Despite the extensive use of IoT and mobile devices in the different applications, their computing power, memory, and battery life are still limited. Multi-Access Edge Computing (MEC) has recently emerged to address the drawbacks of these limitations. With MEC on the network's edge, mobile and IoT devices can offload their computing operations to adjacent edge servers or remote cloud servers. However, task offloading is still a challenging research issue, and it is necessary to improve the overall Quality of Service (QoS) and attain optimized performance and resource utilization. Another crucial issue that is usually overlooked while handling this matter is offloading an application that consists of dependent tasks. In this study, we suggest a Refined Whale Optimization Algorithm (RWOA) for solving the multiuser dependent tasks offloading problem in the Edge-Cloud computing environment with three objectives: 1- minimizing the application execution latency, 2- minimizing the energy consumption of end devices, and 3- the charging cost for used resources. We also avoid the traditional binary planning mechanisms by allowing each task to be partially processed simultaneously at three processing locations (local device, MEC, cloud). We compare RWOA with other Optimizers, and the results demonstrate that the RWOA has optimized the fitness by 52.7% relative to the second best comparison optimizer.