# Introduction to Simulated Annealing - PowerPoint

Document Sample

```					   Introduction to
Simulated Annealing
gw
Inspiration: Metallurgy
 Solid is heated to melting point
– High-energy, high-entropy state
– Removes defects/irregularities

 Temp is very slowly reduced
– Recrystallization occurs (regular structure)
– New internal state of diffused atoms
– Fast cooling induces fragile structure
Simulated Annealing
 Method of sampling search space
– State: feasible solution
– High energy: many solutions still possible
– Cooling: perform local search
– Ground state: optimal solution
Basic Algorithm
Create initial solution

Modify to create
new solution

Evaluate solutions

Stochastically select
a solution

Reduce temperature
Acceptance Criteria
1
P          eval( current)  eval( new)
1 e               T

As a function of Temp                  As a function of evaluation difference

T         e-10/T         P             Δ(eval)       eΔ(eval)/10        P
1010     0.99999         0.50             50          148.41           0.01
100      0.90484         0.52             10            2.72           0.27
10      0.36788         0.73               0           1.00           0.50
1       0.00004         0.99             -10           0.37           0.73
-50           0.01           0.99
Cooling Schedule

 Fast            Slow

http://en.wikipedia.org/wiki/Simulated_annealing
Acceptance Characteristics
 At high temperatures, more likely to accept
“worse” solutions
 At low evaluation differences, more likely to accept
“worse” solution
 Result  wide search of solution space

 Moves towards a region of the search space
containing good solutions
 Moves towards low-energy regions
 Moves downhill (gradient descent)
Parameters
 Initial solution: random
 New solution: select - Gaussian distribution
 Temperature schedule
– Initial
– Decay function: Ti+1 = cTi
– Final
 #Iterations at temp:
– Proportional to neighborhood size
Usage
 Search heuristic
– Global optima in large solution space
 Best for discrete-valued solutions
– Traveling Salesman
– VLSI circuit design
References / Resources
 Optimization by Simulated Annealing
Kirkpatrick, S.; Gelatt, C. D.; and Vecchi, M. P.
Science 220:671-680, 1983.

 Simulated annealing: a proof of convergence
Granville, V., Krivanek, M., and Rasson, J.-P.
IEEE Trans. Pattern Analysis and Machine Intelligence, 16:652-656, 1994.

Simulated Annealing applet for Traveling Salesman problem:
http://www.heatonresearch.com/articles/64/page1.html

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 132 posted: 7/9/2010 language: English pages: 10