model of differential equation for genetic algorithm with neural network (gann) computation in c#

IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959

International Research Journal of Management Science & Technology http:www.irjmst.com Page 331

Model of Differential Equation for Genetic Algorithm with Neural

Network (GANN) Computation in C#

(Kumar Sarvesh1, Kumar Hemant2 Singh R.P.3, Mishra A.4, Kumar

Sailesh5) 1. Sarvesh Kumar, Research Scholar, Dept. of Statistics & Computer Applications, T.M.B.

University, Bhagalpur (India), Email:[email protected]

3. Dr. Rajeshwar Prasad Singh, Bhagalpur College of engineering, Sabour, Bhagalpur,

India,

Email: - [email protected]

4. DR. Akshoy Kumar Mishra, Post graduate of Statistics and computer applications ,

T.M.B. University, Bhagalpur, India, Email: [email protected]

2. Hemant Kumar, Statistician-cum-Optimization, Directorate of Economics & Statistics

(Planning Cadre), GNCT Delhi, India, Email: - [email protected]

5. Shailesh Kumar, Delhi Technical University (DTU/DCE), Delhi, India, Email: -

[email protected]

Abstract

The work is carried on the application of differential equation (DE) and its computational

technique of genetic algorithm and neural (GANN) in C#, which is frequently used in

globalised world by human wings. Diagrammatical and flow chart presentation is the major

concerned for easy undertaking of these two concepts with indication of its present and future

application is the new initiative taken in this paper along with computational approaches in

C#. Little observation has been also pointed during working, functioning and development

process of above algorithm in C# under given boundary value condition of DE for genetic

and neural. Operations of fitness function and Genetic operations were completed for

behavioural transmission of chromosome. Overall working process of model is based on

Initialization and Termination control of chromosome with its intermediates. Discussion is

also extended with the presentation of similar application of neural & genetic concept used in

various multidisciplinary fields. The computational of the DE model is verifies for a

particular function (Mg(x) = exp(x)+sin(x)) which corresponds to the chromosome g for

mailto:[email protected]







different quantities and penalty of fitness. Rule of thumb has been explained for better

understanding of the Decision criteria on when to use Genetic Algorithms versus when to use

Neural Networks to solve a problem is also presented

Index Term: Boundary value Differential equation, Genetic & Neural Algorithm,

Transmission of chromosome, Fitness function & Genetic operations and C# computation.

Introduction

Here we present a method for solving the ordinary differential equations which depends on

the function approximation capacity of the feed forward neural network and returns the

solution of differential equation in a closed analytic and differentiable form. There are

various research work has been carried on the mathematical modelling of neural network and

genetic algorithms in different ways especially in the contest of differential equation but

among which only little no of research has been published for computation of neural and

genetic algorithm by using differential equation under given available environment

condition. In this field this is the unique attempted to compute the mathematical model for

neural and genetic algorithms in c# especially by Ordinary Differential Equation (ODE)

method [1,3,4,8,9]. The concept of Genetic algorithms has been used to solve optimization

problems for artificial neural networks (ANN) in several domains. The choice of the basic

parameter (network topology, learning rate, initial weights) often already determines the

success of the training process. The selection of these parameter follow in practical use rules

of thumb[2,3,5,6], but their value is at most arguable. Genetic algorithms are global search

methods that are based on principles like selection, crossover and mutation[2,3,5,6]. This

thesis examines how genetic algorithms can be used to optimize the network topology etc. of

neural networks. It investigates, how various encoding strategies influence the GA/NN

synergy[2,35,6]. They are evaluated according to their performance on academic and

practical problems of different complexity. A research tool has been implemented, using the

programming language C#[4,7]. Its basic properties are described Genetic algorithms help to

search for optimal hidden-layer architectures, connectivity and used parameters for ANN for

predicting the outputs of chromosomes. Feed-forward back-propagation ANN was trained on

socio demographic, symptom, sign, co morbidity, and radiographic outcome data among.

Binary chromosomes with genes representing network attributes, including the number of

nodes in the hidden layers, learning rate and momentum parameters, and the presence or


International Research Journal of Management Science & Technology http:www.irjmst.com 33

absence of implicit within-layer connectivity using a competition algorithm, were operated on

by various combinations of crossover, mutation, and probabilistic selection. Formations of

artificial neural networks completely alter the progression of human thought. Artificial neural

networks (ANNs) represent models of information processors that resemble biological neural

networks[1,3,5,6,7,15]. While ANNs provide individuals more efficient ways of processing

data, adverse results occur if machines interfere with human cognition. Development of

artificial neural networks remains a fascinating element of scientific discovery, but this

innovation brings about revolutionary changes that benefit and harm development of

individuals’ intelligence. The idea of combining GA and NN came up first in the late 80s, and

it has generated a intense field of research in the 1980s[1,3,5,6,15]. Since both are

autonomous computing methods, why combine them? In short, the problem with neural

networks is that a number of parameter have to be set before any training can begin.

However, there are no clear rules how to set these parameters. Yet these parameters

determine the success of the training. By combining genetic algorithms with neural networks

(GANN)[1,2,3,5,6,15], the genetic algorithm is used to find these parameters. The inspiration

for this idea comes from nature: In real life, the success of an individual is not only

determined by his knowledge and skills, which he gained through, experience (the neural

network training), it also depends on his genetic heritage (set by the genetic

algorithm)[2,3,5,6,15]. One might say, GANN applies a natural algorithm that proved to be

very successful on this planet: It created human intelligence from scratch. The topic of this

paper is the question of how exactly GA and NN can be combined by computational way in

c#[4,7], i.e. especially how the neural network should be represented to get good results from

the GA in the way of computational technique in c#[4,7].

