## 5 Experimental Results
### Novel GVNS Versus Conventional GVNS  
The data in Table 4 reveal that the novel GVNS is indeed an improvement over the classic GVNS. From the data one may conclude that in all cases this new version of GVNS is at least as good as GVNS and in many cases outperforms classical GVNS. This is in accordance with the work in [35], which, through a comparative analysis, also showed that the quantum-inspired GVNS achieves better results than the conventional GVNS. Table 5 contains the experimental results of the novel GVNS on some asymmetric TSP benchmarks. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Benchmark Name** & **Improved NN** & **Repeated NN** & **GVNS BI** & **GVNS FI** & **OV** \\ \hline eil76 & 614 & 608 & 548 & 549 & 538 \\ \hline fri26 & 982 & 965 & 937 & 937 & 937 \\ \hline gil262 & 3027 & 2823 & 2571 & 2558 & 2378 \\ \hline gr17 & 2187 & 2178 & 2085 & 2085 & 2085 \\ \hline gr21 & 3265 & 3003 & 2707 & 2707 & 2707 \\ \hline gr24 & 1769 & 1553 & 1272 & 1272 & 1272 \\ \hline gr48 & 6287 & 5840 & 5048 & 5054 & 5046 \\ \hline gr96 & 70,060 & 65,416 & 56,084 & 56,133 & 55,209 \\ \hline gr120 & 8791 & 8438 & 7197 & 7199 & 6942 \\ \hline gr137 & 93,749 & 84,376 & 72,381 & 72,536 & 69,853 \\ \hline gr202 & 47,460 & 45,030 & 42,419 & 42,287 & 40,160 \\ \hline gr229 & 167,062 & 157,745 & 141,387 & 142,175 & 134,602 \\ \hline gr431 & 218,383 & 197,405 & 184,140 & 184,993 & 171,414 \\ \hline hk48 & 13,052 & 12,137 & 11,498 & 11,531 & 11,461 \\ \hline lin105 & 20,359 & 16,935 & 14,613 & 14,607 & 14,379 \\ \hline lin318 & 54,031 & 49,201 & 45,018 & 45,179 & 42,029 \\ \hline pcd442 & 64,623 & 58,950 & 55,416 & 55,804 & 50,778 \\ \hline pr76 & 154,708 & 130,921 & 109,103 & 109,421 & 108,159 \\ \hline pr107 & 46,765 & 46,680 & 45,183 & 45,464 & 44,303 \\ \hline pr124 & 69,154 & 67,055 & 59,705 & 59,742 & 59,030 \\ \hline pr136 & 127,551 & 114,553 & 99,622 & 100,718 & 96,772 \\ \hline pr144 & 61,904 & 60,964 & 58,776 & 58,991 & 58,537 \\ \hline pr152 & 85,349 & 79,564 & 74,703 & 74,943 & 73,682 \\ \hline pr226 & 95,573 & 92,552 & 81,379 & 81,781 & 80,369 \\ \hline \end{tabular}
\end{table} 
Table 3: The experimental results show that GVNS outperforms the improved and the repeated NN on TSP instances (2/2). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Benchmark Name** & **Improved NN** & **Repeated NN** & **GVNS BI** & **GVNS FI** & **OV** \\ \hline eil76 & 614 & 608 & 548 & 549 & 538 \\ \hline fri26 & 982 & 965 & 937 & 937 & 937 \\ \hline gil262 & 3027 & 2823 & 2571 & 2558 & 2378 \\ \hline gr17 & 2187 & 2178 & 2085 & 2085 & 2085 \\ \hline gr21 & 3265 & 3003 & 2707 & 2707 &  
In order to further test the feasibility of our method, we applied the novel GVNS to some national TSPs (nTSPs) in order to test the behavior on much bigger instances. Table 6 contains the computational results of novel GVNS on nTSPs. Our aim in this paper was the implementation of a method based on a well-known metaheuristic that would be efficient enough to solve real world problems, such as the garbage collection challenge studied here. We wanted to develop an algorithm that would be able to find near-optimal solutions in a relatively short period of time. To achieve our goals, we chose to implement this novel version of GVNS, since we expected to outperform the conventional GVNS. This was indeed confirmed experimentally, as the results in Table 4 show. The bulk of our experiments were meant to determine how GVNS fares against well-established methods that are widely applied for GPS, like the NN and its most important variations. Tables 1-3 contain experimental evidence suggesting that GVNS outperforms the NN, the repeated NN, and the improved NN heuristics in all cases. \begin{table}
\begin{tabular}{c c c c} \hline
**Benchmark** & **OV** & **GVNS FI** & **GVNS BI** \\ \hline ar9152 & 837,479 & 1,648,596 & 1,648,596 \\ \hline gr9882 & 300,899 & 388,944 & 388,944 \\ \hline eg7146 & 172,387 & 220,315 & 220,315 \\ \hline fi10639 & 520,527 & 649,604 & 649,604 \\ \hline \end{tabular}
\end{table} 
Table 6: GVNS on National TSPs.