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AI – Week 5 Implementing your own AI Planner in Prolog – part II : HEURISTICS Lee McCluskey, room 2/09

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Artform Research Group Last Week: Building your own forward searching planner IN PROLOG INITIAL STATE Each node is modelled as a “state” + sequence of operators that lead to the state + heuristic value 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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Artform Research Group 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(State,Soln) 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', Soln++[O])) 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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Artform Research Group 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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Artform Research Group 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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Artform Research Group 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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Artform Research Group 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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Artform Research Group 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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Artform Research Group 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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Artform Research Group The FAMOUS A* Property An A* search algorithm is one that expands a node with the lowest cost, where 1. COST(n) = g(n) + h(n) 2. g(n) is the ACTUAL COST of the path to the current node (usually number of operators/actions required, or amount of resources) 3. h(n) is an ADMISSIBLE estimated cost of reaching the goal from n A* algorithms are OPTIMAL and COMPLETE

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Artform Research Group Adding Heuristics to Prolog Code Heuristic 1: Prune the tree: don't visit/expand the same state twice: eg 5. IF State' NOT EXPANDED BEFORE THEN assert(node(State', Soln++[O])) +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 (= don’t expand a node(S,Soln1) if a state with node(S,Soln2) is already in the open nodes…)

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Artform Research Group 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', Soln++[O], COST) 2. pick a node(State,Soln, 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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Artform Research Group Heuristic 2 -Example INITIAL STATE Goal=set of subgoals: A&B&C&D&E A&B&C&D solved A&B solved A&B&C solved C&D solved A&B solved E solved C&D solved GREADY SEARCH: PICK THIS NODE TO EXPAND Greedy Scores in Red

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Artform Research Group 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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Artform Research Group Heuristic 4 -Example INITIAL STATE Goal condition: A&B&C&D&E A&B&C&D solved A&B solved A&B&C solved C&D solved A&B solved E solved C&D solved PICK THIS NODE TO EXPAND Greedy Scores in Red

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Artform Research Group 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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Artform Research Group 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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Artform Research Group 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)

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