So, there are three computing paradigms, which
is followed in soft computing one is fuzzy
logic, another is genetic algorithm and the
third is artificial neural network. So, today,
we will introduce the genetic algorithm the
computing paradigm for soft computing. Now
genetic algorithm is basically used for solving
optimization problem. Now you know exactly,
what is an optimization problem.
So, the optimization problem essentially solving
the to find the optimum value. That means,
find the minimum or maximum value. As an example
say suppose, this is the value for which the
different.
So, suppose f x, f x is a function which varies
with x. So, if it is x in this direction then
f x this is the f x. Now, so this concept
say suppose the value of f x varies with the
x, using this form, it is like this now. So,
this means the value of f x varies with x
and it takes the form like this and you can
say that x as it varies then it has many values.
So, here basically the for some x, the value
f x is highest, it is the maximum, it is the
another maximum or so on. Similarly, minimum
these are minimum this one. So, it basically
says that how the f x varies with x and if
it is like this and if you have to find which
is the maximum value for which or what is
the maximum value of f x or for which values
of x, it is the maximum.
So, that can be obtained and if you have to
search it then it is called the searching
for an optimum result and. So, far the searching
for an optimum result is concerned, it has
many what is called the values actually, here
these are the value is a highest value is
a peak. All peaks are basically, some values
they are called maxima. Similarly, all this
is the lowest values the valley it is called
the minima.
Now, out of this so many maxima’s there
are some values it is called the global maxima,
if we say that this is the maximum of all
the maxima values. Similarly, it is a local
maxima local minima if it is minimum of all
the minima values there. So, the concept is
local maxima or local minima and then global
maxima or global minima. So, finding an optimum
value; that means, a minimum which is global
maxima or global minima is called the solving
for optimization problem.
Now, we will discuss about the GA. The genetic
algorithm, which basically gives us a unique
and fantastic way to search for all optimum
values. That means, either minima or maxima
before going to discuss about the genetic
algorithm, we will just discuss about, how
mathematically the optimization problem is
defined.
If suppose x 1, x 2 dot, dot x n, are the
input parameter is given to us and we have
to find, the function which is defined by
f and which is discussed with this in terms
of these are the input parameters. That means,
the value of f is decided by the value of
all these parameters x 1, x 2, dot, dot x
n. So, this is a function we call this function
as a objective function. So, this function
is called objective function.
Now, we have to find either say optimum value,
optimum means either minimum value or maximum
value, for a given set of values of these
x 1, x 2, dot, dot x n. Then this is called
the optimise value. So, this optimise value
can be either minimize, if we have to find
the minimum values or we have to either find
maximize if we have to value the maximum maximization
value.
So, objective function always in terms of
either minimization or maximization and this
basically define by means of an objective
function, which takes like this x n, now this
functions this optimization. In fact, subject
to certain constants. So, if it is minimize
and constant may be another function g i x
1, x 2 dot, dot same set of parameters.
Now, this may be equals to 0, where they are
may be one or more constant. So, this i, i
equals to 1 to m, so if m constants are there.
So, these basically this is the objective
function it is like this and this is basically
the constant usually we denote as subject
2. So, there may be g 1, g 2, and dot, dot
g m constant. So, here the finding an optimum
value; that means, finding some values of
the input parameter. So, that this function
returns the optimum value and it should satisfy
all these constant.
Now, this problem is no more trivial problem.
In fact, and this problem cannot be solved
in normal time, that is why we need some pragmatic
approach like say soft computing to solve
the optimization problem. That means, we have
to find the values of input parameters for
which a function f should return on optimum
value minimum value or maximum value and at
the same time, it should satisfy the search
constants number of constants. So, this program
is no more a simple program.
So, traditionally there are many methods are
available and run to solve this kind of optimization
problem, but they have their own limitation
actually the traditional optimization methods
are in fact, computationally expensive. That
mean, they cannot be applied to solve some
optimization problem in real time. It may
take 1 month to solve some problem like and
all the traditional optimization methods usually
not suitable for a discrete objective function
and.
So, they are not suitable for discontinuous
objective function there are some functions
which have some value in some ranges. So,
is a discontinuity they are in the objective
function those method fails and as it is the
time consuming, what is called the task finding
an optimum value. So, usually we advise to
follow parallel computing, but the parallel
computing may not be implementable may not
be realise using traditional optimization.
