{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW2 - HW2 Solutions Fall 2010 Total points possible 20 1 SA...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HW2 Solutions Fall 2010 Total points possible: 20 1. SA Parameter Selection when cost function range = (MaxCost and MinCost) are known: a) (1 pt) If M incost is taken as a lower bound on Cost in the search space, and MaxCost the upper bound, assume you know MaxCost - MinCost = 100. Assuming the distribution of costs is uniformly distributed between MaxCost and Mincost , what is reasonable estimate of Tinitial if you want probability of accepting an uphill move on the first iteration Pinitial = 0.4? ¡¢£ ¤¢¥¦¥§¨©ª « ¬­ ®§¨©ª ¯ ­°±§¨©ª² ³ ´µ¶· « ¸´´¬´µ¶·²¥¥¥¥¥ ¡¢£ ¤¢¥¦¥§¨©ª « ¶·¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥¥ When P initial = 0.4 average Δ cost = 25 ¹ º»º¼º½¾¥ « ¶¿µ¶ b) (2 pt) Write down a general expression for Tinitial in terms of MaxCost, MinCost and Pinitial . If À Á « ¢®Â Ã¯ ¬­ ®§¨©ª ¯ ­°±§¨©ª² ³ ´µ¶· Ä Á ¹ º»º¼º½¾ Å Solving for T initial (i.e. when k=0) ¹ º»º¼º½¾ « ¥ ¯ ¬­ ®§¨©ª ¯ ­°±§¨©ª² ³ ´µ¶· ÆÇ À º»º¼º½¾ ¥¥¥¥¥¥¥È¥Ä É « ¸¥¥ c) (1 pt) Now write a similar expression for Tfinal , the final temperature, in terms of MaxCost , MaxCost , and Pfinal (the probability of accepting an uphill move on the final iteration). ¹ Êº»½¾ « ¥ ¯ ¡¢£ ¤¢¥¦¥§¨©ª ÆÇ À Êº»½¾ ¥¥ d) (1 pt) Suppose you have the following parameters for a simulated annealing algorithm: Tinitial = 100, maxiter = 200, beta = 1, M = 1. What should the value of the cooling parameter alpha be if you want the Probability on the final (200th) simulated annealing iteration to be 0.001? Use MaxCost – MinCost as in part a) HW2 Solutions Fall 2010...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

HW2 - HW2 Solutions Fall 2010 Total points possible 20 1 SA...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online