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Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#
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Model of Differential Equation for Genetic Algorithm with Neural Network (GANN) Computation in C#

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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 …

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.

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  • 1. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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:-sarveshmcasoft@gmail.com 3. Dr. Rajeshwar Prasad Singh, Bhagalpur College of engineering, Sabour, Bhagalpur, India, Email: - dr.rajeshwarprasad@gmail.com 4. DR. Akshoy Kumar Mishra, Post graduate of Statistics and computer applications , T.M.B. University, Bhagalpur, India, Email: -akmishra.tmbu@gmail.com 2. Hemant Kumar, Statistician-cum-Optimization, Directorate of Economics & Statistics (Planning Cadre), GNCT Delhi, India, Email: - iitd.hement@gmail.com 5. Shailesh Kumar, Delhi Technical University (DTU/DCE), Delhi, India, Email: shailesh4751@gmail.com 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 331
  • 2. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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 Page 332
  • 3. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 333
  • 4. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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 multipleoutput 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 334
  • 5. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 335
  • 6. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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 vk 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: n o f (net ) f wj x j ; Where wj is the weight vector, and the function f(net) is an j 1 activation function. The variable net is defined as a scalar product of the weight and input vectors by net wT x w1 x1 .................. wn xn ; where T is the transpose of a International Research Journal of Management Science & Technology http:www.irjmst.com Page 336
  • 7. Volume 4 Issue 3 IRJMST matrix. The output value O is computed as 0 Online ISSN 2250 - 1959 f (net ) {1if wT x ; othrrwise 0} ; Where θ is called the threshold level; and this type of node is called a linear threshold p unit. The internal activity of the model for the neurons is given by: vk wk x j Then j 1 the output of the neuron yk would be the outcome of some activation function on the value of vk . Fixed input x0=± 1 = Activation Function vk ∑ (0) Summin g Junction Threshol d Input signals Synapti c Weights 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 337
  • 8. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 338
  • 9. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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. International Research Journal of Management Science & Technology http:www.irjmst.com Page 339
  • 10. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 Initial Population Selection Mating Recombination Hey User Choose Best Ever Ye s Termination check No 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 340
  • 11. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 341
  • 12. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 342
  • 13. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 343
  • 14. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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‖. International Research Journal of Management Science & Technology http:www.irjmst.com Page 344
  • 15. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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. representatives In of the the first potential phase, an solution, initial is population, created to describing 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. illustrated. The single The chromosomes are manipulation selected and two crossover process randomly point selected is positions of The mutation, the crossover points randomly. termed points’ chromosomes step the bits are in at altered. are any of second where operations two the one The genetic or more 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. Offspring New generation Population (Chromosomes) Decoded strings International Research Journal of Management Science & Technology Genetic Fitness Page 345 http:www.irjmst.com Operators Evaluation Selection Parents (Mating Pool) Manipulation Reproduction
  • 16. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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. Genetics Epigenetics Disease International Research Journal of Management Science & Technology Phenotype http:www.irjmst.com Page 346
  • 17. Volume 4 Issue 3 IRJMST The overall GANNA can be seen in concise way Online ISSN 2250 - 1959 by flow chart and diagrammatical presentation which is presented here with in two parts separately. Fig.5. Occurrence of Diseases INITIALIZE POPULATION FORMULA CONSTRAINTS POPULATION OF NEW FORMULATIONS MUTATION FORMULA CONSTRAINTS FORMULA CONSTRAINTS SELECTION PERFORMANCE EVALUATION YES TEST FOR CONVER GENCE OR STOPPIN G CRITERI A NO Fig.6: Chart of GA (1st Part of GANNA) Architecture /Design Layer Network International Research Journal of Management Science & Technology Neuron http:www.irjmst.com Page 347 Transmission DataSe Network ErrorType Connection
  • 18. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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. International Research Journal of Management Science & Technology http:www.irjmst.com Page 348
  • 19. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 349
  • 20. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 350
  • 21. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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, Where (1) 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( = Where (5) 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 subchromosomes. 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. International Research Journal of Management Science & Technology http:www.irjmst.com Page 351
  • 22. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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) ModelChromosome(N) * x); } return result; } public static double ModelChromosome(double x) { return Math.Exp(x) + Math.Sin(x); } * x) * (x * International Research Journal of Management Science & Technology http:www.irjmst.com Page 352
  • 23. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 /// <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); } } International Research Journal of Management Science & Technology http:www.irjmst.com Page 353
  • 24. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 /// <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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 354
  • 25. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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 2 nd 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 Engine b + + Y_ref Bias data set Operating condition Altitude Mach number Power lever angle V y - Neural Network Estimator Engine model genetic algorithm optimization: Find b that minimized y error 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 355
  • 26. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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. International Research Journal of Management Science & Technology http:www.irjmst.com Page 356
  • 27. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 Monthly average throughfall Monthly average rainfall outside of the forest Monthly average rainfall on top of canopy Water surface evaporation outside the forest Runoff or Evapotranspitatio n Water surface evaporation inside of forest Monthly average temperature Tree ages Input layer Hidden layer Output layer 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 International Research Journal of Management Science & Technology http:www.irjmst.com Page 357
  • 28. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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. International Research Journal of Management Science & Technology http:www.irjmst.com Page 358
  • 29. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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 GA terminology Genetics Terminology Species Terminology Population DNA Population Bit string Chromosome Organism Bit (one or zero) Gene converse Selection Gene Linkage Genome Survival of the fittest Recombination Crossover Inheritance Mutation Mutation Mutation International Research Journal of Management Science & Technology http:www.irjmst.com Page 359
  • 30. IRJMST Volume 4 Issue 3 Online ISSN 2250 - 1959 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. International Research Journal of Management Science & Technology http:www.irjmst.com Page 360
  • 31. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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. International Research Journal of Management Science & Technology http:www.irjmst.com Page 361
  • 32. Volume 4 Issue 3 IRJMST Online ISSN 2250 - 1959 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-cumOptimization,) 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. International Research Journal of Management Science & Technology http:www.irjmst.com Page 362

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