Informed Search Strategies

1
Informed Search Strategies

• Tutorial

2
Informed Search Strategies

• 8-Puzzle Problem

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Heuristics for 8-puzzle

• These heuristics were obtained by relaxing
  constraints (Explain !!!)
• h1 The number of misplaced tiles (squares with
  number).
• h2 The sum of the distances of the tiles from
  their goal positions.

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Heuristics for 8-puzzle I
Current State

• The number of misplaced tiles (not including the
  blank)

Goal State
In this case, only 8 is misplaced, so the
heuristic function evaluates to 1. In other
words, the heuristic is telling us, that it
thinks a solution might be available in just 1
more move.
Notation h(n) h(current state) 1
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Heuristics for 8-puzzle II
3
3
Current State
2 spaces

• The Manhattan Distance (not including the blank)

8
3 spaces
Goal State
8
1
In this case, only the 3, 8 and 1 tiles are
misplaced, by 2, 3, and 3 squares respectively,
so the heuristic function evaluates to 8. In
other words, the heuristic is telling us, that it
thinks a solution is available in just 8 more
moves.
3 spaces
1
Total 8
Notation h(n) h(current state) 8
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Greedy Search(with systematic checking of
repeated states)

• 8-Puzzle with h2()
• h2() Manhattan Distance

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8-Puzzle Problem

• Solve the following 8-puzzle problem using Greedy
  search algorithm as search strategy and Manhattan
  distance as heuristic.

3
2
1
8
4
5
6
7
8
Greedy Search(with systematic checking of
repeated states)

• 8-Puzzle with h1()
• h1() the number of misplaced tiles

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8-Puzzle Problem

• Solve the following 8-puzzle problem using Greedy
  search algorithm as search strategy and h1() as
  heuristic.

3
2
1
8
4
5
6
7
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A Search(with systematic checking of repeated
states)

• 8-Puzzle with h1()
• h1() the number of misplaced tiles

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8-Puzzle Problem

• Solve the following 8-puzzle problem using A
  search algorithm as search strategy and the
  following function f(n) as heuristic
  f(n)g(n)h(n)
• h(n)the number of misplaced tiles
• g(n)the number of steps from the initial state

3
8
2
4
6
1
5
7
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A Search(with systematic checking of repeated
states)

• 8-Puzzle with h2()
• h2() Manhattan Distance

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8-Puzzle Problem

• Solve the following 8-puzzle problem using A
  search algorithm as search strategy and the
  following function f(n) as heuristic
  f(n)g(n)h(n)
• h(n)the Manhattan Distance
• g(n)the number of steps from the initial state

3
8
2
4
6
1
5
7
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IDA Search

• 8-Puzzle with h1()
• h1(n) the number of misplaced tiles

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8-Puzzle Problem

• Solve the following 8-puzzle problem using IDA
  search algorithm as search strategy and the
  following function f(n) as heuristic
  f(n)g(n)h(n)
• h(n)the number of misplaced tiles
• g(n)the number of steps from the initial state

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Informed Search Strategies

• Maze Traversal

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Maze Traversal

• Consider the Maze Traversal Problem

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Maze Traversal

• Give a formulation for this problem
• Solve this problem by using
• Greedy search technique with Manhattan distance
  as heuristic.
• A Algorithm and Manhattan distance as heuristic.
• propose another heuristic h().

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Maze Traversal

• Consider the following problem
• Where A3 is the Starting node and E2 the End
  node.

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Maze Traversal

• Solve this problem by using
• Greedy search technique with Manhattan distance
  as heuristic.
• A Algorithm and Manhattan distance as heuristic.
• IDA Algorithm and Manhattan distance as
  heuristic.

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MAP Searching

• Consider the following Map

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Map Searching
City
h()

• SLD heuristic h()
• Straight Line Distance between any city and
  the End city Munchen
• Is h() admissible ?

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Map searching

• We wish to move from Hannover to Munchen,
  solve this problem using
• Greedy search with SLD heuristic
• A algorithm with SLD heuristic