# Multi-Objective Message Routing in Electric and Flying Vehicles Using a Genetics Algorithm
## 2 System Model
The value of \(\omega_{i,j}\) represents transmission between vehicles \(i\) and \(j\), such that \(\omega_{i,j}<1\) depicts unreliable and incomplete data transmission. Algorithm 1 outlines a novel module to estimate the reliability (\(\omega_{i,j}\)) of a link between vehicle \(i\) and \(j\) by incrementally exploring connectivity time \(\tau_{i,j}\). The process terminates execution when it achieves reliable connectivity (\(\omega_{i,j}\geq 1\)) or both vehicles move out of communication range (\(R_{i,j}\)). A quadratic solution can also predict \(\Delta D_{i,j}(t_{0}+\tau)\), but through extensive trial and error evaluation, it has been identified that often there exist multiple or no solutions, which lead to unreliable prediction. Moreover, Algorithm 1 considers mobility metrics to estimate connectivity time while avoiding the need for any probe message to gather network metrics (throughput, bandwidth, etc.). The proposed reliability check only considers the data in hand (BSM messages, etc. ), and does not require any network information for prediction. The route-reliability procedure in Algorithm 1 increases connectivity time by \(\alpha\) (0.5, 1, etc.) time units (seconds) with every iteration and continuously checks that both vehicles are within communication range (\(\Delta D_{i,j}(t_{0}+\tau)<R_{i,j}\)). The algorithm also converges if the reliability metric (\(\omega_{i,j}\)) reaches 1, which translates to a successful transmission of data (\(Dt_{i,j}\)). Through this ingenious process, the reliability of a communication link can be easily identified without the additional overhead of probe messages. ```
1:Initiate and distribute a vehicle discovery message
2:For all responses regarding the target vehicle
3:if no direct link exists between source and the destination then
4:for all loop-free responses with target vehicle do
5: Route \(\omega_{s,d}=min(\omega_{s,1},\omega_{1,2},\ldots,\omega_{l,d})\),
6:while calculate all \(\omega_{i,j}\) for hops between s and d do
7:while\(\Delta D_{i,j}(t_{0}+\tau)<R_{i,j}\) and \(\omega_{i,j}<1\)do
8:\(\tau_{i,j}=\tau_{i,j}+\alpha\)
9: Find \(\Delta D_{i,j}(t_{0}+\tau)\) for hop i and j. 10: Identify \(\omega_{i,j}=\frac{\tau_{i,j}\times T_{x,j}}{Dt_{i,j}}\)
11:endwhile
12:endwhile
13:if\(\omega_{s,d}<1\)then Remove the response as unreliable
14:endif
15:endfor
16: Call multi-objective genetics algorithm (\(0\)) with remaining responses messages
17:else
18: Direct link between source and the destination supersedes all possible paths. 19:endif
20:Return the optimal route as transmission path. ```  
**Algorithm 1** The algorithm implemented in each communicating vehicle Moreover, the average data rate \(\left(O^{1}\right)\) of the source, and all intermediate nodes in a route (\(p\)) between the source (\(s\)) and destination (\(d\)) can be calculated as:  
\[O^{1}_{s,d}=\left(sum(Tx_{s,i},Tx_{i,j},\ldots,Tx_{l,d})\right)/hops \tag{4}\]  
On the other hand, the minimum residual energy \(\left(O^{2}\right)\) of any vehicle in a route (\(p\)) between the source (\(s\)) and destination (\(d\)) can be calculated as:  
\[O^{2}_{s,d}=min(\bar{s}_{s,i},\bar{\xi}_{i,j},\ldots,\bar{\xi}_{l,d}), \tag{5}\]  
where \(\bar{\xi}_{i,j}\) is residual energy of vehicle \(i\). A reliable route (\(\omega_{i,j}\geq 1\)) having the highest \(O^{1}\) and \(O^{2}\) values, prioritizes UAVs in the path whilst keeping their residual energy float.