ai sesi03 searching heuristic search 4slide

8/3/2019 Ai Sesi03 Searching Heuristic Search 4slide

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Jurusan Teknik Inform atika Universitas Widyatama

Heuristic Search

Pertemuan : 3

Dosen Pembina :Sriyani Violina

Danang Junaedi

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Pertemuan ini mempelajari bagaimana memecahkan

suatu masalah dengan teknik searching.

Metode searching yang dibahas pada pertemuan ini

adalah heuristic search atau informed search yang

terdiri dari: Generate-and Test

Hill Climbing

Best-First Search Greedy Best-First-Search

A*

Iterative Deeping A*

Deskripsi

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Limitations of uninformed search

8-puzzle

Avg. solution cost is about 22 steps

branching factor ~ 3

Exhaustive search to depth 22: 3.1 x 1010 states

E.g., d=12, IDS expands 3.6 million states on average

[24 puzzle has 1024 states (much worse)]

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Recall tree search


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Recall tree search

This strategy is whatdifferentiates different

search algorithms

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Heuristic

Merriam-Webster's Online Dictionary

Heuristic (pron. \hyu-ris-tik\): adj. [from Greekheuriskein to discover.] involving orserving as an aid to learning, discovery, or problem-solving by experimental andespecially trial-and-error methods

The Free On-line Dictionary of Computing (15Feb98)

heuristic 1. A rule of thumb, simplification or educated guess thatreduces or limits the search for solutions in domains that are difficult and poorlyunderstood. Unlike algorithms, heuristics do not guarantee feasible solutions andare often used with no theoretical guarantee. 2. approximationalgorithm.

From WordNet (r) 1.6

heuristic adj 1: (computer science) relating to or using a heuristic rule 2: of or relatingto a general formulation that serves to guide investigation [ant: algorithmic] n : acommonsense rule (or set of rules) intended to increase the probability of solvingsome problem [syn: heuristic rule, heuristic program]

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Informed methods add

domain-specific information

Add domain-specific information to select the best

path along which to continue searching

Define a heuristic function h(n) that estimates the

goodness of a node n. Specifically, h(n) = estimated cost (or distance) of minimal

cost path from n to a goal state.

The heuristic function is an estimate of how close we

are to a goal, based on domain-specific information

that is computable from the current state description.

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Heuristic function

Heuristic:

Definition: using rules of thumb to find answers

Heuristic function h(n)

Estimate of (optimal) cost from n to goal h(n) = 0 if n is a goal node

Example: straight line distance from n to Bucharest

Note that this is not the true state-space distance

It is an estimate actual state-space distance can be higher

Provides problem-specific knowledge to the search algorithm


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Heuristic functions for 8-puzzle

8-puzzle

Avg. solution cost is about 22 steps

branching factor ~ 3

Exhaustive search to depth 22:

3.1 x 1010 states.

A good heuristic function can reduce the search process.

Two commonly used heuristics

h1 = the number of misplaced tiles h1(s)=8

h2 = the sum of the distances of the tiles from their goal positions

(Manhattan distance).

h2(s)=3+1+2+2+2+3+3+2=18

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Heuristics

All domain knowledge used in the search is encoded in theheuristic function h().

Heuristic search is an example of a weak method because of

the limited way that domain-specific information is used to

solve the problem.

Examples:

Missionaries and Cannibals: Number of people on starting river bank

8-puzzle: Number of tiles out of place

8-puzzle: Sum of distances each tile is from its goal position

In general:

h(n) 0 for all nodes n

h(n) = 0 implies that n is a goal node

h(n) = implies that n is a dead-end that can never lead to a goal

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Weak vs. strong methods

We use the term weak methods to refer to methods that are

extremelygeneraland not tailored to a specific situation.

Examples of weak methods include

Means-ends analysis is a strategy in which we try to represent the current

situation and where we want to end up and then look for ways to shrink thedifferences between the two.

Space splitting is a strategy in which we try to list the possible solutions to

a problem and then try to rule out classes of these possibilities.

Subgoaling means to split a large problem into several smaller ones that

can be solved one at a time.

Called weak methods because they do not take advantage of

more powerful domain-specific heuristics

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When to use ?

The input data are limited or inexact.

Optimization model can not be used as for complexreality.

