1. CS621 : Artificial Intelligence Pushpak Bhattacharyya CSE Dept., IIT Bombay Lecture 3 - Search

2. Common Dimensions in Search Methods How does a solution correspond to a search tree? – Solutions can be any nodes – Solutions must be terminal nodes – Solutions are paths through the tree When does a search method stop? – Satisficing: when its finds one solution – Exhaustive: when it has considered all possible solutions – Optimizing: when it has found the best solution – Resource limited: when it has exhausted its computational resources – Due process: when it has searched with a method that has proven adequate for most cases

3. Common Dimensions in Search Methods (contd.) How is the search directed? – Blind: systematic search through possibilities – Directed: heuristics used to guide the search – Hierarchical: abstract solutions used to organize the search How thorough is the search – Complete: If there is a solution in the search space, the system will find it – Incomplete: the system may miss some solutions

4. AI search is always backed up by knowledge Ontological knowledge: a hierarchy of concepts

5. The Hierarchical Assembly in an automobile system Motor System Breaking System Engine System Transmission System Electrical SystemCooling System Cooling hoseRadiator Charging System Starter System Voltage Regulator Generator Battery Solenoid Starter Motor Ignition System Spark PlugsCoil Motor System

6. Informed Search Avoid useless subtrees Important for Web

7. Intelligent Search on Web Root of the Web LiteraturePoetryDramaNovelEconomicsMacroMicroSportsRacketStick Give “Shakespeare's Hamlet”. No point going to Economics subtree. Document clustering and classification needed.

8. Two Cardinal Theorems for A* Admissibility – A* always terminates finding the optimal path. Informedness – More informed heuristic is “better”, i.e., a less informed heuristic will expand at least as many times as a more informed one.

9. Proof of Admissibility S N1N1 N2N2 N i = N G Start Node N is the node on optimal path on open list, All its ancestors are in closed list Goal Node

10. Proof of Admissibility (contd.) If A* does not terminate f values of nodes on open list become unbounded. f(N) = g(N) + h(N) and g(N)>= e.Σarcs e=least cost on the arcs (+ve).

11. Proof of Admissibility (cont.) N is on optimal path. N’s ancestors are all in CL g(N) = g*(N) ; optimal path to N found h(N) <= h*(N), by defn of A* Hence, f(N) <= f*(N) = f*(S) Since for each N on optimal path f* values are equal and equal to the cost of the optimal path from S to G.

12. Proof of Admissibility (cont.) Fact 1: If A* does not terminate f values of nodes on OL become unbounded. Fact 2: Any time before A* terminates there exists on OL a node N with f(N) < f*(S) These two can be reconciled iff A* terminates

13. Intuition of Termination A* keeps wavering and straying. But is brought back to the correct path.