The document describes a problem of a farmer transporting a fox, goose, and grains across a river using a small boat that can only carry one item at a time, outlines the initial state and constraints of not leaving the fox and goose or goose and grains alone together, and proposes using breadth-first search to find the optimal solution path to transport all items across the river.

1. FUNDAMENTALS OF ARTIFICIAL
INTELLIGENCE PROJECT
(CSC463)
Document Reference No: REPORT/1.0/2011
Group member :
Mohd Nazri Bin Ismail
Muhammad Ibrahim Bin Haji Mohamed Soid
Nor Azura Binti Mohamed Salim

2. Farmer and his three possessions
PROJECT (B)

3. Outline
1) Introduction
2) Problem formulation
- State space
- Well-defined problem
3) Solution
4) Conclusion

4. 1.0
Introduction
A farmer wants to transport
himself along with a fox, a
goose, and some grains across
a river. The boat could only
take at most one of his
possessions any trip. The
constraints of this problem are
the fox must not be left
unattended with the goose,
and the goose must not be left
unattended with the grains.

5. Farmer, fox,
goose, grains
2.1 State Space
B A
Farmer, grains Fox, goose Farmer Fox, goose,
grains
B A A
2. Problem Formulation
B
Farmer, goose Fox, grains Farmer, fox Goose, grains
B A B A
Goose Farmer, fox,
grains
B A
Farmer, goose, Fox Farmer, fox, Grains
grains goose
B A B A
Grains Farmer, fox, Fox Farmer, goose,
goose grains
B A B A
Goose, grains Farmer, fox Fox, goose Farmer, grains
B A B A
Farmer, fox, Goose
grains
B A
Initial State
Fox, grains Farmer, goose Terminate
Goal
B A
Farmer, fox,
goose, grains
B A

6. 2.2 Well-Defined Problem
• Initial State
- At A there is a farmer with a fox, a goose and some grains
- At B there is no one.
B A
RIVER
Farmer with a fox, a goose and
some grains

7. • Possible Action
– Farmer need to bring along with him a fox first or a goose first or some
grains first or brings himself only
– Farmer must also consider constrains that is do not left behind the fox
and the goose together or left the goose and the grains together
• Transition Model
– If the farmer chooses to bring a fox first then he will leave a goose and
some grains at place A then goose will eat the grains
– If the farmer chooses to bring the grains first, then the fox will eat the
goose
– Thus, farmer only has one choice that is bring the goose first and left
the fox together with the grains

8. • Goal
- The goal of this problem is to transfer the entire farmer possessions that
is a fox, a goose, and some grains to place B.
B A
RIVER
Farmer with a fox, a goose and
some grains

9. All the farmer action can be summarized as follow:
1) First, the farmer brings the goose from place A to place B.
2) Second, the farmer return back to place A.
3) Third, from place A the farmer brings a fox or some grains to place B.
4) Fourth, from place B the farmer brings back a goose to place A.
5) Fifth, from place A the farmer brings a fox or some grains to place B.
(The one that the farmer does not bring in step 3)
6) Sixth, the farmer return back to place A.
7) Lastly, the farmer brings goose to place B.
• Step Cost
o Step Cost = number of crossing that the farmer must
make in order to bring all of his possessions to place B.
o There are 7 crossing, that is 4 forward and 3 backward
o Thus, the step cost is 7
• Path Cost
o Path cost=number of animal & farmer has crossed the river
o That is from 4 to 0.

10. 3. Search Algorithm
• One algorithm from blind search that is
Breadth First Search (BFS)
• BFS is the shortest solution path from initial
state to goal compare to Depth First Search
(DFS)
• BFS proceed searching all the way across one
level before going to the next level

11. 3.1 Search Strategies
• Space Complexity
– Is proportional to the number of nodes at the deepest level
– Space complexity for BFS at worst case is exponential
– Thus, BFS is often impractical for large problems on systems with
bounded space
• Time Complexity
– Time complexity of BFS is
– O(bd) or exponential since every vertex and every edge will be
explored in the worst case

12. • Completeness
– BFS is complete, thus BFS will find solution regardless of the kind of
graph
– But, if the graph is infinite and there is no solution and BFS will diverge
• Optimality
– For unit-step cost, BFS is optimal
– In general BFS is not optimal since it always returns the result with the
fewest edges between the start node and the goal node
– If the graph is not weighted, and therefore all step costs are equal, BFS
will find the nearest and the best solution
– BFS use 2 lists that are Open list and Close list

13. 3.2
B
F
S
BFS TRAVERSAL:
A B C D E F G H I J K L M N O P Q

14. STATE OPEN CLOSE
0 [A] [ ] BFS TRAVERSAL:
1 [B, C, D, E] [A] A B C D E F G H I J K L M N O P Q
2 [C, D, E] [B, A]
3 [D, E, F] [C, B, A]
4 [E, F] [D, C, B, A]
5 [F] [E, D, C, B, A]
6 [G, H] [F, E, D, C, B, A]
7 [H, I, J] [G, F, E, D, C, B, A]
8 [I, J, K, L] [H, G, F, E, D, C, B, A]
9 [J, K, L] [I, H, G, F, E, D, C, B, A]
10 [K, L, M] [J, I, H, G, F, E, D, C, B, A]
11 [L, M, N] [K, J, I, H, G, F, E, D, C, B, A]
12 [M, N] [L, K, J, I, H, G, F, E, D, C, B, A]
13 [N, O] [M, L, K, J, I, H, G, F, E, D, C, B, A]
14 [O, P] [N, M, L, K, J, I, H, G, F, E, D, C, B, A]
15 [P, Q] [O, N, M, L, K, J, I, H, G, F, E, D, C, B, A]
16 [Q, R] [P, O, N, M, L, K, J, I, H, G, F, E, D, C, B, A]

15. SOLUTION PATH:
A C F G J M O Q

16. Conclusion
• BFS is complete, optimal search strategy with
exponential time and space complexity
• Problem size is small
• BFS is easier to implement

17. - Nazri –
- Ibrahim –
- Azura -
Question??