# A Survey on Search Strategy of Evolutionary Multi-Objective Optimization Algorithms
## 3 Classification of Multi-Objective Evolutionary Algorithms from the View of Search Strategy
### Evaluation Index-Based MOEA Algorithms
#### 3.3.1 S-Metric Selection Based Evaluative Multi-Objective Optimization Algorithm  
We will introduce HV in Section 4. [PERSON] and [PERSON] first suggested the HV metric, also referred to as the S-metric, and they referred to it as the size of the coverage space or the dominated space. As a crude approximation to the Pareto frontier, the EMO method produces a set of points in the performance space. To calculate how close the predicted data points are to the real Pareto front, quantitative measures are needed [92]. The HV  
Figure 8: The implementation steps for NSGA-II’s elite strategy. The new population is ranked non-dominantly; in this example, the population is divided into six Pareto ranks, and non-dominant individuals with Pareto rank 1 and 2 are placed in a new set of parents, after which their crowding is determined before ranking those with Pareto rank 3 and excluding all those with ranks 4 to 6. This figure is adopted from [16]. indicator, which estimates the HV between the Pareto front (P) and the reference point (R), is one of these measurements. As shown in Figure 9, a key characteristic of SMS-EMOA is that it updates using a steady-state strategy in which a single offspring is generated in each iteration and immediately evaluated before being integrated into the evolution of the next generation. This means that each generation only produces one new person. Algorithm 1 describes the basic algorithm, starting from the initial population, using a random mutation operator to generate a new individual [93]. Unlike some other methods for maintaining a collection of non-dominant individuals, SMS-EMOA maintains a constant population size for both dominant and non-dominant individuals. To decide which individuals are removed during the selection process, it is necessary to set the parameter selection in the dominant solution. Algorithm 2 describes a replacement program that reduces employment. To select the individuals that make up the population, SMS-EMOA uses a ranking system based on the Pareto frontier, a concept derived from the well-known NSGA-II algorithm. 1. The fast non-dominant sorting algorithm is used to calculate the Pareto front of the non-dominant level until \(R_{i}\) cannot be put down in the population G (put the parent generation (N individuals) and the offspring (N individuals) together, then selects the first N better individuals). 2. After that, an individual is dropped from the worst ranking. If front \(R_{i}\) contains \(|R_{i}|>1\) (domination of the individual is greater than an individual, then for s \(\in R_{i}\)\(R_{i}\) layer included in the Pareto frontier s) of the individual will be eliminated, minimize it.The \(\triangle S\) (s, \(R_{i}\)) represents the HV of \(s\). The smaller the HV, the smaller the role of this individual should be removed. The point with the worst non-dominant leading edge is selected in each of the two objective functions and ranks them by the original objective function \(f_{1}\)'s value. We then receive a second sequence that is arranged according to \(f_{2}\), because none of these points dominates the others. \(\triangle S\) (s, \(R_{i}\)) is calculated as follows in Equation (5). For \(R_{i}\): \(R_{i}\) = \(\{s_{1\cdots}\) s \(|\)\(R_{i}\) }  
\[\triangle S(s_{i},R_{i})=(f_{1}(s_{i+1})-f_{1}(s_{i}))\cdot(f_{2}(s_{i-1})-f_{ 2}(s_{i})). \tag{5}\]  
The SMS-EMOA algorithm is a promising Pareto optimization algorithm. It is especially useful when a few solutions are needed and a balanced solution is important. However, it has a high selection time complexity and is typically only applied when there  
Figure 9: The operation mechanism of the SMS-EMOA algorithm. An offspring is produced in each iteration and evaluated immediately before integration into the next generation of evolution, with poor individuals being eliminated as a new subpopulation. This figure is adopted from [90]. is only one layer of the non-dominant level [94]. Despite this, SMS-EMOA tends to produce good results.