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Best-First Search – an algorithm in which a node is selected for expansion based on an evaluation function f(n)

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- 1. AI: Chapter 4: Informed Search and Exploration 1 Introduction to Artificial Intelligence Chapter 4 Solving problems by searching Informed (heuristics) Search
- 2. AI: Chapter 4: Informed Search and Exploration 2 Informed (Heuristic) Search Strategies • Informed Search – a strategy that uses problem-specific knowledge beyond the definition of the problem itself • Best-First Search – an algorithm in which a node is selected for expansion based on an evaluation function f(n) – Traditionally the node with the lowest evaluation function is selected – Not an accurate name…expanding the best node first would be a straight march to the goal. – Choose the node that appears to be the best
- 3. AI: Chapter 4: Informed Search and Exploration 3 Informed (Heuristic) Search Strategies • There is a whole family of Best-First Search algorithms with different evaluation functions – Each has a heuristic function h(n) • h(n) = estimated cost of the cheapest path from node n to a goal node • Example: in route planning the estimate of the cost of the cheapest path might be the straight line distance between two cities
- 4. AI: Chapter 4: Informed Search and Exploration 4 A Quick Review • g(n) = cost from the initial state to the current state n • h(n) = estimated cost of the cheapest path from node n to a goal node • f(n) = evaluation function to select a node for expansion (usually the lowest cost node)
- 5. AI: Chapter 4: Informed Search and Exploration 5 Greedy Best-First Search • Greedy Best-First search tries to expand the node that is closest to the goal assuming it will lead to a solution quickly – f(n) = h(n) – “Greedy Search” • Implementation – expand the “most desirable” node into the fringe queue – sort the queue in decreasing order of desirability • Example: consider the straight-line distance heuristic hSLD – Expand the node that appears to be closest to the goal
- 6. AI: Chapter 4: Informed Search and Exploration 6 Greedy Best-First Search
- 7. AI: Chapter 4: Informed Search and Exploration 7 Greedy Best-First Search • hSLD(In(Arad)) = 366 • Notice that the values of hSLD cannot be computed from the problem itself • It takes some experience to know that hSLD is correlated with actual road distances – Therefore a useful heuristic
- 8. AI: Chapter 4: Informed Search and Exploration 8 Greedy Best-First Search
- 9. AI: Chapter 4: Informed Search and Exploration 9 Greedy Best-First Search
- 10. AI: Chapter 4: Informed Search and Exploration 10 Greedy Best-First Search
- 11. AI: Chapter 4: Informed Search and Exploration 11 Greedy Best-First Search • Complete – No, GBFS can get stuck in loops (e.g. bouncing back and forth between cities) • Time – O(bm ) but a good heuristic can have dramatic improvement • Space keeps all the nodes in memory • Optimal – No!
- 12. AI: Chapter 4: Informed Search and Exploration 12 A* Search • A* (A star) is the most widely known form of Best-First search – It evaluates nodes by combining g(n) and h(n) – f(n) = g(n) + h(n) – Where • g(n) = cost so far to reach n • h(n) = estimated cost to goal from n • f(n) = estimated total cost of path through n
- 13. AI: Chapter 4: Informed Search and Exploration 13 A* Search • When h(n) = actual cost to goal – Only nodes in the correct path are expanded – Optimal solution is found • When h(n) < actual cost to goal – Additional nodes are expanded – Optimal solution is found • When h(n) > actual cost to goal – Optimal solution can be overlooked
- 14. AI: Chapter 4: Informed Search and Exploration 14 A* Search • A* is optimal if it uses an admissible heuristic – h(n) <= h*(n) the true cost from node n – if h(n) never overestimates the cost to reach the goal • Example – hSLD never overestimates the actual road distance
- 15. AI: Chapter 4: Informed Search and Exploration 15 A* Search
- 16. AI: Chapter 4: Informed Search and Exploration 16 A* Search
- 17. AI: Chapter 4: Informed Search and Exploration 17 A* Search
- 18. AI: Chapter 4: Informed Search and Exploration 18 A* Search
- 19. AI: Chapter 4: Informed Search and Exploration 19 A* Search
- 20. AI: Chapter 4: Informed Search and Exploration 20 A* Search
- 21. AI: Chapter 4: Informed Search and Exploration 21 A* Search • A* expands nodes in increasing f value – Gradually adds f-contours of nodes (like breadth-first search adding layers) – Contour i has all nodes f=fi where fi < fi+1
- 22. AI: Chapter 4: Informed Search and Exploration 22 A* Search • Complete – Yes, unless there are infinitely many nodes with f <= f(G) • Time – The better the heuristic, the better the time • Best case h is perfect, • same as BFS • Space – Keeps all nodes in memory and save in case of repetition – worse – A* usually runs out of space before it runs out of time • Optimal – Yes, cannot expand fi+1 unless fi is finished
- 23. AI: Chapter 4: Informed Search and Exploration 23 Memory-Bounded Heuristic Search • Iterative Deepening A* (IDA*) – Similar to Iterative Deepening Search, but cut off at (g(n)+h(n)) > max instead of depth > max – At each iteration, cutoff is the first f-cost that exceeds the cost of the node at the previous iteration • Simple Memory Bounded A* (SMA*) – Set max to some memory bound – If the memory is full, to add a node drop the worst (g+h) node that is already stored – Expands newest best leaf, deletes oldest worst leaf
- 24. AI: Chapter 4: Informed Search and Exploration 24 Exercise For the case of a Romania Example if a person needs to go from the city of Oradea to Bucharest determine: 1. The state space graph 2. By using the five uninformed search strategies determine the successor functions 3. By using a greedy best and A* heuristics search strategies determine the path to reach the goal city 4. Which search strategy provide you an optimal solution for the problem? Why?

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