## 3 Related Studies  
In this part, the most recent approaches to the multi-objective task graph scheduling problem are briefly reviewed. In [14], several algorithms were applied to a bi-objective (Makespan and reliability index) Gaussian elimination graph with 18 nodes by [PERSON] et al. They also evaluated the performance of the algorithms using the randomly generated graphs. the standard genetic algorithms (SGA) and evolutionary programming (EP) were applied by the authors, and they used a weighted-sum approach to combine the objectives into one objective. Moreover, the authors applied the multi-objective GA (MOGA) [30; 31] and multi-objective evolutionary programming (MOEP) [32; 33], and outcomes illustrated that the MOEP provides better distribution in Pareto-front than SGA, EP, and MOGA. Carrying out the comparison only between the GA and EP as well as using very small graphs can be taken into account as constraints in the study. [PERSON] et al. [17] suggested the HEFT-NSGA method to optimize the Makespan as well as the reliability index in the multi-objective task graph scheduling. Evaluations were carried out using some application graphs and random task graphs. the authors compared the outcomes with the Heterogeneous Earliest Finish Time (HEFT) method [34] and Critical Path GA (CPGA) [35] to illustrate that HEFT-NSGA extracts better solutions. The multi-objective mean field annealing (MFA) is another metaheuristic used by [PERSON] et al. [11] for solving the task graph scheduling problems. The authors evaluated their introduced method against the NSGAII [36] and MOGA [31] metaheuristics, and outcomes proved that the MFA extracts better Pareto-front in comparison to NSGAII and MOGA. The constraint of the study is that only very small graphs have been used for evaluation. To solve the three-objective task graph scheduling problem, [PERSON] et al. [12] consumed the weighted sum GA [37], weighted sum MOEP [32], evolutionary programming (EP) [38; 39], and MOGA [31] methods over a Gaussian elimination graph. There are no metrics calculations and no comparisons with state-of-the-art algorithms in the study. For the bi-objective task graph scheduling problem, [PERSON] and [PERSON] [40] proposed a firefly-based algorithm for optimizing Makespan and reliability solutions. In addition, comparisons and evaluations were done against modified GA (MGA) [41] and bi-objective GA (BGA) [42]. The findings indicated that the firefly method performs faster than MGA and BGA. Using a weighted-sum approach to merge objective values is the limitation of the suggested method. Likewise, no statistical analysis or metrics calculation can be found in [40]. [PERSON] et al. [14] merged multi-objective metaheuristics with a simple local search method to solve the bi-objective scheduling problem. SPEA2 and NSGAII metaheuristics were compared in their pure and hybrid versions. [PERSON] [8] proposed a strategy to combine six metaheuristics to solve two- and three-objective task graph scheduling problems. According to the proposed strategy, six metaheuristics collaborate and cooperate together to improve a shared population. The common population is divided into the subpopulations to be improved by metaheuristics, and all non-dominated solutions found so far are kept in a common archive. Also, each metaheuristic has its own local archive to keep non-dominated solutions during individual execution. Evaluations were done over different task graphs and compared to most of the state-of-the-art methods. Consequently, the evaluation results showed that the proposed ensemble method outperformed all considered competitors. Likewise, there is a wide literature on new evolutionary algorithms that have been recently proposed by researchers [43; 44; 45; 46]. [PERSON] et al. suggested the NSGA-II-WA algorithm to enhance the NSGAIII standard. When it comes to the evolution strategy and weight vector modification, their suggested NSGA-II-WA outperforms NSGAIII [43].