So, we need something which basically suitable
for parallel computing and it is observed
that traditional optimization approaches are
not good enough to deal with the discrete
values of the input parameters. So, if the
input parameters are having discrete values
then the existing optimization technique cannot
solve them, and another limitation of the
existing approaches is that they are not necessarily
adaptive.
Adaptive in the sense that the same algorithm
that you have developed, if you have to apply
to m number of parameters instead of n, where
n maybe greater than m or less than m; that
means, if the input parameter increases then
you have to rewrite the method the program
totally differently. If the say, input parameter
type is different a earlier it was for integer.
Now, you have to see it real type so, then
it cannot be. So, they are actually they are
not adaptive; adaptive means if the environment
changes, input changes, that input parameter
type changes then the traditional approach
is not easy to adapt them.
So, we need some new method, which basically
address all these limitations and we will
see the evolutionary algorithm, it is an alternative
approaches to the traditional optimization
approaches that can solve and then address
all these problem. So, genetic algorithm is
basically one special type of evolutionary
algorithms.
Now, so far the evolutionary algorithms are
concerned how they are different than the
traditional approach. So, they are different
in terms of their the way they solve the problem.
In fact, the evolutionary algorithms they
follow few concepts and the concept is called
the, they follow certain biological and physical
behaviours, which is around our globe in our
world.
So, genetic algorithm which we are going to
discuss is basically follow, the concept of
genetics and evolution. Genetics is a well
known concept in biology and evolution is
also an well known concept in biology. So,
these are biological concepts. So genetics
and evolution is followed to solve the optimization
problem then this is called the genetic algorithm
and popularly it is abbreviated as GA.
Now, the way the ant they collect the food
or they invite others fellows to a particular
food source. It has been, followed to solve
optimization problem and this is called ant
colony optimization. So, it is also some sort
of behaviour of ant, which has been followed
and their behaviour is basically adapted into
solve optimization problem it is called the
ant colony optimization called ACO.
Now like there are how our nervous system
work, if we follow the concept then and if
we apply it then you can solve any problem
this is called the artificial neural network
or ANN. So, these are the classes belong to
the biological behaviours there are some physical
behaviours, the matters how they work. Now
annealing process is the one process which
is used to prepare the metals and if we follow
the annealing process to solve a type of optimization
problem or optimization problem, then it is
called the simulated annealing, it is abbreviated
SA.
Now particle how this swarm in a stream or
flow the same concept can be followed to solve
another optimization type of problem is called
the particle swarming optimization problem
or PSO. We have learned about fuzzy logic,
how fuzzy logic can be used to learn. So,
this is also another physical behaviour. So
all this concept are basically the concept,
which is followed in evolutionary algorithms.
Now, in this lecture we will basically focus
on specific evolutionary algorithm, it is
called the genetic algorithm, As I told you
genetic algorithm like ant colony optimization,
particle swarm optimization is another type
of evolution algorithm and it follows the
two important biological processes called
the genetics and evolution and particularly
it has been observed that genetic algorithm
is tremendous successful, in case of solving
the problem which are basically called combinatorial
optimization problem; that means, the problems
which cannot be solve in real time.
It is also called NP-Hard problem, or you
can say that additional methods if we apply
to solve this kind of problem. That means,
NP-Hard problems it is computationally very
expensive and cannot be computed in real time.
So, it is the problem and then genetic algorithm
have been applied to solve this kind of problem
and we can see the result in real time. And
more significantly, the genetic algorithm
is best suitable for those kind of problem
for which any specific mathematical model
or a suitable algorithm is possible to define
how to solve the problem. If we are not have
that specific algorithm are steps to solve
the problem, when we can apply the genetic
algorithm to solve this kind of problem.
So, the problem which is very difficult to
module mathematically or specific algorithm
is available then we can apply the genetic
algorithm to solve this kind of problem. And
if a problem involves a large number of parameters,
the parameters maybe discrete or maybe continuous
or anything then the traditional approach
is very difficult to use it, but genetic algorithm
can be used to solve this kind of problem
efficiently and effectively.
So, this is the idea, this is the history
behind the genetic algorithm and which we
can follow it. Now I just want to start with
a little background about genetic algorithm.
So, it is as early as in 1965, Professor John
Holland, from Michigan university. He first
proposed the concept, concept of genetic algorithm
in 1965, although he has proposed the idea,
but ultimately it was acceptable to the research
community much later in around 1975.
