Basic Searching for Artificial Intelligence, Lecture notes of Artificial Intelligence

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PRINCIPLES OF ARTIFICIAL INTELLIGENCE

COURSE CODE: SOF

LECTURER : Dr. Shamini Raja Kumaran

Problem solving and search technology PART 1

OUTLINE

• (^) BASIC SEARCHING:
  • (^) Learn the basics of state space representation
  • (^) Learn the basics of search in state space
    • (^) Game: How to tackle N queens game?
    • (^) Conditions: What’re the conditions for searching?
    • (^) Formulation: How to formulate searching?
    • (^) Category: How to categorize searching?
    • (^) Solution: How to solve searching problems?
    • (^) Measurement: How to measure searching?

4 Search and AI

 Search methods are ubiquitous in AI systems. They often

are the backbones of both core and peripheral modules

 An autonomous robot uses search methods:

• (^) to decide which actions to take and which sensing operations to perform,
• (^) to quickly anticipate collision,
• (^) to plan trajectories,
• (^) to interpret large numerical datasets provided by sensors into compact symbolic representations,
• (^) to diagnose why something did not happen as expected,
• (^) etc...

 Many searches may occur concurrently and sequentially

Category of Searching

• (^) Incremental Formulation
  • (^) This problem involves operators that augment the state description, starting with an empty state.
  • Example: for the N-queens problem, this means that each action adds a queen to the state.
• (^) Complete-State Formulation
  • States are independent for each other.
  • (^) Example: Travel Plan.

Applications

Search plays a key role in many applications, e.g.:

 Route finding: airline travel, networks

 Package/mail distribution

 Pipe routing

 Comparison and classification of protein folds

 Pharmaceutical drug design

 Design of protein-like molecules

 Video games

8

Across history, puzzles and games requiring the

exploration of alternatives have been considered a

challenge for human intelligence:

 (^) Chess originated in Persia and India about 4000 years ago  (^) Checkers appear in 3600-year-old Egyptian paintings  (^) Go originated in China over 3000 years ago So, it’s not surprising that AI uses games to design and test algorithms

Goodness of a search strategy

• (^) Completeness
• (^) Time complexity
• (^) Space complexity
• (^) Optimality of the solution found (path cost = domain cost)
• (^) Total cost = domain cost + search cost search cost

What’re the conditions for

searching?

• (^) Observable
  • (^) You always know what’s going on currently.
  • (^) What’s going on = current state.
• (^) Discrete
  • (^) Given any state, there are only finitely many actions to choose from.

How to formulate

searching?

• (^) States
  • (^) The basic unit for searching.
  • (^) Example: Any arrangement of queens on the board is a state. (legal/illegal)
• (^) Initial State
  • (^) The state that the agent starts in.
  • (^) Example: No queens on the board.
• (^) Actions
  • (^) The operations that you can perform for the current state.
  • (^) Example: Add a new queen to the board.

How to formulate

searching?

• (^) Transition Model
  • The outcome of actions.
  • (^) Example: Returns the board with a queen added to the specified square.
• (^) Goal test:
  • (^) Which determines whether a state is a goal state.
  • (^) Example: N queens are all on the board, none attacked happens.
• (^) Path cost
  • (^) Assign a numeric cost to each path.
  • (^) Example: Attacked path will cost infinite, otherwise will cost 1.

How to solve searching

problems?

• (^) A solution is an action sequence, so search algorithms work by considering various possible action sequences.
• The possible action sequences starting at the initial state form a search tree with the initial state at the root.
• (^) The branches are actions and the nodes correspond to states in the state space of the problem.

Graph theory: The city of Königsberg

• (^) The city is divided by a river. There are two islands at the river. The

first island is connected by two bridges to both riverbanks and is also

connected by a bridge to the other island. The second island two

bridges each connecting to one riverbank.

• (^) Question: Is there a walk around the city that crosses each bridge

exactly once?

• (^) Swiss mathematician Leonhard Euler invented graph theory to solve

this problem.

Example

Graph of the Königsberg bridge system

A labeled directed graph