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Informed Search and Exploration
Uninformed vs Informed
Search Strategies,
Best-First Search Algorithm,
Uniform Cost Search
Algorithm (UCS),
Greedy best-first search
algorithm,
- Complete?,
- Time?,
- Space?,
- Optimal?.
A* search algorithm,
Iterative Deepening Search
Algorithm,
- QueuingFn,
- Expand(state),
Explore: Topics based
Research Areas:
@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)
1. Uninformed Vs Informed Search Strategies
Uninformed Search Strategies:
Uninformed search strategies look for solutions by systematically
generating new states and checking each of them against the goal.
This approach is very inefficient in most cases.
Most successor states are “obviously” a bad choice.
Such strategies do not know because they have minimal problem-
specific knowledge.
Strategies are;
- Breadth-first search,
- depth-first search.
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1. Uninformed Vs Informed Search Strategies (Cont…)
Informed Search Strategies:
Informed search strategies exploit problem-specific knowledge as
much as possible to drive the search.
They are almost always more efficient than uninformed searches
Also, more consistent and optimal.
Main Idea:-
①Use the knowledge of the problem domain to build an evaluation function f.
②For every node n in the search space, f ( n ) quantifies the desirability of expanding
n in order to reach the goal.
③Then, use the desirability value of the nodes in the fringe (destination) to decide
which node to expand next.
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1. Uninformed Vs Informed Search Strategies (Cont…)
Informed Search Strategies:
Informed search strategies deal as best-first search.
Idea: use an evaluation function for each node to estimate of
“desirability”.
Strategy: Always expand most desirable unexpanded node.
Implementation: fringe is a priority queue sorted in decreasing order
of desirability.
Special cases:
Best-first search
Uniform-cost search
Greedy search
A* search
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2. Best-First Search Algorithm
Efficient selection of the current best candidate for extension is
typically implemented using a priority queue.
Best-first search only as good as heuristic.
– Example heuristic for 8 puzzle:
– Manhattan Distance
Example:- Step -1:-
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2. Best-First Search Algorithm (Cont…)
Example:- Step -2:-
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Example:- Step -3:-
2. Best-First Search Algorithm (Cont…)
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Example:- Step -4:-
2. Best-First Search Algorithm (Cont…)
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Example:- Step -5:-
2. Best-First Search Algorithm (Cont…)
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Example:- Step -6:-
2. Best-First Search Algorithm (Cont…)
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Example:- Step -7:-
2. Best-First Search Algorithm (Cont…)
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Example:- Step -8:-
2. Best-First Search Algorithm (Cont…)
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Example:- Step -9:-
Is there any other “GOAL” is possible at specific “Estimated
distance” ????
2. Best-First Search Algorithm (Cont…)
@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)
Example:- Class Evaluation:-
Estimated distance = 24, 37, 49
H
e u i a ai o
a r g g m t s z w tt
h yl
19 6 11 9 14 2317
16 12 826
315 13 14
73 54
31 0 27
2. Best-First Search Algorithm (Cont…)
@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)
Example:- Generate “English dictionary” by using best-first search
algorithm.
2. Best-First Search Algorithm (Class Participation)
Parent Node Total level (max) Total Estimated distance Total number of nodes
S 4 34 18
D 3 46 16
R 2 23 12
A 5 69 27
I 2 18 9
P 3 25 14
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3. Uniform Cost Search Algorithm (UCS)
QueueingFn is SortByCostSoFar.
Cost from root to current node n is g(n).
– Add operator costs along path
First goal found is least-cost solution.
Space & time can be exponential because large subtrees with
inexpensive steps may be explored before useful paths with costly
steps.
If costs are equal, time and space are O(bd).
– Otherwise, complexity related to cost of optimal solution.
