This paper proposes a Neurocomputing application that reorders the Web results obtained from different Web Search Engines emulating the way our brain takes decisions. The proposed application is based on the Random Neural Network with Deep Learning Clusters that evaluates and adapts Web result relevance by associating independently each Deep Learning Cluster to a specific Web Search Engine. In addition, this paper presents a Deep Learning Cluster to perform as a Management Cluster that decides the final result relevance based on the inputs from each independent Deep Learning cluster. The performance of the proposed Management Cluster is evaluated when included as an additional layer to the Deep Learning Clusters. On average; the proposed Deep Learning cluster structure improves Smart Search performance