Implementing Search

1
Implementing Search

• Lecture 2-2
• January 14th/19th, 1999
• CS250

2
8-Puzzle

• States?
• Operators?
• Goal test?
• Path cost?

3
8-Queens

• Place 8 queens on a chess board, with no one
  attacking any other
• Goal test?
• Path cost?
• States
• Operators?

4
Cryptarithmetic

• Puzzles with numbers replaced by letters

FORTY TEN TEN SIXTY
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Missionaries Cannibals

• Three missionaries and three cannibals wish to
  cross a river in a boat that wont hold all three
• States?
• Operators?
• Goal test?
• Path cost?

6
Real-World Problems

• Route finding
• TSP
• VLSI
• Robot navigation
• Paint booth scheduling

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Search Trees
8
Whats in a Node?

• State - what state are we in?
• Parent - Which node generated the current node?
• Operator - Action which generated node from
  parent
• Node depth - Number of nodes from root
• Cost - Path cost from initial node

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Lieutenant Node General Search
function GENERAL-SEARCH(problem, QUEUEING-FN)
returns solution or failure nodes ?
MAKE-QUEUE(MAKE-NODE(INITIAL-STATEproblem)) loo
p do if nodes is empty then return
failure node ? REMOVE-FRONT(nodes) if
GOAL-TESTproblem applied to STATE(node)
succeeds then return node nodes ?
QUEUING-FN(nodes, EXPAND(node, OPERATORSproblem)
) end
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Coding Goals

• Create the initial node list
• Need the right ordering
• Write a loop
• If test
• Functions for
• QUEUEING-FN, REMOVE-FRONT, GOAL-TEST, EXPAND,
  MAKE-NODE

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In Lisp...
(defun general-search (problem queuing-fn) "Expan
d nodes according to the specification of PROBLEM
until we find a solution or run out of nodes to
expand. The QUEUING-FN decides which nodes to
look at first. p 73 (let ((nodes
(make-initial-queue problem queuing-fn)) node
) (loop (if (empty-queue? nodes) (RETURN
nil)) (setq node (remove-front nodes)) (if
(goal-test problem (node-state node)) (RETURN
node)) (funcall queuing-fn nodes (expand node
problem)))))
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A Few Lisp Ends
special form A list (but not a macro), which is
a form with special syntax or special evaluation
rules or both, possibly manipulating the
evaluation environment or control flow or
both. The first element of a special form is a
special operator.
(setq var1 form1 var2 form2 ...)
return terminates a loop and returns the value
of the specified expression as the value of the
loop
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Dumb Smart Searching

• Does the search algorithm use information beyond
  GOAL-TEST?
• Uninformed/blind searching does not
• Informed/heuristic search does

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Factors in Search Strategy

• Completeness - Are we guaranteed to find a
  solution, if one exists?
• Time complexity - How long does it take?
• Space complexity - How much memory?
• Optimality - Find the best of several solutions?

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Different Strokes for Different Searches

• Why is GENERAL-SEARCH general?

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Breadth-First Search

• Go sideways before you go down
• How do we do this in GENERAL-SEARCH?
• How good is it?
• Completeness?
• How long does it take?
• How much memory?
• Optimality?

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Uniform Cost

• BFS No shorter path is a solution, but what
  about cost?
• Uniform cost expands the lowest cost node
• When is BFS also uniform?

g(node) DEPTH(node)
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Depth-first Search

• Go down before you go sideways
• Saves memory over BFS - why?
• How good is it?
• Completeness?
• How long does it take?
• Optimality?
• Depth-limited search

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Iterative Deepening Search

• Repeated depth-limited search
• Depth 0, depth 1, depth 2,
• Same states expanded multiple times
• Higher branching factors make repeated expansion
  less important
• How good is it?
• Good choice when
• Big search space
• Unknown solution depth

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Bidirectional Search

• Start from the beginning and the end, meet in the
  middle
• Divide and conquer
• Cut the depth of each search in half
• From O(bd) to O(2bd/2)
• For b 10, d 6
• BFS searches 1,111,111
• Bidirectional searches 2,222

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Sounds Great, Where do I Sign Up?

• Searching backwards?
• Calculating predecessors can be tricky
• Many goal states are a problem
• Generate a node and ask, Is it in the other half
  of the tree?
• Different halves can have different searches

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Search Comparison
d depth of the goal m max tree depth l
depth limit
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And the Winner is...

• Depth-first iterative deepening
• Asymptotically optimal in time
• Asymptotically optimal in space
• among blind searches that find optimal solutions

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Constraint Satisfaction Search

• Constraint Satisfaction Problem (CPS) additional
  structural properties
• States are values of a set of variables
• Goal test specifies constraints on variable
  values
• Unary - cryptarithmetic
• Binary - 8-Queens
• 3rd and higher-order
• Absolute or just nice to have

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Why Bother?

• Less general than the notion of problem
• More efficient algorithms
• Constraints are fine-grained

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Domains

• Variables Vi have domains, Di
• Discrete or continuous?

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AIMA Code (for homework)

• Code from AIMA

/courses/current/CS250/Code/AIMA/doc/overview.html