AI

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AI Week 6 Implementing your own AI Planner in
Prolog part II HEURISTICS

• Lee McCluskey room 2/09
• Email lee_at_hud.ac.uk
• http//scom.hud.ac.uk/scomtlm/cha2555/

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Last Week Building your own forward searching
planner IN PROLOG
Each node is modelled as a state sequence of
operators that lead to the state heuristic value
INITIAL STATE
A search algorithm is COMPLETE if it can always
find a solution if there is one A search
algorithm is OPTIMAL if it always finds the
shortest (minimal cost) solution
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RECAP Planning Algorithm in Prolog
breadth-first forward search through state-space

• 1. Store the first node (initial state empty
  solution)
• Repeat
• 2. pick a node(StateSoln)
• 3. pick an operator and parameter grounding -
  O - that can be applied to State
• 4. apply O to State to get State
• 5. assert(node(State SolnO))
• 6. if possible backtrack to 3. and make a
  different choice.
• until a node has been asserted that contains a
  solution

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Heuristic Search - Definitions

• Optimal if a solution is found it is best
  solution (that is it minimises some metric such
  as length of solution or amount of resource
  consumed)
• Complete - guaranteed to find a solution if there
  is one
• Efficiency amount of time / space required to
  find a solution

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Heuristic Search - Definitions

• BEST - FIRST search repeat the following ..
• collect the set of un-expanded (ie OPEN) nodes
• -- pick a node from the set to expand if a
  heuristic function gives it the best value
• -- mark it as closed and expand it giving new
  open nodes to the set

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Heuristic Search - Definitions

• Variation GREEDY search
• pick a node to expand if it appears to be
  nearest the goal
• That is pick a node which appears to have the
  minimum distance between the node and a goal
  node
• GREEDY search takes no account of the effort
  spent in getting to that node in the first place!
  Hence Greedy.

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Heuristics - Definitions

• NON-GREEDY variation of best-first search
• factor in the cost of getting to the current
  state..
• Let a heuristic value of node n be given by
• COST(n) g(n) h(n)
• where
• g(n) is the ACTUAL COST of the path to the
  current node
• h(n) is the ESTIMATED COST of reaching the goal
  from n

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Heuristics - Example

• Breadth First Search
• As carried out by the planner in last weeks
  practical is best-first in the sense that
• COST(n) g(n) h(n)
• where
• g(n) Count of action applications is the COST
  of the path to get to node n
• h(n) 0
• This makes Breadth First Search OPTIMAL and
  COMPLETE but often hopelessly inefficient.

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Admissable Heuistics

• An ADMISSIBLE heuristic evaluation function is
  one that supplies an estimate of the cost to
  reach a goal state from current state and the
  goal
• and never overestimates that cost.
• Example Goal - get from current position P to a
  Goal position G by the road network.
• an ADMISSIBLE estimated cost is the straight line
  distance between P and G

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The FAMOUS A Property

• An A search algorithm is one that expands a node
  with the lowest cost where
• COST(n) g(n) h(n)
• g(n) is the ACTUAL COST of the path to the
  current node (usually number of operators/actions
  required or amount of resources)
• h(n) is an ADMISSIBLE estimated cost of reaching
  the goal from n
• A algorithms are OPTIMAL and COMPLETE

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Adding Heuristics to Prolog Code

• Heuristic 1 Prune the tree dont visit/expand
  the same state twice
• eg 5. IF State NOT EXPANDED BEFORE
• THEN assert(node(State SolnO))
• ve In some domains cuts down search
  considerably.
• Does not affect completeness of search.
• Does not affect optimality in a breadth
  first search
• - ve overhead in storing and searching through
  all previous states.
• Might not find ALL solutions
• See website for an implementation of this (
  dont expand a node(SSoln1) if a state with
  node(SSoln2) is already in the open nodes)

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Adding Heuristics to Prolog Code

• Heuristic 2 greedy search
• COST estimated effort to reach a solution
  from the current state eg number of goals still
  to be achieved
• 5. assert(node(State SolnO COST)
• 2. pick a node(StateSoln COST)
• ---- WHERE COST HAS THE LOWEST VALUE
  (ignoring the cost/size of Soln)
• eg Evaluate the nodes BEFORE ASSERTING them and
  store them with the cost attached

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Heuristic 2 -Example
ABCD solved
1
AB solved
3
AB solved
3
INITIAL STATE
Goalset of subgoals ABCDE
E solved
4
CD solved
3
ABC solved
2
GREADY SEARCH PICK THIS NODE TO EXPAND
CD solved
3
Greedy Scores in Red
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Adding Heuristics to the Planner

• recall node n (state ops) COST(n)g(n)h(n)
• Heuristic 3 COST(n) how many ops it took to
  get there (g(n) length of ops) and h(n) 0
• minimise cost(n) Breadth first search.
• Is h(n) admissible Is this A
• Heuristic 4 COST(n) how many ops it took to
  get there (g(n) length of ops) h(n) how
  many subgoals still to solve.
• -ve crude - may work in some domains but not in
  others
• ve negligible overhead
• Is h(n) admissible Is this A

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Heuristic 4 -Example
ABCD solved
13
AB solved
33
AB solved
33
INITIAL STATE
Goal condition ABCDE
E solved
42
CD solved
32
ABC solved
21
PICK THIS NODE TO EXPAND
CD solved
31
Greedy Scores in Red
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Adding Heuristics the PlanGraph

• Heuristic 5 Relax the problem take away some
  of the constraints
• To calculate the cost of a node n (state
  ops)
• Calculate solution plan from state ignoring
  delete lists (ie ignoring undoing effects and
  interference) of planning operators. Let h(n)
  length of shortest relaxed plan
• So COST(n) length ops h(n)
• This is admissible as it is always an
  underestimation of the distance to goal - it
  never over estimates.

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Other improvements to Planner..

• See website another world planner
• the WEB SERVICE COMPOSITION world (simulates a
  web agent that needs to plan to achieve goals)
• Improvement I have added the ability to put
  EVALUABLE predicates in states eg maths
  operators assigment

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Summary

• It is easy to add Heuristics to the Breadth first
  state space planner to make it Best first
• Relaxed problem solving can provide a very good
  admissible measure of h(n)