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Network function virtualization enables network operators to implement new services through a process called service function chain mapping. The concept of Service Function Chain (SFC) is introduced to provide complex services, which is an ordered set of Network Functions (NF). The network functions of an SFC can be decomposed in several ways into some Virtual Network Functions (VNF). Additionally, the decomposed NFs can be placed (mapped) as VNFs on different machines on the underlying physical infrastructure. Selecting good decompositions and good placements among the possible options greatly affects both costs and service quality metrics. Previous research has addressed NF decomposition and VNF placement as separate problems. However, in this paper, we address both NF decomposition and VNF placement simultaneously as a single problem. Since finding an optimal solution is NP-hard, we have employed heuristic algorithms to solve the problem. Specifically, we have introduced a multiobjective decomposition and mapping VNFs (MODMVNF) method based on the non-dominated sorting genetic multi-objective algorithm (NSGAII) to solve the problem. The goal is to find near-optimal decomposition and mapping on the physical network at the same time to minimize the mapping cost and communication latency of SFC. The comparison of the results of the proposed method with the results obtained by solving ILP formulation of the problem as well as the results obtained from the multi-objective particle swarm algorithm shows the efficiency and effectiveness of the proposed method in terms of cost and communication latency.