Introduction to search

1
Introduction to search

• Chapter 3

2
Why study search?

• Search is a basis for all AI
• search proposed as the basis of intelligence
• all learning algorithms, e.g., can be seen as
  searching some space of hypothesis

3
Newell Simon physical symbol hypothesis

• A physical-symbol system has the necessary
  sufficient means for general intelligent action

4
Physical-systems

• A physical-system consists of a set of entities,
  called symbols, which are physical patterns that
  can occur as components of another type of entity
  called an expression Thus a symbol structure is
  composed of a number of instances (or tokens) of
  symbols related in some physical way (such as one
  token being next to another). At any instant of
  time, the system will contain a collection of
  these symbol structures. Besides these
  structures, the system also contains a collection
  of processes that operate on expressions to
  produce other expressions processes of creation,
  modification, reproduction, destruction. A
  physical-symbol system is a machine that produces
  through time an evolving collection of symbol
  structures.

5
Intelligence as search

• The solutions to problems are represented as
  symbol structures. A physical-symbol system
  exercises its intelligence in problem-solving by
  search -- that is, by generating progressively
  modifying symbol structures until it produces a
  solution structure.

6
The search task

• Given
• a description of the initial state
• list of legal actions
• preconditions
• effects
• goal test -- tells you if a goal has been reached
• Find
• an ordered list of actions to perform in order to
  go from the initial state to the goal

7
Search as a graph

• Nodes
• search-space states
• Directed arcs
• legal actions from each state to another
• Example
• Rather than being given, however, we often build
  the graph (implicitly) as we go we arent given
  the graph explicitly

8
Trip as search

• State geographical location (city, street, etc.)
• Actions following a road
• Initial state Madison
• Goal state Minneapolis

9
ID3 as search

• Search space space of all decision trees
  possible using feature set
• Operator (action) add a node (expand the tree)
• State (node) decision tree
• Initial state single leaf node
• Goal state tree that properly categorizes
  (separates) the training examples

10
ID3 heuristic

• Problem search space very large given that we
  cant look at all of the possibilities, whats a
  good next state? -- info gain (heuristic)
• Info gain can be seen as a scoring function that
  guides us through the space of possible decision
  trees

11
General search methods

• Given a set of search-space nodes, which one
  should we consider next?
• Youngest depth-first search
• most recently created/expanded node
• Oldest breadth-first search
• least-recently created/expanded node
• Best best-first search
• requires a scoring function
• Random
• simulated annealing

12
Example of search strategies
13
Considering a node

• If goal-state?(node) then done else expand(node)
• expand add previously unvisited children
  (states that be gotten to from node) to the OPEN
  list
• if we want the cheapest path, we must check that
  we cant find a cheaper route
• example

14
General search algorithm
15
Search algorithm explained

• Task find a route from the start node to the
  goal node
• Desire try all/many possible paths
• OPEN list allows backtracking from a path that
  dies out saves other possible ways
• nodes under consideration (to be expanded)
• CLOSED list prevents us from repeatedly trying a
  node ending up in an infinite loop
• nodes that have been processed

16
Search danger infinite spaces

• We must be careful that our search doesnt go
  forever
• the goal we are looking for may not be in the
  search space but because the space is infinite we
  might not know this
• the goal may be in the search space but we go
  down an infinite branch
• example

17
Implementing search strategies

• Breadth
• queue first in, first out
• put new nodes at the back of list
• Depth
• stack last in, first out
• put new nodes at the front of list
• Best
• priority queue
• add new nodes then sort list
• The next node to consider is popped off the front
  of the OPEN list

18
BFS tradeoffs

• pros
• guaranteed to find a solution if it exists
• guaranteed to find the shortest solution (in
  terms of arcs)
• cons
• OPEN becomes too big O(bd)
• example

19
DFS tradeoffs

• pros
• might find solution quickly
• needs less space for OPEN O(b d)
• example
• cons
• can get stuck (run forever) in infinite spaces
• might not find shortest solution

20
Best-first search tradeoffs

• pro
• can use domain specific knowledge
• con
• requires a good heuristic (scoring) function

21
Fixing DFS iterative deepening

• Combines the strengths of breadth- depth-first
  search
• do DFS but with depth limited to k
• if find solution, done (return path, etc.)
• else, increment k start over
• dont save partial solutions from previous
  iterations too much memory required
• due to exponential growth, most work is at the
  bottom
• guaranteed to find the shortest solution, but
  OPEN doesnt get too big (as in BFS)

22
Iterative deepening idea

• We do only a little more work overall, but our
  storage needs are much less
• we get the good aspects of BFS -- shortest
  solution
• without the negative aspects -- OPEN list too big

23
Search space examples

• Water jug problem
• Missionaries cannibals
• Define
• state representation (k-rep)
• initial state
• goal state
• operators
• Then draw search space