is

1. SRI KRISHNA COLLEGE OF ENGINEERING AND TECHNOLOGY
Kuniamuthur, Coimbatore, Tamilnadu, India
An Autonomous Institution, Affiliated to Anna University,
Accredited by NAAC with “A” Grade & Accredited by NBA (CSE, ECE, IT, MECH ,EEE, CIVIL& MCT)
SKCET- LECTURE
Course: Artificial Intelligence
Module: Agents & Its Techniques - Informed Search
Strategies
Faculty : Dr. P. Mohan Kumar,CSE
www.skcet.ac.in
SKCET- EEE MEASUREMENTS
AND INSTRUMENTATION

2. Completion of this lecture students will be able to :
◦ Understand Search Strategies of AI
◦ Students will be able to solve the
problems using Strategic approach
SKCET- CSE AI
SRI KRISHNA COLLEGE OF ENGINEERING AND TECHNOLOGY
Kuniamuthur, Coimbatore, Tamilnadu, India
An Autonomous Institution, Affiliated to Anna University,
Accredited by NAAC with “A” Grade & Accredited by NBA (CSE, ECE, IT, MECH ,EEE, CIVIL& MCT)

3. 3
SKCET- VIDEO LECTURE
Animation
Lecture Video

6.  Heuristic Search
◦ Best-First Search Approach
◦ Greedy
◦ A*
◦ Heuristic Functions
 Local Search and Optimization
◦ Hill-climbing
◦ Simulated Annealing
◦ Local Beam
◦ Genetic Algorithms
6

7.  An informed search strategy uses knowledge
beyond the definition of the problem
 The word "heuristic" means trial-and-error,
exploratory, unguaranteed, rule of thumb.
 The knowledge is embodied in an evaluation
function f(n)
◦ Estimates the distance of node n from the goal
7

8.  A combination of DFS and BFS
 The idea of Best First Search is to use an
evaluation function to decide which adjacent is
most promising and then explore.
 At each step, using an appropriate heuristic
function, the most promising node is selected
 If the node is selected, quit
 Otherwise, add it to the set of nodes generated so
far, and carry on with generating & selecting the
next node
8

9.  An instance of tree or graph search
 Fringe is ordered by f(n)
 Several best-first algorithms
◦ Greedy, A*, …
 Key is the heuristic function h(n)
◦ Heuristic measures distance from n to goal based
solely on the state at n
◦ Problem specific
◦ Constraint: h(n) = 0 if n is a goal node
9

10. function BEST-FIRST SEARCH (problem, Eval fn) returns a solution
sequence
inputs: problem, a problem
Eval fn, an evaluation function
Queueing-Fn  a function that orders nodes by Eval fn
return GENERAL-SEARCH(problem,Queueing-Fn)
10

11. 11

12.  Insert best nodes at beginning of nodes according to h,
that is, f(n)=h(n)
function Greedy-Search(problem) -> solution
input: a problem
best-first-search(problem,h) -> solution
 Consider the route finding problem.
◦ Can we use additional information to avoid costly paths that
lead nowhere?
◦ Consider using the straight line distance (SLD)
12

13. 374
253
366
329
13

14. 14

15. 15
So is Arad->Sibiu->Fagaras->Bucharest optimal?
Possibilities from Arad: Go to Zerind, Timisoara, or Sibiu?
Take as heuristic the air distance:
Zerind (374), Timisoara (329), or Sibiu (253)
Closest air distance Sibiu, hence go to Sibiu.
Possibilities from Sibiu: Arad, Fagaras, Oradea, or Rimnicu Vilcea?
Take as heuristic the air distance:
Arad (366), Fagaras (176), Oradea (380), or Rimnicu Vilcea (193)
Closest air distance Fagaras, hence go to Fagaras.
Possibilities from Fagaras: Go to Sibiu or Bucharest?
Take as heuristic the air distance:
Sibiu (253) or Bucharest (0)?
Closest air distance Bucharest, hence go to Bucharest.
That is 140km +99km +211km = 450km .

16.  Not optimal.
 Not complete.
◦ Could go down a path and never return to try another.
 Time Complexity
◦ O(bm)
 Space Complexity
◦ O(bm)
16

17.  The greedy best-first search does not consider how costly it was to
get to a node.
 It insert best nodes at beginning of nodes according to,
f(n)=g(n)+h(n)
g(n) - actual cost to that node
h(n) - estimated cost to the goal.
 In the A* algorithm the heuristic function h must be optimistic in order
to find the best solution.
function A-star(problem) -> solution
input: a problem
best-first-search(problem, g+h) -> solution
17

18. 18

19. 19
Possibilities from Arad: Go to Zerind, Timisoara, or Sibiu?
Take as heuristic the air distance plus cost to town:
Zerind (374+75=449), Timisoara (329+118=447), or Sibiu
(253+140=393)
Most promising Sibiu, hence explore going to Sibiu.
Possibilities from Sibiu: Arad, Fagaras, Oradea, or Rimnicu Vilcea?
Take as heuristic the air distance plus cost to town:
Arad (140+140+366=646), Fagaras (140+99+176=415), Oradea
(140+151+380=671), or Rimnicu Vilcea (140+80+193=413)
Overall most promising not expanded Rimnicu Vilcea, hence explore going to
Rimnicu Vilcea

