computeGradientField: Compute the multi-objective gradient vector for a set of...

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

Description

Computes the multi-objective gradients for a matrix of points.

Usage

computeGradientField(points, fn1, fn2, fn3 = NULL, scale.step = 0.5,
  prec.grad = 1e-06, prec.norm = 1e-06, prec.angle = 1e-04,
  parallelize = FALSE, lower, upper)

Arguments

points	[matrix] Matrix of points, for which the multi-objective gradient should be computed. Each row of the matrix will be considered as a separate point, thus the number of rows corresponds to the number of observations and the number of columns to the dimensionality of the search space.
fn1	[function] The first objective used for computing the multi-objective gradient.
fn2	[function] The second objective used for computing the multi-objective gradient.
fn3	[function] The third objective used for computing the multi-objective gradient. If not provided (fn3 = NULL), the gradient field will only consider fn1 and fn2.
scale.step	[numeric(1L)] Scaling factor for the step size in the direction of the multi-objective gradient. The default is 0.5.
prec.grad	[numeric(1L)] Precision value (= step size) used for approximating the gradient. The default is 1e-6.
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.
prec.angle	[numeric(1L)] Precision threshold used for comparing whether the angle (in degree) between two vectors is zero. The default is 1e-4.
parallelize	[logical(1L)] Should the computation of the gradient vectors be parallelized (with parallel::mclapply)? The default is FALSE.
lower	[numeric(d)] Vector of lower bounds.
upper	[numeric(d)] Vector of upper bounds.

Value

[matrix]
Returns matrix of multi-objective gradients. The i-th row of the matrix contains the multi-objective gradient vector of the i-th observation (= row) of the input matrix points.

Examples

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

# Create a grid of points, for which the gradients should be computed:
points = expand.grid(x1 = seq(0, 1, 0.01), x2 = seq(0, 1, 0.05))
gradient.field = computeGradientField(points, fn1, fn2)

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