Background of GANN with Diagrammatical/Flow Chart Presentation

Neural networks consist of cells known as neurons that transmit electrical impulses

throughout the central nervous system. Individual neurons consist of dendrites, soma, axons,

and myelin sheath[1,15]. Dendrites receive signals from other neurons. The soma represents

the cell body, protecting the neuron nucleus. Axons act as terminals for electrical impulses,

with the myelin sheath acting as an insulator[1,15]. Certain neurons perform specific tasks,

such as transmitting signals from sensory or motor organs to the brain. Multiple neurons

transmitting data for a specific purpose form a neural network. An Artificial Neural network

(ANN), usually called "neural network" (NN), is a mathematical model or computational



model that simulates the computational model like the biological neural networks[3,5,11]. It

consists of an interconnected artificial neurons and processes information using a

connectionist approach. In most cases an ANN is an adaptive system that changes its

structure based on external or internal information that flows through the network during the

learning process[1,4]. Another aspect of the artificial neural network is that there are different

architectures[7,15], which requires different types of algorithms [7,15], but compare to other

complex system, a neural network is relatively simple if handled intelligently. The advantage

of the ANN is the feed forward networking and back propagation of error, by which the

network can be trained to minimize the error up to an acceptable accuracy. The benefits of

ANN is that the output of the network for selective number of points can be used to find out

the outcome for any other new point using the same parameters for interpolation and

extrapolation[1,11,15]. Modern scientists continue to improve on creating ANN models that

duplicate the phenomena of biological neurons, enabling inventors to create machines that

perform humanlike tasks[1,15]. Scientists apply artificial neural networks in speech, image

analysis, and robotics. Others utilize ANN setups to provide mathematical models of

biological neural networks. Regardless of purpose, the creation of artificial neural networks

remains complex.ANN is a field which is growing from the last few decades. An enormous

amount of literature has been written on the topic of neural networks. Because neural

networks are applied to such a wide variety of subjects, it is very difficult to mention here all

of available material. A brief history of neural networks has been written to give an

understanding of the subject[1]. Papers on various topics related to this study are detailed to

establish the need for the proposed work in this study[1,5,6,9]. As such, following paragraphs

give a brief literature review for the ANN in general and related to the present problem in

particular[1,3,5,6,10,12].

Networks of linear units are the simplest kind of networks, where the basic questions related

to learning, generalization, and self-organization can sometimes be answered analytically.

Some relevant theoretical results on the asymptotic behavior of finite neural networks have

been exits in the real world, when they are subjected to fixed boundary conditions[8,9].

Previously , the brief introduction was all ready completed by numerical linear algebra

approaches for solving structured nonlinear least squares problems arising from multiple-

output neural-network (NN) model, after then this boundary value problem has been solved

by the development of new model of neural network based on ordinary differential equation

with certain iteration. An interesting method had been developed[3,5,6] for adaptive



behavior of learning in an artificial neural network (ANN). The adaptive behavior of learning

emerges from the coordination of learning rules. Each learning rule is defined as a function of

local information of a corresponding neuron only and modifies the connective strength

between the neuron and its neighbors. Investigated various application of ANN in different

practical problems had been finished by various researcher [ ]. In the finite difference and

finite element methods we approximate the solution by using the numerical operators of the

function’s derivatives and finding the solution at specific pre assigned grids. A few works

have been done for solving ODE’s and PDE’s using ANN, which are refereed to produce this

paper. Last research work on neural network has been also presented in the form of neural

algorithms for solving differential equations [2,12,14] . The presentation of the nonlinear

differential equations has been solved by previous extended work using feed forward neural

networks with continuous work on optimization for multidimensional neural network training

and simulation[17]. The neural network has been classified on the basis of functional

behavior of model are presented here with.

1. The Biological Model: - Artificial neural networks emerged after the introduction of

simplified neurons by McCulloch and Pitts in 1943[11]. These neurons were

presented as models of biological neurons and as conceptual components. The basic

model of the neuron is founded upon the functionality of a biological neuron.

―Neurons are the basic signaling units of the nervous system‖ and ―each neuron is a

discrete cell whose several processes arise from its cell body‖. Figure gives the

structure of a neuron in human body. Human brain has more than 10 billion

interconnected neurons. Each neuron is a cell that uses biochemical reactions to

receive, process, and transmit information. The networks of nerve fibers called

dendrites are connected to the cell body or soma, where nucleus of the cell is located.

The body of the cell is a single long fiber called the axon, which is branched in to

strands and sub strands, are connected to other neurons through the synaptic terminals

or synapses[1,3,5,6,14,15]. The basic processing elements of neural networks are

called artificial neurons, or simply neurons or nodes. In the mathematical model of

neuron, the synaptic effects are represented by connection weights, that modulate the

effect of the input signals and the nonlinear characteristic of neurons is represented by

a activation function [2,14]. The neuron impulse is computed as the weighted sum of

the input signals, transformed by the activation function. The learning capability of an



artificial neuron can be achieved by adjusting the weights in accordance to the chosen

learning algorithm[1,2,3,5,6,14,15].

Fig.1. Structure of biological neural system

2. Mathematical Model: Mathematical definition of artificial neural networks can be

seen by presented neural network models , In which, first inputs x1, . . . ,xn combined

with synapses of the neuron represented as weights. These weights transmit

throughout the neuron, eventually combining at a ―summing junction‖ ∑. Electronic

impulses relay this compilation to the ―activation function‖ that sends out the desired

output. The equation presented below has been defines the biological neurons’

processes through a mathematical function [1].In a biological network; the ―summing

junction‖ represents the spinal cord, while the ―activation function‖ serves as the

brain. Output kv represents the reaction the brain forces a person to perform. A

functional model of a biological neuron has three basic components of importance.

First, the synapses of the neuron which are modeled as weights. The strength of the

connection between an input and a neuron is noted by the value of the weight. An

activation function controls the amplitude of the output of the neuron. An acceptable

range of output is usually between 0 and 1, or -1 and 1. A typical artificial neuron and

the modeling of a multilayered neural network are illustrated in figure. The signal

flow from inputs x1, . . . ,xn are considered to be unidirectional, indicated by arrows to

the neuron’s output signal flow (O). The neuron output signal O is given as:

1

( )n

j j

j

o f net f w x ; Where wj is the weight vector, and the function f(net) is an

activation function. The variable net is defined as a scalar product of the weight and

input vectors by1 1 ..................T

n nnet w x w x w x ; where T is the transpose of a



matrix. The output value O is computed as 0 ( ) {1 ; 0}Tf net if w x othrrwise ;

Where θ is called the threshold level; and this type of node is called a linear threshold

unit. The internal activity of the model for the neurons is given by:1

p

k k j

j

v w x Then

the output of the neuron ky would be the outcome of some activation function on the

value of kv .

