SamplePrelim Fall07_sols - SOLUTIONS CEE 509/CS 572/ORIE...

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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 2-5 yes no 3 13542 3-5 yes no 4 14532 4-3 yes yes 5 24531 2-1 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 3-2 21534 39 25431 38 23541 29 3-4 yes yes 24351 33 24513 32 1-3 no no 54231 31 2-5 yes no
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24351 30 3-5 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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SamplePrelim Fall07_sols - SOLUTIONS CEE 509/CS 572/ORIE...

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