Engineering Optimization: Theory and Practice, Fourth Edition

706 Modern Methods of Optimization

Start with initial vector, X 1 ,

initial temperature and other parameters

(T,n,c)

Findf 1 = f(X 1 ),

Set iteration number i = 1

and cycle number p = 1

Accept or reject Xi+ 1 using

Metropolis criterion

Update iteration number

asi = i + 1

Update the number of

cycles as p = p + 1

Set iteration number i = 1

Reduce temperature.

Stop

Convergence criteria

satisfied?

Is number of

Iterationsi≥n?

Generate new design point Xi+ 1

In the vicinity of Xi. Compute

fi+ 1 = f(Xi+ 1 ) and Df = fi+ 1 – fi

No

Yes

Yes

No

Figure 13.2 Simulated annealing procedure.

Example 13.3 Find the minimum of the following function using simulated annealing:

f (X)= 500 − 20 x 1 − 62 x 2 − 4 x 1 x 2 + 4 x 12 + 3 x 22

SOLUTION We follow the procedure indicated in the flowchart ofFig. 13.2.