## 3 Related Studies
The suggested approach adds a discriminating condition, which speeds up the procedure without affecting performance. The effectiveness of the NSGA-II-WA in terms of convergence and distribution was tested by the authors using the DTLZ benchmark set [43]. In 2017, [PERSON] et al. introduced the VAEA (Vector Angle-Based Evolutionary Algorithm), which is based on angle decomposition [44]. Without the use of reference points, VAEA can adjust search space variety and convergence. The maximum vector-angle-first theory, used by VAEA, ensures that the solution set is wide and uniform. The findings of the authors' evaluation of VAEA using numerous objective benchmarks showed that VAEA effectively tunes convergence and diversity. [PERSON] et al. suggested the RVEA (Reference Vector Guided Evolutionary Algorithm) in 2016 [46], which is based on reference vector guidance. RVEA tunes the weight vectors in accordance with objective functions dynamically. The authors compared the RVEA to five cutting-edge techniques and found that RVEA is efficient and effective. Due to the wide range of state-of-the-art works in literature, it is useful to categorize the developed methods in terms of algorithm type and the problem type they are solving. The first categorization can be carried out in terms of the problem type, which is bi-objective or three-objective task graph scheduling problems. Likewise, the second organization is done based on the algorithm type, which can be either single-objective or multi-objective optimization approaches. The algorithms can also be either improved versions or hybrid types. Table 1 represents the categorization of state-of-the-art methods. Three recently proposed evolutionary algorithms are also considered in the table. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method Title**} & \begin{tabular}{c} **Single-Objective** \\ **Algorithm (Applying** \\ **Weighted-Sum)** \\ \end{tabular} & \begin{tabular}{c} **Multi-Objective** \\ **Algorithm** \\ \end{tabular} & \begin{tabular}{c} **Bi-Objective** \\ **TGS** \\ \end{tabular} & \
\begin{tabular}{c} **Three-Objective** \\ **TSG** \\ \end{tabular} &
\begin{tabular}{c} **Reference** \\ **Number** \\ \end{tabular} \\ \hline SGA & \(\surd\) & \(\mathsf{X}\) & \(\surd\) & \(\mathsf{X}\) & [15] \\ EP & \(\surd\) & \(\mathsf{X}\) & \(\surd\) & \(\mathsf{X}\) & [15] \\ Hybrid GA & \(\surd\) & \(\mathsf{X}\) & \(\mathsf{\surd}\) & \(\mathsf{X}\) & [15] \\ EP & \(\surd\) & \(\mathsf{X}\) & \(\mathsf{X}\) & \(\surd\) & [12] \\ GA & \(\surd\) & \(\mathsf{X}\) & \(\mathsf{X}\) & \(\surd\) & [12] \\ MOGA & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\surd\) & [14; 31] \\ MOEP & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\surd\) & [14; 32] \\ HEFT & \(\surd\) & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & [17; 34] \\ CPGA & \(\surd\) & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & [17; 35] \\ HEFT-NSGA & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\surd\) & [17] \\ MFA & \(\mathsf{X}\) & \(\surd\) & \(\mathsf{X}\) & \(\surd\) & [11] \\ FA & \(\surd\) & \(\mathsf{X}\) & \(\surd\) & \(\mathsf{X}\) & [13] \\ MGA & \(\surd\) & \(\mathsf{X}\) & \(\surd\) & \(\mathsf{X}\) & [42] \\ BGA & \(\surd\) & \(\mathsf{X}\) & \(\surd\) & \(\mathsf{X}\) & [41] \\ MOO+Local & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\mathsf{X}\) & [15] \\ Search & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\surd\) & [8] \\ Ensemble System & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\surd\) & [43] \\ NSGA-II-WA & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\surd\) & [43] \\ VAEA & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\surd\) & [44] \\ RVEA & \(\mathsf{X}\) & \(\surd\) & \(\surd\) & \(\surd\) & [46] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Classification of the current methods in the literature. The single-objective optimization algorithms use the weighted-sum method to be able to optimize more than one objective [47; 48; 49]. The reported results show that most of the multi-objective optimization methods outperform the single-objective and weighted-sum approaches.