Multi-objective optimization in fog computing is an important research area that addresses the challenge of simultaneously optimizing multiple conflicting objectives, such as minimizing latency, reducing energy consumption, improving resource utilization, lowering operational costs, and maximizing Quality of Service (QoS). Research papers in this domain explore heuristic, metaheuristic, and evolutionary algorithms—such as genetic algorithms, particle swarm optimization, ant colony optimization, and NSGA-II—to efficiently handle the trade-offs inherent in fog environments. Studies also integrate machine learning and reinforcement learning approaches to design adaptive, context-aware optimization models capable of responding to dynamic workloads, user mobility, and heterogeneous resource constraints. Recent works investigate joint optimization problems such as computation offloading with resource allocation, service placement with load balancing, and energy efficiency with performance guarantees. Hybrid frameworks that combine fog–edge–cloud resources are emphasized for scalability and reliability, while security- and privacy-preserving multi-objective optimization approaches are gaining attention to ensure trust in sensitive IoT and industrial applications. Applications include smart cities, intelligent transportation systems, real-time healthcare monitoring, and multimedia streaming, where multi-objective optimization ensures both system efficiency and user satisfaction. Overall, research in multi-objective optimization for fog computing provides flexible, adaptive, and sustainable solutions for managing complex trade-offs in next-generation distributed computing infrastructures.