## 2 State-of-the-Art on Evolutionary Multi-Objective Optimization
### Many-Objective Optimization Methods
MOEA/DD, MOEA dominance and decomposition [25] form a hybridization of the MOEA/D [13] and the NSGA-III [24], where the multiple objectives are decomposed into sub-problems and a dominance criterion is used to aggregate the global solution. Different grid-based criteria, such as the grid crowding distance (GCD), the grid ranking (GR) and the grid coordinate point distance (GCD) are integrated in MOEAs to evaluate the fitness function of the MaOP. In addition, the GrEA system [35], is designed to maintain a good balance between convergence and diversity over both the grid dominance and grid difference to evaluate the fitness function and push the system toward the most optimal solutions. Two variants of the Pareto-based evolutionary algorithm using the penalty mechanism (PMEA) are presented in [54]: the MPEA-MP and the MPEA*-MA. The PMEA-MA is developed using the Manhattan-distance and the cosine distance as the convergence and distribution metrics; it includes a population-prepossessing to enhance the diversity. The second variant, PMEA*-MA, is a simplified one, which does not adopt the prepossessing step. The Angle-based Selection algorithm (AnD) [55] is a non-Pareto-based method that aims to maintain the diversity of the population using an angle-based selection technique, then picks optimized members in the same search direction as a sorting solution. A hybridization of the Strength Pareto Evolutionary Algorithm (SPEA) and the shift-based density estimation (SDE) strategy in [39] is denoted by (SPEA/SDE). This estimates the density of the population; then, individuals who do not converge are eliminated to enhance diversity among the divergent solutions. In [56], the SPEAR leverages a reference direction-based density estimator using the standard SPEA algorithm for multi/many-objective optimization problems. The knee point-driven evolutionary algorithm (KnEA), proposed in [40], evolves a population and selects non-dominated solutions based on knee point criterion, which may be assumed to be a Pareto strategy. Furthermore, the two-stage evolutionary algorithm (TSEA) is developed in [57]. In the first stage, several sub-populations are optimized to converge to different regions of the Pareto front; then, the non-dominated solutions of each sub-population are considered as individuals that could be optimized in the second stage. In indicator-based methods, several quality metrics are used to perform the optimization process; for example, the Monto Carlo simulation is used in the HypE algorithm [27] to minimize the computation cost and approximate the results. The preference-based approaches use different adaptation mechanisms like an external memory for convergence and diversity preservation as well as to make a decision regarding the true Pareto front. In [41], the PICEA-g algorithm integrates the co-evolution as a posterior adaptation mechanism with a set of candidate solutions to help with decision-making and approximate the entire of the POF. Two archives are used in the Two_Arch2 [43] system: the first is considered for convergence (CA) and the second is used to maintain diversity (DA). A crossover operator is used as a selector mechanism between the CA and DA and a mutation operator is used in CA memory.