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SOLUTIONS
CEE 509/CS 572/ORIE 533 Prelim
October 30, 2007
(Note these are the posted answers.
However, there is a version of the
exam was re worded
after the exam was taken (revised
or rev in file name)
that has better wording of the
questions.
Put your answers in your test book, show work and explain your reasoning. You enhance your
chances of getting full or partial credit by writing legibly and putting boxes around your final
answers so the people grading the exam understand what you have done.
1.
(25 points)
You are applying Tabu Search to a permutation problem.
Your decision is
the permutation of 5 numbers.
Assume that your initial starting point is 12345 and tabu
search choices are as follows:
Iteration number
Decision Selected
SWAPS
Tabu in 6
th
iter
if m=4
m=2
1
12345
2
15342
25
yes
no
3
13542
35
yes
no
4
14532
43
yes
yes
5
24531
21
yes
yes
6
????
Assume you want to minimize cost.
Assume the neighborhood is defined as all permutations
arising from a swap in location of two numbers.
Assume the tenure is also defined by which
two numbers were swapped. (i.e. if you swap 1 and 5, then all swaps involving
both
of those
number are tabu during the tenure).
Assume you are using the best aspiration criteria.
a. If you consider swaps of any two numbers as the neighborhood, how many members of the
neighborhood are there?
b.
Assume the
best solution found so far is 28
. Below is listed the cost values of
the best 8 neighbors as well as the solution in the 5
th
iteration.
Permutation
Cost
swaps from 24531
Tabu tenure remain
Tabu tenure
m
=
4
m
=
2
24531
40
(solution in 5
th
iteration)
(best eight neighbors below)
34521
34
32
21534
39
25431
38
23541
29
34
yes
yes
24351
33
24513
32
13
no
no
54231
31
25
yes
no
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View Full Document24351
30
35
yes
no
Continuation of problem 1:
Given the costs for part b.), what is the value of the permutation in the 6
th
iteration of Tabu
search if the tenure is 4?
What is the value of the permutation in the 6
th
iteration of Tabu
search if the tenure is 2?
(For each case give the permutation and its cost.)
c.
Assume that everything is the same as in part a and b,
except
that the
best solution
found so far is 34.
What is the permutation in the
6
th
iteration
of Tabu search if the tenure is 4?
What is the
value of the permutation in the next iteration of Tabu search if the tenure is 2? (For each
case give the permutation and its cost.)
Solution a
. By enumeration, there are 10 possible swaps: (1,2), (1,3), (1,4), (1,5), (2,3), (2,4),
(2,5), (3,4), (3,5), and (4,5).
Note that (1,2) and (2,1) are the same swap, so the number of
swaps can be computed as follows: 10 = (5*4)/2 = 10.
Solution b.
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 Fall '11
 Shoemaker

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