## 5 Experiments and Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Instance (N/M)** & **Problem** & **BKS** & **ACO** & **Gap** \\ \hline \multirow{2}{*}{p01 (50/4)} & MDVRP & **576.87** & 607.66 & 5.34\% \\  & M-MDVRP & 237.81 & **152.54** & 55.90\% \\ \hline \multirow{2}{*}{p02 (50/4)} & MDVRP & **473.53** & 495.34 & 4.61\% \\  & M-MDVRP & 169.57 & **125.82** & 34.77\% \\ \hline \multirow{2}{*}{p03 (75/5)} & MDVRP & **641.19** & 670.82 & 4.62\% \\  & M-MDVRP & 207.23 & **136.05** & 52.32\% \\ \hline \multirow{2}{*}{p04 (100/2)} & MDVRP & **1001.59** & 1021.36 & 1.97\% \\  & M-MDVRP & 532.24 & **511.41** & 4.07\% \\ \hline \multirow{2}{*}{p05 (100/2)} & MDVRP & **750.03** & 750.72 & 0.09\% \\  & M-MDVRP & 378.17 & **378.17** & 0.00\% \\ \hline \multirow{2}{*}{p06 (100/3)} & MDVRP & **876.50** & 902.91 & 3.01\% \\  & M-MDVRP & 432.59 & **301.75** & 43.36\% \\ \hline \multirow{2}{*}{p07 (100/4)} & MDVRP & **885.80** & 907.55 & 2.46\% \\  & M-MDVRP & 246.21 & **228.95** & 7.54\% \\ \hline \multirow{2}{*}{p08 (249/2)} & MDVRP & **4437.68** & 4449.65 & 0.27\% \\  & M-MDVRP & 2474.82 & **2224.85** & 11.24\% \\ \hline \multirow{2}{*}{p09 (249/3)} & MDVRP & **3900.22** & 4085.51 & 4.75\% \\  & M-MDVRP & 1836.00 & **1364.70** & 34.54\% \\ \hline \multirow{2}{*}{p10 (249/4)} & MDVRP & **3663.02** & 3825.73 & 4.44\% \\  & M-MDVRP & 1049.12 & **960.76** & 9.20\% \\ \hline \multirow{2}{*}{p11 (249/5)} & MDVRP & **3554.18** & 3732.36 & 5.01\% \\  & M-MDVRP & 808.21 & **749.41** & 7.85\% \\ \hline \multirow{2}{*}{p12 (80/2)} & MDVRP & **1318.95** & 1318.95 & 0.00\% \\  & M-MDVRP & 659.48 & **659.48** & 0.00\% \\ \hline \multirow{2}{*}{p13 (80/2)} & MDVRP & **1318.95** & 1318.95 & 0.00\% \\  & M-MDVRP & 659.48 & **659.48** & 0.00\% \\ \hline \multirow{2}{*}{p14 (80/2)} & MDVRP & **1360.12** & 1365.69 & 0.41\% \\  & M-MDVRP & 686.69 & **682.84** & 0.56\% \\ \hline \multirow{2}{*}{p15 (160/4)} & MDVRP & **2505.42** & 2554.12 & 1.94\% \\  & M-MDVRP & 646.92 & **640.58** & 0.99\% \\ \hline \multirow{2}{*}{p16 (160/4)} & MDVRP & **2572.23** & 2606.22 & 1.32\% \\  & M-MDVRP & 694.27 & **651.55** & 6.56\% \\ \hline \multirow{2}{*}{p17 (160/4)} & MDVRP & **2709.09** & 2709.09 & 0.00\% \\  & M-MDVRP & 690.55 & **677.27** & 1.96\% \\ \hline \multirow{2}{*}{p18 (240/6)} & MDVRP & **3702.85** & 3871.01 & 4.54\% \\  & M-MDVRP & 895.50 & **652.24** & 37.30\% \\ \hline \multirow{2}{*}{p19 (240/6)} & MDVRP & **3827.06** & 3884.81 & 1.51\% \\  & M-MDVRP & 694.27 & **651.55** & 6.56\% \\ \hline \multirow{2}{*}{p20 (240/6)} & MDVRP & **4058.07** & 4058.07 & 0.00\% \\  & M-MDVRP & 690.55 & **681.13** & 1.38\% \\ \hline \multirow{2}{*}{p21 (360/9)} & MDVRP & **5474.84** & 5824.58 & 6.39\% \\  & M-MDVRP & 936.62 & **659.25** & 42.07\% \\ \hline \multirow{2}{*}{p22 (360/9)} & MDVRP & **5702.16** & 5873.41 & 3.00\% \\  & M-MDVRP & 719.64 & **657.90** & 9.38\% \\ \hline \multirow{2}{*}{p23 (360/9)} & MDVRP & **6095.46** & 6124.67 & 0.48\% \\  & M-MDVRP & 690.55 & **686.69** & 0.56\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experiments. optimization criterion, i.e., BKS solutions with the M-MDVRP criterion, and vice versa. All solutions from Table 3 are available for download at [[http://www.unob.cz/en/fml/structure/k110/m-mdvrp](http://www.unob.cz/en/fml/structure/k110/m-mdvrp)]([http://www.unob.cz/en/fml/structure/k110/m-mdvrp](http://www.unob.cz/en/fml/structure/k110/m-mdvrp)). The difference (gap) between BKS and ACO solutions (both for MDVRP and M-MDVRP optimization criteria) are also shown in the last column of Table 3. These values do not indicate the quality of the algorithms, because different optimization criteria were used for optimization. The quality of results in Table 3 can be estimated by comparing the lengths of individual routes within the solution, since this indicates the distribution of the delivery process to individual vehicles; the smaller the differences between the routes, the better the solution. Table 4 shows the average and standard deviation for all benchmark instances.