1. Intelligent Control Methods Lecture 4: Searching in State Space Slovak University of Technology Faculty of Material Science and Technology in Trnava

2. 2 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)

3. 3 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)

4. 4 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

5. 5 Searching to the depth: As the first expands the node, which has been generated as the last one.

6. 6 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:

7. 7 Searching to the width: As the first expands the node, which has been generated as the first one.

8. 8 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.

9. 9 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)

10. 10 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,...