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Abstract This paper studies the virtual network function placement (VNF-P) problem in the context of network function virtualization (NFV), where the end-to-end delay of a requested service function chain (SFC) is minimized and the compute, storage, I/O and bandwidth resources are considered. To address this problem, an integer encoding grey wolf optimizer (IEGWO) is proposed. IEGWO has two significant features, namely an integer encoding scheme and a new wolf position update mechanism. The integer encoding scheme is problem-specific and offers a natural way to represent VNF-P solutions. The proposed wolf position update mechanism divides the wolf pack into two groups in each iteration, where one group performs exploitation while the other focuses on global exploration. It provides the search with a balanced local exploitation and global exploration during evolution. Performance evaluation has been conducted based on 20 test instances and IEGWO is compared with five state-of-the-art meta-heuristics, including the black hole algorithm (BH), the genetic algorithm (GA), the group counseling optimization (GCO), the particle swarm optimization (PSO) and the teaching–learning-based optimization (TLBO). Simulation results demonstrate that compared with BH, GA, GCO, PSO and TLBO, IEGWO achieves significantly better solution quality regarding the mean (standard deviation), boxplot and t-test results of the best fitness values obtained. Graphical abstract Highlights • Study the virtual network function placement problem in a NFV environment. • Propose an integer grey wolf optimizer (IEGWO) with a new wolf position update mechanism. • IEGWO outperforms a number of evolutionary algorithms regarding the solution quality. [ABSTRACT FROM AUTHOR]