# 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
It significantly outperforms CGMA, MBPOS, and DGHS, as confirmed by [PERSON]'s post hoc test (\(p<0.05\)). Although the difference with HSOSHS is \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 & 13,143 & CGMA & **13,143** & 13,140 & 13,142.20 & **13,143** & 1.3493 & - \\  & & MBPSO & **13,143** & 13,140 & 13,141.40 & 13,140 & 1.5222 & - \\  & & DGHS & 13,137 & 13,131 & 13,134.30 & 13,134 & 1.2077 & - \\  & & HOSHS & **13,143** & **13,143** & **13,143** & **13,143** & 0 & - \\  & & SDHS & **13,143** & **13,143** & **13,143** & **13,143** & 0 & 0.09 \\
500 & 21,069 & CGMA & **21,069** & 21,063 & 21,068.00 & **21,069** & 1.6400 & - \\  & & MBPSO & **21,069** & 21,063 & 21,066.10 & 21,066 & 1.4704 & - \\  & & DGHS & 21,060 & 21,054 & 21,056.00 & 21,057 & 1.8194 & - \\  & & HOSOSHS & **21,069** & **21,069** & **21,069** & **21,069** & 0 & - \\  & & SDHS & **21,069** & **21,069** & **21,069** & **21,069** & 0 & 0.16 \\
800 & 34,227 & CGMA & **34,227** & 34,221 & 34,223.90 & 34,224 & 2.2947 & - \\  & & MBPSO & 34,221 & 34,215 & 34,216.40 & 34,215 & 2.1909 & - \\  & & DGHS & 34,209 & 34,197 & 34,201.50 & 34,200 & 2.4600 & - \\  & & HOSHS & **34,227** & **34,227** & **34,227** & **34,227** & 0 & - \\
1000 & 42,108 & CGMA & **42,108** & **42,108** & **42,108** & **0** & - \\  & & MBPSO & **42,108** & 42,099 & 42,104.10 & 42,105 & 2.1066 & - \\  & & DGHS & 42,096 & 42,084 & 42,088.00 & 42,087 & 2.9827 & - \\  & & HOSHS & **42,108** & **42,108** & **42,108** & **42,108** & 0 & - \\  & & SDHS & **42,108** & **42,108** & **42,108** & **42,108** & 0 & 0.36 \\
1200 & 51,585 & CGMA & **51,585** & 51,582 & 51,583.80 & **51,585** & 1.4948 & - \\  & & MBPSO & 51,576 & 51,570 & 51,572.20 & 51,573 & 2.0745 & - \\  & & DGHS & 51,558 & 51,549 & 51,553.80 & 51,552 & 2.4410 & - \\  & & HOSHS & **51,585** & **51,585** & **51,585** & **51,585** & 0 & - \\  & & SDHS & **51,585** & **51,585** & **51,585** & **51,585** & 0 & 0.45 \\ \hline \hline \end{tabular} Note: Bold numbers indicate the algorithm found the relatively best solution.  
\end{table} 
Table 17: Comparison of the SDHS algorithm with four metaheuristics on large-scale profit ceiling 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 & 1914.62 & CGMA & 1905.08 & 1901.03 & 1902.49 & 1902.28 & 1.0721 & - \\  & & MBPSO & 1887.61 & 1884.12 & 1885.70 & 1885.38 & 0.9509 & - \\  & & DGHS & 1915.72 & 1874.84 & 1878.48 & 1876.60 & 8.8626 & - \\  & & HOSHS & 1914.62 & 1912.41 & 1913.55 & 1913.65 & 0.5508 & - \\  & & SDHS & **1918.25** & **1918.24** & **1918.24** & **1918.24** & 0.0014 & 1.26 \\
500 & 3198.62 & CGMA & 3174.57 & 3176.25 & 3171.66 & 3171.79 & 1.5624 & - \\  & & MBPSO & 3149.96 & 3144.21 & 3146.81 & 3146.76 & 1.1317 & - \\  & & DGHS & 3136.95 & 3130.92 & 3133.70 & 3133.39 & 1.8258 & - \\  & & HOSHS & 3198.62 & 3193.24 & 3195.30 & 3195.17 & 1.4499 & - \\  & & SDHS & **3210.52** & **3210.47** & **3210.50** & **3210.50** & 0.0096 & 2.52 \\
7000 & 4444.40 & CGMA & 4410.22 & 4399.96 & 4406.19 & 4406.11 & 2.4319 & - \\  & & MBPSO & 4379.24 & 4373.04 & 4375.35 & 4375.22 & 1.9022 & - \\  & & DGHS & 4366.02 & 4356.18 & 4359.12 & 4358.52 & 2.5196 & - \\  & & HOSHS & 4444.40 & 4436.23 & 4438.50 & 4438.28 & 2.1447 & - \\  & & SDHS & **4469.43** & **4469.24** & **4469.34** & **4469.34** & 0.0348 & 4.16 \\
10000 & 6340.18 & CGMA & 6294.93 & 6284.56 & 6288.19 & 6287.12 & 2.7812 & - \\  & & MBPSO & 6251.53 & 6246.10 & 6249.05 & 6249.12 & 1.6007 & - \\  & & DGHS & 6235.64 & 6227.47 & 6231.33 & 6230.79 & 2.0268 & - \\  & & HOSHS & 6340.18 & 6327.39 & 6333.76 & 6334.03 & 3.2233 & - \\  & & SDHS & **6387.25** & **6386.69** & **6387.02** & **6387.00** & 0.1138 & 7.19 \\ \hline \hline \end{tabular} Note: Bold numbers indicate the algorithm found the relatively best solution.  
\end{table}