## 3 Utilized Design Optimization Algorithms
### Grey Wolf Optimizer (GWO)  
In 2014, [PERSON] et al. [22] proposed the grey wolf optimizer (GWO), a groundbreaking swarm intelligence optimization algorithm that simulates various animals' hunting and searching activities. GWO is a nature-inspired metheuristic that is based on the behavior of a pack of wolves. It explores the search space in hope of finding an optimal solution. It is an iterative method that is used to solve optimization problems. It primarily mimics the natural wolf leadership structure and hunting mechanism. Four types of grey wolves are employed to replicate the leadership structure: alpha, beta, delta, and omega. GWO also executes the three core hunting processes: locating prey, enclosing prey, and attacking prey. [PERSON] et al. [39] summarized the hunting strategy of GWO in first approaching and chasing the prey, followed by an encircling maneuver around the prey until it completely stops moving, and finally attacking of the prey when it is exhausted. In terms of optimization performance, the authors in [22] show that ordinary GWO is better than other optimization algorithms in the same family such as PSO, GSA, DE, and FEP algorithms. The pseudo code of GWO (Algorithm 1) can be summarized as follows:  
```
Initialize the grey wolf population \(X_{i}\), \(i=1\dots n\)  Initialize a, A, and C  Calculate the fitness of each search agent \(X_{\text{alpha}}=\) the best search agent \(X_{\text{beta}}=\) the second best search agent \(X_{\text{gamma}}=\) the third best search agent \(\textbf{While}\ t<\) max number of iterations do  for each search agent do  Randomly initialize \(r_{1}\) and \(r_{2}\)
```  
**Algorithm 1** Grey Wolf Optimizer  
```
Initialize the grey wolf population \(X_{i}\), \(i=1\dots n\)  Initialize a, A, and C  Calculate the fitness of each search agent \(X_{\text{alpha}}=\) the best search agent \(X_{\text{beta}}=\) the second best search agent \(X_{\text{gamma}}=\) the third best search agent \(\textbf{While}\ t<\) max number of iterations do  for each search agent do  Randomly initialize \(r_{1}\) and \(r_{2}\)
```  
**Algorithm 2** Grey Wolf Optimizer  
```
Initialize the grey wolf population \(X_{i}\), \(i=1\dots n\)  Initialize a, A, and C  Calculate the fitness of each search agent \(X_{\text{alpha}}=\) the best search agent \(X_{\text{beta}}=\) the second best search agent \(X_{\text{gamma}}=\) the third best search agent \(\textbf{While}\ t<\) max number of iterations do  for each search agent do  Randomly initialize \(r_{1}\) and \(r_{2}\)
```  
**Algorithm 3** Grey Wolf Optimizer  
```
Initialize the grey wolf population \(X_{i}\), \(i=1\dots n\)  Initialize a, A, and C  Calculate the fitness of each search agent \(X_{\text{alpha}}=\) the best search agent \(X_{\text{beta}}=\) the second best search agent \(X_{\text{gamma}}=\) the third best search agent \(\textbf{While}\ t<\) max number of iterations do  for each search agent do  Randomly initialize \(r_{1}\) and \(r_{2}\



### Genetic Algorithm (Ga)

The genetic algorithm (GA) [23] is an evolutionary optimization (EO) algorithm. GA is modeled after natural selection, in which the fittest individuals are picked for reproduction to produce children for the following generation. The goal of these tactics is to use randomization, mating behavior, and mutations to evolve our solution. A genetic profile is assigned to each particle, which is utilized to determine its fitness. The particles with the highest fitness will reproduce more, whereas those with the lowest fitness will die and be replaced. Crossover reproduction procedures are utilized, mixing both parents' genes, although mutations are possible, allowing the new generation to evolve further. Five phases are considered in GA, intial population; fitness function; selection; crossover; and mutation. GA is used in this study to find the optimal design variables for reducing transmitted forces from the engine to the frame. Mechanical vibrations are decreased or isolated as a result.