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Network function virtualization (NFV) is a novel technology that virtualizes computing, network, and storage resources to decouple the network functions from the underlying hardware, thus allowing the software implementation of such functions to run on commodity hardware. By doing this, NFV provides the necessary flexibility to enable agile, cost-effective, and on-demand service delivery models combined with automated management. Different management and orchestration challenges arise in such virtualized and distributed environments. A major challenge in the selection of the most suitable edge nodes is that of deploying virtual network functions (VNFs) to meet requests from multiple users. This article addresses the VNF placement problem by providing a novel integer linear programming (ILP) optimization model and a novel VNF placement algorithm. In our definition, the multi-objective optimization problem aims to (i) minimize the energy consumption in the edge nodes; (ii) minimize the total latency; and (iii) reducing the total cost of the infrastructure. Our new solution formulates the VNF placement problem by taking these three objectives into account simultaneously. In addition, the novel VNF placement algorithm leverages VNF sharing, which reuses VNF instances already placed to potentially reduce computational resource usage. Such a feature is still little explored in the community. Through simulation, numerical results show that our approach can perform better than other approaches found in the literature regarding resource consumption and the number of SFC requests met.