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Best-first Search

Best-First Search

Definition

Best-first search is a heuristic search technique in artificial intelligence that explores a graph by expanding the most promising node chosen according to a specified rule. It uses an evaluation function to rank nodes and select the best one to explore next.

Key Concepts

  • Evaluation Function (f(n)): A function that assigns a value to each node ( n ) to estimate its desirability for exploration. The node with the best (lowest) evaluation is expanded first.
  • Open List: A priority queue of nodes to be evaluated, sorted by their evaluation function values.
  • Closed List: A set of nodes that have already been evaluated.
  • Heuristic Function (h(n)): An estimate of the cost to reach the goal from node ( n ).
  • Greedy Best-First Search: A variant that uses only the heuristic function ( h(n) ) to guide the search.

Detailed Explanation

  • Procedure:
    1. Initialize the open list with the start node and the closed list as empty.
    2. While the open list is not empty:
      • Remove the node ( n ) with the lowest ( f(n) ) from the open list.
      • If ( n ) is the goal node, return the path from the start node to ( n ).
      • Generate all successors of ( n ) and calculate their ( f ) values.
      • For each successor:
        • If the successor is not in the open list or the closed list, add it to the open list.
        • If it is already in the open list but has a higher ( f ) value, update its ( f ) value and parent pointer.
      • Move ( n ) to the closed list.
  • Optimality: Best-first search is not guaranteed to find the shortest path, as it focuses on exploring the most promising nodes first, which may lead to suboptimal solutions.
  • Efficiency: The performance depends heavily on the heuristic function. A well-designed heuristic can significantly reduce the number of nodes expanded.

Diagrams

  • Best-First Search Process: Best-First Search Process
  • Evaluation Function f(n): Evaluation Function f(n)

Links to Resources

Notes and Annotations

  • Summary of key points:

    • Best-first search uses an evaluation function to prioritize nodes, expanding the most promising node first.
    • It is not guaranteed to find the shortest path but can be efficient with a good heuristic.
    • The algorithm maintains open and closed lists to manage explored and unexplored nodes.

  • Personal annotations and insights:

    • Best-first search is particularly useful in scenarios where finding any solution quickly is more critical than finding the optimal solution.
    • It provides a foundation for understanding more sophisticated algorithms like A* which combine cost and heuristic estimates.
    • The choice of evaluation function ( f(n) ) and heuristic ( h(n) ) are crucial in determining the algorithm's effectiveness.

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