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A. Question No 7, (2004/2005)

Using cutting plane method to solve the ollo!ing

"a#imise (#) $ #2

4.5 #% & #22 ' %

#%, #2  0

*. Question No %+ o uestion pape- dated %5.%2.2007

olve the ollo!ing p-olem using cutting plane method minimie

1%2%1)( +2%

22

2

2

%   −−−−++=   x x x x x x x  f    

su3ect #% & 2#2 & #+ ' 4#%  , 0, i $ %, 2, +

tae the sta-ting point as

=0

0

0

% X  

. Question No %+ o uestion pape- dated 22.%%.200

Using cutting plane method minimie (6) $ #%2 & #2

2  1#% 8 #2 & %0 u3ect to

4#%2 & #2

2 ' 1

+#% & 5#2 ' %5#i 0, i $ %, 2

9ith the sta-ting point 6% $ :%%;<, complete one step o the p-ocess.

=. Question No %+ o uestion pape- dated %5.05.200>o- an optimiation p-olem, the ollo!ing const-aint set is given?

g(6) $ #%2 & 4#2

2  4 @ 0, 0 ' #% ' +

<he cu--ent point is #(t) $ (%, 0.5)<. 9-ite the gene-al p-ocedu-e to solve the p-olem usingcutting plane method and const-uct the cutting plane at #(t).

. Question No %+ o uestion pape- dated %2.%2.200onside- the NBC p-olem ma#imie (#) $ #% & #2

2 su3ect to

25#%2 8#2

2  0

#%2 & #2 '

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0 ' #% ' 5, 0 ' #2 ' %0,

(a) set up and solve the i-st su p-olem o- the cutting plane method.

() calculate the cutting plane at the -esulting point.

>. Question No %4 o uestion pape- dated %5.%2.2007"inimie su3ect to

(#) $ (#% 8 %0)+ & (#2 8 20)+ 

g%(#) $ #% & %+ ' 0

g2(#) $ (#% 8 5)2 8 (#2 8 5)2 & %00 ' 0g+(#) $ (#% 8 1)2 & (#2 8 5)2 8 2.% ' 0

g4(#) $ #2 ≤ 0.

ta-ting o-m the point

=

10.(

+5.%4

% X   use inte-io- penaltD unction method.

E. Question No %4 o uestion pape- dated %2.%2.200

"inimise

(#) $ #%2 & #2

2 & 1#% 8 #2 & %0 su3ect to4#% & #2

2 ' %1,

+#% & 5#2 ' %5,

#i  0, i $ %,2*D using the ollo!ing method !ith sta-ting point $ F%, %G

(a) Hnte-io- penaltD unction method

() #te-io- penaltD unction method

I. Question No %5 o uestion pape- dated %5.%5.200ApplD simple genetic algo-ithm to solve the ollo!ing NBC p-olem.

"in (#% 8 %.5)2 & (#2 8 4)2

<

4#% & #22 % ' 0

2#%#22 8 % 0

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0 ' #%, #2 ' 4

Accu-acD levels -eui-ed o- the va-iales #% and #2  $ 2 decimal places.

(a) >o-mula the const-ained p-olem using -acet ope-ato- penaltD unction.() Io! manD its -eui-ed o- coding the va-ialesJ

(c) 9-ite do!n the itness unction !hich Dou !ould e using in c-oss ove-J

(d) >-om -andomlD gene-ated initial population select t!o ch-omosomes and do the c-ossove- 

(e) Ce-o-m the it!ise mutation o- the osp-ingKs and evaluate the itnessJ

H. Question No %5 o uestion pape- dated %5.%2.2007

"inimie the ollo!ing p-olem using the simulated annealing method "inimie22

2%

2

2

2

%2%   )7()%%(),(   −++−+=   x x x x x x  f  

L. Question No %1 o uestion pape- dated %5.%5.200

Use the simulated annealing algo-ithm to solve the ollo!ing unconst-ained p-olem

"in (#) $ #2 & 54/#

Ce-o-m t!o ite-ations !ith the ollo!ing assumptions?Hnitial point #0 $ %, € $ 0.00%

Hnitial <empe-atu-e < $ +0

 No o ite-ation steps n $ % (neigho-ing points)

M. Question No %1 o uestion pape- dated %2.%2.200

olve the ma#imiation p-olem (#) $2# i # ' 0.+%.5 8 +# i 0.+ # ' 0.5

5# 8 2.5 i 0.5 # ' 0.

2.4 8 2# i # @ 0.

Using simulated annealing !ith initial point #(0) $ 0.2, a standa-d no-mal p-oailitD

dist-iution is used to c-eate a neigho-ing point(a) alculate the p-oailitD o c-eating a point in the gloal asin

() H the tempe-atu-e < $ %0 is used, !hat is the ove-all p-oailitD o accepting a

 point in the gloal asin.