In this paper, we introduce the Enhanced Whale Optimization Algorithm (EWA) to optimize dependent task offloading in a multi-edge cloud computing environment. Our proposed algorithm aims to identify the most suitable offloading scenario for dependent tasks, focusing on minimizing total processing latency, energy consumption, and associated costs. We operate within a system comprising many decentralized Mobile Edge Computing servers (MECs) and a centralized cloud server. Two novel improvement operations, namely Frame Shifting (FS) and Load Redistribution Strategy (LRS), are introduced to enhance the performance of the whale algorithm. Through simulation, our results demonstrate the superior performance of EWA. Specifically, compared to the Whale Optimization Algorithm (WOA), EWA achieves a remarkable reduction in latency by 22.84%, a substantial decrease in energy consumption by 78.28%, and a notable reduction in cost usage by 61.47%. These outcomes underscore the efficacy and practical significance of the proposed EWA in addressing the challenges posed by dependent task offloading in the multi-edge cloud computing landscape.