Heuristic search uses heuristic functions to help optimize problem solving by trying to find solutions in the fewest steps or lowest cost. A heuristic function estimates the cost of reaching the goal state from any given node. There are two types of heuristic functions: admissible functions, which never overestimate cost, and non-admissible functions, which may overestimate cost. Admissible heuristics help guide search towards optimal solutions.

1. Artificial Intelligence
Heuristic Search

2. Heuristic Search and Heuristic Function
▪ Heuristic Search and Heuristic function are used in informed search.
▪ Heuristic search is a simple searching technique that tries to optimize a
problem using Heuristic Function.
▪ Optimization means that we will try to solve a problem in minimum number
of steps or cost.

3. Heuristic Function h(n)
▪ It is a function H(n) that gives an estimation on the cost of getting from
node ‘n’ to the goal state.
▪ It helps in selecting optimal node for expansion.
R1
R2
Mumbai GOA
R1= 340 Km
R2= 270Km
H(300)
H(200)

4. Heuristic Function h(n)
X
Y
Z
(Number of steps to reach the
goal state) or Heuristic value
of x will be :
h(x)=2
(Number of steps to reach the
goal state) or Heuristic value
of x will be :
h(y)=1
Goal State
Start Sate

5. Types of Heuristic Function h(n)
▪ There are two types of Heuristic Functions:
1. Admissible
2. Non-Admissible

6. Admissible Heuristic Function h(n)
▪ A heuristic function is admissible if it never overestimates the cost of
reaching the goal .
h(n) < = h*(n)
Here h(n) is heuristic cost, and h*(n) is the
estimated cost.
So heuristic cost should be less than or
equal to the estimated cost.

7. Non-Admissible Heuristic Function h(n)
▪ A non-admissible heuristic may overestimate the cost of reaching the
goal.
h(n) > h*(n)
Here h(n) is heuristic cost, and h*(n) is the
estimated cost.
So heuristic cost may be greater then to
the estimated cost.
total cost = search cost + path cost

8. Admissible Heuristic Function h(n)
A
B
1
E
Heuristic Cost
Start Sate
G
C
D
F Goal State
B= 1+3=4
3
2
5
1
1
H(C)=4 H(D)=5
H(B)=3 H(D)=5
H(C)=4
H(E)=2
H(F)=3
F(n) = H(n) + G(n)
Cost = Heuristic cost + Actual cost
C= 1+4=5
H(B)=3
D= 1+5=6
Actual cost fromA to G = 1+3+5+2= 11
H(B)=3 so h(n) =3 and h*(n)=11
H(n)<=h*(n)
3<=11
ADMISSIBLE

9. Non-Admissible Heuristic Function h(n)
A
B
1
E
Heuristic Cost
Start Sate
G
C
D
F Goal State
3
2
5
1
1
H(D)=5
H(B)=3 H(D)=5
H(C)=4
H(E)=3
H(F)=3
F(n) = H(n) + G(n)
Cost = Heuristic cost + Actual cost
Actual cost from A to G(via D) = 1+3= 4
H(D)=5 so h(n) =5 and h*(n)=4
H(n)<=h*(n)
5<=4
NON-ADMISSIBLE
3

10. THANK YOU
➢ Subscribe our channel
➢ Follow us on Facebook
✓ Page name : Digital
Wave ( Link in
Description Box)