The Quadratic Assignment Problem (QAP) is an NP-complete problem. Different algorithms have been proposed using different methods. In this paper, the problem is formulated as a minimizing problem of a quadratic function with restrictions incorporated to the computational dynamics and variables Si ∈{1,2,..., n}. To solve this problem a recurrent neural network multivalued (RNNM) is proposed. We present four computational dynamics and we demonstrate that the energy of the neuron network decreases or remains constant according to the Computer Dynamic defined.