findoptima {adana}

Finds peaks and valleys on the curve of a function with single variable

Description

This function finds the peaks and valleys on the curve of user-defined functions with one variable. The function also plots the function curve that can be used to demonstrate the points for local optima and global optimum in a optimization problem.

Usage

findoptima(x, type="max", pflag=TRUE)

Arguments

x

a vector of variable

type

Either “max” (the default) or “min”. The peaks are found when type="max" and the valleys are found when type="max".

pflag

if this is TRUE, the first and last values are also checked.

Details

The findoptima function finds all the peaks and valleys in a given function curve. The points can be colorized with different colors. See the example below.

Value

Returns a vector of indices of the peaks or valleys on the function curve.

Author(s)

Zeynel Cebeci & Erkut Tekeli

References

Cebeci Z. (2021). R ile Genetik Algoritmalar ve Optimizasyon Uygulamalari. Ankara:Nobel Akademik Yayincilik

Examples

fx <- function(x) -sin(x)-sin(2*x)-cos(3*x) + 3
x <- seq(-2*pi, 2*pi, by=0.001)
curve(fx, x)
cr <- curve(fx, x, lwd=2)
xy <- cbind(cr$x, cr$y)
peaks <- findoptima(cr$y, type = "max")
valleys <- findoptima(cr$y, type = "min")

## Finds peaks and valleys
peaks <- findoptima(cr$y, type="max")
valleys <-  findoptima(cr$y, type="min")

## Plotting the function curve and local optima and global optimum
points(xy[peaks,], pch=19, cex=1.2, col=2)
points(xy[valleys,], pch=18, cex=1.2, col=4)
gmin <- valleys[which.min(xy[valleys,2])]
gmax <- peaks[which.min(xy[valleys,2])]
points(xy[gmax,1], xy[gmax,2], pch=19, cex=2, col=2)
points(xy[gmin,1], xy[gmin,2], pch=18, cex=2, col=4)
text(xy[gmax,1], xy[gmax,2], labels="Glob.Max", pos=2, cex=0.8, col=1)
text(xy[gmin,1], xy[gmin,2], labels="Glob.Min", pos=2, cex=0.8, col=1)