## 1 Introduction
Meanwhile, the proposed method applies a variable neighborhood search mechanism (VNS) over the archive after it is updated. This technique allows for more exploration and exploitation of the solutions in the archive to make them more accurate. However, to prevent time-consuming VNS, it is applied over a maximum of 10 solutions in the archive, and there are ten iterations of the inner loop. A description of the VNS method is given in Section 4. Apart from the fact that DE is a straightforward optimization method, it is also robust and powerful. Like many other optimization methods, DE operates based on some parameters and several operators. The aim of optimization methods is to explore a high-quality PF in an acceptable time, preventing early convergence to avoid local optimal solutions. It is obvious that the quality of operators as well as the solution representation scheme affect the ability of DE to find better PF and speed up convergence. Therefore,  
Figure 1: Non-dominated and dominated solutions. there is a rich literature to improve the performance of DE [20]. Likewise, hybridizing DE with other methods is another way to add more power to DE in discovering better PFs [21; 22; 23]. In our proposed method to optimize the well-known scheduling problem, not only operator improvement but also hybridization are applied to have a robust hybrid system to deal with objective functions (makespan, reliability, and flow time). Evaluation of the proposed hybrid method's effectiveness and performance against well-known benchmarks gleaned from cutting-edge literature. In addition, the values of spacing and hyper-volume metrics are calculated. Furthermore, the Wilcoxon signed method is applied to carry out pairwise statistical tests over the obtained results. The proposed method exceeds all the state-of-the-art methods in terms of performance and quality of objective values, according to all findings and test results. As future works, different optimization problems, e.g., task scheduling in cloud computing, digital twins, and the internet of things [24; 25; 26], can be solved by the proposed method. In addition, it is planned to replace the MODE algorithm with recently proposed optimization methods mentioned in Section 3 and see how they affect the performance of the system [27; 28; 29]. The remaining parts of the study are divided into five sections: The full definition of the multi-objective task graph scheduling problem is provided in Section 2. Likewise, Section 2 defines the objectives of the problem and related equations in detail. In Section 3, the most recent approaches to scheduling multi-objective task graphs are briefly discussed. In addition, some recent robust metaheuristics are reviewed in this section. Section 4 contains a description of the suggested unique hybrid technique in details. The section also represents the flowcharts and algorithms applied in the proposed system. The algorithm settings and experimental findings are reported and discussed in Section 5 to prove the high performance of the proposed hybrid system. Finally, Section 6 illustrates the study's findings as well as a few potential future research projects.