## 4 Performance Evaluation
### Result of Solutions
#### 4.2.3 Quadratic Instances  
In a single knapsack, the profit ratio of selected items can be up to 0.1049\(\sim\)0.6767 as shown in Table 3. In terms of closeness to the optimal solution, the proposed algorithm's result shows 99% in overall capacity, and it outperforms other algorithms. The average profit of the proposed algorithm gets 3.171, 5.219, 7.92 more profit than the greedy algorithms in a single knapsack case, three-knapsack case, and in the five-knapsack case, respectively. When solving 1000 problems, the proposed algorithm earns a profit of 5055 more than the greedy algorithm. In terms of capacity as shown in Table 12, the average profit of the proposed algorithm has the highest value in the overall capacity.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(M\) & \(N\) & **Capacity** & **Random** & **Greedy** & **Proposed** & **Optimal** \\ \hline \multirow{4}{*}{1} & & 10 & 42.548 & 0.094 & 3.121 & 10.875 \\  & & 20 & 43.171 & 0.109 & 4.438 & 12.043 \\  & & 40 & 44.491 & 0.109 & 6.256 & 14.060 \\  & & 80 & 47.343 & 0.125 & 8.337 & 16.530 \\  & & 100 & 48.260 & 0.125 & 8.936 & 17.406 \\ \hline \multirow{4}{*}{3} & & 10 & 43.115 & 0.172 & 6.846 & 20.756 \\  & & 20 & 45.137 & 0.172 & 10.267 & 21.039 \\  & & 40 & 48.254 & 0.172 & 11.508 & 25.326 \\  & & 80 & 51.607 & 0.169 & 14.087 & 29.009 \\  & & 100 & 52.505 & 0.172 & 15.318 & 27.187 \\ \hline \multirow{4}{*}{5} & & 10 & 44.645 & 0.203 & 13.324 & 24.618 \\  & & 20 & 47.890 & 0.188 & 11.789 & 29.347 \\  & & 40 & 50.471 & 0.188 & 13.796 & 32.295 \\ \hline \multicolumn{2}{c}{Average} & & 46.880 & 0.154 & 9.848 & 21.576 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Computation time (seconds) in RI.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(M\) & \(N\) & **Capacity** & **Random** & **Greedy** & **Proposed** & **Optimal** \\ \hline \multirow{4}{*}{1} & & 10 & 52.549 & 0.109 & 3.396 & 8.696 \\  & & 20 & 53.002 & 0.141 & 4.910 & 9.176 \\  & & 40 & 44.479 & 0.125 & 6.915 & 10.281 \\  & & 80 & 47.641 & 0.125 & 9.117 & 14.083 \\  & & 100 & 48.550 & 0.109 & 10.374 & 14.842 \\ \hline \multirow{4}{*}{3} & & 10 & 51.214 & 0.188 & 9.360 & 19.139 \\  & & 20 & 45.742 & 0.172 & 12.804 & 27.927 \\  & & 40 & 47.496 & 0.172 & 13.280 & 32.529 \\  & & 80 & 51.170 & 0.172 & 14.493 & 42.591 \\  & & 100 & 51.073 & 0.175 & 15.415 & 28.046 \\ \hline \multirow{4}{*}{5} & & 10 & 44.677 & 0.203 & 11.613 & 33.515 \\  & & 20 & 47.423 & 0.187 & 14.379 & 40.987 \\  & & 40 & 51.020 & 0.172 & 19.191 & 52.013 \\ \hline \multicolumn{2}{c}{Average} & & 48.926 & 0.158 & 11.173 & 25.679 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Computation time (seconds) in LI.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(M\) & \(N\) & **Capacity** & **Random** & **Greedy** & **Proposed** & **Optimal** \\ \hline \multirow{4}{*}{1} & & 10 & 42.438 & 0.109 & 3.222 & 8.800 \\  & & 20 & 43.232 & 0.109 & 3.719 & 9.566 \\  & & 40 & 44.211 & 0.125 & 9.369 & 10.872 \\  & & 80 & 46.144 & 0.125 & 8.274 & 12.444 \\  & & 100 & 47.784 & 0.125 & 12.986 & 12.904 \\ \hline \multirow{4}{*}{3} & & 10 & 43.792 & 0.172 & 6.445 & 16.455 \\  & & 20 & 45.239 & 0.171 & 9.554 & 20.504 \\ \cline{1-1}  & & 40 & 48.214 & 0.172 & 9.661 & 24.433 \\ \cline{1-1}  & & 80 & 51.516 & 0.172 & 14.420 & 22.745 \\ \cline{1-1}  & & 100 & 50.897 & 0.172 & 15.891 & 21.201 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Computation time (seconds) in QI.