trí tuệ nhân tạo cao hoàng trứ chương ter2 problems and search sinhvienzone com

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Problems and Search

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Chapter 2

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Search strategies

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State space search

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Problem characteristics

Design of search programs

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Outline

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CSE Faculty - HCMUT
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State Space Search

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Problem solving = Searching for a goal state

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CSE Faculty - HCMUT
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State Space Search: Playing Chess

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• Each position can be described by an 8-by-8 array.
• Initial position is the game opening position.
• Goal position is any position in which the opponent

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does not have a legal move and his or her king is
under attack.

• Legal moves can be described by a set of rules:

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− Left sides are matched against the current state.
− Right sides describe the new resulting state.

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CSE Faculty - HCMUT
SinhVienZone.com

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State Space Search: Playing Chess

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• State space is a set of legal positions.
• Starting at the initial state.
another.

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• Using the set of rules to move from one state to

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• Attempting to end up in a goal state.

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CSE Faculty - HCMUT
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State Space Search: Water Jug Problem

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“You are given two jugs, a 4-litre one and a 3-litre one.
Neither has any measuring markers on it. There is a
pump that can be used to fill the jugs with water. How
can you get exactly 2 litres of water into 4-litre jug.”

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CSE Faculty - HCMUT
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State Space Search: Water Jug Problem
y = 0, 1, 2, 3

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• Start state: (0, 0).

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x = 0, 1, 2, 3, or 4

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• State: (x, y)

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• Goal state: (2, n) for any n.
• Attempting to end up in a goal state.

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CSE Faculty - HCMUT
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3. (x, y)
if x > 0

Cao Hoang Tru
CSE Faculty - HCMUT
SinhVienZone.com

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Zo

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4. (x, y)
if y > 0

→ (x, 3)

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2. (x, y)
if y < 3

→ (4, y)

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1. (x, y)
if x < 4

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State Space Search: Water Jug Problem

→ (x − d, y)
→ (x, y − d)

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→ (x, 0)

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6. (x, y)
if y > 0

→ (0, y)

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5. (x, y)
if x > 0

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State Space Search: Water Jug Problem

7. (x, y)
→ (4, y − (4 − x))
if x + y ≥ 4, y > 0

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8. (x, y)
→ (x − (3 − y), 3)
if x + y ≥ 3, x > 0

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CSE Faculty - HCMUT
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9. (x, y)
→ (x + y, 0)
if x + y ≤ 4, y > 0

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State Space Search: Water Jug Problem

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10. (x, y)
→ (0, x + y)
if x + y ≤ 3, x > 0
12. (2, y)

→ (2, 0)

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11. (0, 2)

Cao Hoang Tru
CSE Faculty - HCMUT

SinhVienZone.com

→ (0, y)

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State Space Search: Water Jug Problem

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1. current state = (0, 0)

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2. Loop until reaching the goal state (2, 0)

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(0, 0)
(0, 3)
(3, 0)
(3, 3)
(4, 2)
(0, 2)
(2, 0)

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− Apply a rule whose left side matches the current state
− Set the new current state to be the resulting state

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CSE Faculty - HCMUT
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State Space Search: Water Jug Problem

→ (x, 3)

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2. (x, y)
if y < 3

→ (4, y)

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1. (x, y)
if x < 4

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The role of the condition in the left side of a rule
⇒ restrict the application of the rule
⇒ more efficient

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CSE Faculty - HCMUT
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State Space Search: Water Jug Problem

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Special-purpose rules to capture special-case
knowledge that can be used at some stage in solving a
problem
→ (2, 0)

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11. (0, 2)

→ (0, y)

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12. (2, y)

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CSE Faculty - HCMUT
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State Space Search: Summary

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1. Define a state space that contains all the possible
configurations of the relevant objects.

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2. Specify the initial states.

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3. Specify the goal states.
4. Specify a set of rules:

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− What are unstated assumptions?
− How general should the rules be?
− How much knowledge for solutions should be in the
rules?

Cao Hoang Tru

CSE Faculty - HCMUT
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Search Strategies

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Requirements of a good search strategy:

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1. It causes motion

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2. It is systematic

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Otherwise, it will never lead to a solution.
Otherwise, it may use more steps than necessary.

3. It is efficient

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Find a good, but not necessarily the best, answer.

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CSE Faculty - HCMUT
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Search Strategies

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1. Uninformed search (blind search)

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Having no information about the number of steps from the
current state to the goal.

2. Informed search (heuristic search)

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More efficient than uninformed search.

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CSE Faculty - HCMUT
SinhVienZone.com

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(4, 0)

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(0, 0)

(0, 0)

(1, 3)

(4, 3)

(0, 3)

(0, 0)

(3, 0)

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(4, 3)

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Search Strategies

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CSE Faculty - HCMUT
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Search Strategies: Blind Search

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Expand all the nodes of
one level first.

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• Breadth-first search

• Depth-first search

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Expand one of the nodes at
the deepest level.

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CSE Faculty - HCMUT
SinhVienZone.com

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Time

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Space

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Optimal?
Complete?

DepthFirst

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BreadthFirst

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Criterion

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Search Strategies: Blind Search

b: branching factor
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CSE Faculty - HCMUT
SinhVienZone.com

d: solution depth

m: maximum depth
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DepthFirst

bd

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Time

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Space

Yes

No

Yes

No

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Optimal?
Complete?

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BreadthFirst

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Criterion

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Search Strategies: Blind Search

b: branching factor

Cao Hoang Tru
CSE Faculty - HCMUT
SinhVienZone.com

d: solution depth

m: maximum depth
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Search Strategies: Heuristic Search

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• Heuristic: involving or serving as an aid to learning,

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discovery, or problem-solving by experimental and
especially trial-and-error methods.
(Merriam-Webster’s dictionary)

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• Heuristic technique improves the efficiency of a

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search process, possibly by sacrificing claims of
completeness or optimality.

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CSE Faculty - HCMUT
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Search Strategies: Heuristic Search

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• Heuristic is for combinatorial explosion.

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• Optimal solutions are rarely needed.

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CSE Faculty - HCMUT
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The Travelling Salesman Problem

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Search Strategies: Heuristic Search

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“A salesman has a list of cities, each of which he must
visit exactly once. There are direct roads between each
pair of cities on the list. Find the route the salesman
should follow for the shortest possible round trip that
both starts and finishes at any one of the cities.”
1

D

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Cao Hoang Tru
CSE Faculty - HCMUT
SinhVienZone.com

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B
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1. Select a starting city.

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Nearest neighbour heuristic:

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Search Strategies: Heuristic Search

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2. Select the one closest to the current city.

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3. Repeat step 2 until all cities have been visited.

Cao Hoang Tru
CSE Faculty - HCMUT
SinhVienZone.com

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1. Select a starting city.

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Nearest neighbour heuristic:

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Search Strategies: Heuristic Search

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2. Select the one closest to the current city.

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3. Repeat step 2 until all cities have been visited.

Cao Hoang Tru
CSE Faculty - HCMUT

SinhVienZone.com

O(n2) vs. O(n!)

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