3. Find a walk which solves the Travelling Salesman Problem for the following weighted graph and calculate the weight of this walk. Justify your answer. 25 C 12 36 14 13 a d 12 25 26 16 e 25
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- Consider the traveling salesman problem where he needs to pass through 7 cities. We will use a genetic algorithm to find the best solution to this problem. Therefore, explain and exemplify the process of mutation in chromosomes.A salesman visits 4 locations, A, B, C, and D. Distances between A and B; A and D; A and D; B and C; B and D; and C and D are given by 2, 3, 4, 3, 4, 2 respectively. Use an exhaustive search approach to find the best travel route for the salesman. Show all possible routes and their lengths and find the smallest. What is the efficiency of this algorithm?Q_ 1 red, 1 blue, 1 black, 1 yellow and 1 white car are all waiting at the traffic lights behind each other. In how many different ways can they be waiting if the black car and only the black car is between the white and yellow cars?
- Show that travelling salesman problem belongs to NP class?A salesman visits 4 locations, A, B, C, and D. Distances between A and B; A and D; A and D; B and C; B and D; and C and D are given by 6, 2, 5, 3, 4, 4 respectively. Use an exhaustive search approach to find the best travel route for the salesman. Show all possible routes and their lengths and find the smallest.What is the efficiency of this algorithm?If given sufficient time, do all Gradient Descent algorithms generate the same model? Explain.
- a. Write down the factorization of P(D, I, G, S, L) based on the Bayesian network.Linear regression aims to learn the parameters 7 from the training set D = {(f(),y(i)), i {(x(i),y(i)),i = 1,2,...,m} so that the hypothesis ho(x) = ēr i can predict the output y given an input vector š. Please derive the least mean squares and stochastic gradient descent update rule, that is to use gradient descent algorithm to update Ô so as to minimize the least squares cost function JO).Question 45. For what ultimate purposes may algorithms like Nelder-Mead, Newton-Raphson or gradient-descentbe used for?a) To find the minimum of a function.b) To find all zeros of a function.c) To evaluate the derivative of a function.d) To solve a generalised regression proble
- Travelling Salesman Problem Statement: Given n cities with known distances betweeneach pair, find the shortest tour that passes through all the cities exactly once before returning tothe starting city. On the following graph:Use Exhaustive Search to find the shortest path, starting from a, and returning back to a.Show all paths/tour that will be taken into consideration in this approach, compute costs for eachtour involved, and find the most optimal path/tour from your computed costs. (Hint: Optimal path:minimum cost)For what ultimate purposes may algorithms like Nelder-Mead, Newton-Raphson or gradient-descentbe used for?a) To find the minimum of a function.b) To find all zeros of a function.c) To evaluate the derivative of a function.d) To solve a generalised regression problemThe room temperature x in Fahrenheit is converted to y in Celsius through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 = ?