Download In 9122 Applied Soft Computing

SOFT COMPUTING
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8.
A.
B.
Define : - Artificial Intelligence.
Mention the characteristics of an artificial intelligent
problem.
A.
How to represent a problem in State Space Search?
Explain with an example
B.
Discuss on Depth First Search and Breadth First
search.
A.
How knowledge can be represented through
Prepositional Logic?
B.
Explain the importance of Scripts and Frames.
A.
Define – RESOLUTION.
B.
With an Example discuss on UNIFICATION
algorithm.
A.
Define – Fuzzy Sets.
B.
Discuss on Fuzzy Reasoning.
A.
How Membership functions can be included in Fuzzy
Set?
B.
Discuss on Fuzzy relations.
A.
How learning can be done with simple neurons?
B.
Explain the concept of Back Propagation Network.
Discuss the following in Genetic Algorithms:
i.
Rank Method.
j.
Rank Space Method.
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Artificial Intelligence (AI)
Artificial intelligence, commonly abbreviated as AI, also known as
machine intelligence, is the practice of developing algorithms that
make machines (usually computers) able to make seemingly
intelligent decisions, or act as if possessing intelligence of a human
scale.
The branch of computer science concerned with making computers
behave like humans. The term was coined in 1956 by John
McCarthy at the Massachusetts Institute of Technology. Artificial
intelligence includes
o
o
o
o
o
games playing: programming computers to play games such
as chess and checkers
expert systems : programming computers to make decisions
in real-life situations (for example, some expert systems help
doctors diagnose diseases based on symptoms)
natural language : programming computers to understand
natural human languages
neural networks : Systems that simulate intelligence by
attempting to reproduce the types of physical connections
that occur in animal brains
robotics : programming computers to see and hear and
react to other sensory stimuli
Problem Characteristics:
The term heuristic is used for algorithms which find solutions
among all possible ones, but they do not guarantee that the best
will be found, therefore they may be considered as approximately
and not accurate algorithms. These algorithms, usually find a
solution close to the best one and they find it fast and easily.
Sometimes these algorithms can be accurate, that is they actually
find the best solution, but the algorithm is still called heuristic
until this best solution is proven to be the best. The method used
from a heuristic algorithm is one of the known methods, such as
greediness, but in order to be easy and fast the algorithm ignores
or even suppresses some of the problem's demands.
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
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Is the problem decomposable into a set of nearly
independent smaller or easier sub problems?
Can solutions steps be ignored or at least undone
if they prove unwise?
Is the problem’s universe predictable?
Is a good solution to the problem obvious without
comparison to all other possible solutions?
Is the desired solution a state of the world or a
path to a state?
Is a large amount of knowledge absolutely
required to solve the problem, or its knowledge
important only to constrain the search?
Can a computer that is simply given the problem
return the solution, or will the solution of the
problem
require
interaction
between
the
computer and a person?
Is the problem decomposable?
Consider the below problem tree where the computer is trying to
find out a solution to the given problem – ∫x2+3x+sin2xcos2xdx.
∫x2+3x+sin2xcos2xdx
∫x2dx
∫3xdx
∫sin2xcos2xdx
∫x3/3
3∫xdx
∫(1-cos2x)cos2xdx
∫3x2/2
∫cos2xdx
-∫cos4xdx
From the above problem tree, a set of problem equation has been
decomposed into smaller further decomposable segments. To arrive
at this, system checks whether it can be further decomposable or
not at each and every state by a simple recursive integration
program. If the steps leads to an answer, then the answer is
directly returned otherwise it will search will go on. Using this
technique of problem decomposition, we can often solve very large
problems easily.
Let us consider one more example.
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We have got three [3] set of cubes namely {A}, {B} & {C}. These were
to be arranged in such a manner, the Set {A} should be placed top
followed by set {B} and then by set {C}. Given set is like this, Set {B}
is outside and set {A} is at the bottom, and set {C} is at top. The aim
to realign the same as A,B & C from top to bottom.
Start
Goal
A
C
B
A
B
C
ON (C, A)
Steps
1.
2.
3.
4.
5.
6.
7.
8.
9.
ON (B, C) & ON (A, B)
involved in this problem:
CLEAR [x] [block x has nothing on it]
On(x, Table) [Pick up x and put it on the table]
CLEAR (x) and CLEAR (y)
ON(x, y) [put x on y]
ON (B, C) and ON (A, B)
ON (B, C) and ON(A, B)
ON (B, C) and CLEAR (A) and ON (A, B)
ON (B, C) and CLEAR (A) and ON (A, B).
