## 2 State-of-the-Art on Evolutionary Multi-Objective Optimization
### Many-Objective Optimization Methods
The best-known posterior approaches are the Preference-Inspired Co-evolutionary Algorithms (PICEA-\(\beta\)) [41], the novel, two-archive algorithm (TAA) [42], and its improved version (Two_Arch2) [43]. In addition, the Particle Swarm Optimization (PSO) algorithm received a great attention in MaOPs. The Control Dominance Area of Solutions (CDAS) [44] has been used with SMPSO and SigmaMOPSO for MaOPs. Indicator-based PSO systems were proposed to maintain the leader's selection using the R2 indicator, as presented in H-MOPSO [45] or the hypervolume metric in S-MOPSO [46]. A two-stage strategy and a parallel cell coordinate system were adopted in MaOPSO/2s-pccs [47]. A preference-based method was proposed, using a PSO system, focusing on solutions around the knee point and called knee-driven particle swarm optimization (KnPSO) [48]. In [49], the MaPSO method uses the leader's selection from a certain number of historical solutions using scalar projection. In addition, the HGLSS-MOPSO algorithm [50] adopted the Hybrid Global Leader Selection (HGLSS) using two global leader selection mechanisms: the first for exploration and the second for exploitation. A recently published paper [51] presented an adaptive localized decision variable analysis approach under the decomposition-based framework to solve the Large-Scale Multi-Objective Optimization problems and Multi-Tasking Optimization Problems in MaOPs. As a conclusion, all the abovementioned Many-Objective Evolutionary Algorithms (MaOEAs) are presented as highly complex and time-consuming systems, especially when using decomposition-based mechanisms and/or quality indicators to separately deal with convergence and diversity. The high number of objectives is managed through a decomposition-based mechanism to obtain a set of single or multi-objectives problems. The multiple single-objective Pareto sampling (MSOPS) [20] algorithm generates a set of target vectors. Then, it undergoes multiple single-objective optimization processes to solve MaOP. Such a strategy may return moderated results, since it does not correctly manage the multi-objectives of MaOPs. The enhanced MSOPS-II [19] uses a set of target vectors based on the current population to guide the optimization process at each iteration. Then, the aggregation of fitness functions is used to evaluate the performances of the proposed solutions. The MOEA/D [13] algorithm proceeds with a decomposition of the many-objectives into a set of single objectives using a uniformly distributed weight vector. Similar to the weight vectors of the MOEA/D algorithm, the NSGA-III [24] used a number of well-spread reference points to approximate non-dominated solutions; then, it enhances the diversity of the population. Based on the main idea of the NSGA-II, the reference vector-guided evolutionary algorithm (RVEA) [22]adopted two reference vectors: one for selection and the second for adaptation. In the RVEA system, the concept of convergence and diversity are dynamically managed using the Angle Penalized Distance (APD). A vector angle-based evolutionary algorithm (VaEA) [52] is proposed for Unconstrained MaOPs. The VaEA algorithm uses the maximum-vector-angle as a selection mechanism to guarantee a good distribution to approximate to the true Pareto front, while the worse solutions are replaced with newly generated random solutions. The \(\theta\) -DEA [36] system is based on NSGA-III with a new, \(\theta\)-non-dominated concept, which is different to the original dominance operator, as used on the Pareto-based methods. It employs a set of reference points to cluster the solutions set and enhance the exploration phase. The NSGA-II/SDR is a modified version of the NSGA-II, with a Strengthened Dominance Relation (SDR), presented in [53] to solve MaOP. The NSGA-II/SDR adopts the angle and the niching mechanism to select the best converged solutions.