CO2301 Games Development 1 Week 9 Bestfirst Search, Dijkstra's Algorithm

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CO2301 - Games Development 1Week 9Best-first
Search,Dijkstra's Algorithm

• Gareth Bellaby

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• Topic 1
• Introduction to best-first searches

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Reminder about Heuristic

• Heuristic a rule of thumb.
• A directed search which should help to reduce the
  size of the search tree.
• Need an evaluation function which generates a
  numerical value.
• Manhattan Distance. The Manhattan Distance is the
  absolute distance from a location to the goal,
  measured square by square.

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Best first searches and best-first search

• A bit confusing but...
• Used to refer to a particular search algorithm.
• Used by some to refer to the class of algorithms
  that direct the search by some notion of the best
  node.

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Best first searches

• Two considerations
• A heuristic evaluation function which uses the
  information gathered by the search up to that
  point.
• Cost to get to the current node.
• A heuristic that attempts to predict how close
  the end of a path is to a solution.
• Estimation of the distance from the
• current node to the goal.

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Best first searches

• Examples include
• Best first (estimate of distance to goal)
• Dijkstra's algorithm (cost)
• A algorithm (cost estimate)

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• Topic 2
• The Best-first Algorithm

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Best first search algorithm

• Order the search on the basis of the most
  preferred nodes.
• Keep a record of all moves.
• Select the current best state.
• Similar to hill climbing but always selects the
  best available move.
• Open is a priority queue.

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Best first search algorithm

• 1) Create OpenList and ClosedList
• 2) Push the initial state (start) on to OpenList,
  set its parent to 0 and calculate its score
  using the heuristic value.
• 3) Until a goal state is found or OpenList is
  empty do
• (a) Pop the first (best) element from OpenList
  and call it 'current'.
• (b) If OpenList was empty, return failure and
  quit.
• (c) If 'current' is the goal state, return
  success, construct the path and quit.
• (d) For each rule that can match 'current' do
• i) Apply the rule to generate a new state and
  calculate its heuristic value.
• ii) If the new state has not already been
  visited, set its parent to 'current' and push the
  new state on to OpenList (using the heuristic
  value to order the list)
• (e) Add 'current' to ClosedList

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• Topic 3
• Dijkstra's algorithm

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Dijkstra's algorithm

• See "algorithms.doc" on the web site for the
  actual algorithm. It's too long to put up in
  PowerPoint presentation.
• However, it's not difficult to explain.
• Note that the of open list is a priority queue.

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Dijkstra's algorithm

• Draw out the graph and all the costs.
• (You can calculate costs as you generate the
  tree but must ensure alternative paths are
  explored unless demonstrable higher cost)
• Set current to the start position.
• While current is not the goal
• Expand current and calculate cost to all of the
  immediately succeeding nodes (i.e. the children
  of current).
• Set current to the best node that hasn't already
  been visited.

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Shortest road distance
3
7, 8
4
2
6
3
3
5
13,12
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9,8
5
3
2
4
10
4
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Map
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Layout the waypoints
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Turn into graph
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Add costs (the distances)
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8
4
4
4
5
5
1
3
4
3
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Solve
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8
4
4
4
5
5
1
3
4
3
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Dijkstra's algorithm

• Use a priority queue for the open list.
• The node popped from the list is the one which
  currently the best, i.e. the node with the lowest
  cost.
• If a lower cost is found to a node, then set the
  cost to the node to this lower value.
• Can't revisit nodes.