Research on Multi-Objective Optimization in Cloud Computing focuses on developing strategies that simultaneously optimize multiple conflicting objectives, such as cost, energy consumption, execution time, and Quality of Service (QoS), in cloud environments. This area explores algorithmic and heuristic approaches to achieve efficient trade-offs among competing goals in dynamic and heterogeneous cloud infrastructures. Key research directions include multi-objective task scheduling, resource allocation, and load balancing using evolutionary algorithms, swarm intelligence, and hybrid optimization techniques. Other emerging topics involve energy- and carbon-aware optimization, SLA-compliant service provisioning, cost-performance trade-off modeling, and container- or VM-level orchestration. Additionally, integrating machine learning for predictive and adaptive optimization, handling uncertainty and failures in large-scale cloud systems, and optimizing hybrid and federated cloud environments represent promising avenues for advancing intelligent, efficient, and sustainable cloud computing solutions.