8/2/2019 Heurstic

1/8

Term Paper Development & Research

On

Heuristic Search Technique

Name : Bhavin Vaja

Roll_no. : 08mca055

Name : Nikunj Oza

Roll_no. : 08mca026

Submitted to,

Prof. Devendra Vashi

Subject : Seminar

8/2/2019 Heurstic

2/8

Heuristic Search Techniques

Direct techniques (blind search) are

not always possible (they require too

much time or memory).

Weak techniques can be effective if

applied correctly on the right kinds of

tasks.

Typically require domain specificinformation.

Search techniques are general problem-

solving methods. When there is a

formulated search problem, a set of

states, a set of operators, an initial state,

and a goal criterion we can use search

techniques to solve the problem (Pearl

& Korf, 1987). A search algorithm isexplained in simple terms by Cawsey

(1998): Suppose that you are trying to

find your way around in a small town,

which has many one way streets. Your

initial state (A) to the target destination

(B) there are many routes, but you do

not know which ones to take. You can

try as many in real life, although it might

be a difficult process. There might be

much inconvenience in the whole

picture: Once you have passed though

one street you may not be able to go

back, as it is one way, or you may be

stuck in a park. This simplified idea of

searching for a place indicates that we

can actually map out all the possible

routes in such an example; even it is

exhausting you eventually find a way. Insmall scale search problems, as

introduced above, simple search

techniques are sufficient to do

systematic search. However, sometimes

we need systematically search for such

a route, for instance, on a much more

complex map. How do we do that?

Search algorithms are good for solving

such problems. The problems could

refer to physical problems such as

walking or driving from A to B; or it could

be abstract actions such as in a set of

steps in a theorem, which will allow us

to prove from a set of facts.

Heuristic search is an AI search

technique that employs heuristic for its

moves. Heuristic is a rule of thumb that

probably leads to a solution. Heuristics

play a major role in search strategies

because of exponential nature of the

most problems. Heuristics help to

reduce the number of alternatives from

an exponential number to a polynomial

number. In Artificial Intelligence,heuristic

search has a general meaning, and a

more specialized technical meaning. In

a general sense, the term heuristic isused for any advice that is often

effective, but is not guaranteed to work

in every case. Within the heuristic

search architecture, however, the term

heuristic usually

http://intelligence.worldofcomputing.net/ai-search/ai-search-techniques.htmlhttp://intelligence.worldofcomputing.net/ai-introduction/artificial-intelligence-overview.htmlhttp://intelligence.worldofcomputing.net/ai-introduction/artificial-intelligence-overview.htmlhttp://intelligence.worldofcomputing.net/ai-search/ai-search-techniques.html

8/2/2019 Heurstic

3/8

HEURISTIC INFORMATION

In order to solve larger problems,

domain-specific knowledge must be

added to improve search efficiency.Information about the problem include

the nature of states, cost of transforming

from one state to another, and

characteristics of the goals. This

information can often be expressed in

the form of heuristic evaluation function,

say f(n,g), a function of the nodes n

and/or the goals g.

Following is a list of heuristic search

techniques.

Pure Heuristic Search

A* algorithm

Iterative-Deepening A*

Depth-First Branch-And-Bound

Heuristic Path Algorithm

Recursive Best-First Search

COMPLEXITY OF FINDING

OPTIMAL SOLUTIONS

The time complexity of a heuristic

search algorithm depends on the

accuracy of the heuristic function. For

example, if the heuristic evaluation

function is an exact estimator, then A*

search algorithm runs in linear time,

expanding only those nodes on an

optimal solution path. Conversely, with a

heuristic that returns zero

everywhere, A*

algorithm becomes uniform-cost

search, which has exponential

complexity.

In general, the time complexity of A*

search and IDA* search is an

exponential function of the error in the

heuristic function. For example, if the

heuristic has constant absolute error,

meaning that it never underestimates by

more than a constant amount regardless

of the magnitude of the estimate, then

the running time of A* is linear with

respect to the solution cost. A morerealistic assumption is constant relative

error, which means that the error is a

fixed percentage of the quantity being

estimated. The base of the exponent,

however, is smaller than the brute-force

branching factor, reducing the

asymptotic complexity and allowing

larger problems to be solved. For

example, using appropriate heuristic

functions, IDA* can optimally solverandom instance of the twenty-four

puzzle and Rubiks Cube.

Heuristic Search

http://intelligence.worldofcomputing.net/ai-search/heuristic-evaluation-function.htmlhttp://intelligence.worldofcomputing.net/ai-search/pure-heuristic-search.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/iterative-deepening-a-star.htmlhttp://intelligence.worldofcomputing.net/ai-search/depth-first-branch-and-bound.htmlhttp://intelligence.worldofcomputing.net/ai-search/heuristic-path.htmlhttp://intelligence.worldofcomputing.net/ai-search/recursive-best-first-search.htmlhttp://intelligence.worldofcomputing.net/ai-search/heuristic-evaluation-function.htmlhttp://intelligence.worldofcomputing.net/ai-search/heuristic-evaluation-function.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/uniform-cost-search.htmlhttp://intelligence.worldofcomputing.net/ai-search/uniform-cost-search.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/iterative-deepening-a-star.htmlhttp://intelligence.worldofcomputing.net/ai-search/iterative-deepening-a-star.htmlhttp://intelligence.worldofcomputing.net/ai-search/iterative-deepening-a-star.htmlhttp://intelligence.worldofcomputing.net/ai-search/iterative-deepening-a-star.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/uniform-cost-search.htmlhttp://intelligence.worldofcomputing.net/ai-search/uniform-cost-search.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/heuristic-evaluation-function.htmlhttp://intelligence.worldofcomputing.net/ai-search/heuristic-evaluation-function.htmlhttp://intelligence.worldofcomputing.net/ai-search/recursive-best-first-search.htmlhttp://intelligence.worldofcomputing.net/ai-search/heuristic-path.htmlhttp://intelligence.worldofcomputing.net/ai-search/depth-first-branch-and-bound.htmlhttp://intelligence.worldofcomputing.net/ai-search/iterative-deepening-a-star.htmlhttp://intelligence.worldofcomputing.net/ai-search/a-star-algorithm.htmlhttp://intelligence.worldofcomputing.net/ai-search/pure-heuristic-search.htmlhttp://intelligence.worldofcomputing.net/ai-search/heuristic-evaluation-function.html

