AI: Search Methods for Problem Solving · Quiz 2 · May 2024

The figure shows a map with several locations on a grid where each tile is 1x1 in size. The locations are at grid points and are connected by two way edges (roads), where each edge has a cost that is the same in both directions. Observe that the edge costs are not necessarily proportional to the coordinate based distance estimates. The start node is S and the goal node is G, the MoveGen function returns neighbours in alphabetical order. Use Manhattan distance as the heuristic function. **Tie-breaker:** when several nodes have the same best cost, use alphabetical order to break ties.

Emulate A*, WA* and Branch-and-Bound on the given map, then answer the subquestions.

In the map, S is the first node to be refined, determine the next 3 nodes (from the 2nd to 4th node) refined by A*. Enter the nodes in the order they are refined. Enter a comma separated list of node labels. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: W,X,Y,Z

The figure shows a map with several locations on a grid where each tile is 1x1 in size. The locations are at grid points and are connected by two way edges (roads), where each edge has a cost that is the same in both directions. Observe that the edge costs are not necessarily proportional to the coordinate based distance estimates. The start node is S and the goal node is G, the MoveGen function returns neighbours in alphabetical order. Use Manhattan distance as the heuristic function. **Tie-breaker:** when several nodes have the same best cost, use alphabetical order to break ties.

Emulate A*, WA* and Branch-and-Bound on the given map, then answer the subquestions.

For the 3 nodes from the 2nd to 4th node refined by A*, list the f-values of those nodes as a comma separated list. Enter a comma separated list of natural numbers. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 2,7,1,8

The figure shows a map with several locations on a grid where each tile is 1x1 in size. The locations are at grid points and are connected by two way edges (roads), where each edge has a cost that is the same in both directions. Observe that the edge costs are not necessarily proportional to the coordinate based distance estimates. The start node is S and the goal node is G, the MoveGen function returns neighbours in alphabetical order. Use Manhattan distance as the heuristic function. **Tie-breaker:** when several nodes have the same best cost, use alphabetical order to break ties.

Emulate A*, WA* and Branch-and-Bound on the given map, then answer the subquestions.

For the 3 nodes from the 2nd to 4th node refined by A*, list the parent nodes assigned by A*. Enter a comma separated list of parent node labels. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: W,X,Y,Z

The figure shows a map with several locations on a grid where each tile is 1x1 in size. The locations are at grid points and are connected by two way edges (roads), where each edge has a cost that is the same in both directions. Observe that the edge costs are not necessarily proportional to the coordinate based distance estimates. The start node is S and the goal node is G, the MoveGen function returns neighbours in alphabetical order. Use Manhattan distance as the heuristic function. **Tie-breaker:** when several nodes have the same best cost, use alphabetical order to break ties.

Emulate A*, WA* and Branch-and-Bound on the given map, then answer the subquestions.

What is the final path found by A*? Enter the path as a comma separated list. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: S,X,Y,G

The figure shows a map with several locations on a grid where each tile is 1x1 in size. The locations are at grid points and are connected by two way edges (roads), where each edge has a cost that is the same in both directions. Observe that the edge costs are not necessarily proportional to the coordinate based distance estimates. The start node is S and the goal node is G, the MoveGen function returns neighbours in alphabetical order. Use Manhattan distance as the heuristic function. **Tie-breaker:** when several nodes have the same best cost, use alphabetical order to break ties.

Emulate A*, WA* and Branch-and-Bound on the given map, then answer the subquestions.

For w=2, what is the final path found by WA* algorithm? Enter the path as a comma separated list. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: S,X,Y,Z,G

The figure shows a map with several locations on a grid where each tile is 1x1 in size. The locations are at grid points and are connected by two way edges (roads), where each edge has a cost that is the same in both directions. Observe that the edge costs are not necessarily proportional to the coordinate based distance estimates. The start node is S and the goal node is G, the MoveGen function returns neighbours in alphabetical order. Use Manhattan distance as the heuristic function. **Tie-breaker:** when several nodes have the same best cost, use alphabetical order to break ties.

Emulate A*, WA* and Branch-and-Bound on the given map, then answer the subquestions.

What is the cost of the path found by Branch-and-Bound algorithm? Enter a natural number. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 42

The figure shows a map with several locations on a grid where each tile is 1x1 in size. The locations are at grid points and are connected by two way edges (roads), where each edge has a cost that is the same in both directions. Observe that the edge costs are not necessarily proportional to the coordinate based distance estimates. The start node is S and the goal node is G, the MoveGen function returns neighbours in alphabetical order. Use Manhattan distance as the heuristic function. **Tie-breaker:** when several nodes have the same best cost, use alphabetical order to break ties.

Emulate A*, WA* and Branch-and-Bound on the given map, then answer the subquestions.

Is the heuristic admissible in the given map?

