CS 2710, ISSP 2610 Foundations of Artificial Intelligence

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CS 2710, ISSP 2610Foundations of Artificial
Intelligence

• Solving Problems by Searching
• Chapter 3

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Framework

• AI is concerned with the creation of artifacts
  that
• Do the right thing
• Given their circumstances and what they know

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Ideal Rational Agents

• should take whatever action is expected to
  maximize its performance measure on the basis of
  its percept sequence and whatever built-in
  knowledge it has
• Key points
• Performance measure
• Actions
• Percept sequence
• Built-in knowledge

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Rational agents
How to design this?
Sensors
percepts
Environ ment
?
Agent
actions
Effectors
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Goal-based Agents

• Agents that take actions in the pursuit of a goal
  or goals.

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Goal-based Agents

• What should a goal-based agent do when none of
  the actions it can currently perform results in a
  goal state?
• Choose an action that appears to lead to a state
  that is closer to a goal than the current one is.

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Problem Solving as Search

• One way to address these issues is to view
  goal-attainment as problem solving, and viewing
  that as a search through a state space.
• In chess, e.g., a state is a board configuration

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Problem Solving

• A problem is characterized as
• An initial state
• A set of actions
• A goal test
• A cost function

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Problem Solving

• A problem is characterized as
• An initial state
• A set of actions
• successors state ? set of states
• A goal test
• goalp state ? true or false
• A cost function
• edgecost edge between states ? cost

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Example Problems

• Toy problems (but sometimes useful)
• Illustrate or exercise various problem-solving
  methods
• Concise, exact description
• Can be used to compare performance
• Examples 8-puzzle, 8-queens problem,
  Cryptarithmetic, Vacuum world, Missionaries and
  cannibals, simple route finding
• Real-world problem
• More difficult
• No single, agreed-upon description
• Examples Route finding, Touring and traveling
  salesperson problems, VLSI layout, Robot
  navigation, Assembly sequencing

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Toy ProblemsThe vacuum world

• The vacuum world
• The world has only two locations
• Each location may or may not contain dirt
• The agent may be in one location or the other
• 8 possible world states
• Three possible actions Left, Right, Suck
• Goal clean up all the dirt

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Toy ProblemsThe vacuum world

• States one of the 8 states given earlier
• Operators move left, move right, suck
• Goal test no dirt left in any square
• Path cost each action costs one

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Toy ProblemsMissionaries and cannibals

• Missionaries and cannibals
• Three missionaries and three cannibals want to
  cross a river
• There is a boat that can hold two people
• Cross the river, but make sure that the
  missionaries are not outnumbered by the cannibals
  on either bank
• Needs a lot of abstraction
• Crocodiles in the river, the weather and so on
• Only the endpoints of the crossing are important
• Only two types of people

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Toy ProblemsMissionaries and cannibals

• Problem formulation
• States ordered sequence of three numbers
  representing the number of missionaries,
  cannibals and boats on the bank of the river from
  which they started. The start state is (3, 3, 1)
• Operators take two missionaries, two cannibals,
  or one of each across in the boat
• Goal test reached state (0, 0, 0)
• Path cost number of crossings

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Real-world problems

• Route finding
• Specified locations and transition along links
  between them
• Applications routing in computer networks,
  automated travel advisory systems, airline travel
  planning systems
• Touring and traveling salesperson problems
• Visit every city on the map at least once and
  end in Bucharest
• Needs information about the visited cities
• Goal Find the shortest tour that visits all
  cities
• NP-hard, but a lot of effort has been spent on
  improving the capabilities of TSP algorithms
• Applications planning movements of automatic
  circuit board drills

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Real-world problems

• VLSI layout
• Place cells on a chip so that they do not overlap
  and that there is room for connecting wires to be
  placed between the cells
• Robot navigation
• Generalization of the route finding problem
• No discrete set of routes
• Robot can move in a continuous space
• Infinite set of possible actions and states
• Additional problem errors in sensor readings and
  motor controls
• Assembly sequencing
• Automatic assembly of complex objects
• The problem is to find an order in which to
  assemble the parts of some object
• Wrong order some of the previous work needs to
  be undone

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What is a Solution?

