# A Survey on Search Strategy of Evolutionary Multi-Objective Optimization Algorithms
## 3 Classification of Multi-Objective Evolutionary Algorithms from the View of Search Strategy
### Dominant Relation-Based MOEA Algorithms
#### 3.2.4 Non-Dominated Sorting Genetic Algorithm II  
In 1993, [PERSON] and [PERSON] presented the NSGA. There are three key issues with the NSGA. The first is the absence of an ideal individual retention mechanism. Studies of relevance indicate that, for one thing, the performance of MOEA can be improved and the loss of exceptional solutions can be avoided by using the best individual retention mechanism. The issue of common parameters is the second issue. If shared parameters are employed during the evolution process to preserve population distribution, it might be challenging to estimate their size as well as dynamically modify and adapt parameters. Thirdly, one challenge with the Pareto optimal solution set is that it requires a high time complexity to construct, with a cost of \(O(R\times N^{3})\), where \(R\) is the number of objectives and \(N\) is the size of the evolutionary population. This can be problematic because each generation of the evolution process involves constructing a non-dominated set, which can be time-consuming when the size of the evolutionary group is large. To address this issue, the NSGA-II algorithm is proposed as an improvement upon the NSGA algorithm [16]. The NSGA-II algorithm's fundamental concept is as follows. Following non-dominated sorting, the random preliminary population of size \(N\) is produced, and the three fundamental genetic algorithm processes of selection, crossover, and mutation are used to create the first generation of the offspring population. Starting with the second generation, the parental and child populations were mixed to accomplish a rapid non-dominant ranking. The crowding distance of individuals in each non-dominant layer was also determined at this time [82]. To create the new parent population, individuals are selected based on  
Figure 5: The niche sharing. Neither candidate \(A\) nor \(B\) is dominant, but \(A\) is more aggregated than \(B\), so \(A\) has less shared fitness than \(B\) and chooses \(B\) to participate in the next generation of evolution. This figure is adopted from [7]. their non-dominant relationship and crowding distance. The standard genetic algorithm operations are performed to produce the new child population. This process is repeated until the end condition of the program is met. The program flow chart for this process is depicted in Figure 6.  
Fast Non-Dominated Sorting Algorithm  
To perform non-dominant sorting, the algorithm must determine two parameters, Np and Sp, for each individual p in the population P. Np represents individual accounts that dominate individual p [83], and Sp is the group of individuals dominated by p in the population. When traversing the entire population, the combined computational complexity of these two parameters is \(O\left(\text{MmN}^{2}\right)\). The steps to implement the fundamental and formal computational procedure for non-dominant sorting are as follows:  
1. Select the first individual to be the current individual. 2. Compare the current individual's objectives with all the other individual's objectives. 3. Count the individual accounts that dominate the current individual, which is represented by Np. 4. Set the individuals who satisfy the condition Np = 0 as the first front and temporarily delete them from the generation for the time being. Adopt Congestion Degree and Congestion Comparison Operator  
(1) Crowding degree estimation [84]: To assess the degree of crowding around a solution in the population, the mean distance between the two dots on each side of a particular point is computed according to each objective function. The vertex of the cuboid is determined by its nearest neighbor, and the number is utilized to determine its circumference (called the crowding factor). The length of the cuboid surrounding  
Figure 6: The fundamental concept of the NSGA-II algorithm. A random initial population, using selection, crossover, and variation to produce a first generation of offspring populations.