Scheduling tasks in a heterogeneous computing environment can be a challenging problem due to the diverse range of hardware and software resources available. In this comparative study different approaches are investigated for solving multitask scheduling in the heterogeneous computing environment, reviewing the literature on the topic, highlighting the strengths and weaknesses of different scheduling algorithms. Then, formulate a hypothesis about how multitask scheduling can be optimized in a heterogeneous computing environment and design an experiment to test this hypothesis. This study experiment involves running a variety of scheduling algorithms as GRASP, Tabu Search, SA, GA, HEFT and FCFS on a heterogeneous computing platform. This study yields valuable insights on the efficacy of various optimization algorithms for scheduling problems and emphasizes the significance of selecting suitable algorithms based on the problem's specific features. The result of this study indicates that the GRASP algorithm outperforms other scheduling algorithms as HEFT Ranked up, Tabu Search, SA, GA, HEFT Ranked down, and FCFS, producing schedules with shorter completion times. This is a critical factor when evaluating scheduling algorithms. The exceptional performance of GRASP can be credited to its effective navigation of the solution space and its adept utilization of a blend of greedy constructive heuristics and randomized local search methods, which enable it to achieve top-notch solutions. Future studies can examine the suitability of the GRASP algorithm for other scheduling problems and explore methods to further improve its performance. Additionally, it is worth noting that GRASP has shown greater efficiency than other algorithms.