# A Heuristics-Guided Simplified Discrete Harmony Search Algorithm for Solving 0-1 Knapsack Problem
## 5 Comparative Experiments
### Experiment on the Third Set of Large-Scale 0-1 KP Instances
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Dim** & **Opt** & **Method** & **Best** & **Worst** & **Mean** & **Median** & **Std** & **Time (s)** \\ \hline
300 & 17,259 & CGMA & **17,259** & 17,239 & 17,253.67 & 17,259 & 8.9955 & - \\  & & MBPSO & 17,259 & 17,257 & 17,258.83 & 17,259 & 0.5307 & - \\  & & DGHS & 17,239 & 17,219 & 17,234.13 & 17,236 & 5.7878 & - \\  & & HOSOSHS & **17,259** & **17,259** & **17,259** & **17,259** & 0 & - \\  & & SDHS & **17,259** & **17,259** & **17,259** & **0** & 0.09 \\
500 & 29,775 & CGMA & 29,755 & 29,735 & 29,752.33 & 29,755 & 6.9149 & - \\  & & MBPSO & 29,755 & 29,735 & 29,752.13 & 29,755 & 6.1180 & - \\  & & DGHS & 29,735 & 29,697 & 29,714.93 & 29,712 & 9.7660 & - \\  & & HOSOSHS & **29,775** & 29,755 & 29,772.33 & **29,775** & 6.9149 & - \\  & & SDHS & **29,775** & **29,775** & **29,775** & **29,775** & 0 & 0.15 \\
800 & 47,153 & CGMA & 47,133 & 47,113 & 47,120.33 & 47,113 & 9.8027 & - \\  & & MBPSO & 47,113 & 47,092 & 47,106.57 & 47,111 & 7.8111 & - \\  & & DGHS & 47,079 & 47,033 & 47,053.30 & 47,052 & 11.0365 & - \\  & & HOSOSHS & 47,153 & 47,133 & 47,151.67 & 47,153 & 5.0742 & - \\  & & SDHS & **47,173** & **47,153** & **47,167.83** & **47,172** & 7.1609 & 0.28 \\
1000 & 59,575 & CGMA & 59,555 & 59,495 & 59,516.33 & 59,515 & 12.7937 & - \\  & & MBPSO & 59,513 & 59,475 & 59,490.33 & 59,492 & 8.8213 & - \\  & & DGHS & 59,455 & 59,403 & 59,427.83 & 59,431 & 12.6248 & - \\  & & HOSOSHS & **59,575** & 59,555 & 59,566.33 & 59,575 & 10.0801 & - \\  & & SDHS & **59,595** & **59,575** & **59,578.2** & **59,575** & 5.5172 & 0.37 \\
1200 & 69,122 & CGMA & 69,062 & 69,021 & 69,037.67 & 69,042 & 13.9243 & - \\  & & MBPSO & 69,012 & 68,980 & 68,996.53 & 68,998.5 & 6.9319 & - \\  & & DGHS & 68,949 & 68,892 & 68,916.10 & 68,917.5 & 12.8529 & - \\  & & HOSOSHS & **69,122** & 69,082 & 69,103.33 & 69,102 & 8.9955 & - \\  & & SDHS & **69,122** & **69,122** & **69,122** & **69,122** & 0 & 0.43 \\ \hline \hline \end{tabular} Note: Bold numbers indicate the algorithm found the relatively best solution.  
\end{table} 
Table 16: Comparison of the SDHS algorithm with four metaheuristics on large-scale multiple strongly correlated instances. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Dim** & **Opt** & **Method** & **Best** & **Worst** & **Mean** & **Median** & **Std** & **Time (s)** \\ \hline
300 & 14,760 & CGMA & **14,760** & 14,750 & 14,751.00 & 14,750 & 3.0513 & - \\  & & MBPSO & 14,760 & 14,750 & 14,751.77 & 14,750 & 3.2872 & - \\  & & DGHS & 14,750 & 14,738 & 14,743.00 & 14,740 & 4.1936 & - \\  & & HOSOSHS & **14,760** & 14,750 & 14,759.33 & **14,760** & 2.5371 & - \\  & & SDHS & **14,760** & **14,760** & **14,760** & **14,760** & 0 & 0.1 \\
500 & 25,597 & CGMA & 25,587 & 25,577 & 25,578.33 & 25,577 & 3.4575 & - \\  & & MBPSO & 25,587 & 25,577 & 25,578.57 & 25,577 & 3.2872 & - \\  & & DGHS & 25,567 & 25,554 & 25,561.40 & 25,563 & 4.4613 & - \\  & & HOSOSHS & **25,597** & 25,587 & 25,590.67 & 25,587 & 4.9013 & - \\  & & SDHS & **25,597** & **25,597** & **25,597** & **25,597** & **0 & 0.19 \\
800 & 39,940 & CGMA & 39,920 & 39,910 & 39,914.33 & 39,910 & 5.0401 & - \\  & & MBPSO & 39,920 & 39,900 & 39,904.17 & 39,901 & 5.0860 & - \\  & & DGHS & 39,894 & 39,867 & 39,877.20 & 39,877.5 & 5.8804 & - \\  & & HOSOSHS & **39,940** & 39,930 & 39,931.33 & 39,930 & 3.4575 & - \\  & & SDHS & **39,940** & **39,940** & **39,940** & **39,940** & 0 & 0.28 \\
1000 & 48,763 & CGMA & 48,743 & 48,713 & 48,728.27 & 48,732 & 6.2419 & - \\  & & MBPSO & 48,723 & 48,703 & 48,712.40 & 48,712 & 4.4303 & - \\  & & DGHS & 48,699 & 48,671 & 48,679.67 & 48,678 & 8.3101 & - \\  & & HOSOSHS & **48,763** & 48,743 & 48,752.33 & 48,753 & 3.6515 & - \\  & & SDHS & **48,763** & **48,763** & **48,763** & **48,763** & 0 & 0.35 \\ \hline \hline \end{tabular} Note: Bold numbers indicate the algorithm found the relatively best solution.  
\end{table} 
Table 15: _Cont._According to the [PERSON] test results in Table 19, SDHS achieves the highest ranking among the evaluated algorithms.