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back-propagation and GRG2, and other heuristic approaches, such as simulated annealing and tabu heuristic search Unlike some of the previous studies, we use nonbinary GA representation We speci cally investigate the impact of different types of design parameters (crossover operators), group distribution characteristics, and group dispersion on learning and predictive performance of GA based ANN The contributions of our case are the following: we study the learning and predictive performance (with special interest in over tting) of GA based ANN on training and unseen test cases under different data characteristics, rather than focus on the training/learning performance of GA based ANN for forecasting and function approximation problems We investigate the predictive performance of GA based ANN for classi cation problems, which has received little attention in the literature We investigate the performanceofdifferentcrossoveroperatorsonthelearningandpredictiveperformance of GA based ANN for classi cation Most studies in the past used only one type of crossover and benchmarked the performance of GA based ANN with other approaches Unlike studies in the past that were limited with few data sets and functions, we conduct extensive experiments to increase external validity of our study Finally, we use nonbinary representation since there is evidence in the literature that nonbinary representation is intuitively appealing and more ef cient in terms of the use of computer memory and convergence times The results of our study should therefore, be interpreted in the realm of nonbinary GAs In summary, we utilize smart data sets to provide evidence that a management smart data strategy is implemented and operational by demonstrating that (1) IT professionals are performing the right work the right way, (2) information technology organization staf ng is current with the right skills and pro ciencies, (3) state-of-theart mechanisms for data exchange are being utilized, and (4) highly pro cient metadata management is occurring The case also shows ways of enabling technology infrastructure featuring open interoperability with less dependency on rigid standards by alignment of IT metrics with enterprise performance optimization metrics and providing an improved operational footprint and savings ANNs and GAs were developed to mimic some of the phenomena observed in biology The biological metaphor for ANNs is the human brain and the biological metaphor for GAs is evolution of a species An ANN consists of different sets of neurons or nodes and the connections between the neurons Each connection between two nodes in different sets is assigned a weight that shows the strength of the connection A connection with a positive weight is called an excitatory connection and a connection with a negative weight is called an inhibitory connection The network of neurons and their connections is called the architecture of the ANN Let A {N1;N2;N3}, B {N4;N5;N6}, and C {N7} be three sets of nodes for an ANN Set A is called the set of input nodes, set B is called the set of hidden nodes, and set C is called the set of output nodes Information is processed at each node in an ANN For example, at a hidden node, the incoming signal vector (input) from the three nodes in the input set is multiplied by the strength of each connection and is added up
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The result is passed through an activation function and the outcome is the activation for the node In the back-propagation algorithm based learning, the strengths of connections are randomly chosen Based on the initial set of randomly chosen weights, the algorithm tries to minimize the square root of the mean-square error Most supervised learning applications use back-propagation as the learning algorithm Back-propagation as a method has several limitations One limitation is that learning time tends to be slow during neural network training using back-propagation Learning time increases with the increase in the size of the problem A second limitation occurs in the degree of dif culty of the training data itself Researchers have attempted to accelerate the learning that takes place with back-propagation One study used variations in the learning rate and corresponding step size to decrease the learning time Another study used various second-order techniques, which use a second derivative in the optimization process to utilize information related not only to the slope of the objective function but also to its curvature A few studies used least-squares optimization techniques All of these techniques might have offered improvements over the basic backpropagation method Since neural network training is a nonlinear problem, the GRG2 nonlinear optimizer was tested as an alternative to back-propagation GRG2 is a FORTRAN program that is used to solve nonlinear constrained optimization problems by the generalized reduced gradient method GRG2 evaluates the objective function and gradient at points required by the algorithm The weights of the interconnectivity arcs and the bias values of the nodes are the decision variables These variables were initialized to zero Training inputs were supplied to the network, which allowed the net inputs and activation levels of the succeeding nodes to be computed until activation levels were computed for the output layer The sum of the squares of the errors for all of the training patterns was the value of the objective function GRG2 allows the user to choose the method for generating search instructions The Fletcher Reeves formula (a conjugate gradient method) and the Broyden Fletcher Goldfarb Shannon method (a variable metric technique), both using the GRG2 software, nd solutions faster than back-propagation The major limitation of back-propagation is its scalability As the size of the training problem increases, the training time increases nonlinearly GRG2 had scalability problems as well, but to a lesser extent than backpropagation The degree of dif culty in training data has also been studied One study introduced an induction method called feature construction to help increase the accuracy in classi cation, as well as the learning time of the neural network Feature construction is a different way of representing the training data prior to input to the neural network Instead of using raw data as training data, higher level characteristics, or features, are constructed from the raw data These features are then input to the neural network For example, if the purpose of the neural network application is to determine the nancial risk of a corporation, instead of using raw accounting data, the features of liquidity, probability, and cash ow could be used for more ef cient learning by the
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