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In the present book, our objective is to develop a hybrid evolutionary system consisting of Hopfield neural network and genetic algorithm which will be responsible for evolution of weight matrices in order to store some input patterns and analyze the performance of such a system in the terms of correct recalling of these already stored patterns again with evolutionary algorithm by presenting the same or noisy versions of input patterns. In this process, first the patterns of training set have been encoded in the neural network using MC-adaptation rule. It is expected that all the patterns of training set has been successfully stored as the associative memory feature of Hopfield type neural network. As a result of this learning process, we obtain the expected optimized weight matrices. Now, we employ the genetic algorithm to evolve the population of these approximate optimal weight matrices obtained by MC-adaptation rule. The fitness of every evolved population of weight matrices is evaluated by using the two fitness evaluation functions.