CS460Spring 2011

Review of Search

Overview

• Uninformed search• Informed search• Local search• Adversarial search

Search Problem Formulation

One possible heuristic evaluation function for a state would be the amount of time required for the robot to go back to the lander from the location of the state; this is clearly admissible. What would be a more powerful, but still admissible, heuristic for this problem? (don’t worryabout whether it is consistent or not).

One possible stronger heuristic is the maximum, over uncollected rocks r, of the time takento go from current location to r, plus the time taken to get from r to the lander.

Prob1: Uninformed Tree

Prob 2: Informed (heuristic) Graph

“Expanded” List

• Path length is additive– Shortest path from S to G via X = shortest path from S to G + shortest

path from X to G• So, we only need to keep around the single best path from S to

any state X, when , in a priority queue Q. • If we find a new path to a state that is already in Q, then we can

discard the longer one• So, once we expand one path to state X, we don’t need to

consider (extend) any other paths to X. We can keep a list of these states. Call it Expanded List. If the state of the search node we pull off of Q is in the Expanded List, we discard the node. When we use the Expanded List this way, we call it ‘strict”.

Non-strict Expanded List

• When using a heuristic, as in A*, we don’t know for sure whether we have a node with a shortest path, we are partly guessing

• So, discarding the next node on Q might risk losing optimal path

• Non-strict: if the path length from the new node is < path length from node already on expanded list, then replace the old node with the new node.

Adversarial (game) search

Complexity Calculation

Problem 3.5 from textbook (3rd ed). N n queens, Assume each action incrementally adds one queen to the state. The state space has cube root of n-factorial or more states.

Another Search Problem formulation

• 3.3 from text. In traveling from one Romanian city to another, let us say two friends have to get together, and at each stop, we have to wait till the other friend gets to his next stop. Let D(I,j) be the straight-line distance between cities I and j.

• Refer to the text, 3.3 a,b, c,d

5.3 from textbook. Pursuit-evasion game.