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Unformatted text preview: 1 Course 45: Informed search (Heuristics) algorithms Outline ¡ Bestfirst search ¢ Greedy bestfirst search ¢ A * search ¡ Local search algorithms ¢ Hillclimbing search ¢ Simulated annealing search ¢ Local beam search ¢ Genetic algorithms ¡ Basic Optimization Problem and Solution ¢ Linear Programming Search Algorithms ¡ Blind search – BFS, DFS, uniform cost ¢ no notion concept of the “right direction” ¢ can only recognize goal once it’s achieved ¢ A search strategy is defined by picking the order of node expansion ¡ Heuristic search – we have rough idea of how good various states are, and use this knowledge to guide our search 2 Bestfirst search ¡ General approach of informed search: ¢ Bestfirst search: node is selected for expansion based on an evaluation function f(n) ¡ Idea: evaluation function measures distance to the goal. ¢ Choose node which appears best ¡ Implementation: ¢ fringe is queue sorted in decreasing order of desirability. ¢ Special cases: greedy search, A* search A heuristic function ¡ [dictionary] “A rule of thumb, simplification, or educated guess that reduces or limits the search for solutions in domains that are difficult and poorly understood.” ¢ h(n) = estimated cost of the cheapest path from node n to goal node . ¢ If n is goal then h(n)=0 How to design heuristics? Later.. 3 ¡ An A algorithm is a bestfirst search algorithm that aims at minimising the total cost along a path from start to goal. ¢ f(n) = g(n) + h(n) estimate of total estimate of total cost along path cost along path through n through n estimate of estimate of cost to reach cost to reach goal from n goal from n actual cost to actual cost to reach n reach n A heuristic function Romania with step costs in km ¡ h SLD =straightline distance heuristic. ¡ h SLD can NOT be computed from the problem description itself ¡ In this example f(n)=h(n) ¢ Expand node that is closest to goal ¢ greedy bestfirst search 4 Romania with step costs in km Greedy bestfirst search ¡ Evaluation function f(n) = h(n) ( h euristic) ¡ = estimate of cost from n to goal . ¡ e.g., h SLD (n) = straightline distance from n to Bucharest. ¡ Greedy bestfirst search expands the node that appears to be closest to goal. 5 Greedy bestfirst search example Greedy bestfirst search example 6 Greedy bestfirst search example Greedy bestfirst search example 7 Properties of greedy bestfirst search ¡ Complete? No – can get stuck in loops, e.g., Iasi Æ Neamt Æ Iasi Æ Neamt Æ ¡ Time? O(b m ) , but a good heuristic can give dramatic improvement ¡ Space? O(b m )  keeps all nodes in memory ¡ Optimal? No A * search ¡ Idea: avoid expanding paths that are already expensive....
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 Fall '09
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