<p>The rapid growth of the Internet of Things (IoT) has led to the generation of massive amounts of data from diverse applications such as smart cities, healthcare, and industrial automation. While fog computing has emerged as a promising paradigm to overcome the latency and bandwidth limitations of traditional cloud-centric models by enabling edge-level processing. Efficient placement of application modules in fog environments remains a critical challenge. This is primarily due to the heterogeneous nature of fog nodes, resource constraints, and the dynamic behavior of applications. Existing solutions often fall short in achieving optimal trade-offs between performance metrics such as latency, energy efficiency, and bandwidth utilization–particularly under real-time constraints. Further, most of these solutions fails to balance between explorations and exploitation. To address this gap, this study introduces a Quantum-Inspired Evolutionary Algorithm (QIEA) designed to optimize application module placement in fog computing. Unlike conventional heuristics, QIEA effectively tackles the NP-hard nature of the placement problem by leveraging quantum-inspired principles to enhance exploration and exploitation in the solution space. The proposed algorithm aims to minimize latency, energy consumption, and execution time, while ensuring the Quality of Service (QoS) requirements of IoT applications. The effectiveness of the method is demonstrated through a real-world use case called smart car parking system. Results show that, on an average, the proposed approach reduces the energy consumption by 9.5%, network usage by 17.2% and execution time by 54%.</p>