“it is Defined as a Method That Provide a Better

8/14/2019 it is Defined as a Method That Provide a Better

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IT IS DEFINED AS A METHOD THAT PROVIDE A BETTER

GUESS ABOUT THE CORRECT CHOICE TO MAKE AT ANYJUNCTION THAT WOULD BE ACHIEVED BY RANDOM

GUESSING.

OR

IT IS DEFINED AS A METHOD OR AS A RULE OR AS A

TRICK. IT IS A PIECE OF INFORMATION THAT IS USED TOMAKE SEARCH OR ANOTHER PROBLEM SOLVING

METHOD, MORE EFFECTIVE AND MORE EFFICIENT.


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A heuristic is a method that

Direct techniques (blind search) are notalways possible (theyrequire too much time or memory).

Weak techniques can be effective if appliedcorrectly on the rightkinds of tasks.

Might not always find the best solution.But is guaranteed to find a good solution in reasonable time.Heuristics are approximation used to minimize the search processUseful in solving tough problems which

-- could not be solved any other way.

-- solutions take an infinite time or very longtime to compute.


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Thus,

Blind search totally ignores where the goals are.

A heuristic function that gives us an estimate of howfar we are from a goal.


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Heuristic function :a function that estimate thevalue of a state, It is an approximation used tominimize the search process .

Heuristic Knowledge : knowledge of approaches thatare likely to work or of properties that are likely to betrue (but not guaranteed).


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Example


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Some Possible 8-puzzle heuristics

Number of tiles in the correct position.

The higher the number the better.

Easy to compute (fast and takes little memory).

Probably the simplest possible heuristic.

Number of tiles in the incorrect position.

This can also be considered a lower bound on the

number of moves from a solution! The best move is the one with the lowest number

returned by the heuristic.


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Heuristic values based on 2nd


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Another 8 puzzle Heuristic

Count how far away (how many tile movements)each tile is from its correct position.

Sum up this count over all the tiles.

This is another estimate on the number of movesaway from a solution.

12

3

4

5

67

8 1 2 3

4 5 6

7 8

h(N) = sum of the distances of

every tile to its goal position= 2 + 3 + 0 + 1 + 3 + 0 + 3 + 1= 13N goal


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SEARCH TECHNIQUES

Generate-and-test:

Very simple strategy - just keep guessing.

Algo: do while goal not accomplishedgenerate a possible solution

test solution to see if it is a goal

Heuristics may be used to determine the specific rulesfor solution generation.


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Example - Traveling Salesman Problem (TSP)

Traveler needs to visit n cities.

Know the distance between each pair of cities.

Want to know the shortest route that visits all the

cities once.


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14

TSP Example

A B

CD 4

6

35

1 2


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15

TSP - generation of possiblesolutions is done in order ofcities:

1. A - B - C - D

2. A - B - D - C

3. A - C - B - D

4. A - C - D - B

...

Generate-and-test Example

A B C D

B C D

C D C BB D

D C B CD B


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Characteristics

Characteristics with generate-and-test: Requires that an entire possible solution is generated at each step,

which may be expensive. It is a depth first search procedure since complete solutions must

be generated before they can be tested.

It may be difficult to develop a generation scheme that provides agood order.

If problem space is very large , may take very long time.

Assignment: TSP is a bad example because it is hard to see the statespace. Consider a problem like the water jug problem and describehow this algorithm would work in that domain.


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Hill Climbing

Is a variant of generate-and test in which feedbackfrom the test procedure is used to help thegenerator decide which direction to move in searchspace.

The test function is augmented with a heuristicfunction that provides an estimate of how close agiven state is to the goal state.Computation of heuristic function can be done

with negligible amount of computation.Hill climbing is often used when a good heuristic

function is available for evaluating states but whenno other useful knowledge is available.


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Simple Hill Climbing

Use heuristic to move only to states that are betterthan the current state.

Always move to better state when possible.

The process ends when all operators have beenapplied and none of the resulting states are better

than the current state.


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Algorithm:

1. Evaluate the initial state. If it is also goal state, then returnit and quit. Otherwise continue with the initial state as thecurrent state.

2. Loop until a solution is found or until there are no newoperators left to be applied in the current state:a. Select an operator that has not yet been applied to the current state

and apply it to produce a new state

b. Evaluate the new state

i. If it is the goal state, then return it and quit.ii. If it is not a goal state but it is better than the current state, then make

it the current state.

iii. If it is not better than the current state, then continue in the loop.


