Download - 1 Chapter 2 Heuristic Search Techniques. 344-471 AI & ESChapter 2 2 Defining the problem A water jug problem: 4-gallon and 3-gallon - no marker on the.

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Chapter 2Heuristic Search Techniques

344-471 AI & ES Chapter 2 2

Defining the problem

A water jug problem: 4-gallon and 3-gallon

- no marker on the bottle- pump to fill the water into the jug- How can you get exactly 2 gallons of

water into the 4-gallons jug?

4 3


A state space search

(x,y) : order pair x : water in 4-gallons x = 0,1,2,3,4 y : water in 3-gallons y = 0,1,2,3start state : (0,0)goal state : (2,n) where n = any value

Rules : 1. Fill the 4 gallon-jug (4,-) 2. Fill the 3 gallon-jug (-,3) 3. Empty the 4 gallon-jug (0,-) 4. Empty the 3 gallon-jug (-,0)


1 (x,y) (4,y) Fill the 4-gallon jug if x < 42 (x,y) (x,3) Fill the 3-gallon jun if y < 33 (x,y) (x – d,y) Pour some water out of if x > 0 the 4-gallon jun4 (x,y) (x,y – d) Pour some water out of if y > 0 the 3-gallon jun5 (x,y) (0,y) Empty the 4-gallon jun if x > 0 on the ground6 (x,y) (x,0) Empty the 3-gallon jun if y > 0 on the ground

Water jug rules


7 (x,y) (4,y – (4 - x)) Pour water from the if x+y >= 4 and y > 0 3-gallon jug into the 4-gallon jug

until the 4-gallon jug is full8 (x,y) (x – (3 - y),3) Pour water from the if x+y >= 3 and y > 0 4-gallon jug into the 3-gallon jug

until the 3-gallon jug is full9 (x,y) (x+y,0) Pour all water from the if x+y <= 4 and y > 0 from the 3-gallon jug

into the 4-gallon jug10 (x,y) (0,x + y ) Pour all water from the if x + y <= 3 and X > 0 from the 4-gallon jug

into the 3-gallon jug11 (0,2) (2,0) Pour the 2 gallons from the 3-

gallon jug into the 4-gallon jug12 (2,y) (0,y) Empty the 2 gallons in

the 4-gallon jug on the ground

Water jug rules


A water jug solution4-Gallon Jug 3-Gallon Jug Rule Applied

0 00 3 23 0 93 3 24 2 70 2 5 or 122 0 9 or 11

Solution : path / plan


Formal description of a problem

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

2. Specify state/states that describes the situation of start state.

3. Specify state/states that describes the situation of goal state.

4. Specify the set of rules. assumption, generalization


Search Tree

(0,0)

(4,0) (0,3)

(4,3) (0,0) (4,3) (3,0)(1,3) (0,0)

Water jug problem.


Search Graph

Water jug problem. Cycle When will the search terminate?

•(0,0)

•(4,0) •(0,3)

•(4,3) •(4,3) •(3,0)•(1,3)

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Homework 2 (1%) Is there any other solution for a

water jug problem? If there is some other solution,

describe in an order pair of how to solve it.

due date ................................

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Question answering question

Marcus was a man.Marcus was a Pompeian.Marcus was born in 40 A.D.All men are mortal.All Pompeians died when the volcano

erupted in 79 A.D.No mortal lives longer than 150 years.It is now 1991 A.D.

Is Marcus alive?

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Solution 1

1. Marcus was man. axiom 14. All men are mortal. axiom 48. Marcus is mortal. 1,43. Marcus was born in 40 A.D. axiom 37. It is now 1991 A.D. axiom 79. Marcus’ age is 1951 years. 3,76. No mortal lives longer than 150 years axiom 610. Marcus is dead. 8,6,9

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7. It is now 1991 A.D. axiom 75. All Pompeians died in 79 A.D. axiom

511. All Pompeians are dead now. 7,5

2. Marcus was a Pompeian. axiom

212. Marcus is dead. 11,2

Solution 2

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The bank president ate a dish of pasta salad with the fork.

