Efficient Virtual Machine (VM) placement is a critical challenge in optimizing resource utilization in cloud data centers. This paper explores both exact and approximate methods to address this problem. We begin by presenting an exact solution based on a Multi-Objective Integer Linear Programming (MOILP) model, which provides an optimal VM Placement (VMP) strategy. Given the NP-completeness of the MOILP model when handling large-scale problems, we then propose an approximate solution using a Tabu Search (TS) algorithm. The TS algorithm is designed as a practical alternative for addressing these complex scenarios. A key innovation of our approach is the simultaneous optimization of three performance metrics: the number of accepted VMs, resource wastage, and power consumption. To the best of our knowledge, this is the first application of a TS algorithm in the context of VMP. Furthermore, these three performance metrics are jointly optimized to ensure operational efficiency (OPEF) and minimal operational expenditure (OPEX). We rigorously evaluate the performance of the TS algorithm through extensive simulation scenarios and compare its results with those of the MOILP model, enabling us to assess the quality of the approximate solution relative to the optimal one. Additionally, we benchmark our approach against existing methods in the literature to emphasize its advantages. Our findings demonstrate that the TS algorithm strikes an effective balance between efficiency and practicality, making it a robust solution for VMP in cloud environments. The TS algorithm outperforms the other algorithms considered in the simulations, achieving a gain of 2% to 32% in OPEF, with a worst-case increase of up to 6% in OPEX.