Reliable and exact algorithm is not available. It is possible to improve the efficiency of the

optimization process.

Symbolic rather than numerical processing is involved.

Quick decision must be made .

Computerization is not feasible.


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Advantages

Simple to understand.

Easier to implement and explain.

Save formulation time.

Save computer programming and storage requirements.

Save computational time and thus real time in decision making.

Often produce multiple acceptable solution.

Usually it is possible to state a theoretical or empirical measure ofthe solution quality.

Incorporate intellegence to guide the search.

It is possible to apply efficient heuristics to models that could besolved with mathematical programming.

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Disadvantages

An optimal solution can not be guaranteed.

There may be too many exceptions to the rules.

Sequential decision choices may fail to anticipate

the future consequences of each choice.

The interdependencies of one part pf a system

can sometime have a profound influence on the

whole system.

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Generate-and-Test

It is a depth first search procedure since complete solutions mustbe generated before they can be tested.

In its most systematic form, it is simply an exhaustive search ofthe problem space.

Operate by generating solutions randomly. Also called as British Museum algorithm

If a sufficient number of monkeys were placed in front of a set oftypewriters, and left alone long enough, then they wouldeventually produce all the works of shakespeare.

Dendral: which infers the struture of organic compounds usingNMR spectrogram. It uses plan-generate-test.

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Generate-and-Test Algorithm

1. Generate a possible solution. For some problems, this

means generating a particular point in the problem

space. For others it means generating a path from a

start state2. Test to see if this is actually a solution by comparing

the chosen point or the endpoint of the chosen path to

the set of acceptable goal states.

3. If a solution has been found, quit, Otherwise return to

step 1.


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Hill Climbing

Is a variant of generate-and test in which feedback fromthe test procedure is used to help the generator decidewhich direction to move in search space.

The test function is augmented with a heuristic functionthat provides an estimate of how close a given state is tothe goal state.

Computation of heuristic function can be done withnegligible amount of computation.

Hill climbing is often used when a good heuristicfunction is available for evaluating states but when noother useful knowledge is available.

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Hill climbing

Perform depth-first,

BUT:

instead of left-to-right

selection,

FIRST select the child

with thebest heuristicvalue

SS

DD

AA EE

BB FF

GG

SS

AA

Example: using the straight-line distance:

8.98.910.410.4

10.410.4 6.96.9

6.76.7 3.03.0

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Hill climbing algorithm

1.1. QUEUEQUEUE


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Simple Hill Climbing

The key difference between Simple Hill climbing

and Generate-and-test is the use of evaluation

function as a way to inject task specific

knowledge into the control process.

Is on state better than another ? For this algorithm

to work, precise definition of better must be

provided.

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Steepest-Ascent Hill Climbing

This is a variation of simple hill climbing which

considers all the moves from the current state and

selects the best one as the next state.

Also known as Gradient search

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Algorithm: Steepest-Ascent Hill

Climbing

1. Evaluate the initial state. If it is also a goal state, then return itand quit. Otherwise, continue with the initial state as the currentstate.

2. Loop until a solution is found or until a complete iteration

produces no change to current state:a. Let SUCC be a state such that any possible successor of the current statewill be better than SUCC

b. For each operator that applies to the current state do:

i. Apply the operator and generate a new state

ii. Evaluate the new state. If is is a goal state, then return it and quit. If not,compare it to SUCC. If it is better, then set SUCC to this state. If it is not

better, leave SUCC alone.

c. If the SUCC is better than the current state, then set current state toSYCC,

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Hill climbing example2 8 3

1 6 4

7 5

2 8 31 4

7 6 5

2 3

1 8 4

7 6 5

1 38 4

7 6 5

2

3

1 8 4

7 6 5

2

1 3

8 4

7 6 5

2

start goal

-5

h = -3

h = -3

h = -2

h = -1

h = 0h = -4

-5

-4

-4-3

-2

h(n) = -(number of tiles out of place)


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Best First Search

Combines the advantages of bith DFS and BFS into asingle method.

DFS is good because it allows a solution to be foundwithout all competing branches having to be expanded.

BFS is good because it does not get branches on deadend paths.

One way of combining the tow is to follow a single pathat a time, but switch paths whenever some competing

path looks more promising than the current one does.

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BFS

At each step of the BFS search process, we select the mostpromising of the nodes we have generated so far.