The distance matrix for 6 cities are provided below. For each city the distances to other cities are listed in ascending order. For example, the distance from A to D is 42, and from A to F is 48, and so on.

Solve the sub-questions using the TSP Branch-and-Bound algorithm. **Attention:** Infer as much as possible (and as early as possible) about the permanent segments in the partial solutions. A segment is a two-way edge between two cities.

What is the lower bound on the cost of the tours (S0) as per the TSP BnB algorithm discussed in class? Enter a natural number. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 17

The distance matrix for 6 cities are provided below. For each city the distances to other cities are listed in ascending order. For example, the distance from A to D is 42, and from A to F is 48, and so on.

Solve the sub-questions using the TSP Branch-and-Bound algorithm. **Attention:** Infer as much as possible (and as early as possible) about the permanent segments in the partial solutions. A segment is a two-way edge between two cities.

Infer all the permanently included segments in the node (S0,AD,~AF,EF,CD,~AE) in the TSP BnB search tree. Enter the total number of permanently included segments in the text box. Enter a natural number. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 17

The distance matrix for 6 cities are provided below. For each city the distances to other cities are listed in ascending order. For example, the distance from A to D is 42, and from A to F is 48, and so on.

Solve the sub-questions using the TSP Branch-and-Bound algorithm. **Attention:** Infer as much as possible (and as early as possible) about the permanent segments in the partial solutions. A segment is a two-way edge between two cities.

Infer all the permanently excluded segments in the node (S0,AD,~AF,EF,CD,~AE) in the TSP BnB search tree. Enter the total number of permanently excluded segments in the text box. Enter a natural number. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 17

The distance matrix for 6 cities are provided below. For each city the distances to other cities are listed in ascending order. For example, the distance from A to D is 42, and from A to F is 48, and so on.

Solve the sub-questions using the TSP Branch-and-Bound algorithm. **Attention:** Infer as much as possible (and as early as possible) about the permanent segments in the partial solutions. A segment is a two-way edge between two cities.

How many tours are represented by the node (S0,AD,~AF,EF,CD,~AE) in the TSP BnB search tree? Enter a natural number. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 17

The distance matrix for 6 cities are provided below. For each city the distances to other cities are listed in ascending order. For example, the distance from A to D is 42, and from A to F is 48, and so on.

Solve the sub-questions using the TSP Branch-and-Bound algorithm. **Attention:** Infer as much as possible (and as early as possible) about the permanent segments in the partial solutions. A segment is a two-way edge between two cities.

What is the cost of the node (S0,AD,~AF,EF,CD,~AE) in the TSP BnB search tree? Enter a natural number. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 17.3

The figure shows a game tree with evaluations W (win), D (draw) and L (loss) from Max's perspective. The horizon nodes carry evals (W/D/L) and node labels (1 to 16).

Based on the above data, answer the given subquestions.

What is the outcome (W, D or L) of the game when both players play perfectly? NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: X

The figure shows a game tree with evaluations W (win), D (draw) and L (loss) from Max's perspective. The horizon nodes carry evals (W/D/L) and node labels (1 to 16).

Based on the above data, answer the given subquestions.

Change the value of only one horizon node such that the outcome of the game changes. Which horizon node will you change and what will be its new value? Enter the label of the horizon node and the new value as a comma separated list. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 16,X

The figure shows a game tree with evaluations at the horizon from Max's perspective. The horizon nodes carry evals (numbers) and node labels (A to P).

Based on the above data, answer the given subquestions.

List the horizon nodes in the best strategy. Enter the node labels. Enter the node labels as a comma separated list in ASCENDING order. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: X,Y,Z

The figure shows a game tree with evaluations at the horizon from Max's perspective. The horizon nodes carry evals (numbers) and node labels (A to P).

Based on the above data, answer the given subquestions.

List the horizon nodes pruned by Alpha-Beta algorithm. Enter the node labels as a comma separated list in ASCENDING order. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: X,Y,Z

The figure shows a game tree with evaluations at the horizon from Max's perspective. The horizon nodes carry evals (numbers) and node labels (A to P).

Based on the above data, answer the given subquestions.

List the horizon nodes in the initial cluster formed by SSS* algorithm. Enter the node labels as a comma separated list in ASCENDING order. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: X,Y,Z

The figure shows a game tree with evaluations at the horizon from Max's perspective. The horizon nodes carry evals (numbers) and node labels (A to P).

Based on the above data, answer the given subquestions.

List the horizon nodes assigned SOLVED status by the SSS* algorithm. Enter the node labels as a comma separated list in ASCENDING order. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: X,Y,Z

The domain description of a blocks-world with a single one-armed robot is provided below. **Note:** this is the same domain description used in the weekly assignments.

