Simulated annealing

1. Simulated Annealing Example
Simulated Annealing

2. Simulated Annealing Example
3)sin(*3)*2cos(*2)(  xxxf
Minimizing the below function
using
Simulated Annealing Algorithm:

3. Simulated Annealing Example
Step 1: Initialize – Start with a random initial placement. Initialize
a very high “temperature”.
Step 2: Move – Perturb the placement through a defined move.
Step 3: Calculate score – calculate the change in the score due to
the move made.
Step 4: Choose – Depending on the change in score, accept or
reject the move.
Step 5: Update and repeat– Update the temperature value by
lowering the temperature. Go back to Step 2.
The process is done until “Freezing Point” is reached.Freezing Point
Step 1
Step 5
Step 3
Step 4
Step 2
Algorithm

4. curval=rand*5;
curcost=minfcn(curval);
T=1000;
for i=1:1:100
newval=rand*5;
newcost=minfcn(newval);
if((newcost-curcost)<=0)
curval=newval;
curcost=newcost;
else
if(exp((curcost-newcost)/T)>rand)
curval=newval;
curcost=minfcn(curval);
end
end
T=T/log(100);
RandomBoltzmanNewCostNewValCurCostCurValT
-1.8 3.24.5 4.8 1.0 0.3
4.83.2
1000
500
False
True Boltzman
X:4.5
Y:-1.8
X:3.2
Y:4.8
CureVal
CureCost
  
3)5.4sin(*3)5.4*2cos(*28.1
)(

xxxf
  
3)2.3sin(*3)2.3*2cos(*28.4
)(

xxxf
Simulated Annealing Example

5. curval=rand*5;
curcost=minfcn(curval);
T=1000;
for i=1:1:100
newval=rand*5;
newcost=minfcn(newval);
if((newcost-curcost)<=0)
curval=newval;
curcost=newcost;
else
if(exp((curcost-newcost)/T)>rand)
curval=newval;
curcost=minfcn(curval);
end
end
T=T/log(100);
RandomBoltzmanNewCostNewValCurCostCurValT
-1.8 3.24.5 4.8 1.0 0.3
4.8 0.63.2 5.4
1000
500
  
3)6.0sin(*3)6.0*2cos(*24.5
)(

xxxf
False
Boltzman
1.0 0.9
True
0.6 5.4250
X:3.2
Y:4.8
X:0.6
Y:5.4
Simulated Annealing Example
CureVal
CureCost

6. curval=rand*5;
curcost=minfcn(curval);
T=1000;
for i=1:1:100
newval=rand*5;
newcost=minfcn(newval);
if((newcost-curcost)<=0)
curval=newval;
curcost=newcost;
else
if(exp((curcost-newcost)/T)>rand)
curval=newval;
curcost=minfcn(curval);
end
end
T=T/log(100);
RandomBoltzmanNewCostNewValCurCostCurValT
3.5 1.53.5 4.0 1.0 0.8
4.0 3.01.5 5.3
0.5 5.5 0.2
5.50.5
1000
500
125
  
3)5.0sin(*3)5.0*2cos(*25.5
)(

xxxf
False
0.99 0.3
6.0 5.4250
X:0.5
Y:5.5
X:0.6
Y:5.4
1.0
BoltzmanTrue
Simulated Annealing Example
CureVal
CureCost

7. curval=rand*5;
curcost=minfcn(curval);
T=1000;
for i=1:1:100
newval=rand*5;
newcost=minfcn(newval);
if((newcost-curcost)<=0)
curval=newval;
curcost=newcost;
else
if(exp((curcost-newcost)/T)>rand)
curval=newval;
curcost=minfcn(curval);
end
end
T=T/log(100);
RandomBoltzmanNewCostNewValCurCostCurValT
3.5 1.53.5 4.0 1.0 0.8
2.7 5.5
1000
500
250
125
62.5
  
3)7.2sin(*3)7.2*2cos(*25.5
)(

xxxf
True
4.0 3.01.5 5.3
0.5 5.5
5.50.5
0.99 0.3
3.0 5.3
X:0.5
Y:5.5
X:2.7
Y:5.5
1.0 0.2
2.7 5.5
Simulated Annealing Example
CureVal
CureCost

8. Simulated Annealing Example
curval=rand*5;
curcost=minfcn(curval);
T=1000;
for i=1:1:100
newval=rand*5;
newcost=minfcn(newval);
if((newcost-curcost)<=0)
curval=newval;
curcost=newcost;
else
if(exp((curcost-newcost)/T)>rand)
curval=newval;
curcost=minfcn(curval);
end
end
T=T/log(100);
RandomBoltzmanNewCostNewValCurCostCurValT
-1.8 3.24.5 4.8 1.0 0.3
4.8 0.63.2 5.4
0.5 5.5 0.2
5.50.5
0.762.5 5.3
5.30.7
1000
500
125
31.25
  
3)7.0sin(*3)7.0*2cos(*23.5
)(

xxxf
True
1.0 0.9
0.6 5.4250
2.7 5.5
1.0
2.7 5.5
X:2.7
Y:5.5X:0.7
Y:5.3
CureVal
CureCost

9. Simulated Annealing Example
Software engineering, MSC level
Computational Intelligence
RandomBoltzmanNewCostNewValCurCostCurValT
62.5
1000
500
125
31.25
250
15.625
7.813
3.906
1.953
0.977
0.489
0.245
0.123
0.0615
4.5 -1.8 3.2 4.8 1.0 0.3
3.2 4.8 0.6 5.4 1.0 0.9
0.6 5.4 0.5 5.5 1.0 0.2
0.5 5.5 2.7 5.5
2.7 5.5 0.7 5.3
0.7 5.3 4.1 -1.1
4.1 -1.1 4.5 -1.8
3.1 5.14.5 -1.8 0.6 0.09
1.0 4.6 2.7 5.5 0.8 0.9
4.8 -1.9 0.7 5.3 0.09 0.7
4.7 -1.9 3.2 4.8 0.03 0.03
3.2 4.8 4.2 -0.6
4.2 -0.6 4.6 -1.9 14.2 0.6
4.6 -1.9 3.7 2.2 0.000000053 0.7
4.7 -1.9 3.8 0.000000000001 0.7
4.8 -2.0
1.6
Just like as previous steps ,now
we follow the instruction till the
freezing point is reached:

10. Simulated Annealing Example
X:4.5
Y:-1.8
X:3.2
Y:4.8
X:0.6
Y:5.4
X:0.5
Y:5.5
X:2.7
Y:5.5
X:0.7
Y:5.3
1
4
3
6
5
2
CureVal
CureCost
Visual Outline
X:4.1
Y:-1.1
7
X:4.5
Y:-18
8
X:1.0
Y:4.6
9
X:4.8
Y:-1.9
10
X:4.7
Y:-1.9
11
12
X:3.2
Y:4.8
X:4.2
Y:-0.6
13 X:4.6
Y:-1.9
14
X:4.7
Y:-1.9
15
X:4.8
Y:-2
16
Freezing
point