Brief description of simulated annealing, algorithms, concept, and numerical example

1. simulated annealing
concept, algorithms, and numerical example

2. concepts…
atom
metal
heated
atom
atom
molten
state
1. move freely
2. respect to each other
reduced at fast rate
(attain polycrystalline
state)
reduced at slow and
controlled rate (having
minimum possible
internal energy)
“process of cooling at a
slow rate is known as
annealing”

3. features of simulated annealing
final solution quality not affected by
initial guesses
design variable need not to be
positive
features
the method can be used to solve
mixed-integer, discrete, or
continuous problems
convergence not influenced by
discrete nature of functions,
constrain evaluations, and
convexity status of feasible space

4. acceptance criteria
desired effect
Escape
local minima
adverse effect
Pass global
optima

5. parameter VS results
large number of
search process maybe
HIGH temperature reduction
LOW
incomplete
too much computational
effort to convergence
faster time
reaching convergence
high
computational time
low
computational time

6. iterations VS cost function
AT INIT_TEMP
Unconditional Acceptance
COST FUNCTION, C
HILL CLIMBING
Move accepted with
probability
= e-(^C/temp)
HILL CLIMBING
HILL CLIMBING
AT FINAL_TEMP
NUMBER OF ITERATIONS

7. simulated annealing
VS
greedy algorithms
Initial position
of the ball
Simulated Annealing explores
more. Chooses this move with a
small probability (Hill Climbing)
Greedy Algorithm
gets stuck here!
Locally Optimum
Solution.
Upon a large no. of iterations,
SA converges to this solution.

8. algorithms
start
Accept or reject Xi+1
using Metropolis
criterion. Update
iteration number as
i=i+1
Set initial vector, X1,
initial temperature
and other
parameters (T,n,c)
Convergence
criteria satisfied?
Iteration i ≥ n?
Find f1=f(X1),
set iteration
number i=1
cycle number p=1
Yes
Yes
Reduce
Temperature
end
Generate new design
point Xi+1 In the
vicinity of Xi. Compute
fi+1=f(Xi+1) and ∆ f=fi+1-fi
Update number of
cycles p=p+1
Set iteration
number i=1
No

9. numerical example

10. numerical example

11. numerical example

12. numerical example

13. numerical example

14. MATLAB example

15. MATLAB optimtoolbox

16. references
Rao, S. S. (2009). Engineering Optimization Theory and Practice Fourth Edition. New Jersey: John Wiley & Sons,