The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

Plotting polytopes in 3D - Example 1

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:

library(gMOIP)

We define the model \(\max \{cx | Ax \leq b\}\) (could also be minimized) with three variables:

A <- matrix( c(
   3, 2, 5,
   2, 1, 1,
   1, 1, 3,
   5, 2, 4
), nc = 3, byrow = TRUE)
b <- c(55, 26, 30, 57)
obj <- c(20, 10, 15)

We load the preferred view angle for the RGL window:

view <- matrix( c(-0.412063330411911, -0.228006735444069, 0.882166087627411, 0, 0.910147845745087,
                  -0.0574885793030262, 0.410274744033813, 0, -0.042830865830183, 0.97196090221405,
                  0.231208890676498, 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)

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

The ILP model with LP and ILP faces:

loadView(v = view)
mfrow3d(nr = 1, nc = 2, sharedMouse = TRUE)
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) )
plotPolytope(A, b, faces = c("i","i","i"), type = c("i","i","i"), plotFeasible = FALSE, obj = obj,
             argsTitle3d = list(main = "ILP faces") )

Let us have a look at some MILP models. 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)

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.
Health stats visible at Monitor.