## 6 Conclusions  
This paper introduces two modifications to the F/DR algorithm for channel assignment problems in telecommunication systems, named as the F/DR-k and F/DR-D-k algorithms. These heuristics either match or improve upon the original algorithm's results while maintaining the same level of implementation complexity and execution time. Notably, F/DR-D-10 stands out with the following achievements: (1) In 100% of the benchmarks used, at least one local optimum value (calculated by the modified algorithm) outperforms the conventional algorithm's result, (2) In 95% of instances used to asses the proposed algorithm, the worsening probability was less than 50%. These novel heuristics can be seamlessly integrated into more complex optimization algorithms to enhance the optimization process's outcomes.  
Conceptualization, C.-I.P.-R.; methodology, C.-I.P.-R. and A.F.; software, C.-I.P.-R.; validation,C.-I.P.-R., A.F., M.P., G.Y. and G.P.; formal analysis, C.-I.P.-R., A.F., M.P., G.Y. and G.P.; investigation, C.-I.P.-R.; resources, C.-I.P.-R., A.F., M.P., G.Y. and G.P.; data curation, C.-I.P.-R., A.F., M.P., G.Y. and G.P.; writing--original draft preparation, C.-I.P.-R. and A.F.; writing--review and editing, M.P., G.Y. and G.P.; visualization, C.-I.P.-R. and A.F.; supervision, C.-I.P.-R.; project administration, C.-I.P.-R. and A.F.; funding acquisition, C.-I.P.-R., A.F., M.P., G.Y. and G.P. All authors have read and agreed to the published version of the manuscript. The APC was funded by the Pontificia Universidad Javeriana.  
The corresponding author can provide access to the source code and data used in this study upon request.  
The authors would like to thank the Electronics Department and Electronics laboratory of the Pontificia Universidad Javeriana for providing the required resources to conduct this study. The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
ACC Adjacent interference CCC Co-Channel interference CSC Co-site interference CAP Channel Assignment Problem FAP Frequency Assignment Problem F/DR Frequency Allocation Strategy with Node Degree Reordering Max-FAP Maximum service and minimum blocking Frequency Assignment Problems  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **F/PER** & **F/DR-10** & **F/DR-D-10** & **F/DR-50** & **F/DR-D-50** & **F/DR-90** & **F/DR-D-90** \\ \hline PoOBR & 20\% & 100\% & 100\% & 85\% & 100\% & 85\% & 100\% \\ PoOBE & 10\% & 90\% & 95\% & 60\% & 85\% & 30\% & 75\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Summary of the percentage of cases with improved performance.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multirow{2}{*}{**Optimal Value**} & \multirow{2}{*}{**F/DR [43]**} & **Best Greedy** & **This Work** & **Tabu Search** & **Simulated Annealing** \\  & & & **Algorithms from [60]** & **(Best Result)** & **from [61]** & **from [61]** \\ \hline P1 & 239 & 259 & 250 & 251 & 240 & 239 \\ P2 & 257 & 292 & 284 & 282 & 269 & 260 \\ P3 & 426 & 448 & 447 & 437 & 428 & 428 \\ P4 & 855 & 895 & 894 & 878 & 858 & 858 \\ P5 & 1713 & 1801 & 1800 & 1761 & 1724 & 1724 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Some results of MS-FAP using main heuristic approaches in literature.