Fig.2. Mathematical Neural Model

Genetic Algorithms:-An attractive class of computational models is generally known as

Genetic Algorithms (GA), that mimic the biological evolution process[3,5,6] for solving

problems in a wide domain. The mechanisms under GA have been analyzed and explained by

various ways having three major applications, namely, intelligent search, optimization and

machine learning. The evolutionary approach to Artificial Intelligence (AI) is one of the

neatest ideas of all to understand the GA. We have tried to mimic the functioning of the brain

through neural networks, because - even though we don't know exactly how it works - we

vk

∑ (0)

Synapti

c

Weights

Summin

g

Junction

Input

signals

=

Activation

Function

Threshol

d

Fixed input x0=± 1



know that the brain does work. Similarly, we know that Mother Nature, through the process

of evolution, has solved many problems, for instance the problem getting animals to walk

around on two feet (try getting a robot to do that - it's very difficult). So, it seems like a good

idea to mimic the processes of reproduction and survival of the fittest to try to evolve answers

to problems, and maybe in the long run reach the holy grail of computers which program

themselves by evolving programs. Evolutionary approaches are simple in conception. In

which four are most important [2]. First one is to generate a population of possible answers

to the problem at hand and another is to choose the best individuals from the population

(using methods inspired by survival of the fittest), nest one is to produce a new generation

by combining these best ones (using techniques inspired by reproduction) and the last one is

to stop when the best individual of a generation is good enough (or you run out of

time).Perhaps the first landmark in the history of the evolutionary approach to computing was

John Holland's book "Adaptation in Natural and Artificial Systems"[1,3,5,6,14,15], where he

developed the idea of the genetic algorithm as searching via sampling hyper plane partitions

of the space. It's important to remember that genetic algorithms (GAs), which we look at in

this lecture, and genetic programming (GP), which we look at in the next lecture, are just

fancy search mechanisms which are inspired by evolution.

The main difference between genetic algorithms and genetic programming is the choice of

representation for problem solutions[2,3,5,15]. In particular, with genetic algorithms, the

format of the solution is fixed, e.g., a fixed set of parameters to find, and the evolution occurs

in order to find good values for those parameters. With genetic programming, however, the

individuals in the population of possible solutions are actually individual programs which can

increase in complexity, so are not as constrained as in the genetic algorithm approach. The

main model or algorithms of GA are presented below for better understanding.

1. The Canonical Genetic Algorithm [3,5,6 ] As with all search techniques, one of the

first questions to ask with GAs is how to define a search space which potentially

contains good solutions to the problem at hand. This means answering the question of

how to represent possible solutions to the problem. The classical approach to GAs is

to represent the solutions as strings of ones and zeros, i.e., bit strings. This is not such

a bad idea, given that computers store everything as bit strings, so any solution would

eventually boil down to a string of ones and zeros. However, there have been many

modifications to the original approach to genetic algorithms, and GA approaches now



come in many different shapes and sizes, with higher level representations. Indeed, it's

possible to see genetic programming, where the individuals in the population are

programs, as just a GA approach with a more complicated representation scheme.

Returning to the classical approach, as an example, if solving a particular problem

involved finding a set of five integers between 1 and 100, then the search space for a

GA would be bits strings where the first eight bits are decoded as the first integer, the

next eight bits become the second integer and so on. Representing the solutions is one

of the tricky parts to using genetic algorithms, a problem we come back to later.

However, suppose that the solutions are represented as strings of length L. Then, in

the standard approach to GAs, known as the canonical genetic algorithm, the first

stage is to generate an initial random population of bit strings of length L. By random,

we mean that the ones and zeros in the strings are chosen at random. Sometimes,

rarely, the initialisation procedure is done with a little more intelligence, e.g., using

some additional knowledge about the domain to choose the initial population. After

the initialisation step, the canonical genetic algorithm proceeds iteratively using

selection, mating, and recombination processes, then checking for termination. This is

portrayed in the following diagram: In the next steps, we look in detail at how

individuals are selected, mated, recombined (and mutated for good measure).

Termination of the algorithm may occur if one or more of the best individuals in the

current generation perform well enough with respect to the problem, with this

performance specified by the user. It is very important to note that the best individual

in your final population may not be as good as the best individual in a previous

generation (GAs do not perform hill-climbing searches, so it is perfectly possible for

generations to degrade). Hence GAs should record the best individuals from every

generation, and, as a final solution presented to the user, they should output the best

solution found over all the generations which can be seen by flow chart.



Initial Population

Fig.3.Overview of GA

2. GA Model for Selection, Mating, Recombination and Mutation [3,5,6 ]So, the

point of GAs is to generate population after population of individuals which represent

possible solutions to the problem at hand in the hope that one individual in one

generation will be a good solution. We look here at how to produce the next

generation from the current generation. Note that there are various models for whether

to kill off the previous generation, or allow some of the fittest individuals to stay alive

for a while - we'll assume a culling of the old generation once the new one has been

generated. The overall process can be understood by above flow chart in concise ways

and discussed below one by one.

Selection: The first step is to choose the individuals which will have a shot at

becoming the parents of the next generation. This is called the selection procedure,

and its purpose it to choose those individuals from the current population which will

go into an intermediate population (IP). Only individuals in this intermediate

population will be chosen to mate with each other (and there's still no guarantee that

they'll be chosen to mate, or that if they do mate, they will be successful ). To perform

the selection, the GA agent will require a fitness function. This will assign a real

number to each individual in the current generation. From this value, the GA

calculates the number of copies of the individual which are guaranteed to go into the

intermediate population and a probability which will be used to determine whether an

additional copy goes into the IP. To be more specific, if the value calculated by the

fitness function is an integer part followed by a fractional part, then the integer part

Selection

Mating

Recombination

Termination check Choose

Best

Ever

Hey

User No

Ye

s



dictates the number of copies of the individual which are guaranteed to go into the IP,

and the fractional part is used as a probability: another copy of the individual is added

to the IP with this probability, e.g., if it was 1/6, then a random number between 1 and

6 would be generated and only if it was a six would another copy be added. The

fitness function will use an evaluation function to calculate a value of worth for the

individual so that they can be compared against each other. Often the evaluation

function is written g(c) for a particular individual c. correctly specifying such

evaluation functions is a tricky job, which we look at later. The fitness of an

individual is calculated by dividing the value it gets for g by the average value for g

over the entire population: fitness(c) = g(c)/(average of g over the entire population)

.We see that every individual has at least a chance of going into the intermediate

population unless they score zero for the evaluation function. As an example of a

fitness function using an evaluation function, suppose our GA agent has calculated the

evaluation function for every member of the population, and the average is 17. Then,

for a particular individual c0, the value of the evaluation function is 25. The fitness

function for c0 would be calculated as 25/17 = 1.47. This means that one copy of c0

will definitely be added to the IP, and another copy will be added with a probability of

0.47 (e.g., a 100 side dice is thrown and only if it returns 47 or less, is another copy of

c0 added to the IP).

