The effectiveness of genetic algorithms (GA) can be improved by adjusting genetic operators and integrating an efficient heuristic. These enhancements are integrated into the suggested enhanced hybrid genetic algorithm (e-HGA). The e-HGA begins with an initial population that includes a solution derived from a heuristic, which serves as a guiding point toward achieving an optimal makespan solution. The proposed e-HGA was evaluated in this work for two degrees of fitness, which qualified a chromosome and a gene to be preferred above their other counterpart in a data population. To preserve population variety and avoid premature convergence, parents were randomly picked from the population and crossed over (mated) to generate offspring that were then modified by introducing random geneLists. The conventional hybrid genetic algorithm (HGA) and e-HGA required 9.95 s and 9.148 s, respectively, for task completion. Increasing the number of cloudlets to 40, the conventional HGA and e-HGA took 10.674 s and 9.558 s, respectively. When 50 cloudlets were assigned to 10 virtual machines (VMs) the conventional HGA completed the task in 11.01 s, while the e-HGA required 12.863 s. Subsequently, with 60 cloudlets on 10 VMs, the conventional HGA and e-HGA achieved task completion in 14.74 s and 14.242 s, respectively. For 70 cloudlets on 10 VMs, the conventional HGA and e-HGA required 15.38 s and 17.25 s, respectively. The results contributed to research on task scheduling optimization by scheduling task operations to reduce cost, enable efficient resource allocation, and manage time.