Matakuliah
Tahun
Versi
: T0264/Inteligensia Semu
: Juli 2006
: 2/1
Pertemuan 2
PROBLEMS, PROBLEM SPACES, AND SEARCH
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• << TIK-99 >>
• << TIK-99>>
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Outline Materi
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Materi 1
Materi 2
Materi 3
Materi 4
Materi 5
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Building a Problem-Solving Program
To build a system to solve a particular
problem, needed four things :
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Define the problem precisely
Analyze the problem
Represent the task knowledge
Choose and apply representation and
reasoning technique
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2.1 Defining the Problem as a State
Space Search
One Legal Chess Move
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Another Way to Describe Chess Moves
White pawn at
Square(file e, rank 2)
AND
Square(file e, rank 3)
is empty
AND
Square(file e, rank 4)
is empty
Move pawn from
Square(file e, rank 2)
TO
Square(file e, rank 4)
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A Water Jug Problem
You are given two jugs, a 4-galon one and
a 3-galon one. Neither has any measuring
marker on it. There is pump that can be
used to fill the jugs with water. How can
you get exactly 2 gallons of water into the
4-galon jug ?
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A Water Jug Problem
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Production Rules for the Water Jug
Problem
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Production Rules for the Water Jug
Problem
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One Solution to the Water Jug Problem
Gallon in the 4-gallon Jug
Gallon in the 3-gallon Jug
Rule Applied
0
0
0
3
2
3
0
9
3
3
2
4
2
7
0
2
5 or 12
2
0
9 or 11
2
0
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To Specify a Problem
To provide a formal description of
problem, do the following :
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Define the state space that contain all
possible configurations of the relevan
objects
Specify one or more the initial states
Specify one or more the goal states
Specify a set of rules that describe the
actions (operator) available
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Contoh Kasus
• Seorang Petani akan menyeberangkan
seekor Kambing, seekor Harimau dan
Sayuran dengan sebuah rakit keseberang
sungai. Rakit hanya muat petani dengan
satu penumpang lainya. Jika ditinggal
petani maka kambing dimakan harimau
dan sayuran dimakan kambing.
Buatlah representasi ruang keadaan agar
keempat obyek sampai diseberang sungai
masih lengkap.
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2.2 Production Systems
• A set of rules
• Knowledge / database
• A control strategy
• A rule applier
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Search Techniques
Termasuk dalam Blind Search
Breadth First Search : semua node dikunjungi
sehingga jika ada solusi pasti diketemukan atau
tidak terjebak jalan buntu. Tetapi membutuhkan
memori besar dan waktu pencarian relatif lama.
Dept First Search : node dikunjungi dari ranting
paling kiri. Jika ada solusi bisa diketemukan
lebih cepat, membutuhkan memori kecil dan
waktu pencarian lebih singkat. Tetapi bisa
terjebak dalam jalan buntu.
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2.2.1 Control Strategies
Algorithm : Breadth – First Search
1. Set Node-List to the initial state
2. Until a goal is found or Node-List is empty do :
a. Remove the first element of Node-List and
call it E.If Node-List was empty,quit
b. For each rule match againtst E do :
• Apply the rule to generate a new state
• If the nem state is a goal, quit and return it
• Else,add the new state to the end of Node-List
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Two level of a Breadth-First Search Tree
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Algorithm : Dept-First Search
1.If the initial state is a goal state, quit and
return succes
2.Otherwise,do the following until succes or
failure is signaled :
a. Generate a successors,E,of the initial state.If
there are no more successors,signal failure
b. Call Depth-First Search with E as the initial state
c. If succes is returned,signal success. Otherwise
continue in this loop
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A Depth-First Search Tree
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2.2.2 Heuristic Search
Some Simple Heuristic Functions
Chess
The material advantage of our side over the
opponent
Travelling
Salesman
The sum of the distances so for
Tic-Tac-Toe
1 for each row in which we could win and in
which we already have one piece plus 2
for each such row in which we have two
pieces
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Heuristic Search
• Heuristic Search is a technique that
improves the efficiency of a search
process, possibly by sacrificing claims of
completeness. Heuristic like tour guides.
• Some heuristics help to guide a search
process without sacrificing any claims to
completeness that the process might
previously have had.
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2.3 Problem Characteristics
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Is the problem decomposable ?
Can solution steps be ignored or undone ?
Is the problem’s universe predictable?
Is a good solution absolute or relative ?
Is the desired solution a state of the world or
a path to a state ?
– Is a large amount of knowledge absolutely
required to solve the problem, or is it
important only to constrain the search ?
– Must problem-solving be interactive?
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Decomposable Problem
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2.4 Production System Characteristics
• A monotonic production system is a production system in
which the application of rule never prevents the later
application of another rule that could also have been
applied at the time the first rule was selected.
• A nonmonotonic production system is one in which this is
not true.
• A partially commutative production system is production
system with the property that if the application of a
particular sequence of rules transform state x into state
y, then any permutation of those rules that is allowable
also transform state x into state y.
• A commutative productions system is production system
that is both monotonic and partially commutative.
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Production System Characteristics
The four Categories of Production Systems
Partially commutative
Monotonic
Nonmonotonic
Theorem proving
Robot navigation
Not
Partially Chemical syntesis
commutative
Bridge
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2.5 Design of Search Programs
• Some important issues that arise in all of them :
- The direction in which to conduct the search
(forward vs backward reasoning)
- How to select applicable rules (matching)
- How to represent each node of the search
process (the knowledge representation problem
and frame problem)
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Design of Search Programs
A Search Graph for the Water Jug Problem
(0,0)
(4,0)
(1,3)
(0,3)
(4,3)
(3,0)
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2.6 Additional Problems
– The Missionarries and Cannibals
– The Tower of Hanoi
– The Monkey and Bananas
– Cryptarithmetic
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<< CLOSING>>
End of Pertemuan 2
Good luck
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