Mating: Once our GA agent has chosen the individuals lucky enough (actually, fit

enough) to produce offspring, we next determine how they are going to mate with

each other. To do this, pairs are simply chosen randomly from the set of potential

parents. That is, one individual is chosen randomly, then another - which may be the

same as the first - is chosen, and that pair is lined up for the reproduction of one or

more offspring (dependent on the recombination techniques used). Then whether or

not they actually reproduce is probabilistic, and occurs with a probability pc. If they

do reproduce, then their offspring are generated using a recombination and mutation

procedure as described below, and these offspring are added to the next generation.

This continues until the number of offspring which is produced is the required

number. Often this required number is the same as the current population size, to keep

the population size constant. Note that there are repeated individuals in the IP, so

some individuals may become the proud parent of multiple children. This mating

process has some analogy with natural evolution, because sometimes the fittest



organisms may not have the opportunity to find a mate, and even if they do find a

mate, it's not guaranteed that they will be able to reproduce. However, the analogy

with natural evolution also breaks down here, because individuals can mate with

themselves and there is no notion of sexes.

Recombination: During the selection and mating process, the GA repeatedly lines up

pairs of individuals for reproduction. The next question is how to generate offspring

from these parent individuals. This is called the recombination process and how this

is done is largely dependent on the representation scheme being used. We will look at

three possibilities for recombination of individuals represented as bit strings. The

population will only evolve to be better if the best parts of the best individuals are

combined; hence recombination procedures usually take parts from both parents and

place them into the offspring. In the One-Point Crossover recombination process, a

point is chosen at random on the first individual, and the same point is chosen on the

second individual. This splits both individuals into a left hand and a right hand side.

Two offspring individuals are then produced by (i) taking the LHS of the first and

adding it to the RHS of the second and (ii) by taking the LHS of the second and

adding it to the RHS of the first. In the following example, the crossover point is after

the fifth letter in the bit string: Note that all the a's, b's, X's and Y's are actually ones

or zeros. We see that the length of the two children is the same as that of the parents

because GAs use a fixed representation (remember that the bit strings only make

sense as solutions if they are of a particular length).

In Two-point Crossover, as you would expect, two points are chosen in exactly the

same place in both individuals. Then the bits falling in-between the two points are



swapped to give two new offspring. For example, in the following diagram, the two

points are after the 5th and 11th letters:

Again, the a's, b's, X's and Y's are ones or zeros, and we see that this recombination

technique doesn't alter the string length either. As a third recombination operator, the

inversion process simply takes a segment of a single individual and produces a single

offspring by reversing the letters in-between two chosen points. For example:

Mutation: It may appear that the above recombinations are a little arbitrary,

especially as points defining where crossover and inversion occur are chosen

randomly. However, it is important to note that large parts of the string are kept in

tact, which means that if the string contained a region which scored very well with the

evaluation function, these operators have a good chance of passing that region on to

the offspring (especially if the regions are fairly small, and, like in most GA

problems, the overall string length is quite high). The recombination process produces

a large range of possible solutions. However, it is still possible for it to guide the

search into a local rather than the global maxima with respect to the evaluation

function. For this reason, GAs usually performs random mutations. In this process, the

offspring are taken and each bit in their bit string is flipped from a one to a zero or

vice versa with a given probability. This probability is usually taken to be very small,

say less than 0.01, so that only one in a hundred letters is flipped on average. In

natural evolution, random mutations are often highly deleterious (harmful) to the

organism, because the change in the DNA leads to big changes to way the body



works. It may seem sensible to protect the children of the fittest individuals in the

population from the mutation process, using special alterations to the flipping

probability distribution. However, it may be that it is actually the fittest individuals

that are causing the population to stay in the local maxima. After all, they get to

reproduce with higher frequency. Hence, protecting their offspring is not a good idea,

especially as the GA will record the best from each generation, so we won't lose their

good abilities totally. Random mutation has been shown to be effective at getting GA

searches out of local maxima effectively, which is why it is an important part of the

process.

To summarise the production of one generation from the previous: firstly, an

intermediate population is produced by selecting copies of the fittest individuals using

probability so that every individual has at least a chance of going into the intermediate

population. Secondly, pairs from this intermediate population are chosen at random

for reproduction (a pair might consist of the same individual twice), and the pair

reproduce with a given fixed probability. Thirdly, offspring are generated through

recombination procedures such as 1-point crossover, 2-point crossover and inversion.

Finally, the offspring are randomly mutated to produce the next generation of

individuals. Individuals from the old generation may be entirely killed off, but some

may be allowed into the next generation (alternatively, the recombination procedure

might be tuned to leave some individuals unchanged). The following schematic gives

an indication of how the new generation is produced:

Description of GANNA: - Genetic Algorithms is used along with neural networks and fuzzy

logic for solving more complex problems. Because of their joint usage in many problems,

these together are often referred to by a generic name: ―; soft-computing‖.



Population

(Chromosomes)

A Genetic Algorithms operates through a simple cycle of stages presented below in concise

manner i.e. (i) Creation of a ―population‖ of strings (ii) Evaluation of each string (iii)

Selection of best strings and iv) Genetic manipulation to create new population of strings.

Each cycle in Genetic Algorithms produces a new generation of possible solutions for a

given problem. In the first phase, an initial population, describing

representatives of the potential solution, is created to initiate the search

process. The elements of the population are encoded into bit-strings, called chromosomes.

The performance of the strings, often called fitness, is then

evaluated with the help of some functions, representing the constraints of the

problem. Depending on the fitness of the chromosomes, they are selected for a

subsequent genetic manipulation process. It should be noted that the selection

process is mainly responsible for assuring survival of the best-fit individuals.

After selection of the population strings is over, the genetic manipulation

process consisting of two steps is carried out. In the first step, the crossover

operation that recombines the bits (genes) of each two selected strings

(chromosomes) is executed{3,5,6].Various types of crossover operators are found in

the literature. The single point and two points’ crossover operations are

illustrated. The crossover points of any two

chromosomes are selected randomly. The second step in the genetic

manipulation process is termed mutation, where the bits at one or more

randomly selected positions of the chromosomes are altered. The mutation

process helps to overcome trapping at local maxima. The off springs produced

by the genetic manipulation process are the next population to be evaluated .The cycle of a

Genetic Algorithms is presented below for better understanding of GA.