8/2/2019 Heurstic

4/8

A heuristic is a method that might not

always find the best solution butis

guaranteed to find a good solution in

reasonable time.By sacrificing

completeness it increases efficiency.

Useful in solving tough problems which

could not be solved any other way.

solutions take an infinite time or very

long time to compute.

The classicexample of heuristic search

methods is the travelling salesman

problem.

Heuristic Search methods Generate and

Test Algorithm

generate a possible solution which can

either be a point in the problem space ora path from the initial state.

test to see if this possible solution is a

real solution by comparing the state

reached with the set of goal states.

If it is a real solution, return. Otherwise

repeat from 1.

This method is basically a depth first

search as complete solutions must be

created before testing. It is often called

the British Museum method as it is like

looking for an exhibit at random. A

heuristic is needed to sharpen up the

search. Consider the problem of four 6-

sided cubes, and each side of the cube

is painted in one of four colours. The

four cubes are placed next to one

another and the problem lies in

arranging them so that the four available

colours are displayed whichever way the

4 cubes are viewed. The problem can

only be solved if there are at least foursides coloured in each colour and the

number of options tested can be

reduced using heuristics if the most

popular colour is hidden by the adjacent

cube.

Hill climbing

Here the generate and test method isaugmented by an heuristic function

which measures the closeness of the

current state to the goal state.

Evaluate the initial state if it is goal state

quit otherwise current state is initial

state.

Select a new operator for this state and

generate a new state.

Evaluate the new state

8/2/2019 Heurstic

5/8

if it is closer to goal state than current

state make it current state

if it is no better ignore

If the current state is goal state or no

new operators available, quit. Otherwise

repeat from 2.

In the case of the four cubes a suitable

heuristic is the sum of the number of

different colours on each of the four

sides, and the goal state is 16 four on

each side. The set of rules is simply

choose a cube and rotate the cube

through 90 degrees. The starting

arrangement can either be specified or

is at random.

Best First Search

A combination of depth first and breadthfirst searches. Depth first is good

because a solution can be found without

computing all nodes and breadth first is

good because it does not get trapped in

dead ends. The best first search allows

us to switch between paths thus gaining

the benefit of both approaches. At each

step the most promising node is chosen.

If one of the nodes chosen generates

nodes that are less promising it ispossible to choose another at the same

level and in effect the search changes

from depth to breadth.

If on analysis these are no better then

this previously unexpanded node and

branch is not forgotten and the search

method reverts to the descendants of

the first choice and proceeds,

backtracking as it were.

This process is very similar to steepest

ascent, but in hill climbing once a move

is chosen and the others rejected the

others are never reconsidered whilst in

best first they are saved to enable

revisits if an impasse occurs on the

apparent best path. Also the best

available state is selected in best first

even its value is worse than the value of

the node just explored whereas in hill

climbing the progress stops if there are

no better successor nodes. The best

first search algorithm will involve an OR

graph which avoids the problem of node

duplication and assumes that each node

has a parent link to give the best node

from which it came and a link to all itssuccessors. In this way if a better node

is found this path can be propagated

down to the successors. This method of

using an OR graph requires 2 lists of

nodes OPEN is a priority queue of

nodes that have been evaluated by the

heuristic function but which have not yet

been expanded into successors. The

most promising nodes are at the front.

CLOSED are nodes that have alreadybeen generated and these nodes must

be stored because a graph is being

used in preference to a tree.

8/2/2019 Heurstic

6/8

Heuristics In order to find the most

promising nodes a heuristic function is

needed called f' where f' is an

approximation to fand is made up of

two parts gand h' where g is the cost of

going from the initial state to the current

node; g is considered simply in this

context to be the number of arcs

traversed each of which is treated as

being of unit weight. h' is an estimate of

the initial cost of getting from the current

node to the goal state. The function f' is

the approximate value or estimate of

getting from the initial state to the goal

state. Both gand h' are positive valuedvariables. Best First The Best First

algorithm is a simplified form of the A*

algorithm. From A* we note that f' = g+h'

where g is a measure of the time taken

to go from the initial node to the current

node and h' is an estimate of the time

taken to solution from the current node.

Thus f' is an estimate of how long it

takes to go from the initial node to the

solution. As an aid we take the time togo from one node to the next to be a

constant at 1.

Best First Search Algorithm:

Start with OPEN holding the initial state

Pick the best node on OPEN

Generate its successors

For each successor Do

If it has not been generated before

evaluate it add it to OPEN and record its

parent

If it has been generated before change

the parent if this new path is better and

in that case update the cost of getting to

any successor nodes

If a goal is found or no more nodes left

in OPEN, quit, else return to 2.

8/2/2019 Heurstic

7/8

Example :

Problem :

Solution :

8/2/2019 Heurstic

8/8