inst/examples/ex_criterion.R

In gMOIP: Tools for 2D and 3D Plots of Single and Multi-Objective Linear/Integer Programming Models

### Set up 2D plot
# Function for plotting the solution and criterion space in one plot (two variables)
plotBiObj2D <- function(A, b, obj,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = FALSE,
   labels = "numb",
   addTriangles = TRUE,
   addHull = TRUE)
{
   p1 <- plotPolytope(A, b, type = type, crit = crit, faces = faces, plotFaces = plotFaces,
                      plotFeasible = plotFeasible, plotOptimum = plotOptimum, labels = labels)
   p2 <- plotCriterion2D(A, b, obj, type = type, crit = crit, addTriangles = addTriangles,
                         addHull = addHull, plotFeasible = plotFeasible, labels = labels)
   gridExtra::grid.arrange(p1, p2, nrow = 1)
}


### Bi-objective problem with two variables
A <- matrix(c(-3,2,2,4,9,10), ncol = 2, byrow = TRUE)
b <- c(3,27,90)

## LP model
obj <- matrix(
   c(7, -10, # first criterion
     -10, -10), # second criterion
   nrow = 2)
plotBiObj2D(A, b, obj, addTriangles = FALSE)

\donttest{
## ILP models with different criteria (maximize)
obj <- matrix(c(7, -10, -10, -10), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)))
obj <- matrix(c(3, -1, -2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)))
obj <- matrix(c(-7, -1, -5, 5), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)))
obj <- matrix(c(-1, -1, 2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)))

## ILP models with different criteria (minimize)
obj <- matrix(c(7, -10, -10, -10), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)), crit = "min")
obj <- matrix(c(3, -1, -2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)), crit = "min")
obj <- matrix(c(-7, -1, -5, 5), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)), crit = "min")
obj <- matrix(c(-1, -1, 2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = rep("i", ncol(A)), crit = "min")


# More examples
## MILP model (x1 integer) with different criteria (maximize)
obj <- matrix(c(7, -10, -10, -10), nrow = 2)
plotBiObj2D(A, b, obj, type = c("i", "c"))
obj <- matrix(c(3, -1, -2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = c("i", "c"))
obj <- matrix(c(-7, -1, -5, 5), nrow = 2)
plotBiObj2D(A, b, obj, type = c("i", "c"))
obj <- matrix(c(-1, -1, 2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = c("i", "c"))

## MILP model (x2 integer) with different criteria (minimize)
obj <- matrix(c(7, -10, -10, -10), nrow = 2)
plotBiObj2D(A, b, obj, type = c("c", "i"), crit = "min")
obj <- matrix(c(3, -1, -2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = c("c", "i"), crit = "min")
obj <- matrix(c(-7, -1, -5, 5), nrow = 2)
plotBiObj2D(A, b, obj, type = c("c", "i"), crit = "min")
obj <- matrix(c(-1, -1, 2, 2), nrow = 2)
plotBiObj2D(A, b, obj, type = c("c", "i"), crit = "min")
}

### Set up 3D plot
\donttest{
# Function for plotting the solution and criterion space in one plot (three variables)
plotBiObj3D <- function(A, b, obj,
                        type = rep("c", ncol(A)),
                        crit = "max",
                        faces = rep("c", ncol(A)),
                        plotFaces = TRUE,
                        plotFeasible = TRUE,
                        plotOptimum = FALSE,
                        labels = "numb",
                        addTriangles = TRUE,
                        addHull = TRUE)
{
   plotPolytope(A, b, type = type, crit = crit, faces = faces, plotFaces = plotFaces,
                plotFeasible = plotFeasible, plotOptimum = plotOptimum, labels = labels)
   plotCriterion2D(A, b, obj, type = type, crit = crit, addTriangles = addTriangles,
                   addHull = addHull, plotFeasible = plotFeasible, labels = labels)
}