In fact, the two pioneer who work to make
the GA, most successful they are the two revolutionary
people one is called the Gregor Johan Mendel
and Charles Darwin. Gregor Johan Mendel in
1865, he proposed one revolutionary concept
called the genetics and around 10 years later,
Charles Darwin who proposed the concept it
is called the evolution and that these two
concept are merged together to solve the optimization
problem which become the true I mean origin
of the genetic algorithms.
So, in order to learn the genetic algorithm,
it is better that we should learn about the
two things the genetics and evolution first.
Now, as I told you Gregor Johan Mendel is
the forefather of the concept of genetics.
And genetics is an well-known things, and
you know genetics came from the concept called
gene and gene is basically is a fundamental
things in our life, and it basically say that
our body is consist of a large number of cells,
living cells and each cell is basically a
consists of what is called the one essential
part in the cell it is called the chromosome,
and if we go into details about the chromosome.
In fact, there is a spiral helix form and
they are called the genes and these genes
are basically the characteristics of a particular
cell. So, or in other words a chromosome decides
a particular type whether it belongs to monkey
or it belongs to man or it belongs to cow.
So, it is also observed that chromosome in
terms of number the different species that
we are having had the unique number of chromosome.
For example, mosquito has number of chromosome
6, human has 46, 23 pairs and goldfish 94
out of is goldfish is the one element which
is having the largest chromosome.
Now, so chromosome is one important be things
that is there and. In fact, this chromosome
also plays an important role in our genetic
algorithm, we will learn it exactly how the
chromosome is synonymous to genetic algorithms.
First let us see exactly how the chromosome
actually works it.
Now see, chromosome basically is a code it
is called the genetic code also and we know
that every individual has its own characteristics,
own features, own specification this is because
the genetic code is unique and it is differ
it is complete different from any other individuals
around.
So, a genetic code is basically looks like
a spiral helix, it is basically a protein
substance and this protein is called DNA,
deoxyribonucleic acid and a typical look of
the protein DNA is look like this. So this
is a DNA structure and this DNA, has its own
unique structure for a particular individual
and that is why you say that it is unique,
and if we can represent this DNA code then
we can basically identify the person. In fact,
so that is why this DNA code is used as a
biometric trait that mean by this DNA, we
can identify a person uniquely.
Now, so this is a concept of DNA and then
the, this concept is basically, is also important
in the reproduction, the reproduction as you
know. So, that two what is called a half cells
they are called haploid, to half cells from
the two opposite sex male and female obtained
and then when they merged they form the diploid
and then there this diploid is basically form
a cell.
So, here very important thing is that haploid
is basically one part which has the half number
of chromosomes and this another half number
of chromosomes, and when they merge together
they form the diploid which basically form
the full number of chromosomes. So, here is
basically the division after that unification
and then it produced another unique. What
is called the unique identity or unique elements.
So, this is the concept that is followed in
reproduction and so this is a part of the
life and we just follow the reproduction.
But behind this reproduction there is one
important thing that we have learnt about
that from two haploid we got a diploid and
here is the idea about. So, this is the one
chromosome from one haploid another chromosome
from another haploid and there is one point,
it is called the kinetochore point.
Now, they basically combine this kinetochore
point and then. So, from one element here
and another element here and then if we consider
another element which is basically one part
of here and another part here. So, basically
it, basically gives the one chromosome to
diploid. Similarly, another chromosome to
diploid. Now, here one thing you can note
if we take one part here and one part here.
So, the new chromosome that we get, so it
has the two call a mixture of chromosomes
and that mixture of chromosomes basically
if produce is able to produce a new elements
or new identity.
Now, so this is the fundamental thing that
is followed there, if we follow these kinetochore
points in different position. Then we can
have the infinite number of different possibilities
of having the different unique identity. So,
in this sense the reproduction allows or reproduction
produces a unique element, every time it reproduces
from two chromosomes to another chromosome
or two haploids to another diploid.
So, this is idea that is follows there and
this concept in genetics is called the crossing
over and we will follow it exactly the concept
of chromosome as it is there in genetics.
Similarly, the crossing over or simply it
is called the crossover is also an important
what is called the philosophy that is followed
in optimization technique.
Now, so this is the genetical genetics, which
basically Gregor Johan Mendel proposed first
then how reproduces and every reproduction
produce the unique element. Next evolution
is basically improvement from one level to
another. So, regarding this in evolution the
Charles Darwin is the forefather of this what
he proposes four concepts. So, far the evolution
is concerned the four concepts.
Are basically heredity, diversity, selection
and ranking, so according to the Charles Darwin
heredity? It is basically called information
propagation, information propagation means
that an offspring has many of its characteristics
of its parents and therefore, the property
or characteristics from its parent is basically
passes through its offspring; offspring means
children.
