C M M Awais (LUMS)1 SEARCH METHODS State space search Heuristic search.

c M M Awais (LUMS) 1

SEARCH METHODS

• State space search

• Heuristic search


SEARCH

Introduction:-

• If the general idea and action is known

• The actions that lead to solution is not known

• search methods can be applied

examples:-

• Systematical steps that lead to prove certain theorems

• Sequence of steps that solve a puzzle


BASIC METHODS

(Through all possible actions)

Initial State

Target State

Background

Material required is “GRAPH THEORY”


TYPICAL EXAMPLES OF

SEARCH PROBLEMS

• Toy Problem (The 8 puzzle)

• Route Finding

• Traveling Save Person

• Robot Navigation

• Assembly Sequencing


Eight Puzzle Problem


Route Finding Problem


Suppose Initial State is Library

Goal State is University

Possible Route ?

Problem is simple so all possible paths can be searched systematically to reach the goal

Library via Hospital via newsagent

to

University

What happens if search space is complex ?


ANALYSIS OF SEARCH STRATEGIES

Completeness: is the strategy guaranteed to find a solution where there is one?

Time Complexity: How long does it take to find a solution?

Space Complexity: How much memory does it need to perform the search?

Optimality: Does the strategy find the highest quality solution when there are several different solutions?


Exhaustive Search

One can systematically check every state that is reachable from initial state to end out if it is a goal state.

Search Space

The set of all states is the search space

• For simple/small search space exhaustive search is applicable [BRUTE FORCE or BLIND SEARCH]

• For complex search space HEURISTIC SEARCH is used


GRAPHS AND TREES

Graphs:-

• Consist of a set of nodes with links between them

• links can be directed / undirected

• Path is the sequence of nodes connected nodes via links.

Acyclic graphs = (Paths linking a node

with itself are absent)

Trees???


Tree:-

A tree is a special kind of graph with only one path to each node, usually represented with a special root node at

the top

Relationship between nodes

• Parent

• Children

• Sibling

Ancestor Node, Descendant Node, Leaf Node


Graphs VS Trees

• Compare the searches in the two (which is efficient)

a

b

c

d a

b c

de f g


Type of searches

• What is the value of profit if sales,employees, expenses etc., are given?.

• For a given profit what level of sales,employees, expenses etc., are required


STRATEGIES FOR STATE SPACE SEARCH

DATA DRIVEN SEARCH

(Forward Chaining)

• Start with some given facts

• Set of legal moves are given

• Search proceeds by applying rules to facts to generate new facts

• Process continues unless goal is reached


Goal - Driven Search (Backward Chaining)

• Take the goal

• Find what conditions or rules can produce or generate the goal

• Apply the conditions to generate subgoals

• Continue until the goal is reached


Types: Breadth First/Depth First


Example: Map Problem-1


Example: Map Problem -2


1. Start with queue = [initial - state] and found = FALSE

2. While queue not empty and not found do:

(a) Remove the first node n from queue

(b) if N is a goal state then found = TRUE

(c ) Find all the successor nodes of X, and put them on the end of the queue

Breath First


1. Open = [A]; closed = []

2. Open = [B,C,D]; closed = [A]

3. Open = [C,D,E,F]; closed = [A,B]

4. Open = [D,E,F,G,H]; closed = [C,B,A]

5. Open = [E,F,G,H,I,J]; closed = [D,C,B,A]

6. Open = [F,G,H,I,J,K,L]; closed = [E,D,C,B,A]

7. Open = [G,H,I,J,K,L,M]; closed = [F,E,D,C,B,A]

8. Open = [H,I,J,K,L,M,N]; closed = [G,F,E,D,C,B,A]

9. And so on until either U is found or open = []


1. Start with agenda = [initial - state] and found = FALSE

2. While agenda not empty and not found do:

(a) Remove the first node N from agenda

(b) if N is not in visited then

(I) Add N to visited

(II) if N is a goal state then found = TRUE

(III) Put N’s successors on the front of the stack

Depth First


Example


1. Open = [A]; closed = []

2. Open = [B,C,D]; closed = [A]

3. Open = [E,F, C,D]; closed = [B,A]

4. Open = [K,L,F,C,D]; closed = [E,B,A]

5. Open = [S,L,F,C,D]; closed = [K,E,B,A]

6. Open = [L,F,C,D]; closed = [S,K,E,B,A]

7. Open = [T,F,C,D]; closed = [L,S,K,E,B,A]

8. Open = [F,C,D]; closed = [T,L,S,K,E,B,A]

9. Open = [M,C,D]as L is already on closed;

closed = [F,T,L,S,K,E,B,A]

10. Open = [C,D]; closed = [M,F,T,L,S,K,E,B,A]

11. Open = [G.H.D]; closed = [C,M,F,T,L,S,K,E,B,A]

C M M Awais (LUMS)1 SEARCH METHODS State space search Heuristic search.

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