# XOR Binary Gravitational Search Algorithm with Repository: Industry 4.0 Applications
## 5 Simulation Results
### Application to Knapsack
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & **m** & **N** & **Filename** & **Proposed** & **BGSA** & **IBPSO** & **BPSO** & **BGWO** & **BDA** \\  & & & & & & & [16] & [17] & [15] & [18] & [19] \\ \hline \hline
1 & 100 & 0.25 & 5 & 10 & OR5x100-0.25,1.dat & **21675.33** & 20,742.73 & \(-\)7E+13 & \(-\)1.4E+14 & \(-\)3.6E+14 & 20,278.77 \\ \hline
2 & 100 & 0.25 & 5 & 10 & OR5x100-0.25,2.dat & **21,223.93** & 20,663 & \(-\)9.2E+13 & \(-\)1.4E+14 & \(-\)3.4E+14 & 19,938.63 \\ \hline
3 & 100 & 0.5 & 5 & 10 & OR5x100-0.50,1.dat & **39,835.93** & 39,302.37 & 37,097.47 & 37,573.93 & 37,093.93 & 38,813.2 \\ \hline
4 & 100 & 0.5 & 5 & 10 & OR5x100-0.50,2.dat & **39,812.4** & 39,372.73 & 36,388.13 & 37,300.47 & 36,902.1 & 38,704.93 \\ \hline
5 & 100 & 0.75 & 5 & 10 & OR5x100-0.75,1.dat & **57,626** & 56,945.5 & 52,385.83 & 50,954.87 & 55,652.37 & 56,107.47 \\ \hline
6 & 100 & 0.75 & 5 & 10 & OR5x100-0.75,2.dat & **59,946.2** & 59,272.1 & 55,457.23 & 53,529.87 & 57,861.93 & 58,294.9 \\ \hline
7 & 250 & 0.25 & 5 & 10 & OR5x250-0.25,1.dat & **49,323.17** & 46,860.27 & \(-\)5.9E+14 & \(-\)7.6E+14 & \(-\)1.1E+15 & 46,805.43 \\ \hline
8 & 250 & 0.25 & 5 & 10 & OR5x250-0.25,2.dat & **51,256.37** & 49,071.9 & \(-\)6.1E+14 & \(-\)7.7E+14 & \(-\)1.2E+15 & 48,596.37 \\ \hline
9 & 250 & 0.5 & 5 & 10 & OR5x250-0.50,1.dat & **99,682.27** & 99,393.17 & 94,943.5 & 94,993.6 & 94,801.07 & 97,535.43 \\ \hline
10 & 250 & 0.5 & 5 & 10 & OR5x250-0.50,2.dat & **99,759** & 99,000.57 & 94,482.33 & 94,256.9 & 94,158.23 & 97621.53 \\ \hline
11 & 250 & 0.75 & 5 & 10 & OR5x250-0.75,1.dat & **142,598.2** & 140,975.2 & 120,843.3 & 115,794.4 & 139,086.3 & 139,172.7 \\ \hline
12 & 250 & 0.75 & 5 & 10 & OR5x250-0.75,2.dat & **147,544.4** & 145,975.8 & 124,749.9 & 119,571.7 & 143,700.6 & 144207.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimization results using various optimization algorithms for the maximization of the knapsack problem. In most real-world optimization problems, the cost function evaluation requires high volume of computation. Hence, it would be highly desired for an optimization algorithm to result in superior performance after its single run. Box plot is a graphical method which gives more information about the diversity of the results rather than just its mean value. A small standard deviation leads to a smaller interquartile range which can be interpreted as its ability to avoid local minima. Outliers can also be easily spotted from box plot. In Figure 3 while the interquartile is illustrated using a blue box, the minimum and the maximum associated with data are demonstrated using the black line. There is a 50 percent chance that for a new experience, the result falls within the interquartile range. The outliers in this figure are represented by \"+\" sign. The median values are demonstrated with red line. The box plot obtained using different optimization algorithms for optimization problems 7 to 18 are illustrated. It can be observed from the figure that not only the median values obtained for the proposed approach in 10 cases out of 12 cases are the best, interquartile range obtained for the proposed approach in most cases is smaller meaning that it is more repeatable than in other investigated optimization algorithms. Furthermore, for optimization problems numbers 7, 8, 11 and 12, it can be observed that the interquartile range obtained for the proposed approach is well above the other optimization algorithms. This means that for every single run of the proposed optimization algorithm, there is  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & **m** & **N** & **Filename** & **Proposed** & **BGSA** & **IBPSO** & **BPSO** & **BGWO** & **BDA** \\  & & & & & & [16] & [17] & [15] & [18] & [19] \\ \hline
13 & 500 & 0.25 & 5 & 15 & OR5x500-0.25.1.dat &  
an appreciable chance we can obtain superior performance for the proposed optimization algorithm compared to other investigated optimization methods.