CS 170 Artificial Intelligence

1. CS 170 Artificial Intelligence Prof. Rao Vemuri Search #1: Problem Solving by Searching

2. Searching • Search is needed when a solution requires a sequence of choices • The history of the choices considered forms a tree. • Each node represents a choice. • Each path represents a set of choices that build on each other. • Note: Search tree nodes may be different from problem nodes.

3. The Monkeys & Bananas The Missionaries & Cannibals Wolf, Goat and Cabbage The Towers of Hanoi Route Finding Water Jugs Problem Time Table Problem The 8-Puzzle The 8 Queens Problem Tic-Tac-Toe Game Checkers Chess Bridge Example Problems

4. Canonical Problem Formulation • State: What the world is doing at this time? • State Space: A collection of possible states • Initial State: Where the search starts • Goal State: Where the search ends • Path: A sequence of operators leading from one state to another • Path Cost: Sum of the costs of operators along the path

5. Example1: Route Finding • Find Route From Here to There • State = Current location on a map • Initial State = Starting City, say City A • Goal State = Destination City, say City Z • Operators: Move along a road to another city • Path Costs = Sum of lengths from here to there • Solution = Path from here to there • Issues • What is the Cost of Finding the Route? • What is the Cost of Traversing the Route?

6. Example2: Timetable • Find Lecture Timetable by Incrementally Modifying a Draft to Eliminate Conflicts • State: A version of a time table • Initial state: A draft version of a timetable • Goal State: A timetable with no conflicts • Operators: exchange a pair of assigned time slots • Costs: Time taken to make the exchange and verify conflicts • Solution: A timetable with no time conflicts (Here the path is irrelevant)

7. Search Trees: Terminology • Search is equivalent to building a search tree • Node, Branch, Path, Root node, Leaf node • Parent, Ancestor; Child, Descendent • Expanding: Determining the children • Open: Node is open until expanded, then it becomes closed • Nodes are data structures: Nodes have parents, children, depth (d), etc. • Fringe: is a collection of nodes waiting to be expanded • A Queue is one way to organize the fringe.

8. Search Trees: Terminology • Branching Factor “b” of a Node: The number of children of a node. • Branching Factor of a Tree: If every node has the same branching factor, then it has a branching factor b. • The total number of paths in a tree of depth d with a branching factor b is = bd. • Number of paths explode exponentially with d. • State: Where am I now? What choices do I have? • Strategy: The choice of which state to expand next.

9. Search Space • Three kinds of nodes in search space • Visited nodes: seen, processed, and expanded • May be remembered • Fringe nodes: seen but not processed or expanded. Waiting to be expanded • Must be remembered • Unvisited nodes: not seen yet (implicit)

10. Basic Search Algorithm • Repeat • Take some nodes off the fringe • Expand them (find their neighbors) • Add neighbors to the fringe • Until solution is found

11. General Search Algorithm • Repeat • Initialize parameters of search. • Repeat • Take some nodes off the fringe • Decide whether to stop (1) • Expand them (find their neighbors) • Add neighbors to the fringe • Evaluate neighbors • Add to fringe and reorder fringe • Prune fringe • Decide whether to stop (2) • Until done • Until done

12. Expanding Nodes • (constructing neighbors): • Lots of flexibility: • add step onto end of plan. • add step onto beginning of plan • add step into middle of plan • Even more flexibility: • combine parts of two poor solutions to make a new candidate • e. g. timetables. • (Genetic Algorithms)

13. Adding to the Fringe • (Queue discipline of Fringe) • LIFO = ``Depth First'' • FIFO = ``Breadth first'' • BIFO = ``Best/priority First'' • What counts as best? • Heuristics to guide the search • Constructing good heuristics are an important part of many AI systems.

14. Managing the Fringe • Queue Discipline of fringe • LIFO, Depth First • FIFO, Breadth First • BIFO, Best/Priority First • Keeping the entire fringe is too expensive • Keep just the best node (``Hill Climbing'') • Keep just the best nodes (``Beam Search'') • Keep a random subset of the fringe • Prune all but first duplicate • Prune all but best duplicate (``Dynamic Programming'') • Prune whenever partial solution is already worse than the best solution found so far. (``Branch and Bound'') • What is best? • Heuristics (The heart of AI)

15. Radical Pruning • Keeping the entire fringe is too expensive • Keep just the best node (``Hill Climbing'') • Keep just the best nodes (``Beam Search'') • Keep a random subset of the fringe.

16. Three Varieties of Search • Blind Search • Depth-first search • Breadth first search • Random search • Heuristic Search • Hill climbing = DFS + Quality measurements • Beam search, expands severalpartial paths and purges the rest • Best-first search, Expands the best partial path • Optimal Search • Branch and Bound, Expands least cost partial path • Branch and Bound augmented by under-estimates • A* - B&B plus under estimates plus dynamic programming