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    Lecture05 Informed Search (Part 1)

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    Dream Maker
    The document discusses informed search techniques for problem solving including best first search, greedy search, and A* search. It provides examples of using heuristic functions to estimate the cost of reaching the goal state to guide the search in finding optimal solutions more efficiently. A* search is described as a best first search that combines the path cost with an admissible heuristic estimate to find the lowest total cost path to the goal.

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    Lecture05 Informed Search (Part 1)

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    Dream Maker
    9 views26 pages
    The document discusses informed search techniques for problem solving including best first search, greedy search, and A* search. It provides examples of using heuristic functions to estimate the cost of reaching the goal state to guide the search in finding optimal solutions more efficiently. A* search is described as a best first search that combines the path cost with an admissible heuristic estimate to find the lowest total cost path to the goal.

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    371942_Lecture05 Informed Search (Part 1)

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    The document discusses informed search techniques for problem solving including best first search, greedy search, and A* search. It provides examples of using heuristic functions to estimate the cost of reaching the goal state to guide the search in finding optimal solutions more efficiently. A* search is described as a best first search that combines the path cost with an admissible heuristic estimate to find the lowest total cost path to the goal.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    9 views26 pages

    Lecture05 Informed Search (Part 1)

    Uploaded by

    Dream Maker
    The document discusses informed search techniques for problem solving including best first search, greedy search, and A* search. It provides examples of using heuristic functions to estimate the cost of reaching the goal state to guide the search in finding optimal solutions more efficiently. A* search is described as a best first search that combines the path cost with an admissible heuristic estimate to find the lowest total cost path to the goal.

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    © All Rights Reserved
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    Download as pdf or txt
    of 26

    TAI2151 – ARTIFICIAL INTELLIGENCE

    FUNDAMENTALS

    LECTURE 5 – SOLVING
    PROBLEMS BY SEARCHING
    (INFORMED SEARCHES)
    PART 1

    Solving Problems By Searching – Informed Searches


    LECTURE OUTLINE

    • Part 1: Best First Search


    • Greedy search
    • A* search
    • Part 2: Heuristic functions

    Solving Problems By Searching – Informed Searches


    INFORMED SEARCH

    • Problems:
    • How to achieve goal?
    • Goal: get a solution, get the best solution
    • How to maximise the utility/profit?
    • Ideally, we want AI to know the knowledge and draw
    conclusion
    • Knowledge: a sequence of action that I took
    • Conclusion: predict the result from the actions

    Solving Problems By Searching – Informed Searches


    INFORMED SEARCH
    • Search strategy that uses problem
    specific knowledge beyond the
    definition of the problem itself
    • To fine a goal with less search
    space (that is informed)
    • Can find solutions more efficiently

    Solving Problems By Searching – Informed Searches


    INFORMED VS UNINFORMED SEARCH

    • Uninformed search:
    • Use only available information in the problem
    • For e.g.:
    • From City A to D: look only the available path from A to D

    • Informed search:
    • Use knowledge specific to a particular problem
    • Interpret the problem and available information
    • Involve reasoning
    • For e.g.:
    • From City A to D: getting the shortest path from A to D, is better than the longest path from A
    to D; or find the path with least traffic jam

    Solving Problems By Searching – Informed Searches


    PROBLEM: FINDING A MINIMUM COST PATH
    • Previously we wanted an arbitrary path to a goal.
    • Now, we want the minimum cost path to a goal G
    • Cost of a path = sum of individual transitions along path
    • How to obtain the path cost? By defining a heuristic function, commonly write as h(n)
    • Heuristics: serving to aid discovery
    • An estimation function that estimates how good a node is
    • “Good”, define based on domain specific information. For e.g.: could be the shortest path in a
    map, number of pieces moved for 8-puzzle
    • Examples of path-cost:
    • Navigation
    • path-cost g(n) = distance to node (n) from start node in miles
    • minimum => minimum time, least fuel, least distance

    • 8-Puzzle
    • path-cost = number of pieces moved
    • minimum => least time to solve the puzzle

    Solving Problems By Searching – Informed Searches


    TERMINOLOGY
    • Agent: AI or someone who try to solve the problem
    • States: configuration of the agent in its environment.
    • Initial state: initial starting state
    • Goal state: solution state
    • Operators/Actions: a kind of (movement) that make within a state
    (choices that can be made within a state)
    • Goal test: way to determine whether a given state is a goal state
    • A machine needs some way to encode whether a state happens to be in
    is the goal state
    • Path Cost: numerical cost associated with a given path
    • Transition Model: returns the state resulting from performing action a
    in state s
    • State space: the set of all states reachable from the initial state by any
    sequence of actions

