Resource allocation in the IoT-Fog environment is a challenging and critical problem with profound implications for application performance and service provider profitability. Efficiently distributing tasks across fog nodes enhances quality of service (QoS) metrics like latency for application users and reduces network resource utilization for service providers. This thesis proposes a hybrid meta-heuristic optimization approach, combining non-dominated search genetic algorithm II (NSGA-II) and multi-objective grey wolf optimization (MOGWO) algorithms, to address resource allocation. Comparative evaluations against five multi-objective optimization algorithms reveal the superiority of the proposed NSGA-II-MOGWO algorithm in resembling the Pareto front and generating diverse solutions for benchmarking functions. Additionally, when tested against cloud-based resource placement and NSGA-II, the proposed algorithm significantly improves users’ QoS metrics (e.g. time latency and response time) and reduces service providers’ costs for computation resources utilization and energy consumption. The implementation utilizes the Python fog simulator YAFS.