In recent years, mobile devices have become an essential part of daily life. More and more applications are being supported by mobile devices thanks to edge computing, which represents an emergent architecture that provides computing, storage, and networking capabilities for mobile devices. In edge computing, heavy tasks are offloaded to edge nodes to alleviate the computations on the mobile side. However, offloading computational tasks may incur extra energy consumption and delays due to network congestion and server queues. Therefore, it is necessary to optimize offloading decisions to minimize time, energy, and payment costs. In this article, different offloading models are examined to identify the offloading parameters that need to be optimized. The paper investigates and compares several optimization techniques used to optimize offloading decisions, specifically Swarm Intelligence (SI) models, since they are best suited to the distributed aspect of edge computing. Furthermore, based on the literature review, this study concludes that a Cuckoo Search Algorithm (CSA) in an edge-based architecture is a good solution for balancing energy consumption, time, and cost.