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3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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Step 1:- Open list: C
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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Step 2:- Open list: B(2) T(1) O(3) E(2) P(5)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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Step 3(ordering):- Open list: T(1) B(2) E(2) O(3) P(5)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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Step 4:- Open list: B(2) E(2) O(3) P(5)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{T(1) is excluded}
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Step 5:- Open list: E(2) O(3) P(5)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{B(2) at stack}
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Step 6:- Open list: E(2) O(3) A(3) S(5) P(5) R(6)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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Step 7:- Open list: O(3) A(3) S(5) P(5) R(6)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{E(2) at stack}
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Step 8:- Open list: O(3) A(3) S(5) P(5) R(6) G(7)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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Step 9:- Open list: A(3) S(5) P(5) R(6) G(7)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{O(3) at stack}
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Step 10:- Open list: A(3) I(4) S(5) N(5) P(5) R(6) G(7)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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Step 11:- Open list: I(4) P(5) S(5) N(5) R(6) G(7)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{A(3) is excluded}
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Step 12:- Open list: P(5) S(5) N(5) R(6) Z(6) G(7)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{I(4) at stack}
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Step 13:- Open list: S(5) N(5) R(6) Z(6) F(6) G(7) D(8) L(10)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{P(5) at stack}
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Step 14:- Open list: N(5) R(6) Z(6) F(6) G(7) D(8) L(10)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{S(5) is excluded}
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Step 15:- Open list: R(6) Z(6) F(6) G(7) D(8) L(10)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{N(5) is excluded}
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Step 16:- Open list: Z(6) F(6) G(7)D(8) L(10)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
{R(6) is excluded}
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Step 17:- Open list: F(6) G(7)D(8) L(10)
3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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3. Uniform Cost Search Algorithm (UCS Example) (Cont…)
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3. Uniform Cost Search Algorithm (Class Participation)
A
B
C
D
E
F
Goal
5
8
10
2
16
30
14
26
4
18
3 12
A)
B)
6
2 3 41
5 7 8
9 10 11 12 Goal
2 1 2
5
1
1
8 3
1 5
1
1
15
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Comparison of Search Techniques
DF
S
BF
S
UC
S
Complete N Y Y
Optimal N N Y
Heuristic N N N
Time bm bd+1 bm
Space bm bd+1 bm
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4. Greedy best-first search algorithm
Greedy best-first search expands the node that appears to be
closest to goal.- Less number of nodes,
- shortest time in between compared nodes.
Evaluation function f(n) = h(n) (heuristic) = estimate of cost from
n to goal.
Example; hSLD(n) = straight-line distance from n to Bucharest.
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4. Greedy best-first search algorithm (Example) (Cont…)
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4. Greedy best-first search algorithm (Example) (Cont…)
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4. Greedy best-first search algorithm (Example) (Cont…)
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4. Greedy best-first search algorithm (Example) (Cont…)
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Complete? No – can get stuck in loops, e.g., Iasi Neamt
Iasi Neamt
Time? O(bm), but a good heuristic can give dramatic
improvement
Space? O(bm) -- keeps all nodes in memory
Optimal? No
4. Greedy best-first search algorithm (Cont…)
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5. A* search algorithm
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
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5. A* search algorithm (Example) (Cont…)
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5. A* search algorithm (Example) (Cont…)
Sibiu = cost + estimated cost
Sibiu = 140+253
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5. A* search algorithm (Example) (Cont…)
Arad = (140+140)+366
Arad = 280+366
Fagaras= (140+99)+176
Fagaras= 239+176
Oradea= (140+151)+380
Oradea = 291+380
Rimnicu Vilcea= (140+80)+193
Rimnicu Vilcea = 220+193
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5. A* search algorithm (Example) (Cont…)
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5. A* search algorithm (Example) (Cont…)
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5. A* search algorithm (Example) (Cont…)
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6. Iterative Deepening Search Algorithm
DFS with depth bound.
QueuingFn is enqueue at front as with DFS
- Expand(state) only returns children such that
depth(child) <= threshold
- This prevents search from going down infinite
path.
First threshold is 1
- If do not find solution, increment threshold and
repeat.
Problem:-
What about the repeated work?
Time complexity (number of generated nodes)
[b] + [b + b2] + .. + [b + b2 + .. + bd]@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)
6. Iterative Deepening Search Algorithm (Cont…)
Figure: Example of iterative deepening search
@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)
7. Explore: Topics based Research Areas
(1) Dynamic Walking over Uneven Terrain :-
Proposed architecture of Model
Implemented results
@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)
Assignment # 2(Searching Algorithms)
1. Adversarial Search
2. Bidirectional Search
3. Beam Search
4. Local & International
applications of;
a) Best-First Search
Algorithm,
b) Uniform Cost Search
Algorithm (UCS),
c) Greedy best-first
search algorithm,
d) A* search algorithm.
@Copyrights: Advanced Artificial Intelligence Organized by Dr. Ahmad Jalal (http://portals.au.edu.pk/imc/)