# Resource Assignment Algorithms for Autonomous Mobile Robots with Task Offloading
## 6 Conclusions  
This work has presented some novel algorithms to deal with the unique assignment of radio and CPU resources to a fleet of mobile robots needing task offloading. The assignment is performed to optimize an indicator of the operational efficiency of the robot fleet, such as the average response delay from the offloading servers. Mobile robots can exploit the assigned resources and perform their task in the quickest way possible. We have compared brute force, evolutionary, and reduced complexity search algorithms to find the optimal assignment. After defining a number of scenarios, we have simulated and compared the algorithms' performance in terms of complexity and optimality. Our results show that the proposed simplified algorithm (SM) outperforms the other methods in terms of reduced complexity, with only a slight average latency penalty with respect to the best algorithm (GA).  
Conceptualization, G.B. and L.R.; methodology, G.B. and L.R.; software, G.B.; validation, G.B. and L.R.; formal analysis, G.B. and L.R.; investigation, G.B. and L.R.; writing--original draft preparation, G.B. and L.R.; writing--review and editing, G.B. and L.R.; visualization, G.B. and L.R.; supervision, G.B. and L.R. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Algorithm** & **Complexity** & **Time for _40/60/20_Variable_ (s) \\ \hline VEX & \(\mathcal{O}\big{(}N_{\text{AV}}N_{\text{BS}}N_{\text{DC}}\cdot(\tilde{N}_{ \text{BS}}\tilde{N}_{\text{DC}})^{N_{AV}}\big{)}\) & \(2\times 10^{100}\) (estimated) \\ GA & \(\mathcal{O}(N_{\text{AV}}N_{\text{BS}}N_{\text{DC}}\cdot N_{\text{call}})\) & 109.4 \\ RSAM & \(\mathcal{O}(N_{\text{AV}}N_{\text{BS}}N_{\text{DC}}\cdot N_{\text{call}})\) & 4.5 \\ SM & \(\mathcal{O}\big{(}N_{\text{AV}}N_{\text{BS}}N_{\text{DC}}\cdot\vartheta N_{ \text{AV}}\tilde{N}_{\text{BS}}\tilde{N}_{\text{DC}}\big{)}\) & 0.0356 \\ MLAT & \(\mathcal{O}(N_{\text{AV}}N_{\text{BS}}N_{\text{DC}})\) & 0.0028 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Computational cost of the algorithms, ordered with decreasing complexity.  
Funding: This work was supported by the European Union--Next Generation EU under the Italian National Recovery and Resilience Plan (NRRP), Mission 4, Component 2, Investment 1.3, CUP E83C22004640001, partnership on \"Telecommunications of the Future\" (PE00000001-program \"RESTART\"). Data are contained within the article. Conflicts of Interest: The authors declare no conflicts of interest. Abbreviations The following abbreviations are used in this manuscript: AI Artificial intelligence AV Autonomous vehicle BS Base station CPU Central processing unit CRAN Cloud radio access network DC Data center DCA Difference of convex algorithm GA Genetic algorithm HW Hardware KPI Key performance indicator MIMO Multiple-input multiple-output MBNLP Mixed-binary nonlinear programming MINLP Mixed-integer nonlinear programming MLAT Minimum latency NP Nondeterministic polynomial OS Operating system RSAM Random sampling SM Sequential minimization SVC Service UL Uplink VEL Valid exhaustive