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Problem Solving By Searching . Introduction Solutions and Performance Uninformed Search Strategies Avoiding Repeated States/Looping Partial Information Summary. Introduction. Let’s review a goal-based agent called a “problem-solving agent” They have two characteristics:

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problem solving by searching
Problem Solving By Searching
  • Introduction
  • Solutions and Performance
  • Uninformed Search Strategies
  • Avoiding Repeated States/Looping
  • Partial Information
  • Summary
introduction
Introduction
  • Let’s review a goal-based agent called a
  • “problem-solving agent”
  • They have two characteristics:
  • Find sequences of actions to reach a goal.
  • They are uninformed.
preliminaries
Preliminaries
  • We need to define two things:
  • Goal Formulation
    • Define objectives
  • Problem Formulation
    • Define actions and states
problem formulation
Problem Formulation
  • Four components:
  • The initial state
  • Actions (successor function)
  • Goal test
  • Path Cost
other examples
Other Examples
  • Toy Problems:
    • Vacuum World
    • 8-puzzle
    • 8-queens problem
other examples9
Other Examples
  • Real Problems
    • Route-Finding Problem
    • Robot Navigation
    • Automatic Assembly Sequencing
    • Protein Design
    • Internet Searching
problem solving by searching10
Problem Solving By Searching
  • Introduction
  • Solutions and Performance
  • Uninformed Search Strategies
  • Avoiding Repeated States
  • Partial Information
  • Summary
solutions
Solutions
  • We search through a search tree
  • We expand new nodes to grow the tree
  • There are different search strategies
  • Nodes contain the following:
    • state
    • parent node
    • action
    • path cost
    • depth
search tree
Search Tree

Initial state

Expanded nodes

performance
Performance
  • Four elements of performance:
  • Completeness (guaranteed to find solution)
  • Optimality (optimal solution?)
  • Time Complexity
  • Space Complexity
performance14
Performance
  • Complexity requires three elements:
  • Branching factor b
  • Depth of the shallowest node d
  • Maximum length of any path m
problem solving by searching15
Problem Solving By Searching
  • Introduction
  • Solutions and Performance
  • Uninformed Search Strategies
  • Avoiding Repeated States
  • Partial Information
  • Summary
breadth first search
Breadth-First Search
  • Root is expanded first
  • Then all successors at level 2.
  • Then all successors at level 3, etc.
  • Properties:
  • Complete (if b and d are finite)
  • Optimal (if path cost increases with depth)
  • Cost is O(bd+1)
uniform cost search
Uniform-Cost Search
  • Like breadth-first search
  • Expand node with lowest path cost.
  • Properties:
  • Complete (if b and d are finite)
  • Optimal (if path cost increases with depth)
  • Cost is O(b c*/e)
  • Could be worse than breadth first search
depth first search
Depth-First Search
  • Expand the deepest node at the bottom
  • of the tree.
  • Properties:
  • Incomplete
  • suboptimal
  • Space complexity is only O(bm)

Backtracking even does

better spacewise: O(m)

Only store the nodes on

the current path including

their unexpanded sibling nodes

depth limited
Depth-Limited
  • Like depth-first search but with
  • depth limit L.
  • Properties:
  • Incomplete (if L < d)
  • nonoptimal (if L > d)
  • Time complexity is O(bL)
  • Space complexity is O(bL)
iterative deepening
Iterative Deepening
  • A combination of depth and breadth-first
  • search.
  • Gradually increases the limit L
  • Properties:
  • Complete (if b and d are finite)
  • Optimal if path cost increases with depth
  • Time complexity is O(bd)
bidirectional search
Bidirectional Search
  • Run two searches – one from the initial state
  • and one backward from the goal.
  • We stop when the two searches meet.
  • Motivation:
  • Time complexity: (b d/2 + b d/2 ) < b d

Searching backwards not easy.

problem solving by searching27
Problem Solving By Searching
  • Introduction
  • Solutions and Performance
  • Uninformed Search Strategies
  • Avoiding Repeated States/Looping
  • Partial Information
  • Summary
avoiding looping repeated states
Avoiding Looping & Repeated States
  • Use a list of expanded states; non-expanded
  • states (open and close list)
  • Use domain specific knowledge
  • Use sophisticated data structures to find
  • already visited states more quickly.
  • Checking for repeated states can be quite
  • expensive and slow down the search alg.
problem solving by searching29
Problem Solving By Searching
  • Introduction
  • Solutions and Performance
  • Uninformed Search Strategies
  • Avoiding Repeated States
  • Partial Information
  • Summary
partial information
Partial Information
  • Knowledge of states or actions is incomplete.
  • Sensorless problems
  • Contingency Problems
  • Exploration Problems
figure 3 21
Figure 3.21

Goal State

Goal State

problem solving by searching33
Problem Solving By Searching
  • Introduction
  • Solutions and Performance
  • Uninformed Search Strategies
  • Avoiding Repeated States
  • Partial Information
  • Summary
summary
Summary
  • To search we need goal and problem
  • formulation.
  • A problem has initial state, actions, goal test,
  • and path function.
  • Performance measures: completeness,
  • optimality, time and space complexity.
summary35
Summary
  • Uninformed search has no additional
  • knowledge of states: breadth and depth-first
  • search, depth-limited, iterative deepening,
  • bidirectional search.
  • In partially observable environments, one
  • must deal with uncertainty and incomplete
  • knowledge.