lecture3 ch4

Artificial Intelligence: A Modern Approach

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1 ICS-171:Lecture 3: 1 Lecture 3: Informed Search; Iterative Improvement Methods ICS 171, Summer 2000 ICS-171:Lecture 3: 2 Outline Heuristic search strategies heuristics and heuristic estimates best-first search A*: optimal search using heuristics We will see that A* can find optimal paths and expand relatively few nodes by using heuristics
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2 ICS-171:Lecture 3: 3 Example of Path Costs S G A B D E C F 2 1 2 5 4 2 4 3 5 Optimal (minimum cost) path is S-A-D-E-F-G ICS-171:Lecture 3: 4 Heuristics and Search in general a heuristic is a “rule-of-thumb” based on domain-dependent knowledge to help you solve a problem in search one uses a heuristic function of a state where h(node) = estimated cost of cheapest path from the state for that node to a goal state G h(G) = 0 h(other nodes) > 0 (note: we will assume all individual node-to-node costs are > 0) How does this help in search we can use knowledge (in the form of h(node))to reduce search time generally, will explore more promising nodes before less promising ones
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3 ICS-171:Lecture 3: 5 Example of Heuristic Functions S G A B D E C F 4.0 6.7 10.4 11.0 8.9 6.9 3.0 ICS-171:Lecture 3: 6 Search Method 8: Best First Search Best-First uses estimated path cost from node to goal (heuristic, hcost) ignores actual path cost after each expansion sort nodes according to estimated path-cost from node to goal in effect, it always expands the most promising node on the fringe (according to the heuristic) e.g., finding a route to Seattle, always extend the path from the most northerly city among the existing routes Uniform Cost uses path cost from root to node after each expansion sort nodes according to path-cost from start S to node
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4 ICS-171:Lecture 3: 7 Example of Best-First Search in action S A D 10.4 8.9 E B F G 6.9 6.7 3.0 0 A 10.4 Note: this is not the optimal path for this problem ICS-171:Lecture 3: 8 Properties of Uniform Cost and Best-First Search Completeness Both Best-first and Uniform Cost search are complete Optimality Best-first is not optimal in general why? its ordering of nodes according to estimated cost to goal G: there is no reason this will produce the path which is really lowest-cost first e.g. “most northerly” => route to Seattle might go through Denver! uniform cost is optimal Time and Space Complexity Both could be O(b d ) in the worst case But in practice, best-first usually uses far fewer nodes
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5 ICS-171:Lecture 3: 9 Combining heuristic and path costs So far, we have only considered cost of path from start to current node or separately considered estimate of cost from node to goal We can also use both costs together: fcost(node) = g(S to node) + h(node to G) – Notation: fcost(N) = estimated cost from S to G via N g(N) = path cost from S to N (exact) h(N) = estimate of path cost from N to G If heuristic is accurate we will quickly zero in on goal But in general it is difficult to come up with a good heuristic ICS-171:Lecture 3: 10
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