This is done by applying an appropriate heuristic function to eachof them.

We then expand the chosen node by using the rules to generate itssuccessors

Similar to Steepest ascent hill climbing with two exceptions: In hill climbing, one move is selected and all the others are rejected, never

to be reconsidered. This produces the straightline behaviour that ischaracteristic of hill climbing.

In BFS, one move is selected, but the others are kept around so that theycan be revisited later if the selected path becomes less promising. Further,the best available state is selected in the BFS, even if that state has a valuethat is lower than the value of the state that was just explored. This contrastswith hill climbing, which will stop if there are no successor states withbetter values than the current state.

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Algorithm: BFS

1. Start with OPEN containing just the initial state

2. Until a goal is found or there are no nodes left onOPEN do:

a. Pick the best node on OPEN

b. Generate its successors

c. For each successor do:

i. If it has not been generated before, evaluate it, add it to OPEN, andrecord its parent.

ii. If it has been generated before, change the parent if this new path isbetter than the previous one. In that case, update the cost of getting tothis node and to any successors that this node may already have.

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BFS : simple explanation

It proceeds in steps, expanding one node at each step, until itgenerates a node that corresponds to a goal state.

At each step, it picks the most promising of the nodes that have sofar been generated but not expanded.

It generates the successors of the chosen node, applies theheuristic function to them, and adds them to the list of open nodes,after checking to see if any of them have been generated before.

By doing this check, we can guarantee that each node onlyappears once in the graph, although many nodes may point to it asa successor.


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BFS Ilustration

Step 1 Step 2 Step 3

Step 4 Step 5

A A

B C D3 5 1

A

B C D3 5 1

E F46A

B C D3 5 1

E F46

G H6 5

A

B C D3 5 1

E F46

G H6 5

A A2 1

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Greedy best-first search

Special case of best-first search

Uses h(n) = heuristic function as its evaluation

function

Expand the node that appears closest to goal

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Romania with step costs in km

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Greedy best-first search example


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Optimal Path


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Properties of greedy best-first search

Complete?

Not unless it keeps track of all states visited

Otherwise can get stuck in loops (just like DFS)

Optimal?

No we just saw a counter-example

Time?

O(bm), can generate all nodes at depth m before finding solution

m = maximum depth of search space

Space? O(bm) again, worst case, can generate all nodes at depth m before finding

solution

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A* Search

Expand node based on estimate of total path cost

through node

Evaluation functionf(n) = g(n) + h(n)

g(n) = cost so far to reach n

h(n) = estimated cost from n to goal

f(n) = estimated total cost of path through n to goal

Efficiency of search will depend on quality of

heuristic h(n)

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A* Algorithm

BFS is a simplification of A* Algorithm

Presented by Hart et al

Algorithm uses: f: Heuristic function that estimates the merits of each node we generate.

This is sum of two components, g and h and f represents an estimate of

the cost of getting from the initial state to a goal state along with the paththat generated the current node.

g : The function g is a measure of the cost of getting from initial state to thecurrent node.

h : The function h is an estimate of the additional cost of getting from thecurrent node to a goal state.

OPEN

CLOSED

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A* Algorithm

1. Start with OPEN containing only initial node. Set that nodes gvalue to 0, its h value to whatever it is, and its f value to h+0or h. Set CLOSED to empty list.

2. Until a goal node is found, repeat the following procedure: Ifthere are no nodes on OPEN, report failure. Otherwise picj thenode on OPEN with the lowest f value. Call it BESTNODE.Remove it from OPEN. Place it in CLOSED. See if theBESTNODE is a goal state. If so exit and report a solution.Otherwise, generate the successors of BESTNODE but do notset the BESTNODE to point to them yet.


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A* Algorithm ( contd)

For each of the SUCCESSOR, do the following:

a. Set SUCCESSOR to point back to BESTNODE. Thesebackwards links will make it possible to recover the path once asolution is found.

b. Compute g(SUCCESSOR) = g(BESTNODE) + the cost ofgetting from BESTNODE to SUCCESSOR

c. See if SUCCESSOR is the same as any node on OPEN. If socall the node OLD.

d. If SUCCESSOR was not on OPEN, see if it is on CLOSED. Ifso, call the node on CLOSED OLD and add OLD to the list of

BESTNODEs successors.e. If SUCCESSOR was not already on either OPEN or CLOSED,

then put it on OPEN and add it to the list of BESTNODEssuccessors. Compute f(SUCCESSOR) = g(SUCCESSOR) +h(SUCCESSOR)

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A* search example

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A* search example

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A* search example


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A* search example

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A* search example

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A* search example

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Properties of A*

Complete?

