## 4 Analysis of Single Objective Algorithms Overview
### Learner Performance-Based Behavior
The difficulty is in figuring out the right fitness-sharing radius, which is contingent on the properties of the problem's objective or the choice space [16; 18]. ### Selection Operator

A \((\mu+\lambda)\) selection method is used in the original NSGA-I1, where parents and offspring are combined in order to compete for membership in the following generation. One of the approaches used in this manner is to keep the elite in place while the candidates are being chosen. Individuals are first compared according to their Pareto rankings. Higher-ranking individuals are selected for the following population. In the event of a tie in Pareto ranks, the individuals who will make up the next generation of the population are ascertained using the crowd distance metric. Research by [PERSON] et al. (2003) [16] has demonstrated that using a strong elitism approach does not produce desirable results. Anysolution that ranks higher will be chosen using this fitness evaluation and selection method, regardless of how dense it is within that rank. [PERSON] and [PERSON] (2001) [79] underline the importance of retaining diversity within ranks to allow those in lower positions to advance to the following generation. To determine the solution's proximity to nearby solutions in the objective space and ultimately reducing its fitness to a minimal value, the MODE incorporates an additional parameter called \(\sigma\) crowd. This method might prevent individuals who are closely related from reproduction, which could lead to early convergence. To put it simply, the MODE creates the following generation by selecting the top N individuals solely based on their fitness rating from parents as well as offspring that have been created by the reproduction operator. When compared with fitness sharing algorithms presented by [PERSON] (1989) [50], it is possible to compute crowd distance metrics without the specification of any parameters beforehand. In the proposal, a new parameter (\(\sigma\) crowd) is proposed. Since the major objective of MOEA is to avoid very similar individuals, the sensitivity of MODE is not as important as the sharing radius in terms of how well it functions. In studies, a low value of (\(\sigma\) crowd) is advantageous in many cases [15]. ```
1:Initialization (initialize population with random members)
2:Evaluated
3:For(i = 0,I \(\leq\) n,i++)
4:While (not termination condition stop)
5:Begin
6:Implement a based method for the selection of optimal individual
7:For the mutation operation using Equation (11)
8:Apply Pareto rank assignment to evaluate individuals
9:Using a sharing radius as a boundary to count members of the individuals
10:Using crowding distance metrics for estimating the density of the solutions
11:around certain individuals and panelized fitness of the individual
12:selection operation
13:to reduce the fitness of the solution to a very small value used parameter \(\sigma\) crowd
14:based only on fitness ranking for the selection of optimal N individuals as the following generation from the two parents and offspring that have been produced by the operator of reproduction
15:End for
16:End while
17:Create new offspring
18:Update
19:End
20:Best set of solutions
```
**Algorithm 6** MODE

#### 5.3.3 Multi-Objective Particle Swarm Optimization

In Section 4.3, we noted that, in contrast to global optimization, the solution set of a problem with multiple objectives is not a single solution, indicating that the original approach should be modified to apply the PSO method for tackling MOO problems. Finding several solutions known as the Pareto-optimum set is the aim of MOO. When addressing a multi-objective problem, there are usually three main objectives to emphasize:

1. Increase the quantity of elements in the Pareto-optimum set. 2. Reduce the difference between the algorithm-generated Pareto front and the actual, global Pareto front (assuming we are aware of its position). 3. Maximize the dissemination of solutions to achieve a smooth and uniform distribution of vectors.