    Solving Problems By Searching – Informed Searches


    INFORMED SEARCHES

     Best-First Search
    * Greedy Search
    * A* Search

     Heuristic Functions
    * Designing a Heuristic Function

    Solving Problems By Searching – Informed Searches


    BEST FIRST SEARCH

    • A search algorithm that expands the node (from one state


    to another state) that is closest to the goal
    • We use a heuristic function to make estimation (we guess,
    but guess with mathematics, i.e. probability and statistics
    logic rules & facts)

    Solving Problems By Searching – Informed Searches


    Informed search strategy uses problem-specific knowledge

    Solving Problems By Searching – Informed Searches


    GREEDY SEARCHES

     Search algorithm: expands node that is closest


    to the goal

     Estimate through heuristic function (a function


    that calculates an approximate cost (ranks
    alternatives) in search algorithm at each
    branching step based on available information
    to decide which branch to follow)

     Since it is approximate, so not necessary it will


    be the best solution (most optimize)

    Solving Problems By Searching – Informed Searches


    Minimize estimated cost to reach a goal: Greedy search

    Solving Problems By Searching – Informed Searches


    GREEDY SEARCH
    • Let evaluation function h(n) be an estimate of cost from node n
    to goal; this function is often called a heuristic function
    (heuristic means to find or to discover) and is denoted by h(n).
    e.g., hSLD(n) = straight-line distance from n to Bucharest
    • Greedy search expands the node that appears to be closest to
    goal
    • Contrast with uniform-cost search in which lowest cost path
    from start is expanded
    • Greedy search resembles depth-first search since it prefers to
    follows a single path all the way to the goal, but it will backup
    when it hits a dead end. So
    • it is not complete
    • it is not optimal
    • time complexity is O(bm) and space complexity is O(bm)

    Solving Problems By Searching – Informed Searches


    Map of Romania with road distances in km, and straight-line distances to Bucharest.
    Goal: Bucharest
    Initial state: Arad
    States: various cities
    Actions: drive between cities or choose
    Minimizenext
    estimated
    city cost to reach a goal: Greedy Search
    Solution: Sequence of cities to reach
    Bucharest

    Solving Problems By Searching – Informed Searches


    Solving Problems By Searching – Informed Searches
    GREEDY SEARCH - EXAMPLE

    Solving Problems By Searching – Informed Searches


    GREEDY SEARCH – EXAMPLE (CONT.)

    Solving Problems By Searching – Informed Searches


    GREEDY SEARCH – EXAMPLE (CONT.)

    Arad → Sibiu → Fagaras → Bucharest : not optimal (140 + 99 +211 = 450)


    ( 32 kilometer longer than Arad → Sibiu → Rimnicu → Pitesti → Bucharest): Optimal
    (140 + 80 + 97 + 101 = 418)
    Solving Problems By Searching – Informed Searches
    PROPERTIES OF GREEDY SEARCH
    • Complete:
    No:
    • Fails in infinite-depth spaces -- example
    • Spaces with loops (e.g. going from Lasi to Oradea)
    → Complete in finite spaces with repeated state
    checking
    • Optimal:
    No - optimal path goes through Pitesti.
    O(bm): like depth first, but a good heuristic function
    • Time:
    gives dramatic improvement on average
    O(bm): Potentially keeps all nodes in memory
    • Space:

    Let b: Branching factor


    m: Maximum Depth
    Solving Problems By Searching – Informed Searches
    A*- a special Best-first search
    • Goal: find a minimum total cost path
    • Notation:
    – g(n) = cost of current path from start to node n in the search tree.
    – h(n) = estimate of the cheapest cost of a path from n to a goal.
    – evaluation function: f = g + h
    • f(n) estimates the cheapest cost solution path that goes through n.
    – h*(n) is the true cheapest cost from n to a goal.
    – g(n) is the true shortest path from the start s, to n.

    • If the heuristic function, h(n), always underestimate the true cost (h(n)
    is smaller than h*(n)), then A* is guaranteed to find an optimal
    solution.

    Solving Problems By Searching – Informed Searches


    MINIMIZING THE TOTAL PATH COST: A* IDEA

    Solving Problems By Searching – Informed Searches


    A* Search

    Straight-line distance is admissible because the shortest


    path between any two points is a straight line.

    Solving Problems By Searching – Informed Searches


    EXAMPLE – CONT.

    Solving Problems By Searching – Informed Searches


    EXAMPLE – CONT.

    Solving Problems By Searching – Informed Searches


    EXAMPLE – FINALLY…

    Solving Problems By Searching – Informed Searches


    PROPERTIES OF A*
    • Complete: Yes, unless there are infinitely many
    nodes with f  f(G)
    • Optimal: Yes
    • Time: Exponential with path length
    • Space: Potentially keeps all nodes in memory
    (runs out of space before it runs out of time)

    Note, A* is also optimally efficient


    for a given heuristic: That is, no other
    optimal search algorithm is guaranteed to
    open fewer nodes. Let b: Branching factor
    m: Maximum Depth
    Solving Problems By Searching – Informed Searches

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