Search Algorithms in Artificial Intelligence: A Comprehensive Guide - Prof. Introduction t, Summaries of Material Engineering

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Set 2: State-spaces and Uninformed

Search

ICS 271 Fall 2016

Kalev Kask

271 - fall 2016

You need to know

• State-space based problem formulation

– State space (graph)

• Search space

– Nodes vs. states

– Tree search vs graph search

• Search strategies

• Analysis of search algorithms

– Completeness, optimality, complexity

– b, d, m

271 - fall 2016

Problem-Solving Agents

• Intelligent agents can solve problems by searching a state-space
• State-space Model
  • the agent’s model of the world
  • usually a set of discrete states
  • e.g., in driving, the states in the model could be towns/cities
• Goal State(s)
  • a goal is defined as a desirable state for an agent
  • there may be many states which satisfy the goal
    • e.g., drive to a town with a ski-resort
  • or just one state which satisfies the goal
    • e.g., drive to Mammoth
• Operators(actions)
  • operators are legal actions which the agent can take to move from

one state to another

271 - fall 2016

Example: Romania

271 - fall 2016

Problem Types

• Static / Dynamic

Previous problem was static: no attention to changes in environment

• Observable / Partially Observable / Unobservable

Previous problem was observable: it knew its initial state.

• Deterministic / Stochastic

Previous problem was deterministic: no new percepts

were necessary, we can predict the future perfectly

• Discrete / continuous

Previous problem was discrete: we can enumerate all possibilities

271 - fall 2016

A problem is defined by five items:

states e.g. cities

initial state e.g., "at Arad“

actions or successor function S(x) = set of action–state pairs

• e.g., S(Arad) = { <Arad  Zerind, Zerind>, … } transition function - maps action & state  state

goal test , (or goal state)

e.g., x = "at Bucharest”, Checkmate(x)

path cost (additive)

• e.g., sum of distances, number of actions executed, etc.
• c(x,a,y) is the step cost, assumed to be ≥ 0

A solution is a sequence of actions leading from the initial state to a goal state

271 - fall 2016 State-Space Problem Formulation

Abstraction/Modeling

• Definition of Abstraction (states/actions)
  • Process of removing irrelevant detail to create an abstract representation: ``high-level”, ignores irrelevant details
• Navigation Example: how do we define states and operators?
  • First step is to abstract “the big picture”
    • i.e., solve a map problem
    • nodes = cities, links = freeways/roads (a high-level description)
    • this description is an abstraction of the real problem
  • Can later worry about details like freeway onramps, refueling, etc
• Abstraction is critical for automated problem solving
  • must create an approximate, simplified, model of the world for the computer to deal with: real-world is too detailed to model exactly
  • good abstractions retain all important details
  • an abstraction should be easier to solve than the original problem 271 - fall 2016

Robot block world

• Given a set of blocks in a certain configuration,
• Move the blocks into a goal configuration.
• Example :
  • ((A)(B)(C))  (ACB)

A

C

B

271 - fall 2016

A B C

The State-Space Graph

• Problem formulation:
  • Give an abstract description of states,

operators, initial state and goal state.

• Graphs:
  • vertices, edges(arcs), directed arcs, paths
• State-space graphs:
  • States are vertices
  • operators are directed arcs
  • solution is a path from start to goal
• Problem solving activity:
  • Generate a part of the search space that contains a solution State-space:
    1. A set of states
    2. A set of “operators”/transitions
    3. A start state S
    4. A set of possible goal states
    5. Cost path 271 - fall 2016

• Observable, start in #5.

Solution?

15

Example: vacuum world

Vacuum world state space graph

17

Example: vacuum world

• Unobservable, start in

{ 1,2,3,4,5,6,7,8 } e.g.,

Solution?

18

20

The Traveling Salesperson Problem

• Find the shortest tour that visits all cities without

visiting any city twice and return to starting point.

• State:

– sequence of cities visited

• S

= A

C A D E F B 271 - fall 2016