Mobile Edge Computing (MEC) uses to perform computation operations at the edge of a network for mobile devices. This allows the deployment of more powerful and efficient computing resources in a cost-effective, lightweight and scalable manner. MEC can optimize mobile device performance, enhance security and privacy, improve battery life, provide increased bandwidth, and reduce latency across wireless networks. Cloudlets are a new concept of computations that can perform at the edge of the networks. The service provider can deploy cloudlets services in a MEC environment with the ability for mobile devices to offload their tasks to cloudlets. In the MEC environment, the offloading problem depends on cloudlets' availability of computation resources. Also, the deployment method of cloudlets in the environment will affect the task offloading. This paper investigates the approach to the cloudlet deployment and task offloading problem in the MEC environment. First demonstrate that the problem has to be considered a Multi-objective optimization problem since it needs more than one objective to be optimized. Then prove that the problem is NP-completeness, give an overview of existing solutions using the meta-heuristic algorithms, and suggest future solutions for this problem. Finally, explain the advantages of using Variable-length of solution space with meta-heuristic algorithms for this problem.