Tools for 2D and 3D plots of single and multi-objective linear/integer programming models

The gMOIP package can be used to make 2D and 3D plots of linear programming (LP), integer linear programming (ILP), or mixed integer linear programming (MILP) models with up to three objectives. This include the polytope, integer points, ranges and iso profit curve. Plots of both the solution and criterion space are possible. For instance the non-dominated (Pareto) set for bi-objective LP/ILP/MILP programming models.

The package also include an inHull function for checking if a set of points is inside/at/outside the convex hull of a set of vertices (for arbitrary dimension).

Finally, the package also contains functions for generating (non-dominated) points in $\mathbb{R}_n$ and classifying non-dominated points as supported extreme, supported non-extreme and unsupported.

Usage

Consider the model $\max{cx | Ax \leq b}$ (could also be minimized) with 2 variables:

A <- matrix(c(-3,2,2,4,9,10), ncol = 2, byrow = TRUE)
b <- c(3,27,90)
coeff <- c(7.75, 10)  # coefficients c

The polytope of the LP model with non-negative continuous variables ($x \geq 0$):

plotPolytope(
   A,
   b,
   coeff,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)

The polytope of the ILP model with LP faces ($x\in \mathbb{Z}_0$):

plotPolytope(
   A,
   b,
   coeff,
   type = rep("i", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)

The polytope of the MILP model (first variable integer) with LP faces:

plotPolytope(
   A,
   b,
   coeff,
   type = c("i", "c"),
   crit = "max",
   faces = c("c", "c"),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)

You can do the same 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)
coeff <- c(20, 10, 15)

# LP model
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)   
loadView(v = view)  # set view angle
plotPolytope(A, b, plotOptimum = TRUE, obj = coeff, labels = "n")

Note: interactive 3d plots cannot be displayed in a GitHub README file, and static images or animated gifs are used here instead. Visit the pkgdown online documentation to view plots which can be manipulated in the browser.

For more examples see example("gMOIP-package") or browseVignettes('gMOIP').

LaTeX support

You may create a TikZ file of the plot for LaTeX using

library(tikzDevice)
tikz(file = "plot_polytope.tex", standAlone=F, width = 7, height = 6)
plotPolytope(
   A,
   b,
   coeff,
   type = rep("i", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)
dev.off()

Installation

Install the latest stable release from CRAN:

install.packages("gMOIP")

Alternatively, install the latest development version from GitHub (recommended):

install.packages("remotes")
remotes::install_github("relund/gMOIP")

library(gMOIP)
browseVignettes('gMOIP')
example("gMOIP-package")

The package is highly dependent on the {rgl} package for plotting 3D graphics. If your build of {rgl} does not include OpenGL functions, use rgl::rglwidget() to display results, e.g. via options(rgl.printRglwidget = TRUE).