## NPTEL An Introduction to Artificial Intelligence Week 4 Assignment Answers 2024

1. Which of the following is (are) drawback(s) of Hill Climbing?

- Global Maxima
- Local Maxima
- Diagonal Ridges
- Plateaus

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2. Let x be the expected number of restarts (first try is not included in the number of restarts) in Hill Climbing with Random Restarts Algorithm, if the probability of success, p = 0.23. Let y be the expected number of steps taken to return a solution, given, it takes 4 steps when it succeeds and 3 steps when it fails. What is 3x+y (return the nearest integer)?

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3. Select the INCORRECT statements –

- Local beam search (with k nodes in memory) is the same as k random-start searches in parallel.
- Simulated annealing with temperature T = 0 behaves identically to greedy hill-climbing search
- Enforced Hill Climbing performs a depth-first search from a local minima.
- In Tabu Search, we never make a currently tabu’ed step.

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4. Select the CORRECT statements –

- Genetic Algorithm has the effect of “jumping” to completely new parts of search-space, and making “non-local” moves.
- As the size of the tabu list increases to infinity, tabu search reduces to a systematic search.
- Greedy Hill Climbing with Random Restarts is asymptotically complete, whereas Random Walk is not.
- If the initial temperature in Simulated Annealing is set too small, the search can get stuck at a local optimum.

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5. We define First-Choice Hill Climbing (FCHC) as a stochastic hill-climbing algorithm that generates neighbours randomly until one is found better than the current state. When this happens, the algorithm moves to this new state and repeats.

Select the CORRECT statements:

- FCHC is similar to Simulated Annealing for large values of T.
- FCHC will always return the same solution as Greedy Hill Climbing as we always take a step in the direction of increasing slope.
- FCHC will perform better than Greedy Hill Climbing when each state has a large number of neighbours.
- FCHC combined with Tabu List does not suffer from local maximas/minimas.

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6. onsider the Hill Climbing Search algorithm for the N-Queens problem with N = 4. The image represents the start state. We want to reach a state i.e. configuration of the board with 4 queens such that no two queens attack each other. The objective function we consider is the number of pairs of queens that attack each other and we want to minimise this objective function. The successor function we consider is moving a single queen along its column by one square either directly up or directly down.

Let the objective function for the start state = x , the number of neighbours of the start state = y, the objective function of the neighbour of the start state with the lowest objective function = z, then what is the value of 2x + y + 3z ?

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7. Consider the same setup as question 6, we apply the hill climbing algorithm to minimise the objective function. The hill climbing algorithm stops when the objective function becomes 0 i.e. no two queens attack each other. To break ties b/w two neighbours with the same objective function pick the neighbour obtained by moving the queen in the lower column number (a < b < c < d) and if a tie still exists pick the neighbour obtained by moving the queen downward. The number of steps required by the hill climbing algorithm is:

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8. Assume that we have a function y = (x – 3)4 , starting at x = 4, which of the following values of the step size λ will allow gradient descent to converge to the global minimum?

- 0.005
- 0.25
- 0.5
- 0.75

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9. Consider a state space having 3 states: s1, s2 and s3. The value of each state is V(s1) = 0, V(s2) = 4, V(s3) = 2. There can be transitions from s1 to s2, s2 to s1 and s3, and s3 to s2. Starting at s1, what is the probability that we end up back at s1 after 2 steps of simulated annealing? Assume that we follow a temperature schedule of [10, 5, 1]. Next state is chosen uniformly at random whenever there are multiple possibilities.

Round answer to 3 digits after decimal point (eg, if the answer is 0.1346, return 0.135).

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10. Consider the 1-D state space shown by the image below. For which of the following start state regions using the greedy local search hill-climbing algorithm will we not reach the global maximum ?

- A
- B
- C
- D
- E
- F

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