ECE457A, Spring 2012 Cooperative and Adaptive Algorithms

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University of Waterloo Department of Electrical and Computer Enginneing

Midterm Exam June 7th, 2012

5:30-7:00 pm Please attempt all 4 questions and write your answers in clear and legible writing. Question 1. [25%] Search Methods. (a) [13%] The major four criteria for evaluating search methods are: time complexity, space complexity, optimality, and completeness. Using one or more of these criteria, attempt to justify the following statements:

ECE457A, Spring 2012 Cooperative and Adaptive Algorithms

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(c) [7%] Briefly describe how simulated annealing works. Explain how the algorithm behaves at very high temperatures, and how it behaves at very low temperatures.

Question 2:

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a. [15%] Consider the following game tree in which the evaluation function values are shown below each leaf node. Assume that the root node corresponds to the minimizing player. Assume that the search always visits children left-to-right.

(i) [5%] Compute the backed-up values computed by the minimax algorithm. Show your answer by writing values at the appropriate nodes in the above tree. See figure (ii) [10%] Which nodes will not be examined by the alpha-beta pruning algorithm? See figure 2.b.[10%] Consider the following partial search tree, where edges are labeled with actual costs of the associated action, and each node is labeled

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with its heuristic evaluation. Which node will be expanded next by each of the following search methods?

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Question 3. [25%] a. [10%] Name and describe the main features/elements/steps of Genetic Algorithms (GA).

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b. [15%] Suppose a genetic algorithm uses chromosomes of the form x = abcdefgh with a fixed length of eight genes. Each gene can be any digit between 0 and 9. Let the fitness of individual x be calculated as: f(x) = (a + b) − (c + d) + (e + f) − (g + h) , and let the initial population consist of four individuals with the following chromosomes:

x1 = 6 5 4 1 3 5 3 2

x2 = 8 7 1 2 6 6 0 1

x3 = 2 3 9 2 1 2 8 5

x4 = 4 1 8 5 2 0 9 4

ECE457A, Spring 2012 Cooperative and Adaptive Algorithms

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Question 4 [25%] a. [10%] Explain the search strategy of Tabu Search

b. [15%] Show how would you use Tabu search to compute the minimum spanning tree (MST) of the following graph (MST is a tree that links all nodes of the graph with minimum total edge cost).

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