Now GOAL SET (A, B & C) is achieved.
Figuratively it is achieved as below:
On (b, c) and on (a, b)
on (a, b)
On (b, c)
On (b, c)
clear (a)
clear (a)
SOFT COMPUTING
on (a, b)
on (a, b)
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By this way we can also try to solve puzzle game where it consists
of 9 cubes placed by 3 x 3 matrix. Out of this, one cube will be
empty or space. The remaining 8 cubes of the matrix will have
numbers. The aim of the game is to realign the numbers from the
present position [What we call it as “Start” position] to the new
position [what we call it as “Goal” position]. Here one has to
move the adjacent number to the empty cube. Through this means
one has to move the numbers in such a way that they reach the
goal conveniently.
Is the universe predictable?
It is the planning that is going to pave way for solutions. Whether
such planning has to be done well in advance or to be done at that
time of activity or there is no such possibility of such planning? It
is to be explored and can’t be unique to all problem solving games.
Considering the 8 cube puzzle and bridge card game, where
unknown things are available as commonality. But in the 8 cube
puzzle game before making a move, it is possible to compute the
permutation and combination of the available moves to choose the
one. Even if we make a wrong move, then it is possible to undo
such moves to start from the same position. Whereas, it is not so
in the game bridge, where once committed is once for all
committed. Though planning is a must, it needs proper place to be
implemented.
In the first 8 cube puzzle game, even if planning fails there is
recoverable process. But in the bridge card game, if planning is
failed, it is out once for all. Improper planning and executing the
same is very expensive and risky. It may succeed or may not
succeed. The problem characteristics of this is ignorable versus
recoverable versus irrecoverable and certain outcome versus
uncertain outcome.
Is a Good Solution Absolute or Relative?
Considering the following database that reveals simple facts:
1.
2.
3.
4.
5.
6.
7.
Marcus was man.
Marcus was a Pompeian.
Marcus was born in 40 A. D.
All men are mortal.
All Pompeian died when the volcano erupted in 79 A. D.
No mortal lives longer than 150 years.
It is now 2007 A. D.
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Now, if anybody ask one question, whether Marcus is alive or
Dead? We have to go through the above statement and find out
the answer.
Let us see the methodology of finding out the answer through
predicate logic, and using formal inference methods.
Decisions
8.
9.
10.
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13.
14.
15.
16.
Justifications.
Marcus was a man.
Axiom 1.
All men are mortal.
Axiom 4.
Marcus is mortal.
1, 4.
Marcus was born in 40 A. D.
Axiom 3.
It is now 2007 A. D.
Axiom 7.
Marcus’ age is 1967 years
Axiom 3 & 7.
No mortal lives longer than 150 yrs. Axiom 6.
All Pompeian died when the
Volcano erupted in 79 A. D.
Axiom 5.
So, Marcus is dead.
10, 13 & 14.
Is the solution A State or Path?
It is always best to choose the example of traveling salesmen, who
has to travel from one city to another and a must that he is not
supposed to return to the same city again and finally he has to
reach back to his starting position. For this the law of finding the
solution is n-1!, where n is total number of cities, he has to travel
and assuming that he has to travel from a particular city and that
is reduced. Say for example, he has to travel 6 cities then the
answer path will be 5! [5x4x3x2x1 = 120] solutions are there to
identify the best possible shortest route. So it will be always very
difficult to identify the best possible shortest route for this
salesmen route. Though, one may come to a conclusion that it is
possible to asses certain totally ignoring others for want of time
and other activities and to proceed based on the assumption that
the decision taken already is correct. Someone at some time may
come up with best possible shortest route. Until then, one will go
by the same path.
What is the role of knowledge?
Chess and General opinion poll. For chess it is limited option and
good logic. For general opinion poll, it is lot of reasons. Every time
we have to break our head to identify the reason for our success or
failures.
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Does the task require Human Interaction or not?
Answer to this is always difficult as many times, the reason
assigned by the computer to identify the answer is not known
properly or at times not acceptable to the human.
Someone may thing that it is necessary for human interaction. We
may take the same in the best manner that if the system
[computer] needs, we can say human is assisting computer and if
the human requires assistance, it is then assisting human to make
understand the computer.
The AI Problem:
1.
Mundane tasks:
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
2.
Perception.

