Uninformed search

14 Jan 2004 CSE-IUT 1
Solving problems by
searching
Chapter 3

14 Jan 2004 CS 3243 - Blind Search 2
Outline
 Introduction to state space search
 Problem types
 Problem formulation
 Example problems
 Basic search algorithms

Objective: State space search
 State space representation
 How problems are formulated as state space
search problems
 How implicit state spaces can be unfolded
during search.

Goal directed agent

 Problem formulation: it means choosing a
relevant set of states to consider and a
feasible set of operators for moving from one
state to another.
 Search is the process of imagining
sequences of operators applied to the initial
state and checking which sequence reaches
a goal state.

Search problem

Searching process

8 queens problem

8 queens solution

8 Queens non solution

8 queens problem formulation 1

Search through a state space

Example: The 8-puzzle
 states?
 actions?
 goal test?
 path cost?

Example: The 8-puzzle
 states? locations of tiles
 actions? move blank left, right, up, down
 goal test? = goal state (given)
 path cost? 1 per move
[Note: optimal solution of n-Puzzle family is NP-hard]


Problem types
 Deterministic, fully observable  single-state problem
 Agent knows exactly which state it will be in; solution is a sequence
 Non-observable  sensorless problem (conformant
problem)
 Agent may have no idea where it is; solution is a sequence
 Each action might therefore lead to one of several possible
successor states.
 it could be one of several possible initial
states


 Nondeterministic and/or partially observable  contingency
problem
 The actions are uncertain
 Agent’s percepts provide new information after each action
 Unknown state space  exploration problem
 When the states and actions of the environment are unknown, the
agent must act to discover them.

Search tree

Search tree- terminology

Search strategies
 A search strategy is defined by picking the order of node
expansion
 Strategies are evaluated along the following dimensions:
 completeness: does it always find a solution if one exists?
 time complexity: number of nodes generated
 space complexity: maximum number of nodes in memory
 optimality: does it always find a least-cost solution?
 Time and space complexity are measured in terms of
 b: maximum branching factor of the search tree
 d: depth of the least-cost solution
 m: maximum depth of the state space (may be ∞)



Uninformed search strategies
 Uninformed search strategies use only the
information available in the problem
definition
 Breadth-first search
 Uniform-cost search
 Depth-first search
 Depth-limited search
 Iterative deepening search


Breadth first search

Depth first search

Depth-first search
 Expand deepest unexpanded node
 Implementation:
 fringe = LIFO queue, i.e., put successors at front



Depth-first search
 Implementation:



Drawbacks of DFS
 It can make wrong choice and get stuck
going down a very long(even infinite) path
when a different choice would lead to a
solution near the root of a search tree.
 DFS is not optimal

Properties of depth-first search
 Complete? No: fails in infinite-depth spaces,
spaces with loops
 Modify to avoid repeated states along path
 complete in finite spaces
 Time? O(bm
): terrible if m is much larger than d
 but if solutions are dense, may be much faster than
breadth-first
 Space? O(bm), i.e., linear space!
 Optimal? No



Depth limited search

Iterative deepening depth-first search

Iterative deepening search l =0

Iterative deepening search
 Number of nodes generated in a depth-limited search to
depth d with branching factor b:
NBFS = b0
+ b1
+ b2
+ … + bd-2
+ bd-1
+ bd
 Number of nodes generated in an iterative deepening
search to depth d with branching factor b:
NIDS = d b^1
+ (d-1)b^2
+ … + 3bd-2
+2bd-1
+ 1bd
 For b = 10, d = 5,
 NBFS= 10 + 100 + 1,000 + 10,000 +100,000+ 999990 = 1,111,100
 NIDS = 6 + 50 + 400 + 3,000 + 20,000 + 100,000 = 123,456



Properties of iterative
deepening search
 Complete? Yes
 Time? (d+1)b0
+ d b1
+ (d-1)b2
+ … + bd
=
O(bd
)
 Space? O(bd)
 Optimal? Yes, if step cost = 1




Comparing search strategies

Repeated states
 Failure to detect repeated states can turn a
linear problem into an exponential one!


Avoiding repeated states

Uniform Cost search

Uniform Cost search (UCS)
Initial Graph
Solution Tree After
Applying UCS

Uniform Cost search
Initialization: { [ S , 0 ] }
Iteration1: { [ S->A , 1 ] , [ S->G , 12 ] }
Iteration2: { [ S->A->C , 2 ] , [ S->A->B , 4 ] , [ S->G , 12] }
Iteration3: { [ S->A->C->D , 3 ] , [ S->A->B , 4 ] , [ S->A->C->G , 4 ] , [ S->G , 12 ] }
Iteration4: { [ S->A->B , 4 ] , [ S->A->C->G , 4 ] , [ S->A->C->D->G , 6 ] , [ S->G , 12 ] }
Iteration5: { [ S->A->C->G , 4 ] , [ S->A->C->D->G , 6 ] , [ S->A->B->D , 7 ] , [ S->G , 12 ] }
Iteration6: gives the final output as S->A->C->G

Uniform Cost search (Algorithm)
Insert the root into the queue
While the queue is not empty
      Dequeue the maximum priority element from the queue
      If priorities are same, alphabetically smaller path is
chosen
      If the path is ending in the goal state, print the path and
exit
      Else
         Insert all the children of the dequeued element, with
the cumulative costs as priority

Uniform Cost search
 Full Details: https://algorithmicthoughts.wordpress.com/2012/12/15/artificial-
intelligence-uniform-cost-searchucs/

Suggestion for good exam
 Read books, internet tutorial and video
tutorials available on Youtube for clear
understanding and better performance in
exam.

Uninformed search

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