Genetic

Operators Selection

(Mating Pool)

Fitness

Evaluation

Parents Manipulation Reproduction

Decoded

strings

Offspring

New

generation



Genetics Epigenetics

Phenotype

Disease

Fig.4. cycle of a Genetic Algorithms

The occurrence of diseases in any species has been look at the diagrammed (Fig5) which is

the intersection of genetics, epigenetic and phenotypes. GENOTYPE: The genetic makeup, as

distinguished from the physical appearance, of an organism or a group of organisms. The

combination of alleles located on homologous chromosomes that determines a specific

characteristic or trait. PHENOTYPE: The observable physical or biochemical characteristics

of an organism, as determined by both genetic makeup and environmental influences. The

expression of a specific functionality, such as type of stature or blood group, based on genetic

as per influences of environmental. An individual or group of organisms exhibiting is a part

of particular phenotype. There are numerous environmental factors that we must take into

consideration as we attempt to understand the interplay between genes and their expression.

These variables include the foods we eat, our choice of supplementation, prescription meds,

chemicals, toxins, and poisons that we are exposed to on a daily bases, and of course the most

influential of them all, the thoughts we think and the feelings we feel. That's right, the

thoughts we think and the feelings we feel have momentous affects on our biology, according

to the area of cutting edge science known as EPIGENETICS. Feelings can be so wonderfully

enjoyable, while at the same time they can elicit such deep suffering. Therefore, the science

of epigenetic suggests that choosing to love ourselves, each other and choosing to perceive

our world as a place of beauty, abundance and tranquillity is a perception that leads to a

cornucopia of healthy cells and healing. The science is suggesting that the choice is ours and

ours only. Hence, nothing and no one has more control over the level of health that we will

enjoy than ourselves.



INITIALIZE

POPULATION

FORMULA

CONSTRAINTS

MUTATION

FORMULA

CONSTRAINTS

SELECTION

POPULATION OF

NEW FORMULATIONS

FORMULA

CONSTRAINTS

PERFORMANCE

EVALUATION

TEST

FOR

CONVER

GENCE

OR

STOPPIN

G

CRITERI

A

YES NO

The overall GANNA can be seen in concise way by flow chart and diagrammatical

presentation which is presented here with in two parts separately.

Fig.5. Occurrence of Diseases

Fig.6: Chart of GA (1st Part of GANNA)

Architecture

/Design

Network Layer

Transmission

Neuron

DataSe Network

Iterator

ErrorType Connection



Fig.7: Chart of ANN (2nd

Part of GANNA)

Decision criteria to use GA/ANN/ GANN

The attempted has been carried on to minimise the effort for deciding where we used

GA or ANN or both as a whole i.e. GANN. We aware genetic algorithms are global search

methods that are based on principles like selection, crossover and mutation. This paper

examines how genetic algorithms can be used to optimize the network topology of neural

networks by ODE technique and computation in c#. It investigates how various encoding or

decoding strategies influence the GA/NN synergy. They are evaluated according to their

performance on academic and practical problems of different complexity The most

complicated question arises that’s in which scenario neural and genetic algorithms can be

used for best performance of engine for determining the molecular and genetic functioning.



Sometimes it is very difficult to take the decision to whether we use genetic and neural. To

avoid these difficulties here we present few decision criteria to resolve it by rule of thumb.

Rule Of Thumb:-Most commonly rule of thumb to be used for determines when to use

Genetic Algorithms versus when to use Neural Networks to solve a problem? As we know

there are two types of neural network - supervised and unsupervised. Supervised get training

data from a human, unsupervised feedback into them and are more like GAs in that respect.

Can we work on getting out the non constructive bits in the question? It's a lot around the "set

of examples" as that's very list-y and we don't want to encourage that. The answers are fairly

good, and we'd like to keep it that way. We'll be happy to reopen it once that bit's taken care

of. As a general rule of thumb genetic algorithms might be useful in problem domains that

have a complex fitness landscape as mixing, i.e., mutation in combination with crossover, is

designed to move the population away from local optima that a traditional hill climbing

algorithm might get stuck in. Observe that commonly used crossover operators cannot change

any uniform population. Mutation alone can provide ergodicity of the overall genetic

algorithm process (seen as a Markov chain).

A genetic algorithm (GA) is a search technique used in computing to find exact or

approximate solutions to optimization and search problems. In the other ways the neural

networks are non-linear statistical data modelling tools. They can be used to model complex

relationships between inputs and outputs or to find patterns in data. If we have facing a

problem for quantify the worth of a solution, a genetic algorithm can perform a directed

search of the solution space. (E.g. find the shortest route between two points).

When you have a number of items in different classes, a neural network can "learn" to

classify items it has not "seen" before. (E.g. face recognition, voice recognition). Execution

times must also be considered. A genetic algorithm takes a long time to find an acceptable

solution. A neural network takes a long time to "learn", but then it can almost instantly

classify new inputs. As we aware sometimes genetic algorithm can be used like optimisation

technique. It primarily boils down to you having a number of variables and wanting to find

the best combination of values for these variables. It just borrows techniques from natural

evolution to get there. Neural networks are useful for recognising patterns. They follow a

simplistic model of the brain, and by changing a number of weights between them, attempt to

predict outputs based on inputs. They are two fundamentally different entities but sometimes

the problems they are capable of solving overlap. There are many similarities between them,

so I will only try to outline their differences. Used when you can code attributes that you

http://en.wikipedia.org/wiki/Genetic_algorithms

http://en.wikipedia.org/wiki/Artificial_neural_network





think may contribute to a specific, non-changing problem. The emphasis is on being able to

code these attributes (sometimes you know what they are) and that the problem is to a large

degree unchanging (otherwise evolutions don't converge). Like scheduling airplanes

/shipping. Time tables to finding the best characteristics for a simple agent in an artificial

environment. Neural Networks are used for regression/classification if given a set of (x, y)

examples we want regress the unknown y for some given x. Genetic algorithms are an

optimization technique. Given a function f(x), you want to determine the x which

minimizes/maximizes f(x).Genetic Algorithms (usually) work on discrete data (enums,

integer ranges, etc.). A typical application for GAs is searching a discrete space for a "good

enough" solution when the only available alternative is a brute force search (evaluating all

combinations).Neural Networks on the other hand (usually) work on continuous data (floats,

etc.). A typical application for NNs is function approximation where you've got a set X of

inputs and a set Y of related outputs but the analytical function f: X → Y. Of course there are

thousands of variants of both so the line between them is somewhat blurred. In fact, you can

use Genetic Algorithms as an alternative to the Back propagation algorithm to update weights

in Neural Network

There is no rule of thumb. In many cases you can formulate your problem to make use of

either of them. Machine learning is still an active area of research and which learning model

to use can be debatable.

