Uninformed Search

• One of the oldest AI techniques
• Pioneered by Newell and Simon (Logic Theorist, General Problem Solver)
• Central component of more recent problem-solving systems such as SOAR

Reading

• Textbook sections 3.1 - 4.11
• Supplementary reading #2: Solving Problems by Searching, by Russell and Norvig

Terminology

• world states
• states and state space
• initial state
• operators (or actions)
• successor function
• step cost and path cost
• goal state
• goal test
• problem: initial state, successor function, goal test, path cost function
• search: find an operator sequence that moves agent from initial state to a goal state

Examples of Problem Formulation

Problem-formulation is the most important step in creating a successful search application. How to choose an appropriate level of abstraction for states and operators?

Route planning

• states: individual cities
• operators: driving from one city to the next
• goal: a particular city
• step cost: time, distance, fuel, danger, etc.

Eight-puzzle

• states: tile configurations
• operators: sliding one tile up/down/left/right
• goal: all tiles in some desired order
• step cost: 1

Map coloring

• states: assignments of colors to regions
• operators: assign a color to an uncolored region that does not conflict with other regions
• goal: all regions colored
• step cost: 0

Cryptarithmetic

• states: puzzle with some letters replaced by digits
• operators: replace a letter with a digit
• goal: no letters left, correct sum
• example:

    CATS     6154     (C=6, A=1, T=5, S=4, E=9, M=7, I=0)
  +  EAT    + 915
  ------    -----
    MICE     7069
  

• step cost: 0

Missionaries and cannibals

• states: number of missionaries and cannibals on each side of river, location of boat
• operators: take 1 or 2 people across the river in the boat without leaving more cannibals than missionaries on one side
• initial state: everyone on left side, boat on left
• goal state: everyone on right side, boat on right
• step cost: 1

Water jug puzzle

• states: amount of water in 3-quart pitcher and 4-quart pitcher
• operators:
  • fill up either pitcher from the faucet
  • pour all water from either pitcher down the drain
  • pour water from one pitcher to the other, up to the brim
• initial state: both pitchers empty
• goal state: 3-quart pitcher empty; exactly 2 quarts left in 4-quart pitcher
• step cost: 1

Uninformed Search Strategies

No information about how far we are from a goal state.

Different strategies answer the following questions in different ways:

• Are we guaranteed to find a solution if one exists? (completeness)
• Will the optimal solution always be found? (optimality)
• How long will it take? (time complexity)
• How much memory is needed? (space complexity)

General search algorithm:

SEARCH(problem, strategy) { 

   create a search tree with the initial state at the root 

   repeat { 

      if there are no candidates for expansion 
         return failure 

      choose a leaf node for expansion according to strategy 

      if the node represents a goal state 
         return solution 
      else 
         generate successors and add them to the candidate list 
   } 
}

Keep in mind:

• Distinction between states of state space and nodes of search tree

• States describe features of the world

• Nodes include states, but also lots of other information:

  • state
  • depth of node in the tree
  • parent node
  • cost of the path so far, usually denoted g(n)
  • action that generated this node

Breadth-first search

• expands shallowest node next
• pushes forward uniformly into the search tree
• complete
• optimal (if path cost is a nondecreasing function of depth)
• candidate list is an ordinary queue
• exponential in time and space

Uniform-cost search

• expands least-cost node next
• complete
• optimal (if steps costs are non-negative)
• candidate list is a priority queue ordered by path cost
• exponential in time and space
• same as breadth-first search if step costs are all equal

Nondeterministic search

• expands random node next
• not complete
• not optimal
• candidate list is a randomized set
• exponential in time and space
• can be useful when branching factor is large and long useless paths may exist

Depth-first search

• expands deepest node next
• dives headlong into the search tree
• not complete (may get sidetracked and never return)
• not optimal (may find suboptimal solution first)
• candidate list is a stack
• exponential in time
• efficient in space
• more efficient than breadth-first when many solutions exist

Depth-limited search

• expands deepest node next, up to a point
• complete (only if a solution exists within depth limit)
• not optimal
• exponential in time
• efficient in space
• unclear how to choose depth limit

Iterative-deepening search

• depth-limited search with increasing depth limits
• complete
• optimal
• exponential in time
• efficient in space
• expands some nodes multiple times
• multiple expansion overhead is not a serious problem
• preferred search method when the search space is large and the depth of a solution is not known

Bidirectional search

• searches forward from initial state and backwards from goal state simultaneously, using breadth-first search
• complete
• optimal
• exponential in time and space, but with better bounds: O(b^d/2) instead of O(b^d)
• not applicable to every problem
• works best with single goal state and reversible operators

Summary of time and space complexities of search strategies is given on page 81 of SR #2

Avoiding Repeated States

• Maintain a record of states previously encountered
• Such a record is usually called the closed list

SEARCH(problem, strategy) { 

   create a search tree with the initial state at the root
   create an empty closed list

   repeat {

     if there are no candidates for expansion 
        return failure 

     choose a leaf node for expansion according to strategy 

     if this node's state is already in closed list
        discard node and continue
     else if the node represents a goal state 
        return solution 
     else
        add node's state to closed list
        generate successors and add them to the candidate list 

   } 
}