Understanding.

Speech.
Natural Language.

Understanding.

Generation.

Translation.

Common sense reasoning

Robot Control
Formal Tasks:


Games.

Chess.

Backgammon.

Checkers.

Go.
Mathematics.
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3.

Geometry.

Logic.

Integral Calculus.

Proving properties of Programs.
Expert Tasks:

Engineering.

Design.

Fault Finding.

Manufacturing Planning.

Scientific Analysis.
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Financial Analysis.
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Medical Analysis.
Problems, Problem Spaces ad Search.
1.
Define the problem precisely.
2.
Analyze the problem.
3.
Isolate and represent the task knowledge that is necessary to
solve the problem.
4.
Choose the best problem – solving technique(s) and apply it
to the particular problem.
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Defining the problem as a state space search
A water jug problem:
Aim to fill 2 gallon water in the 4 gallon water jug using 3 gallon
water jug, where both 4 and 3 gallon jug does not have any
marking on it.
May be on look the answer will be very simple.
For god’s sake, the problem does not mention about the quantity of
water to be used to fill 2 gallon of water in 4 gallon jug.
So it is the user’s choice that by spending n number of gallons of
water, he can fill 2 gallons of water.
The steps involved in identifying the same.
1.
There are two jugs without any measurement in it but
identifying itself as 4 gallons and 3 gallons depending
on its size [Large – 4 gallons and smaller – 3 gallons].
2.
Assuming both the jugs is empty. Let us name the
bigger jug as ‘x’ for 4 gallons and smaller jug as ‘y’ for
3 gallons.
3.
Fill 4 gallon jug with water.
4.
Fill 3 gallon jug with water.
5.
Pour all water from 4 gallon jug.
6.
Now, transfer all water from 3 gallon jug to 4 gallon
jug.
7.
Now, 4 gallon jug has 3 gallons of water and 3 gallon
jug is empty.
8.
Fill 3 gallon jug full.
9.
Now, 3 gallon jug has 3 gallon water and 4 gallon jug
as 3 gallon water.
10.
Pour water from 3 gallon jug carefully to 4 gallon jug
till it reaches full [Care has to be taken no to drop any
water down to earth either from 4 gallon jug or 3
gallon jug].
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11.
Now 4 gallon jug has 4 gallon water and 3 gallon jug
after filling the balance 4 gallon jug, now has 2 gallon
water.
12.
Pour all water from 4 gallon jug.
13.
Now, 4 gallon jug is empty and 3 gallon jug has 2
gallon water.
14.
Now, transfer the 2 gallon water from 3 gallon jug to 4
gallon jug so that 4 gallon jug has 2 gallon of water.
The same is represented as table here:
Gallons in the 4
Gallon Jug [x] Bigger
Gallons in the 3
Gallon Jug [y] Smaller
0
0
Both the jugs are empty.
4
0
Fill jug [x] – 4 gallons with
water.
4
3
Fill jug [y] – 3 gallons with
water.
0
3
Empty the 4 gallon jug[x].
3
0
Pour all the water from 3
gallon jug[y] to 4 gallon
jug[x].
3
3
Fill 3 gallon jug[y] with
fresh water.
4
2
Pour water from 3 gallon
jug[y] to 4 gallon jug[x] till
it is full.
0
2
Empty the 4 gallon jug[x]
0
Pour all the water from 3
gallon jug[y] to 4 gallon
jug[x] - RESULT
2
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Rules applied.
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Breadth First Search - How it works
BFS is an uninformed search method that aims to expand and examine all nodes of
a graph systematically in search of a solution. In other words, it exhaustively
searches the entire graph without considering the goal until it finds it. It does not use
a heuristic.
From the standpoint of the algorithm, all child nodes obtained by expanding a node
are added to a FIFO queue. In typical implementations, nodes that have not yet
been examined for their neighbors are placed in some container (such as a queue or
linked list) called "open" and then once examined are placed in the container
"closed".
The breadth-first tree one gets when
running BFS on the given map and
An example map of Germany with some
Animated example of a breadthfirst search
starting in Frankfurt.
connections between cities.
Uninformed search
An uninformed search algorithm is one that does not take into account the specific
nature of the problem. As such, they can be implemented in general, and then the
same implementation can be used in a wide range of problems thanks to
abstraction. The drawback is that most search spaces are extremely large, and an
uninformed search (especially of a tree) will take a reasonable amount of time only
for small examples. As such, to speed up the process, sometimes only an informed
search will do.
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Algorithm (informal)
1. Put the ending node (the root node) in the queue.
2. Pull a node from the beginning of the queue and examine it.

If the searched element is found in this node, quit the search and return a result.

Otherwise push all the (so-far-unexamined) successors (the direct child nodes) of this node
into the end of the queue, if there are any.
3. If the queue is empty, every node on the graph has been examined -- quit the search and return
"not found".
4. Repeat from Step 2.
C++ implementation
This is the implementation of the above informal algorithm, where the "so-far-unexamined" is handled by
the parent array.
Suppose we have a struct:
struct Vertex {
...
std::vector<int> out;
... }; and an array of vertices: (the algorithm will use the indexes of
this array, to handle the vertices)
std::vector<Vertex> graph(vertices); the algorithm starts from start and returns true if there is a
directed path from start to end:
bool BFS(const std::vector<Vertex>& graph, int start, int end) {
std::queue<int> next;
std::vector<int> parent(graph.size(), 0); // 0 means filled with zeros.
parent[start] = -1;
next.push(start);
while (!next.empty()) {
int u = next.front();
next.pop();
// Here is the point where you can examine the u th vertex of graph For example:
if (u == end) return true;
for (std::vector<int>::const_iterator j = graph[u].out.begin(); j != graph[u].out.end(); ++j) {
// Look through neighbors.
int v = *j;
if (parent[v] == 0) {
// If v is unvisited.
parent[v] = u;
next.push(v);
} } }
return false;
}
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