search tech

8/3/2019 Search Tech

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Problem Solving Techniques

Contains algorithms:

Uninformed search

Informed search

Local SearchConstraint Satisfaction Problem

Adversarial search


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Basic Search AlgorithmBasic Search AlgorithmLet L be a list containing the initial state (L= the fringe)

Loopif L is empty return failure

Node select (L)

if Node is a goal thenreturn Node

(the path from initial state to Node)

else generate all successors of Node, andmerge the newly generated states into LEnd Loop


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Evaluating Search strategiesEvaluating Search strategies

1. Completeness: Is the strategy guaranteed to find a solution ifone exists?

2. Optimality: Does the solution have low cost or the minimalcost?

3. Search cost associated :a. Time complexity: Time taken (number of nodes expanded)

(worst or average case) to find a solution.

b. Space complexity: Space used by the algorithm measuredin terms of the maximum size of fringe


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Different search strategy

1. Blind Search strategies or Uninformed searcha. Depth first search

b. Breadth first searchc. Iterative deepening searchd. Iterative broadening search

2. Informed Search

3. Constraint Satisfaction Search4. Adversary Search


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Uninformed search

or

Blind Search


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Blind Search

Algorithm 1 : Breadth First Search

Let fringe be a list containing the initial stateLoop

if fringe is empty return failure-

if Node is a goalthen return the path from initial state to Node

else generate all successors of Node, and

(merge the newly generated nodes into fringe)add generated nodes to the back of fringeEnd Loop


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Blind Search

Algorithm 2: Depth First Search


if fringe is empty return failure-

if Node is a goalthen return the path from initial state to Node

else generate all successors of Node, and

(merge the newly generated nodes into fringe)add generated nodes to the front of fringeEnd Loop


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Blind Search

Algorithm 3: Depth Limited Search


Node remove-first (fringe)if Node is a goal

then return the path from initial state to Node

else if depth of Node = limit return cutoffelse add generated nodes to the front of fringeEnd Loop


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Blind Search

Algorithm 4: Depth First Iterative Deepening

SearchFirst do DFS to depth 0 (i.e., treat start node as having no

, , , , .

until solution found doDFS with depth cutoff c

c = c+1


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Blind Search

Algorithm 5: Uniform Cost Search

1. Similar to Breath-First.2. Pursues the path with less accumulated cost.

The algorithm expands nodes in the order of their costfrom the source.


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Blind SearchAlgorithm 6: Bidirectional Search

Let fringe1 be a list containing the initial state SLet fringe1 be a list containing the initial state G

Loop (while fringe1 and fringe2 are not empty)Node remove-first frin e1

if Node is in fringe2then return the path {SNode concatenated with reverse(GNode)}else generate all successors of Node, andadd generated nodes to the front of fringe1

m remove-first fringe2generate all successors of Node, andadd generated nodes to the front of fringe2

End Loop


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Informed search

or

Heuristic Search


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Heuristic Search

Algorithm 1: Best First Search

Let fringe be a priority queue containing the initial stateLoop

if frin e is em t return failure

Node remove-first (fringe)if Node is a goal

then return the path from initial state to Nodeelse generate all successors of Node, and

put the newly generated nodes into fringeaccording to their f values

End Loop


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Heuristic Search

Algorithm 2: A* Search

1. Put start state onto queue.2. If queue is empty then fail.3. If head of queue is goal then succeed.4. Else remove head of queue, expand it, place in queue,

and sort entire queue with least cost-so-far + estimatedcost remaining nodes in front.5. If multiple paths reach a common goal, keep only lowest

so far path.

6. Recurse to step 2.


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Heuristic Search

Algorithm 3: IDA* Algorithm

Iterative deepening A* or IDA* is similar to iterative-deepeningdepth-first, but with the following modifications:The depth bound modified to be an f-limit

1. Start with limit = h(start)2. Prune any node if f(node) > f-limit3. Next f-limit=minimum cost of any node pruned

The cut-off for nodes expanded in an iteration is decided by the f-value of the nodes.


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Heuristic Search

Algorithm 3: RBFS: Recursive Breadth First Search

RBFS uses only linear space. It mimics best first search.

It keeps track of the f-value of the best alternative pathavailable from any ancestor of the current node.

If the current node exceeds this limit, the alternative path isexplored.RBFS remembers the f-value of the best leaf in the forgottensub-tree.


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Local search


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Local Search

Algorithm 1: Hill climbing Search

1. Put start state onto queue.

2. If queue is empty then fail.3. If head of queue is goal then succeed.4. Else remove head of queue, expand it, place children sorted by

n n ron o e queue.5. Recurse to step 2.

Or , Algorithm:

1. Determine successors of current state2. Choose successor of maximum goodness (break ties randomly)3. If goodness of best successor is less than current state's

goodness, stop

4. Otherwise make best successor the current state and go to step 1


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Local Search

Algorithm 2: Beam Search

1. Put start state onto queue.2. If queue is empty then fail.3. If head of queue is goal then succeed.4. Else remove head of queue, expand it, place children at

t e en o t e queue.5. If finishing a level, keep only w best nodes in the queue.6. Recurse to step 2.


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Local Search

Algorithm 3: Simulated annealing Search

1. From current state, pick a random successor state;2. If it has better value than current state, then accept the

transition, that is, use successor state as current state;3. Otherwise, do not give up, but instead flip a coin and accept

t e trans t on w t a g ven pro a ty t at s ower as t esuccessor is worse).4. So we accept to sometimes un-optimize the value function a

little with a non-zero probability.


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Adversarial search


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Adversarial Search

Algorithm : MINIMAX

MAXIMIN(n, alpha, beta)

If n is at the search depth, RETURN V(n)For each child m of nvalue = MINIMAX(m, alpha, beta)if value > alpha, alpha = value

= ,

RETURN alpha

MANIMAX(n, alpha, beta)If n is at the search depth, RETURN V(n)

For each child m of nvalue = MAXIMIN(m, alpha, beta)if value < beta, beta = valueif alpha


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Adversarial Search

Algorithm : MINIMAX

Minimax(player,board)

if(game over in current board position)return winnerchildren = all legal moves for player from this board

'

return maximal score of calling minimax on all the childrenelse (min's turn)

return minimal score of calling minimax on all the children


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Adversarial Search

Algorithm : Alpha-beta pruningEvaluate (node, alpha, beta)

if node is a leaf return the heuristic value of nodeif node is a minimizing node

for each child of nodebeta = min (beta, evaluate (child, alpha, beta))

if beta


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Syllabus for Mid sem :

Problem solving using Search techniques

Knowledge & reasoning

All the Best

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