• A sequence of actions that when performed will
  transform the initial state into a goal state
  (e.g., the sequence of actions that gets the
  missionaries safely across the river)
• Or sometimes just the goal state (e.g., infer
  molecular structure from mass spectrographic
  data)

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Our Current Framework

• Backtracking state-space search
• Others
• Constraint-based search
• Optimization search
• Adversarial search

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Initial Assumptions

• The agent knows its current state
• Only the actions of the agent will change the
  world
• The effects of the agents actions are known and
  deterministic
• All of these are defeasible likely to be wrong
  in real settings.

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Another Assumption

• Searching/problem-solving and acting are distinct
  activities
• First you search for a solution (in your head)
  then you execute it

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Generalized Search

• Start by adding the initial state to a
• list, called fringe
• Loop
• If there are no states left then fail
• Otherwise remove a node from fringe, cur
• If its a goal state return it
• Otherwise expand it and add the resulting nodes
  to fringe

Expand a node generate its successors
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Evaluation Criteria

• Completeness
• Does it find a solution when one exists
• Time
• The number of nodes generated during search

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Search Criteria

• Space
• Maximum number of nodes in memory at one time
• Optimality
• Does it always find a least-cost solution?
• Cost considered sum of the edgecosts of the
  path to the goal (the g-val)

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Time and Space Complexity Measured in Terms of

• b maximum branching factor of the
• search tree
• d depth of the shallowest goal
• m maximum depth of any path in the state space
  (may be infinite)

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Blind Search Strategies

• Lets define and evaluate the following
  algorithms
• Breadth-first search
• Uniform-cost search
• Depth-first search
• (On the board)

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Generalized Search

• Start by adding the initial state to a
• list, called fringe
• Loop
• If there are no states left then fail
• Otherwise remove a node from fringe, cur
• If its a goal state return it
• Otherwise expand it and add the resulting nodes
  to fringe

Expand a node generate its successors
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Implementation issues

• Nodes versus states
• Search a tree or general graph checking for
  duplicate states

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def treesearch (qfun,fringe) qfun
queuing function fringe a list
containing the initial node while
len(fringe) gt 0 cur fringe0
fringe fringe1 if goalp(cur)
return cur fringe qfun(makeNodes(succes
sors(cur)),fringe) return
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def graphsearch (qfun,fringe) expanded
while len(fringe) gt 0 cur
fringe0 fringe fringe1
if goalp(cur) return cur if not
(expanded.has_key(cur.state) and\
expandedcur.state.gval lt cur.gval)
expandedcur.state cur
fringe qfun(makeNodes(successors(cur)),fringe)
return
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def iterativeDeepening(start) result
depthlim 1 startnode Node(start) while
not result result depthLimSearch(startno
de,depthlim) depthlim depthlim 1
return result
def depthLimSearch (fringe,depthlim) while
len(fringe) gt 0 cur fringe0
fringe fringe1 if goalp(cur)
return cur if cur.depth lt depthlim
fringe makeNodes(successors(cur))
fringe return
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Bidirectional search

• Search forward from the initial state and
  backward from the goal
• Stop when the two searches meet in the middle

Start
Goal
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Bidirectional SearchGo from Timisoara to
Bucharest
Oradea
Neamt
Iasi
Zerind
Sibiu
Fagaras
Arad
Vaslui
Rimnicu Vilcea
Timisoara
Urziceni
Hirsova
Lugoj
Pitesti
Mehadia
Bucharest
Eforie
Dobreta
Craiova
Giurgiu
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Bidirectional search

• Bidirectional search merits
• Big difference for problems with branching factor
  b in both directions
• A solution of length d will be found in O(2bd/2)
  O(bd/2)
• For b 10 and d 6, only 2,222 nodes are needed
  instead of 1,111,111 for breadth-first search
• Bidirectional search issues
• Predecessors of a node need to be generated
• Difficult when operators are not reversible
• For each node check if it appeared in the other
  search
• Needs a hash table of O(bd/2)