Uninformed Search
Reading: Chapter 3 by today, Chapter 4.1-4.3 by
Wednesday, 9/12
Homework #2 will be given out on Wednesday
DID YOU TURN IN YOUR SURVEY? USE
COURSEWORKS AND TAKE THE TEST
Pending Questions
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Class web page:
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http://www.cs.columbia.edu/~kathy/cs
4701
Reminder: Don’t forget assignment
0 (survey). See courseworks
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When solving problems, dig at
the roots instead of just hacking
at the leaves.
Anthony J. D'Angelo, The College
Blue Book
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Agenda
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Introduction of search as a problem-solving
paradigm
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Uninformed search algorithms
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Example using the 8-puzzle
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Formulation of another example: sodoku
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Transition to greedy search, one method for
informed search
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Goal-based Agents
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Agents that work towards a goal
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Select the action that more likely achieve
the goal
Sometimes an action directly
achieves a goal; sometimes a series
of actions are required
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Problem solving as search
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Goal formulation
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Problem formulation
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Actions
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States
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Uninformed
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Search through the space of
possible solutions
Use no knowledge about which path
is likely to be best
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Characteristics
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Before actually doing something to solve
a puzzle, an intelligent agent explores
possibilities “in its head”
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Search = “mental exploration of
possibilities”
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Making a good decision requires exploring
several possibilities
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Execute the solution once it’s found
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Formulating Problems as Search
Given an initial state and a goal, find the sequence
of actions leading through a sequence of states to
the final goal state.
Terms:
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Successor function: given action and state, returns
{action, successors}
State space: the set of all states reachable from the
initial state
Path: a sequence of states connected by actions
Goal test: is a given state the goal state?
Path cost: function assigning a numeric cost to each path
Solution: a path from initial state to goal state
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Example: the 8-puzzle
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How would you use AI techniques
to solve the 8-puzzle problem?
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8-puzzle URLS
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http://www.permadi.com/java/puzzle8
http://www.cs.rmit.edu.au/AISearch/Product
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8 Puzzle
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States: integer locations of tiles
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(0 1 2 3 4 5 6 7 B)
(0 1 2)(3 4 5) (6 7 B)
Action: left, right, up, down
Goal test: is current state = (0 1 2 3 4 5
6 7 B)?
Path cost: same for all paths
Successor function: given {up, (5 2 3 B 1
8 4 7 6)} -> ?
What would the state space be for this
problem?
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What are we searching?
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State space vs. search space
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Nodes
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State represents a physical configuration
Search space represents a tree/graph of
possible solutions… an abstract configuration
Abstract data structure in search space
Parent, children, depth, path cost, associated
state
Expand
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A function that given a node, creates all
children nodes, using successsor function
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Data structures:
Searching data
AI: Searching solutions
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Uninformed Search Strategies
The strategy gives the order in which
the search space is searched
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Breadth first
Depth first
Depth limited search
Iterative deepening
Uniform cost
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Breadth first Algorithm
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Depth-first Algorithm
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Complexity Analysis
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Completeness: is the algorithm
guaranteed to find a solution when there
is one?
Optimality: Does the strategy find the
optimal solution?
Time: How long does it take to find a
solution?
Space: How much memory is needed to
perform the search?
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Cost variables
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Time: number of nodes generated
Space: maximum number of nodes stored
in memory
Branching factor: b
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Depth: d
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Maximum number of successors of any node
Depth of shallowest goal node
Path length: m
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Maximum length of any path in the state
space
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Can we combine benefits of both?
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Depth limited
Select some limit in depth to explore the
problem using DFS
 How do we select the limit?
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Iterative deepening
DFS with depth 1
 DFS with depth 2 up to depth d
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Properties of the task environment?
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Fully observable
Deterministic
Episodic
Static
Discrete
Single agent
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Partially
observable
Stochastic
Sequential
Dynamic
Continuous
Multiagent
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Three types of incompleteness
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Sensorless problems
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Contingency problems
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Adversarial problems
Exploration problems
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End of Class Questions?
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Sodoku
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Informed Search
Heuristics
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Suppose 8-puzzle off by one
Is there a way to choose the best
move next?
Good news: Yes!
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We can use domain knowledge or
heuristic to choose the best move
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0
1
2
3
4
5
6
7
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Nature of heuristics
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Domain knowledge: some
knowledge about the game, the
problem to choose
Heuristic: a guess about which is
best, not exact
Heuristic function, h(n): estimate
the distance from current node to
goal
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Heuristic for the 8-puzzle
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# tiles out of place (h1)
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Manhattan distance (h2)
Sum of the distance of each tile from its
goal position
 Tiles can only move up or down  city
blocks
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0
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2
3
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5
6
7
Goal State
0
1
2
0
2
5
3
4
5
3
1
7
7
6
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h1=1
h2=1
4
h1=5
h2=1+1+1+2+2=7
Best first searches
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A class of search functions
Choose the “best” node to expand
next
Use an evaluation function for each
node
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Estimate of desirability
Implementation: sort fringe, open
in order of desirability
Today: greedy search, A* search
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Greedy search
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Evaluation function = heuristic
function
Expand the node that appears to be
closest to the goal
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Greedy Search
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OPEN = start node; CLOSED = empty
While OPEN is not empty do
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Remove leftmost state from OPEN, call it X
If X = goal state, return success
Put X on CLOSED
SUCCESSORS = Successor function (X)
Remove any successors on OPEN or CLOSED
Compute heuristic function for each node
Put remaining successors on either end of OPEN
Sort nodes on OPEN by value of heuristic function
End while
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End of Class Questions?
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