Artificial Intelligence

Transcription

1 Artificial Intelligence Dr Ahmed Rafat Abas Computer Science Dept, Faculty of Computers and Informatics, Zagazig University

2 State-Space Search 2

3 State-Space Search The state-space is the configuration of the possible states and how they connect to each other. It s required to search the state-space to find an optimal path from a start state to a goal state. Uninformed search can only decide where to go by considering the possible moves from the current state, and trying to look ahead as far as possible. 3

4 example: Searching a graph link(g,h). link(g,d). link(e,d). link(h,f). link(b,f). Initial State D A E B F Goal State C State-Space go(x,y,[x T]):- link(x,z), go(z,y,t). G?- go(a,f,x). X = [a,e,f] X = [a,b,f] H Simple search algorithm Consultation 4

5 State-Space Representation link(g,h). link(g,d). link(e,d). link(h,f). link(b,f). D E F C A F C Initial state is the root B C 5

6 Searching for the optimum State-space search is finding in a state-space an optimal path to the goal state/node. For a route-finder which searches for shortest routes between towns `optimal path' means the shortest path between two towns. 6

7 Prolog implementation In Prolog the state-space search is implemented by : 1. representing a state 2. generating all of the next states reachable from a given state; go(x,y,[x T]):- link(x,z), go(z,y,t). 3. determining whether a given state is the goal state using an evaluation function; 4. controlling how we search the space. 7

8 Depth-First Search go(x,y,[x T]):- link(x,z), go(z,y,t). E A B?- go(a,c,x). X = [a,e,f,c]? X = [a,b,f,c]? X = [a,b,c]? ; D F C F C C the depth-first search algorithm: finds the first link from the current node. follows the left-most branch of the search tree down until either finds: the goal state or a leaf node with no successors. backtracks to find another branch to follow. 8

9 Iterative Deepening Depth-first search usually does not find the optimal solution that is the shortest path from the initial state to the goal state. Alternatively, the depth needs to be varied iteratively to look for a goal after exhausting all nodes at a particular depth. Depth-First go(x,y,[x T]):- link(x,z), go(z,y,t). Iterative Deepening go(x,y,[y T]):- go(x,z,t), link(z,y). Check if current node is goal. Find an intermediate node. Check whether intermediate Node links with goal. 9

10 Iterative Deepening: how it works??- go(a,c,sol). Z=a go(a,z,[a]). link(z,c). link(a,c). link(g,h). link(g,d). link(e,d). link(h,f). link(b,f). go(x,y,[y T]):- go(x,z,t), link(z,y).?- go(a,c,s). 10

11 Iterative Deepening: how it works??- go(a,c,sol). go(a,z,sol). link(z,c). Z1=a go(a,z1,sol). link(z1,z). link(a,z). link(g,h). link(g,d). link(e,d). link(h,f). link(b,f). go(x,y,[y T]):- go(x,z,t), link(z,y).?- go(a,c,s). 11

12 Iterative Deepening: how it works??- go(a,c,sol). go(a,e,[e,a]). link(e,c). Z1=a go(a,z1,[a]). link(g,h). link(g,d). link(e,d). link(h,f). link(b,f). go(x,y,[y T]):- go(x,z,t), link(z,y).?- go(a,c,s). 12

13 Iterative Deepening: how it works??- go(a,c,[c,b,a]). go(a,b,[b,a]). Z1=a go(a,z1,[a]). link(g,h). link(g,d). link(e,d). link(h,f). link(b,f). go(x,y,[y T]):- go(x,z,t), link(z,y).?- go(a,c,s). S = [c,b,a]? 13

14 Iterative Deepening: how it works??- go(a,c,sol). go(a,z,sol). link(z,c). go(a,z1,sol). link(z1,z). go(a,z2,sol). link(z2,z1). link(g,h). link(g,d). link(e,d). link(h,f). link(b,f). go(x,y,[y T]):- go(x,z,t), link(z,y).?- go(a,c,s). S = [c,b,a]?; 14

15 Iterative Deepening: how it works??- go(a,c,sol). go(a,f,sol). go(a,e,sol). go(a,a,sol). link(g,h). link(g,d). link(e,d). link(h,f). link(b,f). go(x,y,[y T]):- go(x,z,t), link(z,y).?- go(a,c,s). S = [c,b,a]?; S = [c,f,e,a]? 15

16 Iterative Deepening Iterative Deepening search: reaches a solution quickly, requires minimal memory as at any point in the search it maintains only one path back to the initial state. However: on each iteration it has to re-compute all previous levels and extend them to the new depth; may not terminate (e.g. loop); 16