state space representations and search strategies spring 2007, juris vīksna
TRANSCRIPT
State space representations and search strategies
Spring 2007, Juris Vīksna
Sample problems - 8-puzzle
[Adapted from C.Arany, R.Barak, M.Dang]
Sample problems - 8-puzzle
[Adapted from C.Arany, R.Barak, M.Dang]
Sample problems - 8 queens
[Adapted from C.Arany, R.Barak, M.Dang]
Sample problems - 8 queens
[Adapted from C.Arany, R.Barak, M.Dang]
Sample problems - 8 queens
[Adapted from C.Arany, R.Barak, M.Dang]
Sample problems - Cryptarithmetic
[Adapted from C.Arany, R.Barak, M.Dang]
Sample problems - Cryptarithmetic
[Adapted from C.Arany, R.Barak, M.Dang]
Sample problems - River crossing puzzles
[Adapted from C.Arany, R.Barak, M.Dang]
Sample problems - River crossing puzzles
[Adapted from C.Arany, R.Barak, M.Dang]
Real world problems
[Adapted from C.Arany, R.Barak, M.Dang]
Real world problems - Route finding
[Adapted from C.Arany, R.Barak, M.Dang]
Real world problems - Travelling salesman
[Adapted from C.Arany, R.Barak, M.Dang]
Real world problems - VLSI layout
[Adapted from C.Arany, R.Barak, M.Dang]
State spaces
<S,P,I,G,W> - state space
S - set of statesP= {(x,y)|x,yS} - set of production rulesIS - initial stateGS - set of goal states W: PR+ - weight function
State spaces
<S,P,I,G,W> - state space
The problem
• find a goal state• find a path from the initial state to a goal state• find a shortest path from the initial state to a goal state• find a path with minimal weight from the initial state to a goal state
River crossing puzzle
[Adapted from R.Shinghal]
River crossing puzzle[Adapted from R.Shinghal]
River crossing puzzle
[Adapted from R.Shinghal]
River crossing puzzle
[Adapted from R.Shinghal]
River crossing puzzle
[Adapted from R.Shinghal]
8-puzzle
[Adapted from R.Shinghal]
8-puzzle
[Adapted from G.Luger, W.Stubblefield]
Search strategies - Data Driven
[Adapted from G.Luger, W.Stubblefield]
Search strategies - Goal Driven
[Adapted from G.Luger, W.Stubblefield]
Search strategies - Bi-directional
[Adapted from G.Luger, W.Stubblefield]
Search strategies - Bi-directional
[Adapted from G.Luger, W.Stubblefield]
Search strategies -
BFS
[Adapted from G.Luger, W.Stubblefield]
Search strategies - BFS
[Adapted from G.Luger, W.Stubblefield]
Search strategies - BFS
BreadthFirstSearch(state space =<S,P,I,G,W>)Open {I}Closed while Open do
x DeQueue(Open)if Goal(x, ) then return xInsert(x,Closed)for y Child(x ,) do
if yClosed and yOpen thenEnQueue(y,Open)
return fail
Open is implemented as queue (FIFO); Closed can be an arbitrary data structure for sets
Search strategies - Uniform Cost Search
UniformCostSearch(state space =<S,P,I,G,W>)Open {<0,I>}Closed while Open do
<wx,x> ExtractMin(Open)if Goal(x, ) then return xInsert(x,Closed)for y Child(x ,) do
if yClosed thenwy wx + W((x,y))Insert(<wy,y>,Open)
return fail
Open is implemented as a priority queue
Search strategies - DFS
[Adapted from G.Luger, W.Stubblefield]
Search strategies -
DFS
[Adapted from G.Luger, W.Stubblefield]
Search strategies - DFS
[Adapted from J.Pearl]
Search strategies - DFS
DepthFirstSearch(state space =<S,P,I,G,W>)Open {I}Closed while Open do
x Pop(Open)if Goal(x, ) then return xInsert(x,Closed)for y Child(x ,) do
if yClosed and yOpen thenPush(y,Open)
return fail
Open is implemented as stack (LIFO); Closed can be an arbitrary data structure for sets
Search strategies - DFS
DepthFirstSearch(state space =<S,P,I,G,W>)Closed return DFSVisit(I,Closed,)
DFSVisit(x,Closed,) if Goal(x, ) then return xInsert(x,Closed)
for y Child(x ,) doif y Closed then
value DFSVisit(y,Closed,) if value fail then return value
return fail
Search strategies - Backtracking
[Adapted from J.Pearl]
Search strategies - Backtracking
BacktrackingSearch(state space =<S,P,I,G,W>)Open {I}Closed while Open do
x Pop(Open)if Goal(x, ) then return xInsert(x,Closed)if there exists y Child(x ,) and yClosed
and yOpen then Push(y,Open)
return fail
Open is implemented as stack (LIFO); Closed can be an arbitrary data structure for sets
Heuristic function
<S,P,I,G,W> - state space
S - set of statesP= {(x,y)|x,yS} - set of production rulesIS - initial stateGS - set of goal states W: PR+ - weight function
d: SR+
d(x) - a shortest distance fromx to the closest goal state
f: SR+ - heuristic estimate of d
(if xG we usually assume f(x)=0)
Search strategies - Hill climbing
HCSearch(state space =<S,P,I,G,W>,f)HCVisit(I,,f)
HCVisit(x,,f) if Goal(x, ) then return xfind y Child(x ,) with the smallest f(y) valueHCVisit(y,,f)
Search strategies - Best first
[Adapted from J.Pearl]
Search strategies - Best first
BestFirstSearch(state space =<S,P,I,G,W>,f)Open {<f(I),I>}Closed while Open do
<wx,x> ExtractMin(Open)if Goal(x, ) then return xInsert(x,Closed)for y Child(x ,) do
if yClosed thenInsert(<f(y),y>,Open)
return fail
Open is implemented as a priority queue
Search strategies
[Adapted from J.Pearl]
Search strategies
[Adapted from R.Shinghal]