Cooling Schedule in Simulated Annealing

Exponential

x<-seq(1:20)
y<-x
z<-x
w<-x
T0<-1
y[1]<-T0
z[1]<-T0
w[1]<-T0

for(i in 2:length(x))
{
  y[i]<-y[i-1]*0.70
  
}


for(i in 2:length(x))
{
  z[i]<-z[i-1]*0.85
  
}


for(i in 2:length(x))
{
  w[i]<-w[i-1]*0.95
  
}
plot(x,y,type="o",xlab="Iterations", ylab="Temperature", col="red")
lines(lowess(x,y,f=1/15), col="red")
points(x,z,col="blue")
lines(x,z, col="blue")
points(x,w,col="green")
lines(x,w, col="green")

legend("topright", legend=c("0.70", "0.85","0.95"),
       col=c("red", "blue","green"), lty=1, cex=0.8)

title(main="Exponential cooling schedule")

Linear

x<-seq(1:20)
y<-x
z<-x
w<-x
T0<-1
y[1]<-T0
z[1]<-T0
w[1]<-T0


for(i in 2:length(x))
{
  y[i]<-y[i-1]-0.05
  
}
for(i in 2:length(x))
{
  z[i]<-z[i-1]-0.02
  
}
for(i in 2:length(x))
{
  w[i]<-w[i-1]-0.01
  
}

plot(x,y,type="o",xlab="Iterations", ylab="Temperature", col="red")
lines(lowess(x,y,f=1/15), col="red")
points(x,z,col="blue")
lines(x,z, col="blue")
points(x,w,col="green")
lines(x,w, col="green")

legend("topright", legend=c("0.05", "0.02","0.01"),
       col=c("red", "blue","green"), lty=1, cex=0.8)

title(main="Linear cooling schedule")

Cauchy

x<-seq(1:20)
y<-x

T0<-1
y[1]<-T0



for(i in 2:length(x))
{
  y[i]<-T0/(1+i)
  
}

plot(x,y,type="o",xlab="Iterations", ylab="Temperature", col="red")
lines(lowess(x,y,f=1/15), col="red")


legend("topright", legend=c("Cauchy"),
       col=c("red"), lty=1, cex=0.8)

title(main="Cauchy cooling schedule")

Boltzmann

x<-seq(1:20)
y<-x

T0<-1
y[1]<-T0



for(i in 2:length(x))
{
  y[i]<-T0/log(1+i)
  
}

plot(x,y,type="o",xlab="Iterations", ylab="Temperature", col="red")
lines(lowess(x,y,f=1/15), col="red")


legend("topright", legend=c("Boltzmann"),
       col=c("red"), lty=1, cex=0.8)

title(main="Boltzmann cooling schedule")