Homework7-solutions

Homework7-solutions - Neural Networks, CAP 6615 Spring 2011...

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Neural Networks, CAP 6615 Spring 2011 Homework 7, Due 18 April 2011 1. (Haykin Problem 11.3) Consider the Markov chain depicted in Figure P11.3, which is reducible. Identify the classes of states contained in this state transition diagram. Figure P11.3 The classes of this Markov chain are {x 1 } and {x 2 , x 3 } 2. (Haykin Problem 11.4) Calculate the steady-state probabilities of the Markov chain shown in Fig. P11.4 Figure P11.4 The stochastic matrix for this Markov chain is P = [ 3 / 4 1 / 4 0 0 2 / 3 1 / 3 1 / 4 0 3 / 4 ] yielding equations π i i ( 3 / 4 )+π 2 ( 0 )+π 3 ( 1 / 4 ) π 2 1 ( 1 / 4 )+π 2 ( 2 / 3 )+π 3 ( 0 ) π 3 1 ( 0 )+π 2 ( 1 / 3 )+π 3 ( 3 / 4 ) thus, π 1 3 , π 2 1 ( 3 / 4 ) . We also have π 1 2 3 = 1 by definition. Thus, π 1 1 ( 3 / 4 )+π 1 = 1 so π 1 3 = 4 / 11 and π 2 = 3 / 11 . 1/3 2/3 3/4 1/4 1/2 1/2 x 1 x 2 x 3 1/4 1/4 1/3 3/4 3/4 2/3 x 1 x 2 x 3
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Neural Networks, CAP 6615 Spring 2011 Homework 7, Due 18 April 2011 3. (Haykin Problem 11.7) In this problem, we consider the use of simulated annealing for solving the traveling-salesman problem (TSP). You are given the following: N cities the distance between each pair of cities, d a tour represented by a closed path visiting each city once, and only once. The objective is to find a tour (i.e., permutation of the order in which the cities are visited) that is of minimal total length L . In this problem, the different possible tours are the configurations, and the total length of a tour is the cost function to be minimized. (a) Devise an iterative method of generating valid configurations.
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Homework7-solutions - Neural Networks, CAP 6615 Spring 2011...

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