OPERATIONS OF ODE MODEL FOR GANNA[2,3,5,8,12,13,14]

To solve a given deferential equation the proper boundary / initial conditions must be stated.

The algorithm has the following phases:

1. Initialization.

2. Fitness evaluation.

3. Genetic operations.

4. Termination control.

1. Initialization: In the initialization phase the values for mutation rate and replication rate

are set. The replication rate denotes the fraction of the number of chromosomes that will go

through unchanged to the next generation(replication). That means that the probability for



crossover is set to 1-replication rate. The mutation rate controls the average number of

changes inside a chromosome.

2 Fitness evaluations: ODE case: We express the ODE’s in the following form:

=0, (1)

Where denotes the n-order derivate of y. Let the boundary or initial conditions be given

by: (2)

Where is one of the two endpoints a or b. The steps for the fitness evaluation of the

population are the following:

1. Choose N equidistant points ( ) in the relevant range.

2. For every chromosome i

a) Construct the corresponding model , expressed in the grammar described

earlier.

b) Calculate the quantity

(3)

c) Calculate an associated penalty P( as show below.

d) Calculate the fitness value of the chromosome as:

(4)

The penalty function P depends on the boundary conditions and it has the form:

P( = (5)

Where is a positive number.

3. Genetic operations. The genetic operators that are applied to the genetic population are

the initialization, the crossover and the mutation. The initialization is applied only once on

the first generation. For every element of each chromosome a random integer in the range

[0..255] is selected. The crossover is applied every generation in order to create new

chromosomes from the old ones, that will replace the worst individuals in the population. In

that operation for each couple of new chromosomes two parents are selected, we cut these

parent - chromosomes at a randomly chosen point and we exchange the right-hand-side sub-

chromosomes. The detail of the selection process has been explained in next section.

4. Termination control. The genetic operators are applied to the population creating new

generations, until a maximum number of generations is reached or the best chromosome in

the population has fitness better than preset threshold.



COMPUTATIONAL APPROACHES OF ODE MODEL FOR GANNA IN C#.

This paper gives a computational method to solve the ordinary differential

equations[2,3,4,5,7,8,12,13,14]. We introduce a trial function which can be used to train input

data at arbitrary nodes. This trial function is based on two facts. First, satisfies the boundary

conditions (BC’s) of the differential equation. Second, is the sum of two terms, involving

perception parameters. This technique is not only applicable to ordinary differential

equations, but also can used to solve partial differential equations, that can be considered in

the future works of computation. The detail soft computational of artificial neural network by

ODE has been presented below .Justification of soft computing part of c# has been justified

for the particular case of ODE with the boundary conditions y(0) =

0 and y’(0) = 10. We take in the range [0; 1] N = 10 when Mg(x) = exp(x)+sin(x). When we

classified ODE in the form of linear ODE and Non-linear ODE then soft computing in C# has

been also covered for the particular function for linear ODE is y’ = 2x-1/x; with

initial condition by y(0)=20.1 with solution Mg(x)=y(x)=x+2/x and for Non-linear ODE is

y’=1/2y; where solution Mg(x)=y(x)= .

public double ModelEMi(double N, double x) { double result=0; for (int i = 0; i < N - 1;i++ ) { result += (x * ModelChromosome(N) * x); } return result * result; } public double ModelPMi(double N, double x) { double result = 0; for (int i = 0; i < N - 1; i++) { result += (x * ModelChromosome(N) * x) * (x * ModelChromosome(N) * x); } return result; } public static double ModelChromosome(double x) { return Math.Exp(x) + Math.Sin(x); }



/// <summary> /// Linear ODE's /// </summary> public class LinearODE { double ODE_One(double x) { return (x + (2 / x)); } double ODE_Two(double x) { return (Convert.ToDouble((x + 2)) / Math.Sin(x)); } double ODE_Three(double x) { return Math.Exp(-x / 5) * Math.Sin(x); } double ODE_Four(double x) { return Math.Sin(10 * x); } double ODE_Five(double x) { return 2 * x * Math.Exp(3 * x); } double ODE_Six(double x) { return Math.Exp(-x / 5) * Math.Sin(x); } double ODE_Seven(double x) { return Math.Sin(10 * x); } double ODE_Eight(double x) { return (1 - x); } double ODE_Nine(double x) { return Math.Exp(-x / 5) * Math.Sin(x); } }



/// <summary> /// Non - linear ordinary di_erential equations /// </summary> class NonLinearOrdinaryDifferentialEquations { double NLODE_One(double x) { return 1 / (2 * x); } double NLODE_Two(double x) { return x + Math.Sin(x); } double NLODE_Three(double x) { return Math.Log(x * x); } double NLODE_Four(double x) { return Math.Log(Math.Log(x)); } }

APPLICATIVE APPROACHES OF GENETIC ALGORITHM FOR NEURAL

NETWORK

The above discussed diagrammatical presentation or flow chart(Fig.8&Fig.9) gives the brief

idea regarding working process of any engine & its performance within internal activates can

be seen by wide applicative approaches of mixed concept of genetic and neural, especially for

natural and artificial activities of neurons as well as molecules. This type of free body

diagram helps for developing the optimization model for contribution of each part of engine.

Deviation of molecular activities can be check out by calculation the standard errors. The

concept of artificial neural network is frequently used in the field of discussing the ages of



Engine

+ b V

+ -

y

Operating condition

Altitude

Mach number

Power lever angle

Y_ref

Bias

data set

Neural

Network

Estimator

Engine

model

genetic algorithm optimization: Find b that minimized y error

forest area depends on the variation of average rainfall in that particular locality in the form

of input, output performance and connection of hidden activities. The above discussed

mathematical model can be applied in the growth pattern of forestry gene of molecular

activities. In every generation the following steps are performed. In the 1st step :-The

chromosomes are sorted with respect to their fitness value, in a way that the best chromosome

is placed at the beginning of the population and the worst at the end. In the 2nd

step c = (1 - s)

* g new chromosomes are produced by the crossover operation, where s is the replication rate

of the model and g is the total number of individuals in the population. The new individuals

will replace the worst ones in the population at the end of the crossover. And In the final

step:-The mutation operation is applied to every chromosome excluding those which have

been selected for replication in the next generation.

