## 4 Analysis of Single Objective Algorithms Overview
### Learner Performance-Based Behavior
\[fw=\left|\frac{\sum_{o=1}^{n}*x_{i,ffitness}}{\sum_{o=1}^{n}Xi,ffitness} \right|-wf \tag{16}\]

where \(\sum_{o=1}^{n}*x_{i,ffitness}\) represents a summation of cost function of the global best individual, n represents the number of objectives, and \(\mathrm{o}=\{1,2,3,\ldots n\}\); the \(\sum_{o=1}^{n}Xi,ffitness\) represents the summation of current individual's cost function, again n represents number of the objectives, and \(\mathrm{o}=\{1,2,3,\ldots n\}\). Lastly, the weight factor wf in Equation (16) has a value of either 0 or 1. It is possible to observe that wf = 0 has no effect on the equation and can be disregarded. Readers who are interested in learning more about single-objective FDO are directed to [20]. The algorithm structure of MOFDO as seen in Algorithm 8 is somewhat similar to that of a single objective FDO, but it also has a few more advantages, which are as follows: for the goal of holding Pareto front solutions throughout optimization, an archive (repository) is utilized, since this is the practice of much published research [73; 81]. Pareto front solutions undergo a polynomial mutation prior to the non-dominated solution being added to the archive. As a variation operator, the polynomial mutation was used in MOEAs [67]. ```
1: Initialize the artificial scout bee population randomly Xt,i (i = 1,2,3,... n, t = 1,2,3,...m). 2: Creating an archive for non-dominated solutions with specific sizes. 3: Generate Hybrid cube Grid
4: While (t) iteration limit not reached (m)or solution good enough. 5: For every one of the artificial scout bee Xt,i
6: Find the ideal artificial scout bee Xt,best
7: Generation of the random walk r in [-1, 1] range
8: Estimate weight fitness value Using Equation (14) //checking Equations (12)-(14) conditions
9: if (fitness weight \(\geq\) 1 or fitness weight \(\leq\)\(-\)1 or summation of Xt,best fitness = 0)
10: fitness weight = r
11: EndIf
12: Calculate Xt + 1,i using Equation (12)
13: If (Xt + 1,i fitness dominate on Xt,i fitnesses)
14: Otherwise
15: Calculation of Xt + 1,i using Equation (12) with previous pace saved
16: If (Xi,t + 1 fitness dominates on Xt,i fitnesses)
17: Move accepted, and saved pace
18: Otherwise
19: The current position is maintained// (do not move)
20: EndIf
21: Apply polynomial mutation
22: Add non-dominated ants (solutions) to the archive. 23: Keep only non-dominated members in the archive
24: Update Hypercube Grid indices
25: End for
26: End while
```
**Algorithm 8** MOFDOMore information is included in the method (8), yet MOFDO begins by allocating the search individuals at random across the search space. Hypercube grids are constructed, and an archive with a specific size is established. Line (4) will then initiate the main algorithm loop, which is mostly dependent on a certain number of iterations or to the point where a predetermined condition is satisfied. Line (5) states that, based on the number of individuals, individual (artificial scout bee) procedures from Line 6 to Line 27 will be repeated for each search. The activities that are stated are determining the global best search agent; determining fw with the use of Equation (15); calculating a new search agent position utilizing Equation (14); and Line 10-Line 12, applying conditions from Equations (12)-(14) to compute pace. The method always determines if the new result (cost function) outperforms the old result when a new search agent is found (14). If so, as indicated in Line (15), the new position will be acknowledged and the pace will be saved for possible future use. If not, the previously saved pace will be utilized in place of the new one in the hopes of producing a better result--that is, if the search agent doesn't maintain the present position [see Lines (17-22)]. Line (24) will see the application of the polynomial mutation to obtain further variant solutions. Lines 25 and 26 will then verify whether or not the solution fits inside the archive. Hypercube grid indices are constantly updated in Line (27) by changes in the search landscape for more detailed about MOFDO see in[48].