# Q-MeaMetaVC: An MVC Solver of a Large-Scale Graph Based on Membrane Evolutionary Algorithms
## 5 Analysis of Experimental Results
### Experimental Results and Analysis
#### 5.2.2 Comparison of Experimental Results between Q-MeaMetaVC and Other Solvers  
To verify the performance of Q-MeaMetaVC, we list the experimental results of Q-MeaMetaVC on the test set and other excellent solvers, including MetaVC2, MetaVC, PEAVC, NuMVC2+, and FastVC2+p in Table 3. Figure 16 shows the number of instances of the best solution obtained by each solver. \begin{table}
\begin{tabular}{c c c c c} \hline
**Instances** & **15,000** & **30,000** & **45,000** & **60,000** \\ \hline inf-roadNet-CA & **999,512.9**(999,510)**1050.04** & 999,513.7(**999,509**)1144.41 & 999,519.2(999,513)1131.58 & 999,519.6(999,511)1129.13 \\ inf-roadNet-PA & **554,207.9(554,205,2050)**91.93** & 554,210.3(**554,205)**882.88** & 554,211.4(554,208)1268.53 & 554,213.1(554,210)1035.96 \\ inf-road-usa & **11,519,521.2(111,519,273)692.58** & 115,519,304.8(115,519,293)67.01 & 11,519,315.1(11,519,303)822.2 & 11,519,334.6(11,519,324)851.13 \\ sc-nasasrb & 51,241.6(51,241)**385.57** & 51,239.6(512,238)1054.64 & 51,238.88(**512,238)953.8 & 51,238.7(**512,238)1217.07 \\ sc-pkustk13 & 89,220.2(89,220)1449.56 & 89,218.3(**89,217**)842.32 & 89,217.7(**89,217**)659.31 & 89,217.1(**89,217**)1389.19 \\ sc-pvtk & 207,682.3(207,681)1654.35 & 207,681.4(207,679)1427.4 & **207,681**(207,679)136.3**19 & 207,681.1(**207,677**)1660.61 \\ sc-shipsc1 & 117,207.8(117,008)**2799.44** & **117,203.0(**117,002)**2856.26 & 117,1208.8(117,010)319.39 & 117,038.2(117,010)2084.11 \\ sc-shipsc5 & 146,863.1(146,837)8928.28 & **146,864.2(146,844)**961.54 & 146,870.9(146,844)**262.52 & 146,807.0(146,858)**2771.67 \\ soc-delicious & **85,2988(85,2980)**4.22** & **85,2988(85,2980)**6.8 & **85,2988(85,2983)**93.99 & **85,2988(85,2980)**4.44 \\ soc-digg & **103,234(103,234)**0.15** & **103,234(103,234)**1.05** & **103,234(103,234)**1.05** & **103,234(103,234)**1.05** \\ socf-Berkeley13 & 17,209.8(17,209)**165.36 & 17,209.9(17,209)**139.89** & **17,209.5(17,209)**1032.55 & 17,209.6(17,209)**630.72 \\ socf-CMU & **4986(4986)**26.24** & **4986(4986)**26.21** & **4986(4986)**54.54** & **4986(4986)**26.56 \\ socf-Duke14 & **7683(7683)**33.73 & **7683(7683)**27.76** & **7683(7683)**65.65 & **7683(7683)**5.87 \\ socf-Indiana & **23,313.3(23,313)**1151.95 & 23,313.7(**23,313**)988.93 & 23,313.7(**23,313**)**651.67 & 23,313.5(**23,313**)1254.63 \\ socf-MIT & **4657(46570)**7.01 & 4657(46570)**57.37 & 4657(46570)**57.04 & **4657(46570)**58.84 \\ socf-OR & **36,547(36,547)**721.8 & 36,547(36,547)**513.17 & **36  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Kavora**} & \multicolumn{2}{c}{**Kavora**} & \multicolumn{2}{c}{**Kav**} & \multicolumn{2}{c}{**Kav**} & \multicolumn{2}{c}{**Kav**} \\  & **Optimal** & **Q************MetaMeVC** & **MeVC2** & **MeVC** & **MeVC** & **MeVC** & **MeVC** & **MeVC** & **MeVC** & **MeVC** \\  
The following can be observed from the experimental results:  
(1) Q-MeaMetaVC only performs averagely in \"sc-pwtk\", \"sc-shipsec1\", \"sc-shipsec5\", \"soc-orkut\", and \"soc-pokec\"; however, it performs well in other instances. (2) The optimal solution obtained by Q-MeaMetaVC in 82.9% (29/35) instances has the best quality--more than 65.7%, 28.6%, 25.7%, 31.4%, and 28.6% of MetaVC2, MetaVC, PEAVC, NuMVC2+p, and FastVC2+p. The average quality of the solution obtained by Q-MeaMetaVC in 80% (28/35) of the instances is the best, far exceeding 42.9%, 17.1%, 28.6%, 20%, and 20%.of MetaVC2, MetaVC, PEAVC, NuMVC2+p, and FastVC2+p. (3) Figure 17 shows an example distribution of the difference between the quality of the solutions of MetaVC2, MetaVC, PEAVC, NuMVC2+p, and FastVC2+p and the quality of the solutions of Q-MeaMetaVC. Among them, Iasd(x) and Iosd(x) are calculated according to Formulas (4) and (5), respectively. \[ \begin{array}{l}\text{Iasd(x) = average quality of solution of algorithm x -- average quality of}\\ \text{solution of algorithm Q-MeaMetaVC}\end{array}  \tag{4}\]  
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