intro to astar

8/6/2019 Intro to Astar

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Introduction ToInformed Search & A*

G51IAI Introduction to AI

Andrew Parkeshttp://www.cs.nott.ac.uk/~ajp/


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PLE ASE NOTEMOND AY OCT 30thNO

FORM

AL LECTUR

E!Question & Answer instead (y ou ask the questions!), especiall y regarding the coursework (s).

Bring Questions!


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Shortest Path ProblemsWhen the graph becomes too large blindsearch is no longer practicalProblem is that blind search does not look inthe right placesT o see this think of the search pattern ofU niform C ost SearchO n the next 2 slides we will see an examplebased on a map of R omania from AI M A These include an animation of how UCS performs thesearch, hence printed version will be a mess! (BTW I removed the Oradea -Sibiu edge to simplif y the

animation and fix an error in an earlier version)


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Study this map of Romania. Note the distances between cities and try and calculatethe shortest route between Sibiu and Bucharest . Then press space to see theoptimal route marked in red.

Arad

Bucharest

OradeaZerind

Faragas

Neamt

Iasi

Vaslui

Hirsova

Eforie

Urziceni

Giurgui

Pitesti

Sibiu

Dobreta

Craiova

Rimnicu

Mehadia

Timisoara

Lugoj

87

92

142

86

98

86

211

101

90

99

71

75

140118

111

70

75

120

138

146

97

80

140

80

97

101

Sibiu

Rimnicu

Pitesti

Optimal route is (80+97+101) = 278 miles

The optimal route between the two cities takes us through Rimnicu and Pitesti.Press space to continue with the slideshow.


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RemarksWe expanded Arad and Zerindeven though they are in totally thewrong direction!T he search pattern was

expanding concentric circles


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Uniform Cost Search in GraphsSearch Pattern:smaller costnodes beforelargerFringe in red

Visited in blue

Blind: still ignoresgoals

goal

outline of graph

increasing cost

start

T his region isbasicallywasted effort


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Heuristic SearchD esired SearchPattern: biased indirection of goal(s)

Fringe in red Visited in blueWhen reaches goalwill have had toexplore less of the

graphR educes time andmemory usage

goal

outline of graph

increasing cost

start


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Heuristic SearchWant to achievethis pattern but

stay complete optimal

If bias the search too much thencould miss goalsor miss shorterpaths

goal

outline of graph

increasing cost

start


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More Realistic PictureIn real problems thegraphs are messy andthe search pattern notclean

What we think iscorrect directionmight be ultimatelywrongStandard solution tostay complete andoptimal: A* search pronounced A star

But first do a moregeneral heuristicmethod: B est First Search

goal

outline of graph

increasing cost

start


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Heuristic SearchSupposehave someestimates,

h , of thecost from a(fringe) nodeto the goalWant tofavour smallhExpand Afirst?

goal

outline of graph

increasing cost

start A

B

g A

gB

h A

hB


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Best First Search (BestFS)Give each node, n, a score or fullcost : f(n)U sually f(n) is based g and h Small f values are better.

BestFS is same asUC

S except use f(n) instead of justg(n)

Search nodes with f before those of f+1

BestFS Queue: explicitly store the f value of a node with that node want smallest f value first if using REMOVE-FIRST then sort the queue in increasing order alternativel y, instead of REMOVE-FIRST, just scan all queue and

use REMOVE-SM ALLEST-SCORE


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Best First SearchPROCEDURE BestFS( problem, S CORE_FN )1. fringe M AKE-E M P T Y-Q U EU E()2. fringe I N SERT ( start _n ode ) // with its f value

3. loop {1. if fringe is empt y then return false // finished without goal2. node REMOVE-SM ALLEST-SCORE(fringe)3. if node is a goal

1. print node and g2. return true // that found a goal

4. Lf

EXP AND(node) // Lf

is set of n eighbours with th e ir f values // ob tain ed us ing SCORE_FN

5. f ring e INSERT-IF-NEW(Lf , fringe ) // ignore revisi t ed nodes // unless th ey a re be tt er

}


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UCS & BestFS

UC S just uses f = g

P ROC EDUR E UC S( problem )

return BestFS( problem , g )


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Greed y SearchGreedy First:try to move to nodes that are as close tothe goal as possibleD o not know true cost to goal, so justuse the estimate hWant to implement Expand small hfirst : simply use f = h

P ROC EDUR E Greedy( problem)return BestFS( problem, h )


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Greed y SearchD ives inwhat hsays isthe bestdirection

T his

directionis just anestimateand canbe wrong

goal

outline of graph

start


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Properties of Greed y SearchIncomplete: if nodes are not checked for revisiting thenit can be incomplete it can get stuck in a loop.Nonoptimalit y: sometimes the best short -term decisionis sub -optimal in the long term not surprising because it ignores the actual path cost g

P ractical: It is often a good wa y to solve big problems it is fast the memor y usage is small because the search dives towards a

solution (this makes it more like Depth -First Search) often the solutions are acceptable even when sub -optimalSelf -Stud y: Carefull y go through the map of Romaniaexamples in heuristic -searches.htm in the heuristicsearches section or the course notes


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P erfect Information SearchSuppose that by magic (by an oraclein C S parlance) we knew the T rue

minimum cost from any node N to thegoalI.e. suppose we know h T (n)In UC S we can expect to know g T (n)T rue min cost, f T(n) for going via n ,

fT (n) = g T(n) + h T(n)


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P erfect Information SearchSupposing that could use the true costin the search, we could do

BestFS( problem, f T(n) )Properties: it would never expand a node that was not on

some minimum cost path because such non perfect nodes will never be at the front

of the queue the search would never make a mistake


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Comparisons1. UC S: BestFS( g )

complete, optimal, high memor y usage

2. Perfect-Info: BestFS( g T (n) + h T(n) )complete, optimal, low memor y usage

3. Greedy: BestFS( h )incomplete, suboptimal, low memor y usage


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A* SearchC annot implement Perfect Info!T ry to get best combination use g (n) : best path cost so far use heuristic h (n), as do not have the true h T(n)

A* Search is B estFS ( g + h )

T hat is, define f(n) = g(n) + h(n) estimated minimum cost via n and use BestFS ( f (n) )


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Effects of h choicesT wo extreme cases h= 0 A* becomes UCS : complete&optimal but search

pattern undirected

h too large : if h is large enough to dominate g thenbecomes like Greed y. uses less memor y but lose optimalit y.U sually when we say A* we exclude the lastcase, and imply that we have an:

Admissible Heuristic: h(n) h T (n) we never over -estimate distance h(n) must provide a valid lower bound on cost to the goal the g term does not get swamped and misled, but the

search pattern improves A* is complete and optimal, and memor y usage can be

much lower than UCS


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A* with Admissible HeuristicC omplete and O ptimal Search as for Uniform Cost Search

Search Pattern seeks out goals Reduced memor y and time usage

It is good on maps/graphsIt is essential on planning and puzzles


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Summar yBest First Search similar to Uniform Cost Search but with a general score derived

from g and h Greed y Search: use h onl y dive towards goals, but can miss best

paths A* search with Admissible Heuristic

Self-study: heuristic searches section of the websiteExpectations: Given an example,

e,g, a map or graph or a small planning problem or puzzle,

then you should be able to work through what BestFirst, UCS,Greed y, and A* would doN ext lecture: T he example of A* in astar.ppt


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