20. 20
Possibilities from Rimnicu Vilcea: Sibiu, Pitesti, or Craiova?
Take as heuristic the air distance plus cost to town:
Sibiu (140+80+80+253=553), Pitesti (140+80+97+100=417), or Craiova
(140+80+146+160=526)
Overall most promising not expanded Fagaras, hence explore going to
Fagaras (from Sibiu)
Possibilities from Fagaras: Sibiu, or Bucharest?
Take as heuristic the air distance plus cost to town:
Sibiu (140+99+99+253=591), or Bucharest (140+99+211+0=450)
Overall most promising not expanded Pitesti, hence explore going to Pitesti
(from Rimnicu Vilcea)

21. 21
Possibilities from Pitesti: Rimnicu Vilcea, Craiova, or Bucharest?
Take as heuristic the air distance plus cost to town:
Rimnicu Vilcea (140+80+97+97+193=607), Craiova
(140+80+97+138+160=615) or Bucharest (140+80+97+101+0=418)
Overall most promising go to Bucharest from Pitesti.
Since there is no way to get on a shorter route to Bucharest the last one is
taken.

22.  A heuristic function h(n) is admissible if the estimated cost is
never more than the actual cost from the current node to the
goal node.
 To understand this, we can imagine a diagram as depicted below.
The direct path (heuristic) from A to C will never be more than the
actual cost (distance taking the path A -> B -> C).
 Theorem:
If h(n) is consistent, A* using GRAPH-SEARCH is optimal
22

23.  A heuristic is consistent if the cost from the current node to a
successor node, plus the estimated cost from the successor node to
the goal is less than or equal to the estimated cost from the
current node to the goal
 In an equation, it would look like this: C(n, n’) + h(n’) ≤ h(n)
Theorem:
If h(n) is consistent, A* using GRAPH-SEARCH is optimal
23

24.  Consider the heuristic such that h(n) = the minimum cost
from a successor of n to one of its own successors,
unless the successor is a goal node, in which case it is 0.
 (i,e)h(n) = the minimum cost of it’s successor’s
successor.
 So if we were to traverse A -> B -> C, h(A) would be
calculated from B -> C and NOT from A -> B
24

25.  In this case h(1) =15 , but h(2) = 0 ,
so, 13, c(1,3) + h(3) > h(1)  20 >15
23 , c (2, 3) + h(3) > h(2)  15 > 0,
which violates consistency.
 Note that the heuristic is still admissible because
h(1) =15 ≤ 20 = g (1),
h(2) = 0 ≤15 = g(2)
 h(1) = 15 because by definition, h(1) is from 2 -> 3. C(1,
2) + h(2) = 5 because C(1, 2) = 5 and h(2) = 0 because
as stated above, since 3 is the goal node, as well as
2’s successor node, h(2) = 0.
25

26.  Complete
◦ Yes! Same as above.
 Time and Space Complexity
◦ Depends on h(n)
◦ Sub-exponential if where h*(n) is true cost of getting from n to
goal
◦ Optimally efficient
26
))
(
(log
)
(
)
( *
*
n
h
O
n
h
n
h 


27. 27

28.  Expand S:
{S,A} f = 1+5 = 6
{S,B} f = 2+6 = 8
 Expand A:
{S,A} f = 1+5 = 6
{S,B} f = 2+6 = 8
{S,A,X} f = (1+4)+5 = 10
{S,A,Y} f = (1+7)+8 = 16
 Expand B:
{S,B} f = 2+6 = 8
{S,A,X} f = (1+4)+5 = 10
{S,B,C} f = (2+7)+4 = 13
{S,A,Y} f = (1+7)+8 = 16
{S,B,D} f = (2+1)+15 = 18
28

29. 29
Nodes H value
S 7
A 6
B 2
C 1
G 0
A
S
B
C G
1
4
2
5
12
3
2

30.  h1 = number of misplaced tiles
 h2 = sum of distances of tiles to goal position.
30

31.  Is h1
◦ admissible?
◦ consistent?
 Is h2
◦ admissible?
◦ consistent?
31

32.  Heuristics are often obtained from relaxed
problem
◦ Simplify the original problem by removing constraints
◦ The cost of an optimal solution to a relaxed problem is an
admissible heuristic.
32

33.  Original
◦ A tile can move from A to B if A is horizontally or
vertically adjacent to B and B is blank.
 Relaxations
◦ Move from A to B if A is adjacent to B
 h2 by moving each tile in turn to destination
◦ Move from A to B if B is blank
◦ Move from A to B
 h1 by simply moving each tile directly to destination.
33

34.  What heuristic is obtained from
Move from A to B if B is blank?
 Gaschnig’s heuristic (1979)
34

35.  Suppose now that the bananas are hung from
the ceiling and the monkey needs to climb on a
box to get the bananas. In addition, walls exist in
the environment.
 Box, monkey, and bananas placed randomly
 Monkey can see the entire world.
 Actions: N,S,E,W,Grab,Drop,Climb,Eat
35

36.  Describe the problem as a search problem.
◦ Initial state, successor function, goal, path cost
 In what way(s) can we relax the problem to obtain
a heuristic?
36

37.  If h2(n)  h1(n) for all n, then h2 dominates h1
◦ h2 is better for use with searching
 For the 8-puzzle, h2 does dominate h1
◦ If a tile is out of place, it is at least a distance of 1 away
from its correct position. Since h1 counts the number of
out of place tiles, and h2 totals all of the distances,
h2(n)  h1(n) for all n.
37

38. 38
ASSESSMENT
Assignment Quiz