With `gMOIP`

you can make plots of the criterion space for
bi-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 both the solution and criterion
space.

First we load the package:

`library(gMOIP)`

We define functions for plotting the solution and criterion space:

```
<- function(A, b, type = rep("c", ncol(A)),
plotSol faces = rep("c", ncol(A)),
plotFaces = TRUE, labels = "numb")
{#loadView(v = view, close = F, zoom = 0.75)
plotPolytope(A, b, type = type, faces = faces, labels = labels, plotFaces = plotFaces,
argsTitle3d = list(main = "Solution space"))
}
<- function(A, b, obj, crit = "min", type = rep("c", ncol(A)), addTriangles = TRUE,
plotCrit labels = "numb")
{plotCriterion2D(A, b, obj, type = type, crit = crit, addTriangles = addTriangles,
labels = labels) +
::ggtitle("Criterion space")
ggplot2 }
```

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

```
<- matrix( c(
Ab 1, 1, 2, 5,
2, -1, 0, 3,
-1, 2, 1, 3,
0, -3, 5, 2
nc = 4, byrow = TRUE)
), <- Ab[,1:3]
A <- Ab[,4]
b <- matrix(c(1, -6, 3, -4, 1, 6), nrow = 2) obj
```

We load the preferred view angle for the RGL window:

```
<- matrix( c(-0.452365815639496, -0.446501553058624, 0.77201122045517, 0, 0.886364221572876,
view -0.320795893669128, 0.333835482597351, 0, 0.0986008867621422, 0.835299551486969,
0.540881276130676, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
```

LP model (solution space):

`plotSol(A, b)`

LP model (criterion space):

`plotCrit(A, b, obj, addTriangles = FALSE) `

ILP model (solution space):

`plotSol(A, b, type = c("i","i","i"))`

ILP model (criterion space):

`plotCrit(A, b, obj, type = c("i","i","i"))`

MILP model with variable 2 and 3 integer (solution space):

`plotSol(A, b, type = c("c","i","i"))`

MILP model with variable 2 and 3 integer (criterion space):

`plotCrit(A, b, obj, type = c("c","i","i"))`

MILP model with variable 1 and 3 integer (solution space):

`plotSol(A, b, type = c("i","c","i"))`

MILP model with variable 1 and 3 integer (criterion space):

`plotCrit(A, b, obj, type = c("i","c","i"))`

MILP model with variable 1 and 2 integer (solution space):

`plotSol(A, b, type = c("i","i","c"))`

MILP model with variable 1 and 2 integer (criterion space):

`plotCrit(A, b, obj, type = c("i","i","c"))`

MILP model with variable 1 integer (solution space):

`plotSol(A, b, type = c("i","c","c"), plotFaces = F)`

MILP model with variable 1 integer (criterion space):

`plotCrit(A, b, obj, type = c("i","c","c"))`

MILP model with variable 2 integer (solution space):

`plotSol(A, b, type = c("c","i","c"), plotFaces = F)`

MILP model with variable 2 integer (criterion space):

`plotCrit(A, b, obj, type = c("c","i","c"))`

MILP model with variable 3 integer (solution space):

`plotSol(A, b, type = c("c","c","i"), plotFaces = F)`

MILP model with variable 3 integer (criterion space):

`plotCrit(A, b, obj, type = c("c","c","i"))`