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The Hopfield Neural Network is a parallel, distributed information processing structure consisting of many processing elements connected via weighted connections. The objective function was then expressed as quadratic energy function and the associated weights between neurons were computed using the gradient descent of energy function. This paper reports a development of a Hopfield type neural network model to solve minimum cost delay leap multicast routing problem. The multicast tree is obtained by recursively obtaining the delay leap optimized path from source to various destinations and combining them by union operator. The union operator ensures that a link is appearing only once in the multicast tree. The minimum energy function is obtained with minimization of constrained parameter as per a defined annealing schedule, which increases the probability of visiting lower energy states. Finally, the goal of minimization of objective function (minimum cost delay leap route) is achieved by using mean filed approximation with stochastic annealing process of reducing constrained parameter.