gMOIP (version 1.1.0)

criterionPoints: Calculate the criterion points of a set of points and find the set of non-dominated points (pareto points) and classify them into extreme supported, non-extreme supported, non-supported.

Description

Calculate the criterion points of a set of points and find the set of non-dominated points (pareto points) and classify them into extreme supported, non-extreme supported, non-supported.

Usage

criterionPoints(points, c1, c2, crit)

Arguments

points

A data frame with columns x1 and x2.

c1

2D vector for first criterion.

c2

2D vector for second criterion.

crit

Either max or min.

Value

A data frame with columns x1, x2, z1 = c1*x, z2 = c2*x, z = z1 + z2, lbl = label, nD = non-dominated, ext = extreme, nonExt = non-extreme supported.

Examples

# NOT RUN {
# Define the LP max/min coeff*x st. Ax<=b, x>=0
A <- matrix(c(9,10,2,4,-3,2), ncol = 2, byrow = TRUE)
b <- c(90,27,3)
coeff <- c(7.75, 10)

# Corner points of the polytope
cPoints<-cornerPoints(A, b)
# Integer points in the polytope
iPoints<-integerPoints(A, b)

# Plot of the polytope
plotPolytope(cPoints)
plotPolytope(points = cPoints)
plotPolytope(points = iPoints)
plotPolytope(cPoints, cPoints, iso = coeff, crit = "max")
plotPolytope(cPoints, iPoints, iso = coeff, crit = "max")
plotPolytope(cPoints, iPoints, showLbl = TRUE)
plotPolytope(cPoints, iPoints, iso = c(3,-3), crit = "min")
plotPolytope(cPoints, iPoints) + xlab("x") + ylab("y")

# Plot of criterion points given a bi-objective vector
zPoints<-criterionPoints(iPoints, c1 = c(coeff[1], 0), c2 = c(0, coeff[2]), crit = "max")
head(zPoints)
plotCriterion(zPoints)
plotCriterion(zPoints, addHull = FALSE, addTriangles = TRUE)
# mimimize
zPoints<-criterionPoints(zPoints, c1 = c(-1, 1), c2 = c(1, -1), crit = "min")
plotCriterion(zPoints, addHull = TRUE, addTriangles = TRUE, crit = "min")
# identify solutions (x1,x2) corresponding to (z1,z2)
plotPolytope(cPoints, zPoints, showLbl = TRUE)
plotCriterion(zPoints, addHull = TRUE, addTriangles = TRUE, crit = "min", showLbl = TRUE)
# max and min
zPoints<-criterionPoints(iPoints, c1 = c(-2, -1), c2 = c(1, 4), crit = "max")
plotPolytope(cPoints, zPoints, showLbl = TRUE, shape = zPoints$nD)
plotCriterion(zPoints, addHull = TRUE, addTriangles = TRUE, crit = "max", showLbl = TRUE)
zPoints<-criterionPoints(iPoints, c1 = c(-2, -1), c2 = c(1, 4), crit = "min")
plotCriterion(zPoints, addHull = TRUE, addTriangles = TRUE, crit = "min", showLbl = TRUE)

# }
# NOT RUN {
# Generate tikz file for LaTeX
library(tikzDevice)
tikz(file = "plot_polytope.tex", standAlone=F, width = 7, height = 6)
plotPolytope(cPoints, zPoints, showLbl = TRUE)
dev.off()
# }
# NOT RUN {
# }