Heuristic Search
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Transcript of Heuristic Search
Mahgul Gulzai
Moomal Umer
Rabail Hafeez
Introduction Definition of heuristic searchAlgorithms of heuristic search
Best first search Hill climbing strategy Implementing heuristic evaluation functions
Admissibility, Monotonicity and Informedness Using heuristic in games
Artificial Intelligence www.csc.csudh.edu
Human generally consider number of alternative strategies on their way to solving a problem .
To obtain the best possible strategy, humans use search.
For example : A chess player consider number of possible moves, A Doctor examine several possible diagnoses .
Human Problem solving seems to be based on judgmental rules that guide our search to those portion of state Space that seems some how promising.
These rules are known as “Heuristics”
Artificial Intelligence www.csc.csudh.edu
George Polya defines Heuristics as, “The study of methods and rules of discovery and invention”.
A heuristic is a method that might not always find the best solution . but is guaranteed to find a good solution in
reasonable time. By sacrificing completeness it increases
efficiency. Useful in solving tough problems which
could not be solved any other way. solutions take an infinite time or very long time
to compute. Artificial Intelligence www.csc.csudh.edu
Heuristic Search is used in AI in two situations:1.When a problem doesn’t have an exact
solution.2.There is an exact solution but the
computational cost of finding it exceeds the limit.
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Consider the game of tic-tac-toe. Even if we use symmetry to reduce the
search space of redundant moves, the number of possible paths through the search space is something like 12 x 7! = 60480.
That is a measure of the amount of work that would have to be done by a brute-force search.
Artificial Intelligence www.csc.csudh.edu
First three levels of the tic-tac-toe state space First three levels of the tic-tac-toe state space reduced by symmetryreduced by symmetry
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The “most wins” heuristic applied to the first children in tic-tac-toe
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CSC411Artificial Intelligence
Heuristically reduced state space for tic-tac-toe
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Using this rule, we can see that a corner square has heuristic value of 3, a side square has a heuristic value of 2, but the centre square has a heuristic value of 4.
So we can prune the left and right branches of the search tree.
This removes 2/3 of the search space on the first move.
If we apply the heuristic at each level of the search, we will remove most of the states from consideration thereby greatly improving the efficiency of the search.
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Heuristic search is implemented in two parts: The heuristic measure. The search algorithm.
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Use heuristic to move only to states that are better than the current state.
Always move to better state when possible.The process ends when all operators have
been applied and none of the resulting states are better than the current state.
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• Will terminate when at local optimum.• The order of application of operators can
make a big difference.• Can’t see past a single move in the state
space
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The local maximum problem for hill-climbing with 3-level look ahead
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Also heuristic search – use heuristic (evaluation) function to select the best state to explore
Can be implemented with a priority queue Breadth-first implemented with a queue Depth-first implemented with a stack
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The best-The best-first first search search algorithmalgorithm
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Heuristic search of a hypothetical state space
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A trace of the execution of best-first-search
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Heuristic search of a hypothetical state space with open and closed states highlighted
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Heuristics can be evaluated in different ways
8-puzzle problem Heuristic 1: count the tiles out of places
compared with the goal state Heuristic 2: sum all the distances by which the
tiles are out of pace, one for each square a tile must be moved to reach its position in the goal state
Heuristic 3: multiply a small number (say, 2) times each direct tile reversal (where two adjacent tiles must be exchanged to be in the order of the goal)
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The start state, first moves, and goal state for an example-8 puzzle
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Three heuristics applied to states in the 8-puzzle
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Use the limited information available in a single state to make intelligent choices
Empirical, judgment, and intuitionMust be its actual performance on problem instancesThe solution path consists of two parts: from the
starting state to the current state, and from the current state to the goal state
The first part can be evaluated using the known information
The second part must be estimated using unknown information
The total evaluation can be f(n) = g(n) + h(n)
g(n) – from the starting state to the current state nh(n) – from the current state n to the goal stateArtificial Intelligence www.csc.csudh.edu
The heuristic f applied to states in the 8-puzzle
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State space generated in heuristic search of the 8-puzzle graph
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The successive stages of open and closed that generate the graph are:
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Open and closed as they appear after the 3rd iteration of heuristic search
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evaluation function for the states in a search space, you are interested in two things:
g(n): How far is state n from the start state? h(n): How far is state n from a goal state? Evaluation function. This gives us the
following evaluation function: f(n) = g(n) + h(n) where g(n) measures the actual length of the path from the start state to the state n, and h(n) is a heuristic estimate of the distance from a state n to a goal state.
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Expert System employ confidence measures to select the conclusions with the highest likelihood of the success through heuristics implementation.
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A best-first search algorithm guarantee to find a best path, if exists, if the algorithm is admissible.
A best-first search algorithm is admissible if its heuristic function h is monotone.
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Admissibility and Algorithm A*Admissibility and Algorithm A*
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Monotonicity and InformednessMonotonicity and Informedness
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Comparison of state space searched using heuristic search with space searched by breadth-first search. The proportion of the graph searched heuristically is shaded. The optimal search selection is in bold. Heuristic used is f(n) = g(n) + h(n) where h(n) is tiles out of place.Artificial Intelligence www.csc.csudh.edu
Games Two players attempting to win Two opponents are referred to as MAX and
MINA variant of game nim
A number of tokens on a table between the 2 opponents
Each player divides a pile of tokens into two nonempty piles of different sizes
The player who cannot make division losses
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State space for a variant of nim. Each state partitions the seven matches into one or more piles
Exhaustive SearchExhaustive Search
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Principles MAX tries to win by maximizing her score, moves to a
state that is best for MAX MIN, the opponent, tries to minimize the MAX’s score,
moves to a state that is worst for MAX Both share the same information MIN moves first The terminating state that MAX wins is scored 1,
otherwise 0 Other states are valued by propagating the value of
terminating statesValue propagating rules
If the parent state is a MAX node, it is given the maximum value among its children
If the parent state is a MIN state, it is given the minimum value of its children
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Exhaustive minimax for the game of nim. Bold lines indicate forced win for MAX. Each node is marked with its derived value (0 or 1) under minimax.
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If cannot expand the state space to terminating (leaf) nodes (explosive), can use the fixed ply depth
Search to a predefined number, n, of levels from the starting state, n-ply look-ahead
The problem is how to value the nodes at the predefined level – heuristics
Propagating values is similar Maximum children for MAX nodes Minimum children for MIN nodes
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Minimax to a hypothetical state space. Leaf states show heuristic values; internal states show backed-up values.
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Heuristic measuring conflict applied to states of tic-tac-toe
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Two-ply minimax applied to the opening move of tic-tac-toe
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Two ply minimax, and one of two possible MAX second moves
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Two-ply minimax applied to X’s move near the end of the game
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Alpha-beta pruning to improve search efficiencyProceeds in a depth-first fashion and creates two
values alpha and beta during the searchAlpha associated with MAX nodes, and never
decreasesBeta associated with MIN nodes, never increasesTo begin, descend to full ply depth in a depth-first
search, and apply heuristic evaluation to a state and all its siblings. The value propagation is the same as minimax procedure
Next, descend to other grandchildren and terminate exploration if any of their values is >= this beta value
Terminating criteria Below any MIN node having beta <= alpha of any of its MAX
ancestors Below any MAX node having alpha >= beta of any of its MIN
ancestorsArtificial Intelligence www.csc.csudh.edu
Artificial Intelligence www.csc.csudh.edu