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**Properties Of A∗ With Reopening In State-Space Search**.pdf

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Preview of **Properties of A∗ with Reopening in State-Space Search**
🔗 Source: ai.dmi.unibas.ch
📊 Size: 177 KB
👤 Author: Malte Helmert
⬇️ Downloads: 34

Summary

Foundations of Artificial Intelligence - State-Space Search: Properties of A∗ (Part I)

This chapter explores the optimality of the A∗ search algorithm with reopening for heuristic-based pathfinding in state spaces. Key takeaways include:

1. Optimality of A∗with Reopening:

A∗with reopening is proven to be optimal when using admissible heuristics.

2. Core Concepts:

Solvable States: A state is solvable if there exists a path with finite cost to reach it from the initial state.
Optimal Paths: The cost of the cheapest (optimal) path from the initial state to a given state.
 Settled States: A state considered "erledigt" (settled) during search when its optimal cost is known and matches the cost stored in the distance table.

3. Optimal Continuation Lemma:

This lemma establishes that if a state is settled, its solvable successor states are either also settled or A∗ maintains a node with the correct g-value (cost) for reaching them.
This ensures progress towards finding optimal paths to settled states and ultimately the goal state.

4. f-Bound Lemma:

This lemma guarantees that at the beginning of each iteration, A∗with reopening maintains a node in its open list with a cost estimate (f-value) less than or equal to the optimal solution cost.
This property is crucial for bounding search space exploration and ensuring termination.

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Description

This section explores state-space search algorithms, focusing on A* with Part I covering optimality properties, including the Optimal Continuation Lemma, f-Bound Lemma, and the algorithm's optimality with reopening.

Technical Information

  • File Format: PDF
  • File Size: 177 KB
  • Pages: 7
  • Language: EN
  • Author: Malte Helmert
  • Total Downloads: 34
  • Last Updated: 2 weeks ago

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**Properties guide**Properties tutorialA∗ guideA∗ tutorialwith guidewith tutorialReopening guideReopening tutorialState-Space guideState-Space tutorialSearch** guideSearch** tutorial

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