**Tie-breaker:** When actions are chosen non-deterministically, choose actions that lead to a plan. Throw away the actions that lead to deadends and cycles. **Tie-breaker:** Treat the goal description, preconditions and effects as lists that are accessed from left to right. When the elements in a list are pushed one by one to a stack, the last element in the list will be at the top of the stack. It has the effect of reversing the list. A planning problem is given below, find a plan using the operators and predicates defined in the blocks-world domain.

Based on the above data, answer the given subquestions.

What is the length of the optimal plan? Enter the number of actions in the optimal plan. NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS. Answer format: 42

The domain description of a blocks-world with a single one-armed robot is provided below. **Note:** this is the same domain description used in the weekly assignments.

**Tie-breaker:** When actions are chosen non-deterministically, choose actions that lead to a plan. Throw away the actions that lead to deadends and cycles. **Tie-breaker:** Treat the goal description, preconditions and effects as lists that are accessed from left to right. When the elements in a list are pushed one by one to a stack, the last element in the list will be at the top of the stack. It has the effect of reversing the list. A planning problem is given below, find a plan using the operators and predicates defined in the blocks-world domain.

Based on the above data, answer the given subquestions.

Which of the following are **applicable** actions in the start state for the given planning problem?

The domain description of a blocks-world with a single one-armed robot is provided below. **Note:** this is the same domain description used in the weekly assignments.

**Tie-breaker:** When actions are chosen non-deterministically, choose actions that lead to a plan. Throw away the actions that lead to deadends and cycles. **Tie-breaker:** Treat the goal description, preconditions and effects as lists that are accessed from left to right. When the elements in a list are pushed one by one to a stack, the last element in the list will be at the top of the stack. It has the effect of reversing the list. A planning problem is given below, find a plan using the operators and predicates defined in the blocks-world domain.

Based on the above data, answer the given subquestions.

Which of the following are **relevant** actions for the goal description in the given planning problem?

The domain description of a blocks-world with a single one-armed robot is provided below. **Note:** this is the same domain description used in the weekly assignments.

**Tie-breaker:** When actions are chosen non-deterministically, choose actions that lead to a plan. Throw away the actions that lead to deadends and cycles. **Tie-breaker:** Treat the goal description, preconditions and effects as lists that are accessed from left to right. When the elements in a list are pushed one by one to a stack, the last element in the list will be at the top of the stack. It has the effect of reversing the list. A planning problem is given below, find a plan using the operators and predicates defined in the blocks-world domain.

Based on the above data, answer the given subquestions.

For the subgoal ordering given in the goal description (and using the given tie breaking rules) which of the following can be pushed as the first four elements onto the stack by the Goal Stack Planning algorithm? In the representation below, the bottom of the stack is on the right end, marked by BOTTOM.

The domain description of a blocks-world with a single one-armed robot is provided below. **Note:** this is the same domain description used in the weekly assignments.

**Tie-breaker:** When actions are chosen non-deterministically, choose actions that lead to a plan. Throw away the actions that lead to deadends and cycles. **Tie-breaker:** Treat the goal description, preconditions and effects as lists that are accessed from left to right. When the elements in a list are pushed one by one to a stack, the last element in the list will be at the top of the stack. It has the effect of reversing the list. A planning problem is given below, find a plan using the operators and predicates defined in the blocks-world domain.

Based on the above data, answer the given subquestions.

For the subgoal ordering given in the goal description (and using the given tie breaking rules), which of the following is the first action popped out of the stack in Goal Stack Planning?

The domain description of a blocks-world with a single one-armed robot is provided below. **Note:** this is the same domain description used in the weekly assignments.

**Tie-breaker:** When actions are chosen non-deterministically, choose actions that lead to a plan. Throw away the actions that lead to deadends and cycles. **Tie-breaker:** Treat the goal description, preconditions and effects as lists that are accessed from left to right. When the elements in a list are pushed one by one to a stack, the last element in the list will be at the top of the stack. It has the effect of reversing the list. A planning problem is given below, find a plan using the operators and predicates defined in the blocks-world domain.

Based on the above data, answer the given subquestions.

For the subgoal ordering given in the goal description (and using the given tie breaking rules), does the Goal Stack Planning algorithm find an optimal plan?

The domain description of a blocks-world with a single one-armed robot is provided below. **Note:** this is the same domain description used in the weekly assignments.

**Tie-breaker:** When actions are chosen non-deterministically, choose actions that lead to a plan. Throw away the actions that lead to deadends and cycles. **Tie-breaker:** Treat the goal description, preconditions and effects as lists that are accessed from left to right. When the elements in a list are pushed one by one to a stack, the last element in the list will be at the top of the stack. It has the effect of reversing the list. A planning problem is given below, find a plan using the operators and predicates defined in the blocks-world domain.

Based on the above data, answer the given subquestions.

If the subgoals in the goal description (list) are reversed then does the Goal Stack Planning algorithm find an optimal plan?