Greedy Best First Search Algorithm

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Questions and Answers

Explain how informed search strategies leverage problem-specific knowledge to enhance search efficiency, contrasting this with uninformed strategies.

Informed search strategies use problem-specific knowledge beyond the problem definition to find solutions more efficiently, while uninformed strategies don't use such knowledge.

How does a best-first search algorithm prioritize node expansion, and what role does the evaluation function play in this process?

Best-first search selects nodes for expansion based on an evaluation function, $f(n)$. Traditionally, the node with the lowest evaluation is selected for expansion.

What is the primary objective of using a heuristic function in search algorithms, and how is it denoted mathematically?

A heuristic function's main goal is to estimate the cost of the cheapest path from a node to the goal node. It is mathematically denoted as $h(n)$.

Explain how greedy best-first search operates and why it may not always yield the optimal solution.

Greedy best-first search expands the node closest to the goal, evaluating nodes by using just the heuristic function: $f(n) = h(n)$. It may not be optimal because it focuses solely on immediate proximity to the goal. Signup and view all the answers

What are the key differences between greedy best-first search and depth-first search, and what common defects do they share?

Greedy best-first search resembles depth-first search in following a single path to the goal but backtracks when it hits a dead end. Both are not optimal and incomplete, as they can start down infinite paths. Signup and view all the answers

What is the evaluation function used in A* search, and how does it combine different factors to estimate the total solution cost?

The A* search uses the evaluation function $f(n) = g(n) + h(n)$, where $g(n)$ is the cost to reach the node and $h(n)$ is the estimated cost to get from the node to the goal. Signup and view all the answers

Explain the conditions under which A* search is considered both complete and optimal.

A* search is complete and optimal if the heuristic function $h(n)$ is admissible, meaning it never overestimates the cost to reach the goal. Signup and view all the answers

Define an admissible heuristic and explain why the straight-line distance heuristic ($h_{SLD}$) is considered admissible.

An admissible heuristic never overestimates the cost to reach the goal. Straight-line distance is admissible because the shortest path between two points is a straight line and is therefore an underestimate. Signup and view all the answers

Describe the property of consistency in heuristics and explain its importance for A* search when used with GRAPH-SEARCH.

A heuristic $h(n)$ is consistent if for every node $n$ and successor $n'$, $h(n) <= c(n, a, n') + h(n')$. When A* search uses GRAPH-SEARCH, consistency ensures optimality. Signup and view all the answers

What is the relationship between consistency and admissibility in heuristics, and why is consistency considered a stricter requirement?

Every consistent heuristic is also admissible, but not every admissible heuristic is consistent. Consistency is stricter because it places additional constraints on the heuristic's estimates between nodes. Signup and view all the answers

Explain the significance of nondecreasing f(n) values along any path in the context of A* search with a consistent heuristic and GRAPH-SEARCH.

If $h(n)$ is consistent, the values of $f(n)$ along any path are nondecreasing. This means the first goal node selected for expansion must be an optimal solution. Signup and view all the answers

Describe what 'contours' represent in the state space when using A* search, and explain how the accuracy of the heuristic influences their shape.

Contours represent nodes with the same $f$-cost in the state space. More accurate heuristics cause the bands to stretch toward the goal state and become more narrowly focused around the optimal path. Signup and view all the answers

Explain why A* search is considered optimally efficient among optimal algorithms that extend search paths from the root.

A* search is optimally efficient because no other optimal algorithm is guaranteed to expand fewer nodes than A*, except possibly through tie-breaking among nodes with $f(n) = C*$. Signup and view all the answers

How does Recursive Best-First Search (RBFS) attempt to mimic standard best-first search while using only linear space?

RBFS mimics best-first search by tracking the $f$-value of the best alternative path available from any ancestor and unwinding recursion when the current node exceeds this limit. Signup and view all the answers

In the context of RBFS, explain how the algorithm updates the $f$-value of nodes along the path as the recursion unwinds, and why this is important.

As the recursion unwinds, RBFS replaces the f-value of each node along the path with the best f-value of its children. This enables RBFS to decide whether it's worth reexpanding the subtree later. Signup and view all the answers

Describe the key idea behind the AO* algorithm and how it differs from the A* algorithm in handling AND-OR graphs.

The key idea behind the AO* algorithm is to solve problems that can be divided into subproblems, using AND-OR graphs. AO* can re-examine expanded nodes to select the current best path, unlike A*. Signup and view all the answers

Explain how the AO* algorithm propagates revised cost estimations backward through the graph and why this is necessary for selecting the current best path.

AO* propagates revised cost estimations backward to re-evaluate expanded nodes, ensuring that the current best path is selected, as expanded nodes are re-examined. Signup and view all the answers

In the context of local search algorithms, explain what a 'state space landscape' represents and how it helps in understanding the search process.

A 'state space landscape' represents the search problem with 'location' (defined by the state) and 'elevation' (defined by the value of the heuristic cost or objective function). It helps visualize the search. Signup and view all the answers

Describe the hill-climbing search algorithm and explain its limitations in finding the global optimum.

Hill-climbing search moves continually in the direction of increasing value until it reaches a 'top' where no neighbor has a higher value. It does not maintain a search tree and does not look ahead beyond immediate neighbors. Signup and view all the answers

Explain the challenges posed by local maxima, ridges, and plateaux for hill-climbing algorithms, and provide strategies to mitigate these issues.

