1. Simulated Annealing
Bladimir Lenis Gil
University of Puerto Rico, Mayaguez Campus
Physics Graduate Seminar
Nov. 18 2010
Dr. Angel Lopez
Professor

2. Simulated Annealing
Contents
1. Introduction
2. S.A. Cooling Schedule
3. Exponential Cooling
4. Problem Specific Decisions
5. S.A. Block Diagram
6. Sample Problems by S.A.
7. Summary

3. Introduction
• Others names:
– MonteCarlo Annealing
– Statistical Cooling
– Probabilistic Hill Climbing
– Stochastic Relaxation
– Probabilistic Exchange Algorithm
• Motivated by the physical annealing process

4. Introduction
• Material is heat and slowly cooled into a
uniform structure
• Simulated annealing mimic this process
• The first S.A. algorithm was developed in 1953
(Metropolis)

5. S.A. Cooling Schedule
• Starting Temperature
• Final Temperature
• Temperature Decrement
• Iterations at each temperature

6. Exponential Cooling
• Can also do
linear or step-
wise cooling
• But exponential
cooling often
work best.

7. Problem Specific Decisions
• Cost Function
• Neighbourhood
• Performance

8. S.A. Block Diagram

9. Sample Problems by S.A.
• Matlab “Peaks” Function
• “Peaks” Convergence
• Traveling Salesman Problem
• Structural Optimization
• Networks and Graphs Problems
• Telescope Array Optimization

10. Summary
• SA is a general solution method that is easily
applicable to a large number of problems
• Generally the quality of the results of SA is
good, although it can take a lot of time
• Results are generally not reproducible:
another run can give a different result
• Proven to find the optimum under certain
conditions; one of these conditions is that you
must run forever

11. Thanks!!!