## 4 Analysis of Single Objective Algorithms Overview
### Practical Swarm Optimization
Each particle moves across the search space during a predetermined number of iterations, modifying its location in accordance with Equations (3) and (4), updating its own best, and after that updating the leader. ```
1: Begin
2: Swarm Locate leader Initialization
3: g = 0
4: While g < termination condition
5: For every particle
6: Update Position (Flight)
7: Evaluation
8: Update pbest
9: EndFor
10: Update leader
11: g++
12: EndWhile
13: End

### Fitness Dependent Optimizer

A population of artificial scouts is first randomly initialized inside the search space (\(i=1,2,\ldots n\)) through the algorithm; every point of a scout bee corresponds to a recently discovered hive (i.e., solution). In order to find excellent hives, scout bees randomly explore their surroundings. They ignore the hive they had previously found once they find a superior one. As a result, the previously found answer is ignored every time the algorithm finds a new and better one. Additionally, the artificial scout bee will continue on its previous trajectory in the hopes that it will lead it to a more ideal solution if its current movement fails to reach a better solution (hive). The current solution is the best choice found so far; if the previous path does not produce a better answer, the algorithm will go on to the current solution. In the wild, scout bees randomly look for hives. Using a random walk-in conjunction with a fitness weight mechanism, this system uses artificial scouts to first randomly scout the landscape. As such, when an artificial scout bee moves forward by speeding up from where it is now, it is doing so in order to explore a better choice. The following describes how artificial scout bees move:

\[X_{i,t+1}=X_{t,i}+pace \tag{5}\]

Assuming x is the artificial scout bee (search agent), t represents the current iteration, and i represents the current search agent, assuming pace is the artificial scout bee's movement rate and direction. Pace is mostly dependent upon physical fitness level. Nonetheless, the orientation of _Pace_ is dependent upon a stochastic mechanism. This is why it is possible to compute the objective function for minimization problems as follows:

\[fw=\left|\frac{*x_{i,tfitness}}{Xi_{i},tfitness}\right|-wf \tag{6}\]

The fitness value of the optimal global solution discovered so far is denoted as the fitness function value \(*x_{i,tfitness}\) of \(Xi_{i},tfitness\). The user's text is unclear and incomplete. The weight factor _wf_, whose value could just be 1 or 0, represents the fitness function regarding the current solution and is used to influence the _fw_. A minimum likelihood of coverage and a substantial degree of convergence are indicated if the value is equal to 1. On the other hand, if _wf_ = 0, it has no effect on Equation (4) and can be ignored. The search is more stable when _wf_ = 0. Because the fitness function value is dependent upon the optimization problem, there are times when the opposite occurs. Nonetheless, the _fw_ value should be between 0 and 1. However, there are several situations in which _fw_ could equal 1. This might happen, for instance, if the present solution is the global best or if the fitness value of the current solution and the global best solution are the same. Additionally, there is a possibility that the value of _fw_ is equal to zero, which takes place in the case when the fitness of \(*x_{i,fitness}\) equals 0. In the case where Xi is equal to zero, it is crucial to avoid dividing by zero. Therefore, it is recommended to follow these guidelines:

\[\left\{ \begin{aligned} & fw=1\;or\;fw=0\;or\;fw=X\;i,t\;fititness=0\;pace=X_{i,t}*r \;(7)\\ & fw>0\;and\;fw<1\left\{\begin{aligned} & r<0,pace=(X_{i,t}-Xi_{i},t^{*})*fw*-1\;(8)\\ &\{r\geq 0,pace=(X_{i,t}-Xi_{i},t^{*})*fw*\}\;(9)\end{aligned} \right\}\end{aligned} \right\}\]

within this context, \(r\) denotes a randomly generated integer that is between \(-1\) and \(1\). There are several ways to construct the random walk, yet Levy flight was chosen because of its well-distributed curve, which provides higher stability.