computeCumulatedPathLengths: Compute the Cumulated Path Lengths.

In kerschke/mogsa: A Multi-Objective Optimization Algorithm Based on Multi-Objective Gradients

Description

Given a grid of points in the search space, along with their corresponding multi-objective gradients, this function will compute (for each point of the grid) the length of the cumulated path from a point towards its attracting local efficient point.

Usage

computeCumulatedPathLengths(centers, gradients,
  prec.vector.length = 0.001, prec.norm = 1e-06, check.data = TRUE)

Arguments

centers	[matrix] Matrix containing the points of a grid of cells, for which the lengths of cumulated gradient paths should be computed. Each row corresponds to a single point.
gradients	[matrix] Matrix containing the multi-objective gradients for each point of centers.
prec.vector.length	[numeric(1L)] Precision value (= threshold) for the length of the multi-objective gradient. Based on this threshold, the function will classify the corresponding point as locally efficient (or not). The default value is 1e-3.
prec.norm	[numeric(1L)] Precision threshold when normalizing a vector. That is, every element of the vector, whose absolute value is below this threshold, will be replaced by 0. The default is 1e-6.
check.data	[logical(1L)] Should sanity checks be performed? The default is TRUE. Note that the checks should only be turned off (e.g., for a slight speed up), if you are sure that you provide the input data in the correct format.

Value

[data.frame]
Returns a data.frame, which appends the cumulated path lengths to the points provided by centers.

Note

ATTENTION: Only turn off the sanity checks (check.data = FALSE), if you can ensure that all input parameters are provided in the correct format.

Examples

# Define two single-objective test problems:
fn1 = function(x) sum((x - c(0.2, 1))^2)
fn2 = function(x) sum((x - c(0.5, 0.5))^2)

# Define a grid of points:
points = as.matrix(expand.grid(x1 = seq(0, 0.7, 0.005), x2 = seq(0, 1.25, 0.005)))

# Compute the corresponding gradients:
gradients = computeGradientField(points, fn1, fn2)

# Now, compute the cumulated path lengths:
x = computeCumulatedPathLengths(points, gradients)

# Finally, we can visualize the resulting multi-objective "landscape":
ggplotHeatmap(x, hide.legend = TRUE)

kerschke/mogsa documentation built on July 11, 2019, 11:52 p.m.