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The key difference between Simple Hill climbing andGenerate-and-test is the use of evaluation function asa way to inject task specific knowledge into thecontrol process.


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Steepest-Ascent Hill Climbing

This is a variation of simple hill climbing whichconsiders all the moves from the current state andselects the best one as the next state.


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Algorithm: Steepest-Ascent Hill Climbing

1. Evaluate the initial state. If it is also a goal state, then returnit and quit. Otherwise, continue with the initial state as thecurrent state.

2. Loop until a solution is found or until a complete iterationproduces no change to current state:

a. Let SUCC be a state such that any possible successor of the currentstate will 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 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 notbetter, leave SUCC alone.

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


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Draw backs: Hill-climbing

This simple policy has three well-knowndrawbacks:

1. Local Maxima: a local maximum.all neighboring states are worse or thesame.

2. Plateaus: An area of the searchspace where evaluation function is

flat, thus all neighboring states are thesame as the current state.

3. Ridge: local optimum that is caused by

inability to apply 2 operators at once.

Assignment: Suggest some possible ways ofdealing with this drawbacks.

(a)

(b)

(c)

Figure 5.9 Local maxima, Plateaus and

ridge situation for Hill Climbing


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Best first search

A combination of DFS & BFS.

DFS is good because a solution can be found withoutcomputing all nodes and BFS is good because it

doesnt get trapped in dead ends.The best first search allows us to switch between

paths going the benefit of both approaches.One way of combining the tow is to follow a single path at a

time, but switch paths whenever some competing pathlooks more promising than the current one does.


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S

A

B

C

D

E

F

G

H

I

J

K

L

M

3

6

5

9

8

12

14

75

6

1

Q

2


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Step Node beingexpanded

Children Available

Node

Nodechosen

1 S (A:3)(B:6)(c:5) (A:3)(B:6)(c:5) (A;3)

2 A (D:9)(E:8) (B:6)(c:5) (D:9)(E:8) (C:5)

3 C (H:7) (B:6) (D:9) (E:8) (H:7) (B:6)

4 B (E:12) (G:14) (E:12) (G:14) (D:9) (E:8) (H:7) (H:7)

5 H (I;5) (J:6) (E:12) (G:14) (D:9) (E:8) (I;5) (J:6) (I:5)

6 I K L M All L


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Best First Search Vs Hill Climbing

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

This is done by applying an appropriate heuristic function to each ofthem.

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 behavior that ischaracteristic of hill climbing.

In BFS, one move is selected, but the others are kept around so that they can 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 value that islower than the value of the state that was just explored. This contrasts withhill climbing, which will stop if there are no successor states with bettervalues than the current state.


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OR-graph

It is sometimes important to search graphs so that duplicate paths willnot be pursued.

An algorithm to do this will operate by searching a directed graph inwhich each node represents a point in problem space.

Each node will contain: Description of problem state it represents Indication of how promising it is Parent link that points back to the best node from which it came List of nodes that were generated from it

Parent link will make it possible to recover the path to the goal once thegoal is found.

The list of successors will make it possible, if a better path is found toan already existing node, to propagate the improvement down to itssuccessors.

This is called OR-graph, since each of its branches represents analternative problem solving path


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Implementation of OR graphs

We need two lists of nodes: OPEN nodes that have been generated and have had

the heuristic function applied to them but which have notyet been examined. OPEN is actually a priority queue in

which the elements with the highest priority are thosewith the most promising value of the heuristic function. CLOSED- nodes that have already been examined. We

need to keep these nodes in memory if we want to searcha graph rather than a tree, since whenever a new node is

generated, we need to check whether it has beengenerated before.


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Algorithm: BFS

1. Start with OPEN containing just the initial state2. Until a goal is found or there are no nodes left on

OPEN 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, and record its parent.

ii. If it has been generated before, change the parent if this newpath is better than the previous one. In that case, update thecost of getting to this node and to any successors that thisnode may already have.


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BFS : simple explanation

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

At each step, it picks the most promising of the nodes thathave so far 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 opennodes, after checking to see if any of them have beengenerated before.

By doing this check, we can guarantee that each node only

appears once in the graph, although many nodes may pointto it as a successor.


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BFS-Tree

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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“it is Defined as a Method That Provide a Better