# A Heuristics-Guided Simplified Discrete Harmony Search Algorithm for Solving 0-1 Knapsack Problem
## 5 Comparative Experiments
### Experiment on the Second Set of Large-Scale 0-1 KP Instances
Additionally, the comparison summary reveals no instances where SDHS underperformed relative to its counterparts as reflected by the \((+/=/-)\) notation sums (e.g., 0/0/12 for CSGHS and BMBO). Collectively, these results highlight the exceptional and consistent performance of SDHS across all evaluated scenarios, positioning it as a leading algorithm in this comparative analysis. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Ins** & **Opt** & **Method** & **Best** & **Worst** & **Mean** & **Median** & **Std** & **Time (s)** \\ \hline KP01 & 40,686 & CSGHS & 40,342 & 40,056 & 40,182 & 40,190 & 68.87 & - \\  & & BMBO & 40,232 & 39,765 & 40,035 & 40,036 & 105.8 & - \\  & & CMBO & **40,686** & 40,683 & 40,683 & 40,683 & 0.71 & - \\  & & OMBO & **40,686** & 40,683 & 40,684 & 40,683 & 0.86 & - \\  & & NM & 40,685 & 40,684 & 40,684.88 & 40,685 & 0.22 & - \\  & & LBSA & **40,686** & 40,684 & 40,684.9 & 40,685 & 0.18 & - \\  & & SDHS & **40,686** & **40,686** & **40,686** & **40,686** & **0** & 0.38 \\ KP02 & 50,592 & CSGHS & 50,027 & 49,717 & 49,846 & 49,835 & 84.36 & - \\  & & BMBO & 50,024 & 49,336 & 49,699 & 49,689 & 135.3 & - \\  & & CMBO & **50,592** & 50,590 & 50,590 & 50,590 & 0.49 & - \\  & & OMBO & **50,592** & 50,590 & 50,590 & 50,590 & 0.70 & - \\  & & NM & **50,592** & **50,592** & **50,592** & **50,592** & **0** & - \\  & & LBSA & **50,592** & 50,591 & 50,591.98 & **50,592** & 0.04 & - \\  & & SDHS & **50,592** & **50,592** & **50,592** & **50,592** & **0** & 0.55 \\ KP03 & 61,846 & CSGHS & 60,951 & 60,616 & 60,788 & 60,791 & 79.79 & - \\  & & BMBO & 61,109 & 60,214 & 60,677 & 60,660 & 165.8 & - \\  & & CMBO & 61,845 & 61,840 & 61,841 & 61,840 & 1.38 & - \\  & & OMBO & 61,845 & 61,840 & 61,842 & 61,843 & 1.82 & - \\  & & NM & **61,846** & 61,845 & 61,845.32 & 61,845 & 0.44 & - \\  & & LBSA & **61,846** & 61,845 & 61,845.27 & 61,845 & 0.40 & - \\  & & SDHS & **61,846** & **61,846** & **61,846** & **61,846** & **0** & 0.79 \\ KP04 & 77,033 & CSGHS & 75,889 & 75,452 & 75,639 & 75,631 & 112.3 & - \\  & & BMBO & 75,761 & 75,062 & 75,464 & 75,482 & 193.3 & - \\  & & CMBO & **77,033** & 77,031 & 77,031 & 77,031 & **0.31** & - \\  & & OMBO & **77,033** & 77,031 & 77,031 & 77,031 & 0.56 & - \\  & & NM & **77,033** & 77,032 & 77,032.92 & **77,033** & 0.15 & - \\  & & LBSA & **77,033** & 77,032 & 77,032.76 & **77,033** & 0.37 & - \\  & & SDHS & **77,033** & **77,033** & **77,033** & **77,033** & **0** & 0.9 \\ KP05 & 102,316 & CSGHS & - & - & - & - & - & - \\  & & BMBO & - & - & - & - & - & - \\  & & CMBO & **102,316** & 102,313 & 102,314 & 102,313 & 0.93 & - \\  & & OMBO & **102,316** & 102,313 & 102,314 & 102,313 & 1.11 & - \\  & & NM & **102,316** & **102,316** & **102,316** & **102,316** & **0** & - \\  & & LBSA & **102,316** & 102,315 & 102,315.9 & **102,316** & 0.20 & - \\  & & SDHS & **102,316** & **102,316** & **102,316** & **102,316** & **0** & 1.15 \\ \hline \hline \end{tabular} Note: Bold numbers indicate the algorithm found the relatively best solution.  
\end{table} 
Table 10: Comparison of the SDHS algorithm with six metaheuristics on large-scale uncorrelated 0-1 KP instances.