<p>Edge computing is a computational paradigm that addresses the computational and storage needs of end-users. Due to the exponential increase in service demand, edge data centres require continuous performance improvement. Efficient scheduling is a crucial component of edge computing for maximizing capacity, minimizing response time, reducing energy consumption, and optimizing resource utilization. This paper presents an efficient method to minimize the energy overhead of time-constrained applications modelled by directed acyclic graphs in heterogeneous edge computing environments. The technique is divided into two phases. In the first phase, a novel approach for calculating request priorities is designed, and an energy-aware scheduling algorithm based on genetic and ant colony optimization is proposed to obtain an initial scheduling result with reduced energy consumption. In the second phase, considering the slack time among requests and their deadlines, an upward and downward proportionally detection slack algorithm is proposed to further reduce energy overhead using Dynamic Voltage and Frequency Scaling (DVFS) techniques. Simulation results indicate that the proposed method reduces both overall energy consumption and request completion times. On average, the results demonstrate a 0.65 reduction in energy consumption and a 0.20 reduction in completion time compared to randomly constructed Directed Acyclic Graph (DAG) algorithms.</p>