## 4 Analysis of Single Objective Algorithms Overview  
### Evolutionary Optimization  
The primary ways that classical optimization approaches and evolutionary optimization concepts differ are explained in the following [8; 50]. Gradient information is frequently not used by an evolutionary optimization technique during the search phase. EO methods are methods of direct search that are applicable to a large class of optimization problems. An evolutionary optimization process employs multiple solutions simultaneously in an iteration, contrasting with classical optimization algorithms that update only one solution per iteration. Utilizing a population has several benefits; an evolutionary optimization process employs stochastic operators, as opposed to deterministic operators commonly seen in traditional optimization methods. Operators aim to attain a certain result by favoring higher probabilities for favorable outcomes rather than relying on established and unchanging transition rules. EO algorithms can effectively navigate many optima and complications, offering a global perspective during the search process as seen in Algorithm 1. ```
1: Start
2: Initialization population solutions randomly
3: Evaluated
4: For (i = 0, i \(\leq n\), i++)
5: While (not termination condition stop)
6: Begin
7: Selection
8: Crossover
9: Mutation
10: Elite--preservation
11: End for
12: End while
13: Create new offspring
14: Update
15: End
16: Best optimal solution
```  
**Algorithm 1** EO  
The process of initialization frequently involves generating solutions at random. When generating the initial population, it is best to leverage information about known good solutions for a given problem. According to another source, a customized initialization can speed up the search process and be useful for handling complex real-world optimization problems [25]. To fill an intermediate mating pool, the selection operator selects solutions from the improved population that are above average and have a greater likelihood. For this aim, the literature on evolutionary optimization has a variety of stochastic selection operators. Essentially, two solutions could be randomly selected from the evaluated population, and the best of the two (depending on the assessed order) could be selected. This process is known as tournament selection. The \"variation\" operator is a set of operators which are used to produce a modified population, such as mutation and crossover. Through sharing information between the parent solutions, crossover operator creates one or more solutions through randomly selecting at least two solutions (i.e., parents) from the mating pool. When using the crossover operator, the fraction of the population that participates in the crossover operation is represented by the crossover probability (pc \(\in[0,1]\)). The changed child population receives a direct replication of the remaining proportion of the population, which is equal to 1 minus pc. Every variable can be crossed separately in real-parameter optimization with n real-value variables as well as a crossover involving two parent solutions. Two new numerical values are often generated as offspring values positioned around the two parent values using a distribution of probability depending on the difference between values of the two parent variables. To preserve the relationship between variablesfrom parent solutions to the offspring solutions, vector-wise recombination operators are advised along with variable-wise recombination operators [1]. Every one of the child solutions is first created by a crossover operator and changed after that by a mutation operator [42; 51]. With a chance of pm, which is often calculated as 1/n (the number of variables), each variable is mutated, leading to an average of one mutated variable per solution. A simple Gaussian probability distribution with a set variance, centered on the value of the child variable, could be used for real-parameter optimization [1].