Yes (unless there are infinitely many nodes with ff(G) )

Optimal?

Yes

Also optimally efficient: No other optimal algorithm will expand fewer nodes, for a given heuristic

Time?

Exponential in worst case

Space?

Exponential in worst case


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Improving A* - memory-bounded heuristic

search

Iterative-deepening A* (IDA*) Using f-cost(g+h) rather than the depth

Cutoff value is the smallest f-cost ofany node that exceeded the cutoff onthe previous iteration; keep these nodes only

Space complexity O(bd)

Recursive best-first search (RBFS)

Best-first search using only linear space (Fig 4.5)

It replaces the f-value of each node along the path with the best f-value ofits children (Fig 4.6)

Space complexity O(bd) with excessive node regeneration

Simplified memory bounded A* (SMA*) IDA* and RBFS use too little memory excessive node regeneration

Expanding the best leaf until memory is full

Dropping the worst leaf node (highest f-value) by backing up to its parent

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Iterative Deepening A* (IDA*)

Idea: Reduce memory requirement of A*by applying cutoff on values of f

Consistent heuristic function h

Algorithm IDA*:1. Initialize cutoff to f(initial-node)

2. Repeat:a. Perform depth-first search by expanding all

nodes N such that f(N) cutoff

b. Reset cutoff to smallest value f of non-expanded(leaf) nodes

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8-Puzzle

4

6

f(N) = g(N) + h(N)with h(N) = number of misplaced tiles

Cutoff=4

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8-Puzzle

4

4

6

Cutoff=4

6



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8-Puzzle

4

4

6

Cutoff=4

6

5


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8-Puzzle

4

4

6

Cutoff=4

6

5

5


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4

8-Puzzle

4

6

Cutoff=4

6

5

56


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8-Puzzle

4

6

Cutoff=5



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8-Puzzle

4

4

6

Cutoff=5

6


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8-Puzzle

4

4

6

Cutoff=5

6

5


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8-Puzzle

4

4

6

Cutoff=5

6

5

7


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8-Puzzle

4

4

6

Cutoff=5

6

5

7

5



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8-Puzzle

4

4

6

Cutoff=5

6

57

5 5


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8-Puzzle

4

4

6

Cutoff=5

6

57

5 5

f(N) = g(N) + h(N)

with h(N) = number of misplaced tiles

5

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Advantages/Drawbacks of IDA*

Advantages: Still complete and optimal

Requires less memory than A*

Avoid the overhead to sort the fringe Drawbacks:

Cant avoid revisiting states not on thecurrent path Essentially a DFS

Available memory is poorly used( memory-bounded search, see R&N p. 101-104)

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Referensi

1. Suyanto.2007.Artificial Intelligence .Informatika. Bandung

2. -.2009. Heuristic (Informed) Search[online].http://www.cse.fau.edu/~xqzhu/courses/cap4630_09spring/lectures/Heuristic_Search_Part2.ppt.Tanggal Akses : 12 Februari 2011

3. Tim Finin et.al..2011.Informed Search [online],http://www.cs.swarthmore.edu/~eeaton/teaching/cs63/slides/InformedS

earchPart1.ppt, Tanggal Akses : 12 Februari 20114. Surma Mukhopadhyay.-.Heuristic

Search[online].url:http://student.bus.olemiss.edu/files/Conlon/Others/BUS669/Notes/Chapter4/HEURISTIC%20%20%20SEARCH.ppt.Tanggal Akses: 12 Februari 2011

5. Dr. Suthikshn Kumar.-. Heuristic SearchTechniques[online].url:http://www.cs.rpi.edu/~beevek/files/ai-heuristic-search.pdf.Tanggal Akses: 12 Februari 2011

6. -.2007. Informed/HeuristicSearch[online].url:http://www.ics.uci.edu/~smyth/courses/cs271/topic3_heuristicsearch.ppt.Tanggal Akses: 12 Februari 2011

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