mcsm (version 1.0)

maximple: Graphical representation of a toy example of simulated annealing

Description

For the toy function $h(x)=(cos(50*x)+sin(20*x))^2$, this function represents simulated annealing sequences converging to a local or global maxima as paths on top of the function $h$ itself. The simulated annealing parameters ratemp and powemp can be changed, as well as the stopping rule tolerance.

Usage

maximple(tolerance = 10^(-5), ratemp = 5, powemp = 2)

Arguments

tolerance

maximal difference in the target value needed to stop the simulated annealing algorithm

ratemp

scale factor of $temp$ that determines the scale of the random walk

powemp

power of $1/(1+t)$ used to set the temperature schedule

Value

The value of this function is a list, with components

x

coordinates of the successive values of the random walk produced by the simulated annealing algorithm

y

corresponding values of $h(x)$, of the same length as x

References

From Chapter 5 of EnteR Monte Carlo Statistical Methods

See Also

dyadic

Examples

# Section 5.2.2, artificial function example 5.8

h=function(x){(cos(50*x)+sin(20*x))^2}
par(mar=c(4,4,1,1),mfrow=c(2,2))
for (tt in 1:4){

  curve(h,from=0,to=1,n=10001,col="grey",lwd=2)
  sam=maximple()
  xgo=sam$x
  hgo=sam$y
  lines(xgo,hgo,col="steelblue4",lwd=2)
  points(xgo,hgo,col="steelblue4",cex=.5,pch=19)
  }