Simulated annealing is a combination of Optimizations technique based on random evaluation of the objective function in such a way that transition out of local minimum are possible.

1. OPTIMIZATION-
SIMULATED ANNEALING
PREASENTED BY: ABHISHEK PANDEY
M.Tech (HYDRAULICS)

2. CONTENTS
 INTRODUCTION TO OPTIMIZATION
 WHAT IS SIMULLATED ANNEALING ?
 MOTIVATION
 THE PROCESS
 Ball on terrain example – Simulated Annealing
 APPLICATION
 CONCLUSION
 REFERENCES

3. INTRODUCTION TO
OPTIMIZATION
 Finding an alternative with the most cost effective or highest achievable performance under the
given constraints, by maximizing desired factors and minimizing undesired ones.
 It is the selection of a best element (with regard to some criterion) from some set of available
alternatives.
 Practice of optimization is restricted by the lack of full information, and the lack of time to
evaluate what information is available (see bounded reality for details). In computer simulation
(modeling) of business problems, optimization is achieved usually by using linear programming
techniques of operations research.

4. WHAT IS SIMULLATED ANNEALING ?
Simulated annealing
Simulated annealing is a combination of Optimizations technique based on random
evaluation of the objective function in such a way that transition out of local
minimum are possible.
The name of the method is derived from simulations of thermal annealing of
critically heated solids. Oslo and control cooling of a heated solid ensure proper
solidification with highly ordered, crystalline state that corresponds to the lowest
internal energy. Cooling, on the other hand causes defects inside the material

5. Motivation
 The connection between this algorithm and mathematical minimization was first
noted by Pincus.
 He proposed that it forms the basis of an optimization technique for
combinatorial (and other) problems.
 SA's major advantage over other methods is an ability to avoid becoming
trapped at local minima.
 The algorithm employs a random search which not only accepts changes that
decrease objective function f, but also some changes that increase it.

6. THE PROCESS
Generate a random solution
Assess its cost
Find a neighboring solution
Assess its cost!

9. Ball on terrain example – Simulated
Annealing
The ball is initially placed at a random position on the terrain. From the current
position, the ball should be fired such that it can only move one step left or
right.What algorithm should we follow for the ball to finally settle at the lowest point
on the terrain?

10. Ball on terrain example – SA

11. APPLICATION OF SIMULATED ANEALING
 The wide utilization of heat exchangers in industrial processes, their cost
minimization is an important target for both designers and users.
 Traditional design approaches are based on iterative procedures which gradually
change the design and geometric parameters to satisfy a given heat duty and
constraints.
 The present study explores the use of non-traditional optimization technique
called simulated annealing.
 The SA approach is able to reduce the total cost of the heat exchanger

12. CONCLUSION
 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
 SA can leave an optimal solution and not find it again (so try to remember the
best solution found so far)
 Proven to find the optimum under certain conditions

13. REFERENCES
 Aarst, “Simulated annealing and Boltzman machines”, Wiley, 1989.
 Duda Hart Stork, “Pattern Classification”, Wiley Interscience, 2001.
 Otten, “The Annealing Algorithm”, Kluwer Academic Publishers, 1989.
 Sherwani, “Algorithms for VLSI Physical Design Automation”, Kluwer Academic
Publishers, 1999