So, this is called the heredity. That means
we inherit something from our parents. So,
that is the concept heredity and population
diversity. So, Charles Darwin termed it as
diversity only, so it is basically called
the variation in characteristics in the next
generation.
So, if we see the different generation no
two generation we can obtain which have the
same identity always it have at least some
minor difference maybe, but differences are
there. Next premises is called the selection,
that is very important and this selection
Charles Darwin termed is at survival for existence.
So, basically out of many offspring only a
small percentage of the offspring is basically
able to survive in to adulthood and other
basically go to I mean dies to exist, there
they cannot sustain much more.
So, that is the selection and our world is
basically followed, this selection procedure
and that selection is basically called the
survival of the best. So, Darwin call is a
survival of the best. That means, only those
offspring they survive depends on their inherited
characteristics. So, it is based on the ranking,
so these are the four things, four premises
rather which is followed they are in so far
the evolution is concerned.
So, evolution will be carried forward and
Charles Darwin shows that these are the four
primary things by which the evolution can
takes place and evolution is followed there
and this evolution also Charleston called
the natural selection initially so, but will
termed is a evolution.
And we will see exactly how these two concepts
are followed in genetic algorithm and then
genetic algorithm has been proposed. Now,
other than this genetic algorithm concept,
there is another is called the mutation will
discuss about the mutation a mutation means
all of a sudden there are some changes. So,
two parents those are the fair skin all of
sudden their offspring may be black also.
So, it is the due to the mutation all of a
sudden there are some changes. That means,
there are certain drastic differences in their
chromosome property and that is the mutation.
So, mutation is also one part of our natural
what is called the process and natural generation
production or genetics.
Now, so this concept is basically followed
there and will learn about that how the concept
of biological process namely genetics and
evolution is followed there I just briefly
summarise the concept that we have learned
so far. So, if we have a population which
is the population initially and then from
this population, we follow the mating pool,
mating pool means we just simply see that,
who can be that can be fitted for mating another’s.
So, there is a mating selection like marriage
or whatever it is there. So, after the mating
selection is there then it starts a mating
and is basically. So, genetics is followed
there. So, that is a mating and then from
the mating, we have we follow whatever the
crossover mechanism or cross crossing over
that then and they produce there they produce
the reproduction.
So, this reproduction produce, the new offspring
and new offspring all together produce the
new generation. So eventually the idea is
that from the current population following
the reproduction procedure, we obtain the
new population and here in between there are
genetics and evolution involved. Now these
are the concept that is followed there and
in genetic algorithm. So, we are basically
using the same concept.
So, I can start with the genetic algorithm
concept, it is basically the is an algorithm
and this algorithm is a population based and
is a probabilistic search, probabilistic search
means the mating and the reproduction is a
probabilistic random and then optimization.
It is basically selecting the best candidate,
from there and which works based on the concept
of genetics and then evolution.
So, this is a concept of genetic algorithm
so the fundamental thing it is there the genetic
algorithm is basically, is a population based
probabilistic search that is important. Now
we will learn about how the population based
probabilistic search can be achieved and using
the genetics and then the concept of evolution.
So, this is the our objective study objective
and we will see exactly how this can be done.
Now, quickly I will start with first the architecture
genetic algorithm. So, this is basically the
flow chart of genetic algorithm. So, we start
with any population so we can say that initial
population randomly we select some population
actually and then there is a concept call
the converge. That means, if we say there
is no improvement in the next population then
we can say that stop it here no more progress,
but if we say there is some possibility of
progressing.
So, then we can go and then selection it basically
out of these populations select the best and
those best basically responsive for reproduction
if generates the next population. So, it will
go there and again start there with the next
population is converge, converge mean we can
achieve our goal or not that mean complete
or not. So, this way this algorithm is basically
is a process you continuous or iterative process
which run for long until we can come to the
converge. So, converge means in the sense
that we can search the optimum result. So,
that is the converge now here many things
are hidden.
So, how this population is related to our
problem solving, and how the selection and
reproduction can be realised. So, that from
one population the another population can
we obtained. So, the another population means
it is basically towards the better solution
and these are the process selection and reproduction
is basically is a fundamental block for probabilistic
searching. So, we will discuss about this
concept in details in the next class so fine.
So, this is the basic framework of the genetic
algorithm and based on this basic framework
there are many other framework also have been
proposed, all this things we will discuss
in the next class.
Thank you.