Understanding a sentence

bank = financial institution / a side of a riverdish = eat dish / eat pastapasta salad : dog food food with dog meat?with a fork : with ....her friend. / with vegetable.

solution : state of the world

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A blocks world

on(c,a). on(b,d).ontable(a).ontable(d).clear(b).clear(c). hand_empty.

a

c

d

b

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Seven problem characteristics

1. Decomposable Problem• Block world problem

2. Can solution steps be ignored or undone?

• Ignorable : theorem provingsolution steps can be ignored

• Recoverable : 8 puzzle solution steps can be undone (backtracking)

• Irrecoverable : chesssolution steps can not be undone

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3. Is the universe predictable?8-puzzel (yes)bridge (no) but we can use probabilities of each

possible outcomescontrolling robot arm gear of the arm might stuckhelping the lawyer to decide how to defend his client

against a murder charge.

4. Is a good solution absolute or relative? - formal inference methods

- More than one solution? - traveling salesman problem

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5. Is the solution a state or a path?- consistent interpretation for the sentence- water jug problem path / plan

6. What is the role of knowledge?knowledge for perfect program of chess (need knowledge to constrain the search)

newspaper story understanding (need knowledge to recognize a solution)

7. Does the task require interaction with a

person? solitary/ conversational

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Production system

1. A set of rules.2. Knowledge contains information

for a particular task.3. A control strategy.

resolve conflict rule. Breadth-first search Depth-first search

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Breadth-first search

Algorithm BFS:1. Create a variable called NODE-LIST and set it

to the initial state.2. Until a goal state is found or NODE-LIST is empty

do: Remove the first element from NODE-LIST and call it E. If NODE-

LIST was empty, quit. For each way that each rule can match the state described in E do:

Apply the rule to generate a new state. If the new state is a goal state, quit and return this state. Otherwise, add the new state to the end of NODE-LIST.

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Advantage BFS

1. will not trapped exploring a blind alley (ไม่�ลงล�กไปทางใดทางหนึ่��งเฉพาะ ท��อาจจะไม่�ใช่�คำ�าตอบ)

2. if there is a solution, DFS is guaranteed to find it.

3. if there are multiple solutions, a minimum solution will be found.

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Depth-first search Algorithm DFS:

1. If the initial state is a goal state, quit and return success.

2. Otherwise, do the following until success or failure is signaled:

Generate a successor, E, of the initial state. If there are no more successors, signal failure.

Call Depth-First Search with E as the initial state. If success is returned, signal success. Otherwise continue in this

loop.

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Advantage DFS

1. require less memory 2. may find a solution without

examining much of the search space.

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Production System Working memory Production set = Rules Figure 5.3 Trace Figure 5.4

Data driven Figure 5.9 Goal driven Figure 5.10

Iteration # Working memory Conflict sets Rule fired

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Production System

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Production System

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Production System

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Production System

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And-Or Graph start

Data driven Goal driven

b c d

e f goal

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Heuristic SearchHeuriskein to discover (Greek word)Heuristic is a technique that improves the

efficiency of the search process. - It is often useful to introduce heuristics based

on relatively unstructured knowledge.- can not use Mathematical analysis.

Heuristic function : is the function that maps from problem state descriptions to measures of desirability, usually represent as number guide the most profitable direction

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Generate-and-test

Generate all possible solutions DFS + backtracking Generate randomly Test function ANSWER yes/no Algorithm page 64....

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Hill Climbing Similar to generate-and-test Test function + heuristic function

Tell how close to the goal state EX : In unfamiliar city without a map...

downtown = tall building...

heuristic function = distance between downtown and tall building

Stop Goal state meet No alternative state to move

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Simple Hill Climbing Task specific knowledge into the control

process Is one state better than another If the new state is ...better... than the

current state then make it the current state

Algorithm page 66.....

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Steepest-Ascent Hill Climbing

Consider all moves from the current state

Select the best one as the next state

Algorithm page 67....

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Hill Climbing Characteristic

Local method It decides what to do next by looking only at

the immediate consequences of its choice (rather than by exhaustively exploring all of the consequence)

Look only one more ahead

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Local heuristic function

Block world figure 3.1 p. 69....

Local heuristic function1. Add one point for every block

that is resting on the thing it is supposed to be resting on.

