Podcast
Questions and Answers
What is the first step in the basic idea of search?
What is the first step in the basic idea of search?
Which of the following best describes the term 'successor states'?
Which of the following best describes the term 'successor states'?
In the context of search, what is the significance of expanding from a start state?
In the context of search, what is the significance of expanding from a start state?
What might occur if a search does not consider successor states?
What might occur if a search does not consider successor states?
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Which of the following is NOT part of the basic search process described?
Which of the following is NOT part of the basic search process described?
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What does the root node of a 'what if' tree represent?
What does the root node of a 'what if' tree represent?
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What do the children of a node represent in the 'what if' tree?
What do the children of a node represent in the 'what if' tree?
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Which statement is true regarding a 'what if' tree?
Which statement is true regarding a 'what if' tree?
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In a 'what if' tree, which aspect is typically not represented?
In a 'what if' tree, which aspect is typically not represented?
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How can a 'what if' tree be utilized effectively?
How can a 'what if' tree be utilized effectively?
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Study Notes
Search: Basic Idea (Lec 10)
- Start with a starting state, expand to possible successor states
- Successor states are the second state from the starting state
- Successor states are put in a frontier (or fringe)
- Frontier is the boundary of states reachable currently
- Frontier states can be: reachable but not visited, goal state or not, have children or not
- Each search algorithm selects a state from the frontier differently
- If a goal state is found, return the complete path from start to end.
- If not, expand the children of the selected state
Search Tree (What-if tree)
- Search algorithms choose nodes/states from the fringe
- What-if tree shows possible actions/outcomes, not actions in the environment
- It's a tree of possibilities to reach the goal
- The root node represents the starting state
Tree Search Algorithm Outline
- Initialize the frontier with the starting state
- While the frontier is not empty:
- Choose a frontier node using a search strategy and remove it
- If the node is the goal state, return the solution
- Else expand the node and add its children to the frontier.
- Stopping criteria: reaching the goal or an empty frontier
Handle Repeated States
- Add each expanded state to an "explored" set
- Don't add already explored states to the frontier again
- If a node already exists in the frontier with a higher path cost, replace it with the new one
Backtracking Search
- A technique to systematically try all paths in a state space
- Considered a blind or uninformed search algorithm
- Starts at the start state and moves along a path until reaching/finding a goal state
- If a dead end is reached, backtrack to the last unexamined node and try a different branch
- Known as Depth-First Search
Backtracking Implementation
- Uses three lists:
- State list: current path (solution path if a goal is found)
- New state list: nodes awaiting evaluation (frontier/open list)
- Dead end list: states that failed to contain the goal node
- Current state: pointer to the current state
- Dead end states should be checked before adding to the new state list to prevent cycles
Blind vs. Heuristic Strategies (Lec 11)
- Blind strategies do not use information within the state
- Blind strategies are uninformed, exhaustive, brute-force methods
- Blind strategies evaluate every possible option systematically
- Heuristic strategies use information from the domain to evaluate nodes
- Heuristic strategies prioritize promising nodes, increasing the chance of finding a good solution faster
Blind Strategies
- Breadth-First Search (BFS):
- Bidirectional Search
- Depth-First Search (DFS):
- Depth-Limited Search
- Iterative Deepening Search
- Uniform-Cost Search (UCS)
Uniform-Cost Search (Lec 12)
- Cost of traversing each edge is not necessarily equal to 1
- Cost values on edges represent the traversing cost between nodes
- Cost must be positive and greater than zero
- The total cost to reach a state is the summation of the costs of the steps
Depth-Limited Strategy (Lec 12)
- Search depth is limited to a specified level
- Does not explore nodes below the specified level
- Can lead to a solution in a limited set of nodes or a failure if node falls out of the range
- Outcomes include solution, failure, cut-off
Iterative Deepening Strategy (Lec 12)
- Increasingly deeper depth-first searches
- Gradually increases the maximum depth in each search
- Combines the efficiency of depth-first search with the completeness of breadth-first search
Comparing Depth, Breadth, & Iterative Deepening Search Algorithms (Lec 13)
- Breadth and iterative deepening guarantee shortest solution
- Breadth-first: high space complexity (needs to store all possible states at each level)
- Depth-first: low space complexity
- Iterative deepening: best performance
Bidirectional Search (Lec 13)
- Searches forward from the start state and backward from the goal state
- Stops when the two searches meet
Complexity of Basic Search Algorithms
- Calculated by evaluating the number of nodes at the lowest level
- Branching factor (b): number of children each node has
- Solution depth (d): height of the tree
- Total nodes at a single specific level = b^d
Avoiding Repeated States
- Depth and Breadth-first strategies:
- Keep records of all states in the current path
- Discard if a new node's state already exists.
- Keeps a record of all states generated, discarding new nodes with existing states
Best-First Search (Lec 13)
- Uses a priority queue (open list) to order states, prioritizing states presumed to be closer to the goal
- Uses a heuristic function to estimate the value of a node
Heuristic Function (Lec 14)
- Function used to estimate how far a node is from the goal
- Can be based on trial and error
- Used in heuristic search algorithms.
Adversarial Search (Lec 14)
- Search in a tree with multiple players (opponent).
- Search in a game where one player's gain is the other's loss.
- Players have the same knowledge (state space)
- Both players aim to maximize their chances of winning
Minimax Procedure (Lec 15)
- Algorithm used in adversarial search
- Evaluates all possible moves for both players to determine the best option for starting player ("maximizer")
- Recursively evaluates moves for both players, trying to maximize one's gain and minimize the other player's gain
Minimax to a Fixed Ply Depth (Lec 15)
- Limits search depth to a fixed number of moves
- Calculates heuristic value for each state
- Maximizer tries to find favorable states while minimizer tries to find unfavorable ones.
Alpha-Beta Pruning Procedure (Lec 15)
- Pruning technique to improve efficiency of adversarial search (Minimax)
- Prunes unnecessary branches in the search tree based on alpha(max) and beta(min) values
- Used to improve search efficiency and reduce the number of nodes evaluated
Search...What's the issue? (Lec 16)
- Use when algorithms like genetic algorithms and simulated annealing do not work well
- When a search space is too large to find the optimal option with current search techniques
- When heuristic functions are needed but not available
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Description
This quiz explores key concepts in search algorithms, including the roles of starting states, successor states, and frontiers. It outlines the search tree and the tree search algorithm process, detailing how nodes are selected from the frontier to find a goal state. Test your understanding of these foundational principles in algorithm design.
