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Heuristic Search Techniques

Heuristic Search Techniques

Definition

Heuristic search techniques are strategies in artificial intelligence that use heuristics to guide the search process towards a goal. Heuristics are rules of thumb or informed guesses that aim to improve the efficiency of the search by estimating the cost or distance to the goal.

Key Concepts

  • Heuristic Function (h(n)): A function that estimates the cost to reach the goal from node ( n ).
  • Evaluation Function (f(n)): Often defined as ( f(n) = g(n) + h(n) ), where ( g(n) ) is the cost from the start node to ( n ).
  • Admissibility: A heuristic is admissible if it never overestimates the cost to reach the goal.
  • Consistency (Monotonicity): A heuristic is consistent if ( h(n) \leq c(n, n') + h(n') ) for every node ( n ) and its successor ( n' ), where ( c(n, n') ) is the cost of reaching ( n' ) from ( n ).

Detailed Explanation

  • Best-First Search: A search algorithm that uses the heuristic function ( h(n) ) to select the next node to explore. The node with the lowest ( h(n) ) value is expanded first. It is not guaranteed to find the shortest path.
  • A Search*: Combines the cost to reach a node (( g(n) )) and the estimated cost to the goal (( h(n) )) in its evaluation function ( f(n) = g(n) + h(n) ). A* is both complete and optimal if the heuristic ( h(n) ) is admissible and consistent.
  • Greedy Best-First Search: Selects the node that appears to be closest to the goal, using ( h(n) ) alone. It is faster but not necessarily optimal or complete.
  • Hill-Climbing Search: A local search algorithm that continuously moves towards the neighbor with the highest value according to a heuristic. It can get stuck in local maxima.
  • Simulated Annealing: A probabilistic technique that explores the search space by allowing occasional moves to worse states to escape local maxima, with a probability that decreases over time.

Diagrams

  • Best-First Search Tree: Best-First Search Tree
  • A Search Algorithm*: A* Search Algorithm

Links to Resources

Notes and Annotations

  • Summary of key points:

    • Heuristic functions guide search algorithms by estimating the cost to the goal.
    • Admissibility and consistency are crucial for the optimality and completeness of A* search.
    • Different heuristic search techniques balance exploration and exploitation in various ways.

  • Personal annotations and insights:

    • A* is highly effective in pathfinding problems in robotics and game development due to its balance of optimality and performance.
    • Hill-climbing, while simple, requires enhancements like random restarts or simulated annealing to be more robust in practice.
    • The choice of heuristic greatly influences the efficiency of the search; domain-specific knowledge can help craft better heuristics.

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