CS.462 Artificial Intelligence SOMCHAI THANGSATHITYANGKUL Lecture 02 : Search

Searching for Solutions The state space model provides a formal definition of a problem and what constitutes a solution to a problem. State space is the set of all states reachable from the initial state by any sequence of operators/actions. Operators -- generate new states from existing states A solution is a state (called a goal state) whose attributes have certain properties and maybe a sequence of operators that will change the initial state to a goal state  A solution is found by searching through the state space until a (goal) state with “specific” properties is found Artificial IntelligenceChapter 12

What is a Solution in this type of Search? A solution to a search problem is a sequence of operators that generate a path from the initial state to a goal state. An optimal solution is a minimal cost solution. Solution cost versus search cost -- which one to optimize? Artificial IntelligenceChapter 13

4 A directed graph in state space

5 Three coins problem Given three coins arrange as in the picture, which is the initial state I. These are goal state G.

6 Three coins problem Operation : Flipping the coin one at a time Let A represent flipping the first coin Let B represent flipping the middle coin Let C represent flipping the last coin The search problem: find a path from a state in I to a state in G. Draw the state space Graph

7 Three coins problem State space graph

8 Three coins problem Let put some rule into the problem Rule : Use exactly 3 flips. This means that 1flip cannot reach the goal and 2 flips also cannot reach the goal. For example: state I : HHT  c HHH not goal State I : HHT  B HTT  A TTT not goal Let draw the state space

9 Three coins problem State space tree

10 Search Many AI problems can be formulated as search. Iterative deepening is good when you don’t know much. First Method of Search Uninformed Search

11 Depth First Search (DFS) Search Put start state in the agenda Loop Get a state from the agenda If goal, then return Expand state (put children in agenda) Avoiding loops Don’t add a node to the agenda if it’s already in the agenda Don’t expand a node (or add it to the agenda) if it has already been expanded.

12 DFS Graph:

13 DFS Agenda: –Expansion: put children at top of stack –Get new nodes from top of stack Expand nodeNodes list s {s} {A s,B s,C s }

14 Try this Find a path from node A to the goal nod B. Use DFS method. A B Z O SF C P R T L M D

15 Breadth First Search (BFS) Search Put start state in the agenda Loop Get a state from the agenda If goal, then return Expand state (put children in agenda) Avoiding loops Don’t add a node to the agenda if it’s already in the agenda Don’t expand a node (or add it to the agenda) if it has already been expanded.

16 BFS Graph:

17 BFS Agenda: –Expansion: put children at end of queue –Get new nodes from the front of queue Expand nodeNodes list s {s} {A s,B s,C s }

18 Try this Find a path from node A to the goal nod B. Use BFS method. A B Z O SF C P R T L M D