 4)

The LP polytope:

loadView(v = view, close = F, zoom = 0.75)
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "coord")

Note you can zoom/turn/twist the figure with your mouse (rglwidget).

The ILP model (note since the vertices are integer the LP and ILP faces are equal):

loadView(v = view, close = F, zoom = 0.75)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","i"), plotOptimum = TRUE, obj = obj, 
             argsTitle3d = list(main = "With LP faces"), argsPlot3d = list(box = F, axes = T) )

Let us have a look at some MILP models (we use static images). MILP model with variable 1 and 3 integer:

loadView(v = view, close = T, zoom = 0.75)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","c","i"), plotOptimum = TRUE, obj = obj)

MILP model with variable 2 and 3 integer:

loadView(v = view, zoom = 0.75)
plotPolytope(A, b, faces = c("c","c","c"), type = c("c","i","i"), plotOptimum = TRUE, obj = obj)

MILP model with variable 1 and 2 integer:

loadView(v = view, zoom = 0.75)
plotPolytope(A, b, faces = c("c","c","c"), type = c("i","i","c"), plotOptimum = TRUE, obj = obj)

MILP model with variable 1 integer:

loadView(v = view, zoom = 0.75)
plotPolytope(A, b, type = c("i","c","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)

MILP model with variable 2 integer:

loadView(v = view, zoom = 0.75)
plotPolytope(A, b, type = c("c","i","c"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)

MILP model with variable 3 integer:

loadView(v = view, zoom = 0.75)
plotPolytope(A, b, type = c("c","c","i"), plotOptimum = TRUE, obj = obj, plotFaces = FALSE)