Computational offloading allows lightweight battery-operated devices such as IoT gadgets and mobile equipment to send computation tasks to nearby edge servers to be completed, which is a challenging problem in the multi-access edge computing (MEC) environment. Numerous conflicting objectives exist in this problem; for example, the execution time, energy consumption, and computation cost should all be optimized simultaneously. Furthermore, offloading an application that consists of dependent tasks is another important issue that cannot be neglected while addressing this problem. Recent methods are single objective, computationally expensive, or ignore task dependency. As a result, we propose an improved Gorilla Troops Algorithm (IGTA) to offload dependent tasks in the MEC environments with three objectives: 1-Minimizing the execution latency of the application, 2-energy consumption of the light devices, 3-the used cost of the MEC resources. Furthermore, it is supposed that each MEC supports many charge levels to provide more flexibility to the system. Additionally, we have extended the operation of the standard Gorilla Troops Algorithm (GTO) by adopting a customized crossover operation to improve its search strategy. A Max-To-Min (MTM) load-balancing strategy was also implemented in IGTA to improve the offloading operation. Relative to GTO, IGTA has reduced latency by 33%, energy consumption by 93%, and cost usage by 34.5%. We compared IGTA with other Optimizers in this problem, and the results showed the superiority of IGTA.