### Bi-objective problem with three variables
loadView <- function(fname = "view.RData", v = NULL) {
   if (!is.null(v)) {
      rgl::view3d(userMatrix = v)
   } else {
      if (file.exists(fname)) {
         load(fname)
         rgl::view3d(userMatrix = view)
      } else {
         warning(paste0("Can'TRUE load view in file ", fname, "!"))
      }
   }
}

## Ex
view <- matrix( c(-0.452365815639496, -0.446501553058624, 0.77201122045517, 0, 0.886364221572876,
                  -0.320795893669128, 0.333835482597351, 0, 0.0986008867621422, 0.835299551486969,
                  0.540881276130676, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
Ab <- matrix( c(
   1, 1, 2, 5,
   2, -1, 0, 3,
   -1, 2, 1, 3,
   0, -3, 5, 2
), nc = 4, byrow = TRUE)
A <- Ab[,1:3]
b <- Ab[,4]
obj <- matrix(c(1, -6, 3, -4, 1, 6), nrow = 2)

# LP model
plotBiObj3D(A, b, obj, crit = "min", addTriangles = FALSE)

# ILP model
plotBiObj3D(A, b, obj, type = c("i","i","i"), crit = "min")

# MILP model
plotBiObj3D(A, b, obj, type = c("c","i","i"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","c","i"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","i","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","c","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("c","i","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("c","c","i"), crit = "min")


## Ex
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)
loadView(v = view)
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 <- matrix(c(1, -6, 3, -4, 1, 6), nrow = 2)

# LP model
plotBiObj3D(A, b, obj, crit = "min", addTriangles = FALSE, labels = "coord")

# ILP model
plotBiObj3D(A, b, obj, type = c("i","i","i"))

# MILP model
plotBiObj3D(A, b, obj, type = c("c","i","i"))
plotBiObj3D(A, b, obj, type = c("i","c","i"), plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("i","i","c"))
plotBiObj3D(A, b, obj, type = c("i","c","c"), plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("c","i","c"), plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("c","c","i"))


## Ex
view <- matrix( c(-0.812462985515594, -0.029454167932272, 0.582268416881561, 0, 0.579295456409454,
                  -0.153386667370796, 0.800555109977722, 0, 0.0657325685024261, 0.987727105617523,
                  0.14168381690979, 0, 0, 0, 0, 1), nc = 4)
loadView(v = view)
A <- matrix( c(
   1, 1, 1,
   3, 0, 1
), nc = 3, byrow = TRUE)
b <- c(10, 24)
obj <- matrix(c(1, -6, 3, -4, 1, 6), nrow = 2)

# LP model
plotBiObj3D(A, b, obj, crit = "min", addTriangles = FALSE, labels = "coord")

# ILP model
plotBiObj3D(A, b, obj, type = c("i","i","i"), crit = "min", labels = "n")

# MILP model
plotBiObj3D(A, b, obj, type = c("c","i","i"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","c","i"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","i","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("i","c","c"), crit = "min")
plotBiObj3D(A, b, obj, type = c("c","i","c"), crit = "min", plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("c","c","i"), crit = "min", plotFaces = FALSE)


## Ex
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)
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 <- matrix(c(1, -6, 3, -4, 1, -1), nrow = 2)

# LP model
plotBiObj3D(A, b, obj, crit = "min", addTriangles = FALSE, labels = "coord")

# ILP model
plotBiObj3D(A, b, obj, type = c("i","i","i"), crit = "min", labels = "n")

# MILP model
plotBiObj3D(A, b, obj, type = c("c","i","i"), crit = "min", labels = "n")
plotBiObj3D(A, b, obj, type = c("i","c","i"), crit = "min", labels = "n", plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("i","i","c"), crit = "min", labels = "n")
plotBiObj3D(A, b, obj, type = c("i","c","c"), crit = "min", labels = "n")
plotBiObj3D(A, b, obj, type = c("c","i","c"), crit = "min", labels = "n", plotFaces = FALSE)
plotBiObj3D(A, b, obj, type = c("c","c","i"), crit = "min", labels = "n")
}