Fig.8.ANN used for Engine System

Using Neural Algorithms: While scientists know what artificial neural networks consist of,

researchers disagree on whether or not there exists a ―central planner‖ that collects

information from any location in the system. In the human body, the brain represents a

―central planner,‖ and experiments prove the organ’s ability to comprehend multiple sources

of data in which certain ANNs, independent devices employ themselves in separate locations,

each with an individual pathway to convert sensory inputs into actions. However, they

believe that for an ANN to act like a human there must be a centralized network similar to the



brain. Humans connect sensory input together when hearing, touching, and seeing at the same

time. Through methods such as ballistic reaching, preset trajectories, and motor emulation,

then the brains log repetitious actions, decreasing the time it takes for the brain to recognize

what is occurring. When the brain identifies what it must do, the signal transmits to the output

device. Discoveries in neuroscience lead to intriguing inventions in artificial intelligence and

provide humans with computational power unrivalled in the past. As an example, computers

prove theories proposed by mathematicians hundreds of years ago. Solutions to the

approximate sum of an infinite series of numbers could only be deciphered by a writing

utensil and paper. Only individuals blessed with minds like Newton or Einstein contemplated

how to solve these problems, but today, ANNs aid all people with a scientific calculator in

resolving an infinite series by hitting a few buttons. How digital technology enables humans

to ignore distance as a limiting factor of production. Researchers discovered patterns of

neural signals throughout the brain of an owl monkey. Once documented, these patterns

entered a computer that predicted the future movements of the neural networks. Signals from

the monkey brain transmitted throughout the computer and controlled a robotic arm receiving

the signal of the laboratory noted that the experiment provided the monkey brain with an arm

of several miles away With this type of technology, organizations like NASA possess the

ability to control probes in other areas of the solar system, and human knowledge bases

extend further than their physical area. Views a cell phone as another link for a person to

theoretically be in two places at once Hundreds of years ago, the actions of a human in one

area would not effect a situation far away. Today, an individual can eat lunch, run their

business in America, and deal with foreign import companies at the same time. While these

artificial networks enhance the ability to focus on multiple projects, they divide the person’s

attention span into separate places. This leads us to the detriments of artificial neural

networks, specifically the fact that it separates humans from actual experience.



Hidden layer Output layer Input layer

Runoff or

Evapotranspitatio

n

Monthly average throughfall

Monthly average rainfall

outside of the forest

Monthly average rainfall

on top of canopy

Water surface evaporation

outside the forest

Water surface evaporation

inside of forest

Monthly average temperature

Tree ages

Fig.9.ANN used in Rainfall and genesis of Forest

If all computer systems crash, the world economy will collapse. However, the greatest

controversy regarding the development of artificial neural networks in particular involves

whether the progress limits the comprehension levels of human beings. For an artificial

neural network to function, it seems that some sort of sensory mechanism must employ itself

in the machine. According to German philosopher Immanuel Kant, ―any phenomenon

consists of sensations, which are caused by particular objects themselves.‖These sensations

help the mind create schemas, mental representations of objects or places. Through computer

imaging and digital technology, humans study realms of knowledge on scales larger and

smaller than what the typical individual understands. Without technological aids, the concept

of space would not exist. However, when humans rely on technology to study, they lose the

direct connection to their project, creating only an abstract assumption of what truly goes on.

In the experiment linking the monkey brain to the robotic arm, electronic impulses transferred

from the monkey’s brain to the robot. This connection replaces human touch, eliminating that

aspect of the human experience. Growing accustom to a strictly digital education results in a

human’s inability to learn through varied methods, including a classroom environment. The



most commonly uses of ANN can be surmised below with certain explanations:-

Character Recognition:-The idea of character recognition has become very important as

handheld devices like the Palm Pilot are becoming increasingly popular.

Image Compression - Neural networks can receive and process vast amounts of information

at once, making them useful in image compression.

Stock Market Prediction - The day-to-day business of the stock market is extremely

complicated. Many factors weigh in whether a given stock will go up or down on any given

day. Since neural networks can examine a lot of information quickly and sort it all out.

Traveling Saleman's Problem - Interestingly enough, neural networks can solve the

traveling salesman problem, but only to a certain degree of approximation.

Medicine, Electronic Nose, Security, and Loan Applications - These are some applications

that are in their proof-of-concept stage, with the acceptation of a neural network that will

decide whether or not to grant a loan, something that has already been used more

successfully.

Miscellaneous Applications - These are some very interesting (albeit at times a little absurd)

applications of neural networks.

Demographic indicators: Mortality and Morbidity rates to be also calculated based on

neural concept of input and output point such as intensive care, dental caries for hospital

complications for health sector.

Portfolio Management:-The analysis of assets and investments is a major component in the

management of an insurance enterprise for financial intermediary, and uniform functions

performed are determined for those companies. Thus, insurers are involved with market and

individual price forecasting, the forecasting of currency futures, credit decision-making,

forecasting direction and magnitude of changes in indexes, and so on.

Geological Technique:- In particular, the papers include regression based weight generation

algorithm in neural network for estimation of frequencies of vibrating plate, neural network

based simulation for response identification of two storey shear building subject to

earthquake motion and response prediction of single storey building structures subject to

earthquake motions. Prediction of response of structural systems subject to earthquake

motions has also been investigated by various way using ANN.

Monsoon Forecasting:- The comparison of neural network configurations in the long range

forecast of southwest monsoon rainfall over India.

http://www-cs-faculty.stanford.edu/~eroberts/courses/soco/projects/2000-01/neural-networks/Applications/daveapps.html



Gene Linkage

Hence all these are also reflects by input, output and hidden layers of investment in market

and life secure policy. The complete mathematical model and computation can be understood

by above discussed algorithms.

How to Use Genetic Algorithms?: Problems which appear to be particularly appropriate for

solution by genetic algorithms includes timetabling and scheduling problems, and many

scheduling software packages are based on GAs. GAs has also been applied to engineering.

Genetic algorithms are often applied as an approach to solve global optimization problems. If

we want to more about evolutionary approaches of GA, then we encounter terminology

which makes the analogy to natural evolutionary processes at the species level and at the

genetics level (remember that it is the evolution of our genetic material that has shaped our

evolution as a species). It is worth remembering however, that, as with artificial neural

networks, this analogy is very loose, because people use different analogies, the analogies’

don't actually fit sometimes and real evolutionary processes are extremely complicated

affairs. If we are able to answer the following four questions, then we are eligible to use a GA

approach for problem solving task:

What is the fitness function? How is an individual represented? How are the

individuals selected?

How do individuals reproduce?