2. Subtract one point for every block that is sitting on the wrong thing.

Initial state score = 4 (6-2) C,D,E,F,G,H correct = 6 A,B wrong = -2

Goal state score = 8 A,B,C,D,E,F,F,H all correct

Heuristic function : max value

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Local heuristic functionCurrent state : figure 3.1

หยิ�บ A วางบนึ่โต!ะ B C D E F G H วางเรี�ยิงเหม่#อนึ่เด�ม่ Score = 6 (B C D E F G H correct)

Block world figure 3.2 p. 69case a : Next state score = 4 (6-2)

case b : Next state score = 4 (6-2)

case c : Next state score = 4 (6-2)

All 3 cases a,b,c ...have no better score than the current state = 6

so we... Stop

Local minimum problemต�ดอยิ$�ในึ่กล%�ม่รีะด&บ local ม่องไปไม่�พ'นึ่อ�าง


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Global heuristic function

Block world figure 3.1 p. 69.... Global heuristic function

For each block that has the correct support structure (บรี�เวณฐานึ่ของม่&นึ่ต'องถู$กหม่ด)add one point for every block in the support structure.

For each block that has an incorrect support structure, subtract one point for every block in the existing support structure.

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initial state score = -28 C = -1, D = -2, E = -3, F = -4,

G = -5, H = -6, A = -7

C บรี�เวณฐานึ่ของม่&นึ่ต'องผิ�ด 1 ต&วD บรี�เวณฐานึ่ของม่&นึ่ต'องผิ�ด 2 ต&ว...

Goal state score = 28 B = 1, C = 2, D = 3, E = 4,

F = 5, G = 6, H = 7

B บรี�เวณฐานึ่ของม่&นึ่ต'องถู$กหม่ด 1 ต&ว

C บรี�เวณฐานึ่ของม่&นึ่ต'องถู$กหม่ด 2 ต&ว....


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Current state : figure 3.1

หยิ�บ A วางบนึ่โต!ะ B C D E F G H วางเรี�ยิงเหม่#อนึ่เด�ม่Score = -21 (C = -1, D = -2, E= -3, F = -4, G= -5, H = -6)

Block world figure 3.2 p. 69

Next state : move to case(c)

case a = -28 same as initial state

case b = -16 (C = -1, D = -2, E= -3, F = -4, G= -5, H = -1)

case c = -15 (C = -1, D = -2, E= -3, F = -4, G= -5)

No Local minimum problem It’s work


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New heuristic function

1. Incorrect structure are bad and should be taken apart.More subtract score

2. Correct structure are good and should built up.Add more score for the correct structure.

สิ่��งท��เรีาต'องพ�จารีณาHow to find a perfect heuristic function?

เข'าไปในึ่เม่องท��ไม่�เคำยิไปจะหล�กเล��ยิงทางต&นึ่ dead end ได'อยิ�างไรี

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Best first search Heuristic function : min value

page 74

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OR GRAPH : each of its branches represents an alternative problem-solving pattern

we assumed that we could evaluate multiple paths to the same node independently of each other

we want to find a single path to the goal use DFS : select most promising path use BSF : when no promising path/ switch part to receive

the better value old branch is not forgotten solution can be find without all completing branches having

to expanded

Best first search

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f’ = g + h’ g: cost from initial state to current stateh’: estimate cost current state to goal statef’: estimate cost initial state to goal stateOpen node : most promising nodeClose node : keep in memory, already discover node.

Best first search

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Best First Search Algorithm

page 75-76

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A* algorithm h’ : count the nodes that we step down the path,

1 level down = 1 point, except the root node.

Underestimate : we generate up until f ’(F)= 6 > f ’(C) =5

then we have to go back to C.

1 level

2 level

3 level

f’(E) = f’(C) = 5

f’ = g + h’

Heuristic function : min value

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A* algorithm f’ = g + h’

1 level

2 level

3 level

ปั�ญหา Overestimate : Suppose the solution is under D but we will not generate D because f’(D) = 6 > f’(G) = 4.

page 76


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And-Or Graph / Tree

can be solved by decomposing them into a set of smaller problems And arcs are indicated with a line connecting all the components

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And-Or Graph / Tree each arc with the successor has a cost of 1

3+4+1+1

15+10+1+1

9+27+1+1

choose lowest value = f’(B) = 5+1

ABEF = 17 + 1


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And-Or Graph / Tree

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To solve a problem1. Define the problem precisely. Specify the

problem space, and the starting and goal state (s).

2. Analyze the problem to determine where it falls with respect to seven important issues.

3. Identify and represent the knowledge required by the task.

4. Choose one or more techniques for problem solving , and apply those techniques to the problem.

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