## 2 State-of-the-Art on Evolutionary Multi-Objective Optimization
### Existing Crow Search-Based Methods  
The Crow Search Algorithm (CSA) [9] was first proposed in 2016 to solve constrained engineering optimization problems. In [58], [PERSON] et al. published a new overview paper to present all modified versions of the CSA algorithm. A set of novel CSA algorithms are extended for solving MOPs. A Multi-Objective Crow Search Algorithm (MOCSA) is proposed in [59], in which chaos and orthogonal opposition-based operators are used to hybridize CSA, (M2O-CSA) with a focus on solving MOPs. Also, a hybridization of the CSA algorithm with a clustering model is published and denoted by the Multi-objective Taylor Crow Optimization algorithm (MOTCO) considered for solving the clustering-aware wireless sensor network [60]. Furthermore, two binary versions of the CSA algorithm are proposed in [61; 62]. The first one is the BCSA [61], which is used as a V-shaped transfer function to obtain a binary representation of continuous data with applications in feature selection. The second binary CSA algorithm [62] consists of applying a sigmoid transformation for solving the 2D bin packing problem. Several modified versions of the CSA algorithm tend to manage the loss of diversity in the search space based on the Gaussian distribution for diversity enhancement as in [63]. A priority-based technique is used to determine the sufficient flight length for each crow and update their position based on a followed crow. This technique is considered for electromagnetic optimization of the usability factors' hierarchical model in a prediction model [64] as well as for the economic load dispatch problem [65]. Also, a modified crow search algorithm is proposed for solving a power system problems and aims to modify the standard CSA parameters such as the awareness probability and the random perturbation by a dynamic awareness probability (DAP) and a Levy flights to simulate the evasion behavior of each crow [66]. Furthermore, [PERSON] et al. [67] proposed a hybrid CSA algorithm (HCSA) based on the Variable Neighborhood Search (VNS) and the standard SCA method. The HCSA algorithm is proposed for dealing with an NP-hard combinatorial optimization problem, such as the permutation flow shop scheduling problem (PFSP), aiming to retrieve an actionable permutation order and handle a large number of jobs. An Improved Crow Search Algorithm was proposed by [PERSON] et al. [68], to solve complex energy problems. The authors aim to modify the awareness probability (AP) and the random perturbation of the standard CSA algorithm with a new dynamic awareness probability (DAP) and Levy flight distribution to balance exploration and exploitation in the search space. The robustness of the CSA algorithm is proven when solving different complex problems. [PERSON] et al. [69] proposed a novel meta-heuristic approach based on the crow search algorithm (CSA) to solve the optimal reactive power dispatch (ORPD) problem. \begin{table}
\begin{tabular}{c c} \hline Decomposition-based approaches & MSOPS [20] and MSOPS-II [19] \\  & MOEA/D [13] \\  & MOEA/DD [25] \\  & TSEA [57] \\  & MPEA-MP and MPEA*-MA [54] \\ Indicator-based approaches & HypE [27] \\ Diversity-based selection criterion & NSGA-III [24] \\  & SPEA/SDE [39] \\  & KnE [40] \\  & SPEAR [56] \\ Modified dominance relation-based & GrEA [35] \\ approaches & VaEA [52] \\  & 6-DEA [36] \\  & NSGA-II/SDR [53] \\  & AnD[55] \\ Preference-based approaches & RVEA [22] \\  & PICEA-g[41] \\  & Two\_Arch2 [43] \\ \hline \end{tabular}
\end{table} 
Table 2: Classification of the MOEAs for MaOPs. A set of mechanisms has been used to improve the CSA algorithm, including a search bounds limits management strategy [70], adding an archive component [71], and restructuring awareness probabilities [72] to enhance the random perturbation and the dynamic probability of the CSA system. Several operators were added to achieve a good balance between convergence and diversity, such as the Roulette wheel selection tool and the inertia weight, the Levy flight and the adaptive adjustment factors.