Problem solving in state spaces

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Problem solvinginstate spaces

• State representation
• and
• the problem solving agent algorithm

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Problem-solving agent

• environment described as state space
• agent actions can change one state to some others
• current situation is one state in space
• goal situation is another state
• problem solving agent finds sequence of actions
  to move from current to goal state

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Problem-solving agent - example

• A farmer agent traveling with a bag of grain, a
  fox and a duck comes to a river he must cross on
  the way to market. There is on the shore a boat
  so small that he can only take one of his market
  products across at a time. He cannot leave the
  fox alone with the duck, nor the duck with the
  grain. How does he get his produce safely across
  the river?

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What kind of problem?

• fully / partly observable
• deterministic / stochastic
• sequential / episodic
• static / dynamic
• discrete / continuous
• single- / multi-agent

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What kind of problem?

• fully / partly observable
• deterministic / stochastic
• sequential / episodic
• static / dynamic
• discrete / continuous
• single- / multi-agent

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Utility-based agent

• internal state representing environment
• goals expressed in terms of environment and/or
  agent states
• performance measure rationality
• NOT REFLEX tries actions internally and tests
  results against goals AND performance measure

• Algorithm
• Perceive state
• If no plan exists, develop a plan
• Act according to plan

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Utility-based agents view

• Crossing river problem state space which bank
  are farmer and produce on?
• Possible actions cross river alone or with one
  item
• Current state all on left bank
• Goal state all on right bank
• Problem plan a sequence of crossings to get from
  start (left bank) to goal (right) while avoiding
  other terminal states.

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Internal model

• State of environment data structure
• Perceptions and actions
• Current state
• Goal state
• Intelligence to develop a plan
• Possible form of plan
• Look-up table or rules or list of actions
• (perception -gt action)

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The simple problem solver

• Restricted form of general agent Figure 3.1,
  p.61
• function Simple-Problem-Solving-Agent( percept)
  returns action
• seq an action sequence, initially empty
• state some description of the current world state
  
• goal a goal, initially null
• problem a problem formulation
• state Update-State(state, percept)
• if seq is empty (ie do plan (search) first
  time only)
• goal Formulate-Goal(state)
• if (stategoal) return nil
• problem Formulate-Problem(state, goal)
  performance
• seq Search(problem)
• action First(seq) (no replanning)
• seq Rest(seq)
• return action

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Problem-solving agent

• State space possible locations of four objects
  Agent, fox, duck, grain on left or right bank
• e.g.
• Agent left
• fox left
• duck left
• grain right
• State space has 24 16 states

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Problem-solving agent

• Possible actions Agent can cross river, taking
  any object on same side with it.

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Problem-solving agent

• Start state
• Goal state

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Problem-solving agent

• Performance measure
• get to goal state
• minimize number of trips
• avoid losing produce
• Constraints
• possible actions
• boat size
• dangerous combinations of position

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Problem-solving agentstate-space and actions
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Problem-solving agent (formulate problem)STATES
TO AVOID
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Problem-solving agent example
Node in search space
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Problem-solving agent example
A solution sequence
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The simple problem solver

• Restricted form of general agent Figure 3.1,
  p.61
• function Simple-Problem-Solving-Agent( percept)
  returns action
• seq an action sequence, initially empty
• state some description of the current world state
  
• goal a goal, initially null
• problem a problem formulation
• state Update-State(state, percept)
• if seq is empty (ie do plan (search) first
  time only)
• goal Formulate-Goal(state)
• if (stategoal) return nil
• problem Formulate-Problem(state, goal)
  performance
• seq Search(problem)
• action First(seq)
• seq Rest(seq)
• return action

Fd F Ff Fd Fg F Fd
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General search algorithms

• Review breadth-first
• and depth-first
• traversals
• in graphs