Local maxima can cause the hill-climbing algorithms to get stuck. Ridges cause a series of local maxima. Plateaux are areas where the evaluation function is flat. Strategies to mitigate this involve sideways moves and random restarts. Signup and view all the answers

What is the approach to Random-restart hill climbing and why can it achieve completeness (with probability approaching 1)?

Random-restart hill climbing conducts a series of hill-climbing searches from randomly generated initial states, stopping when a goal is found. It will eventually generate a goal state as the initial state if there are few local maxima and plateaux. Signup and view all the answers

Explain how local beam search differs from running k random restarts in parallel.

In a random-restart search, each search process runs independently of the others. In a local beam search, useful information is passed among the k parallel search threads. Signup and view all the answers

Describe how stochastic beam search can help to alleviate the problem of lack of diversity among k states in local beam search.

Stochastic beam search chooses $k$ successors at random from the pool of candidate successors, with the probability of choosing a given successor being an increasing function of its value. Signup and view all the answers

Explain how genetic algorithms utilize crossover and mutation operations to evolve solutions, and discuss the advantages and disadvantages of the crossover operation.

Genetic algorithms combine two parent states through crossover and introduces random changes through mutation. Though it combines useful functions, if the code is permuted initially in a random order, crossover conveys no advantage. Signup and view all the answers

Define the concept of a 'schema' in the context of genetic algorithms.

A schema is a substring in which some of the positions can be left unspecified. It is a underlying pattern, which if present means something to the overall performance. Signup and view all the answers

Describe what a constraint satisfaction problem(CSP) is and its three main components, what is the goal of solving it?

A CSP consists of variables X, domains D, and constraints C. The goal is to find a complete, consistent assignment of values to variables from their domains that satisfies all constraints. Signup and view all the answers

What are node consistency, arc consistency and path consistency in constrait satisfaction problems, and how do they contribute to solving CSPs?

Node, arc, and path consistency are techniques for constraint propagation. They reduce the search space by removing inconsistent values and assignments, thereby simplifying the CSP and helping to find a solution more efficiently. Signup and view all the answers

Explain the concept of global constraints and provide an example of how they can be used in constraint satisfaction problems.

Global constraints involve a large number of variables and provide a succinct way to express certain types of constraints. An example is the Atmost constraint, which limits the total number of personnel assigned to tasks. Signup and view all the answers

In the context of constraint satisfaction, explain the purpose and mechanism of 'bounds propagation'.

Bounds propagation reduces the domains of variables by considering the minimum and maximum possible values based on constraints. It tightens the domains. Signup and view all the answers

Describe the Alldiff constraint, providing an example utilizing sudoku puzzles.

The Alldiff constraint specifies that all variables involved must have different values. In Sudoku, each row, column, and box of 9 squares must satisfy an Alldiff constraint. Signup and view all the answers

What is cryptarithmetic problem, what is the purpose of allDiff constraint with it and what does each letter stand for?

It is a problem involving mathematical equations in which letters represent digits, the allDiff constraint ensures each letter stands for a distinct digit. The purpose is to find a substitution of digits for letters. Signup and view all the answers

What are the components of a game, from the point of view of adversarial search.

A game is fomrally defined as a kind of search problem where we include the board, who's turn it is, the successor function, the state, how the game ends. Signup and view all the answers

Describe the minimax algorithm for game playing and explain how it determines the optimal move for the maximizing player.

The minimax algorithm determines the optimal strategy in a game tree by calculating the minimax value of each node which represents the utility of being in that state. It assumes players will play optimally. Signup and view all the answers

How is the minimax algorithm extended to handle multiplayer games, and what does the utility value of a node represent in this context?

In multiplayer games, a vector of utilities (one for each player) is associated with each node. The backed-up value represents the utility vector of whichever successor has the highest value for the player choosing at the node. Signup and view all the answers

How does alpha-beta pruning improve the efficiency of the minimax algorithm, and why does it not affect the final minimax decision?

Alpha-beta pruning improves the efficiency is prunes away branches that cannot possibly influence the final decision. The value of the root has has to do with with z, not x or y, so what the values are. This improves efficiency because it doesn't need to check extraneous values. Signup and view all the answers

Define the alpha and beta parameters used in alpha-beta pruning and explain how they are used to determine bounds on the backed-up values during the search.

Alpha is the value of the best (i.e., highest-value) choice we have found so far at any choice point along the path for MAX. Beta is the value of the best (i.e., lowest-value) choice we have found so far at any choice point along the path for MIN. Signup and view all the answers

Under what conditions can can alpha-beta reduce nodes to pick the best more, and what factor is improved for minimax?

Alpha-beta can reduce nodes with perfect oredering, which means only needs to check 0(b^(m/2)) nodes to pick the best more. So, instead of b, if we utilize alpha-beta pruning, with perfect ordering the search needs to check square root b. Signup and view all the answers

Flashcards

Informed Search

Uses problem-specific knowledge beyond the definition of the problem to find solutions efficiently.

Best-First Search

Selects a node for expansion based on an evaluation function, estimating distance to the goal; uses a priority queue.

Heuristic Function (h(n))

Estimated cost of the cheapest path from a node to a goal node; key for best-first search algorithms.

Greedy Best-First Search

Expands the node that is supposedly closest to the goal, based on straight line distance. Evaluates nodes using the heuristic function f(n) = h(n).