Intelligent Control Methods

Lecture 4: Searching in State Space

Slovak University of TechnologyFaculty of Material Science and Technology in Trnava

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Basic Concepts:

A Task is every time in some state. A set of all possible states: State space

Example: chess

Task representation: Initial state Goal state (a set of goal states, they are listened or

given by condition) Operators set (operator = action for transformation of

a state into another one)

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Basic Concepts (2):

To solve a task = to find an operators sequence, which transforms the initial state into the goal one.

The state space is represented by a graph. States – nodes Operators – branches

To solve the task in a graph = to find a path in a graph (from initial into goal state)

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Graph is too large. => Graph (graph parts) forms during task

solution Node creation = node generation Generation of all node successors = node expansion

Depends on nodes expansion order: Searching to the depth Searching to the width

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Searching to the depth: As the first expands the node, which has been generated as the last one.

1 2

1 1 1 2

3

9 1 0

5

7 8

6

4

0

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Advantages: Easy implementation (LIFO) Systematical searching

Disadvantages: The goal node can be missed. Necessary: The depth of searching

Example: Game „8“

Searching to the depth:

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Searching to the width: As the first expands the node, which has been generated as the first one.

1 2 1 3

4 5 6 7

1

8 9

2

1 0 1 1

3

0

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Searching to the width:

Advantages: Easy implementation (FIFO) The first solution is funded Systematical searching

Disadvantages: Too systematical (inefficient)

Example: Game „8“

S. to the depth + s. to the width = blind searching.

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Heuristic searching:

Opposite to blind searching More complicate, but more effective Exploits information from the task for nodes

evaluation f(n) = g(n) + h(n) g(n) – evaluation of path from begin to node n h(n) – evaluation of past from node n to goal h(n) – unknown, substituted by assessment h´(n)

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Searching examples:

Game „8“ 3 missionaries and 3 cannibals Wolf, goat and cabbage Hanoi tower Monkey and banana (in robotics) Operations planning Games with coins, matches, weighting

machines, ...