This analogy is presented in Fig.10 as follows:

GA terminology Genetics Terminology Species Terminology

Population DNA Population

Bit string Chromosome Organism

Bit (one or zero) Gene converse Genome

Selection

Survival of the fittest

Recombination Crossover Inheritance

Mutation Mutation Mutation

GA



Application of genetic algorithms include: mirrors designed to funnel sunlight to a solar

collector, antennae designed to pick up radio signals in space and walking methods for

computer figures. Many of their solutions have been highly effective, unlike anything a

human engineer would have produced, and inscrutable as to how they arrived at that solution.

GAs are similar to ANNs in as much as they might not be exactly the best (most efficient,

etc.) way to proceed, but they do provide you with a quick and easy way of tackling the

problem. As we saw with the transport application described above (carried out by

undergraduates), such initial efforts can often produce surprisingly good results, and it's not

fair to say that GAs should only be used as a first try. Indeed, as we shall see in the next

lecture, evolutionary approaches such as genetic programming can sometimes rival human

performance and be the most suitable AI technique to use.

CONCLUSION AND FUTURE SCOPE

The computational development of GANN model for ordinarily differential equation model is

the unique attempted for providing the accuracy of the differentiable solutions of neurons &

genetic in a closed analytic form. It gives an excellent function approximation and satisfies

the initial/boundary conditions. The method provides excellent generalization as the

derivation at test points never deviates more to that of exact one. It was observed that the

parameters of ANN remains fixed while the dimension can be increased by taking more test

points in the form of provided initial and boundary valve condition of ODE. But in this

process the time required for the GANN training will be more for getting better result. The

neural network architecture has been considered as fixed for all the simulation experiments.

Certainly the result may be good if we take more number of hidden nodes and no of

chromosome g for different penalty of fitness. As such it will be a challenge to see how far

the result becomes better for GANN Model by taking different number of hidden layers,

nodes, chromosomes and fitness function. The other factor is the variation of test points with

respect to the error minimization, because we only considered equidistance points. So better

result could be expected by taking more number of test points where the error values are

more. This paper helps for easy understating the GNNA concept and where it’s uses in real

life. The bottleneck of this new model is that the computational part of work only restricted

for defined fitness function and particular case of ODE. The computational process may be

extended for several programming and salutation will be obtained by approximation

technique of numerical analysis and Partial DE.



REFERENCES

1. Abraham A. (2004) Meta-Learning Evolutionary Artificial Neural Networks, Neuro

computing Journal, Vol. 56c, Elsevier Science, Netherlands, (1–38).

2. A. Malek *, R. Shekari Beidokhti; ―Numerical solution for high order differential

equations using a hybrid neural network—Optimization method‖; Applied

Mathematics and Computation 183 (2006) 260–271

3. Cao, H., Kang, L., Chen, Y., Yu, J., Evolutionary Modeling of Systems of Ordinary

Deferential Equations with Genetic Programming, Genetic Programming and

Evolvable Machines, vol.1,pp.309-337, 2000.

4. Christian Nagel, Bill Evjen, Jay Glynn, Morgan Skinner, Karli Watson, ―Professional

C# 2008‖, 2008

5. Iba,H., Sakamoto,E.: "Inference of Deferential Equation Models by Genetic

Programming‖, Proceedings of the Genetic and Evolutionary Computation

Conference (GECCO 2002),pp.788-795, 2002.

6. J. R. Koza, Genetic Programming: On the programming of Computer by Means of

Natural Selection. MIT Press: Cambridge, MA, 1992.

7. Kumar Sarvesh, Singh R.P., Mishra A., Kumar Hemant; ― computation of neural

network using C# with respect to bioinformatics‖ :International journal of scientific

and research publications, volume 3, issue 9, sept. 2013.

8. Lambert J.D. (1983), Computational Methods in Ordinary Differential Equations,

John Wiley and Sons, New York,.

9. Lee H., Kang I.S. (1990), Neural algorithms for solving differential equations, Journal

of Computational Physics 91 110–131.

10. Lagaris I.E., Likas A., Fotiadis D.I. (1998), Artificial neural networks for solving

ordinary and partial differential equations, IEEE Transactions on Neural Networks 9

(5) 987–1000.

11. Likas A., Karras D.A., Lagaris I.E. (1998), Neural-network training and simulation

using a multidimensional optimization system, International Journal of Computer

Mathematics 67 33–46.

12. Meade Jr A.J., Fernandez A.A. (1994), The numerical solution of linear ordinary

differential equations by feed forward neural networks, Mathematical and Computer

Modelling 19 (12) 1–25.



13. Meade Jr A.J., Fernandez A.A. (1994), Solution of nonlinear ordinary differential

equations by feed forward neural networks, Mathematical and Computer Modelling

20 (9) 19–44.

14. Malek A., Beidokhti R. Shekari (2006), Numerical solution for high order differential

equations, using a hybrid neural network—Optimization method, Applied

Mathematics and Computation 183,260–271.

15. Zurada J. M. (1992), Introduction to artificial neural systems, West Publishing

Company, St. Paul, United States of America

Acknowledgment: I am very grateful to gives the thanks to my supervisor& co-supervisor

Dr. Rajeshwar Prasad Singh, and DR. Akshoy Kumar Mishra for accelerating towards

writing & publishing the research work in reputed journals in the field of computer science.

The correcting and improving in paper is the major contribution of these two authors as a

supervisor. I am also thankful to Sh. Shailesh Kumar for his valuable cooperation and

suggestions in improving the soft-computing part in C#.The most valuable research part of

this paper has been covered by under the guidance of Sh.Hemant Kumar (Statistician-cum-

Optimization,) in the direction of innovation of new work in the field of neural and genetic.

The better understanding of mathematical model and the concept of GANN and its

computational technique has been possible by him with gives the unique approaches to

present the concept in flow charts and diagrams. He has received M.Phil in Operational

Research , Department of Operational Research, University of Delhi (India) with

specialization in Software Reliability Modelling(2009) after finishing the M.Sc in

Operational Research from St.Stephen’s College of Delhi University . He also admitted in

Indian Institute of Technology, Delhi (IITD) for M.Sc (Mathematics, 2004) after completed

graduation degree in Mathematics from Science College,Patna(Bihar) .He has almost two

year teaching experience in S.S. College of Business Studies , University of Delhi. Presently

he is serving for Govt of NCT of Delhi (India) in Planning cadre as a statistician from last

four years. He has given valuable guidance and correspondence author in four research paper

in the field of operation research. This work has been finished under the blessing of my father

and mother.

model of differential equation for genetic algorithm with neural network (gann) computation in c#

Education

genetic neural algorithm

concept of genetic algorithms

computation of neural

neural gann

model of differential

artificial neural networks

c kumar sarvesh1

c computation