![Inexact Search
When all leaf nodes are feasible(even some are
better than others), H.C. needs no backtracking.
We then must use Forgetful H.C.
Forgetful H.C.: keeps track of current node
and forget where we’ve been [no open list].](https://image.slidesharecdn.com/lecture6ai-astar-230114020045-31dc4d3d/85/lecture-6-AI-A-star-pdf-27-320.jpg)
lecture 6 AI - A star.pdf
- 2. 1 2 3 4 6 7 8 5 goal Best first search
- 6. Combining cost-so-far and heuristic function • Since what we're really looking for is the optimal path between the initial state, and some goal state, a better measure of how promising a state is, is the sum of the cost-so-far, and our best estimate of the cost from there to the nearest goal state. • For a state n, with a cost-so-far g(n), and a heuristic estimate of the cost to goal of h(n), what we want is: • f(n) = g(n) + h(n) 6
- 7. Algorithm A* •Idea: avoid expanding paths that are already expensive. • •Evaluation function f(n) = g(n) + h(n) • • g(n) = cost so far to reach n • h(n) = estimated cost from n to goal • f(n) = estimated total cost of path through n to goal • •This proves to be a very effective strategy for controlling state-space search. When used with best-first search, as a way of sorting the agenda where the agenda is sorted so that the states with the lowest values of f(n) come first, and are therefore expanded first-> this is known as Algorithm A*.
- 8. A* Algorithm H.C. and B.F. (given heuristics) can find solutions faster than exhaustive searches. However, it can’t tell whether the found solution is the best one. Problem: The heuristic guides us to the good nodes but doesn’t give enough information to guarantee we’ve found the optimum. Solution: Branch and bound method The cost of the path to a node serves as a lower bound on the cost of the nodes below it. We need a heuristic function ev(n,p) with this property to guarantee optimum solution.
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- 15. A* search and admissibility • The choice of an appropriate heuristic evaluation function, h(n), is still crucial to the behaviour of the search algorithm. • In general, we want to choose a heuristic evaluation function h(n) which is as close as possible to the actual cost of getting to a goal state. • A heuristic is admissible if it never overestimates the cost to the goal.
- 16. • The A* algorithm always finds the optimal solution path whenever a path from the start to a goal state exists. • When the agenda is sorted according to the function f(n) = g(n) + h(n) and where the function h(n) is admissible, can be proven to always find an optimal solution.
- 17. Dominance • We say that a search strategy which searches less of the state-space in order to find a goal state is more informed. Ideally, we'd like a search strategy which is both admissible (so it will find us an optimal path to the goal state), and informed (so it will find the optimal path quickly.) • Admissibility requires that the heuristic evaluation function, h(n) doesn't overestimate, but we do want a function which is as close as possible to the actual cost of getting to the goal.
- 18. Admissible Heuristics • Finding heuristics: • Relaxing the problem restrictions (simplifying the problem), e.g. the rules for moving tiles. • Learning heuristics from experience: learning a function as weighted sum of features (quantitative properties of the states). • e.g. 8’s puzzle • Number of tiles out of place • h1= the number of tiles that are in the wrong position. This is admissible because any tile that is out of place must be moved at least once. 2 8 1 6 4 7 5 1 2 3 8 4 7 6 5 (4) 3
- 20. The heuristic f applied to states in the 8- puzzle
- 27. Inexact Search When all leaf nodes are feasible(even some are better than others), H.C. needs no backtracking. We then must use Forgetful H.C. Forgetful H.C.: keeps track of current node and forget where we’ve been [no open list].
- 28. Why Inexact Search • As the search space become very large (exhaustive) even when guided by heuristics it’ll be impractical.
- 29. Blind Search VS Heuristic Search • Blind Search: Very basic. Follow an algorithm, taking no account of how close we might be to a solution. • Informed (Heuristic) Search: Uses guesses, rules to aid the search. It involves making an estimate of how far we are from a solution after each possible next move & going to the move with the lowest estimate.
- 30. Informed Search Summary • Best-first search Is general search where the minimum cost nodes (according to some measure) are expanded first. • Hill-climbing search • When chose to follow a node, it continues to do so in depth first way. • Even though the children of the node(say a) has heuristic information worst than that for a node in the same level of node (say a). • Forgetful Hill-climbing search keep only a single state in memory, but can get stuck on local optima.
- 31. A* search • A* algorithm is a modified form of best first algorithm. • It is a branch and bound method with cost associated by path. • It’s used in path problems where the cost of a path is the sum of the costs of the moves. • Guarantee to find best solution. • f(n) = g(n) + h(n) and handles state repetitions and h(n) never overestimates. • A* is complete, optimal and optimally efficient but its space complexity is still bad.