## 2 Related Work
### Multi-Objective Optimization Routing in Satellite Networks  
Heuristic-based QoS-oriented satellite routing using a software-defined framework for integrated space-terrestrial satellite communication was proposed with a decision factor \(u_{a}\) for choosing a path based on the type of service as  
\[u_{a}=w_{1}BandWidth-w_{2}Delay-w_{3}PacketLoss,\]  
where \(w_{1},w_{2}\), and \(w_{3}\) are weights [39]. A sustainable heuristic algorithm was proposed to satisfy the QoS requirements of multi-layered satellite network users to select a path based on an evaluation function \(fee\) defined as below. \[fee=\alpha\,delay+\beta\,utilization+\gamma\,packetLossRate,\]  
where \(\alpha\), \(\beta\), and \(\gamma\) are balance weights [40]. A software-defined space-ground-integration-network-based deep reinforcement learning algorithm was proposed, which computes reward \(r\) to evaluate the performance of a link as  
\[r=\alpha\,bandwidth+\beta\,throughput+\gamma\,\frac{1}{delay}+\delta\,\frac{1}{ packetLossRate}+\epsilon\,\frac{1}{jitter},\]  
where \(\alpha\), \(\beta\), \(\gamma\), \(\delta\), and \(\epsilon\) are adjustment factors [41]. A priority-and-failure-probability-based (PFPR) routing was proposed to fulfill the QoS requirements of different services in LEO/MEO satellite communication links using an objective function \(penalty()\) that uses a linear sum as below. \[min:penalty()=\sum service_{j}\,Fault_{busines(j)}+\gamma\sum\delta(l)C(l),\]  
where \(service_{j}\) is the weight of different priority services, \(Fault_{busines(j)}\) is the failure rate, \(gamma\) is the weight for the delay, \(\delta(l)\) denotes the presence or absence of a link \(l\), \(j\) is the service type, and \(C(l)\) is the delay on the link [42]. A centralized QoS-aware algorithm using the software-defined networking controller was proposed with a linear cost function:  
\[score=k_{1}\,AB+\frac{k_{2}}{latency}+k_{3}\,(1-PDR)+\frac{k_{4}}{jitter}+k_{5} \,stability-flag,\]where \(AB\) is the available bandwidth of a link, \(PDR\) is the packet loss rate, \(stability-flag\) denotes the presence of an intra-orbit link, and \(k1\), \(k2\), \(k3\), and \(k4\) are the importance weights for each metric [43]. A multi-QoS adaptive routing algorithm was proposed using an SDN-based satellite networking architecture to satisfy the QoS requirements of different types of services. A link's weight is calculated using a linear combination as  
\[W=\alpha\ delay+\beta\,logloss,\]  
where \(alpha\) or \(\beta\) will be increased to improve their proportion if the delay or loss rate cannot be satisfied by the flow demand in the previous path [44]. An agent-based load balancing and QoS routing for LEO satellite networks was proposed to use a cost function:  
\[C_{i}=\lambda\frac{TotalDelay(p_{i})}{\sum_{i=1}^{k}TotalDelay(p_{i})}+\mu\frac{ TotallLoss(p_{i})}{\sum_{i=1}^{k}TotalLoss(p_{i})},\]  
where \(\lambda\) and \(mu\) are weights and \(i\) is the link in a path \(p\)[45]. A routing model based on the membership function of uncertain links in mobile edge computing satellites networks has been proposed and solved using a grey wolf optimization algorithm to select a link with the minimum comprehensive value of the metrics delay, packet loss rate, and bandwidth. The comprehensive evaluation of a link is given as  
\[ld=\sqrt{(m_{gk}^{td}-1)^{2}+(m_{gk}^{lr}-1)^{2}+(m_{gk}^{bd}-1)^{2}},\]  
where \(td\), \(lr\), and \(bd\) are the membership degree functions of the delay, packet loss rate, and bandwidth [46]. The shortest path routing approach was proposed to service delay-sensitive traffic and other traffic separately [47]. This work used a linear cost function to compute the delay on a link using the queuing delay, average delay, and service time, where the average delay is computed for a link between two nodes \(i\) and \(j\) as  
\[D_{avg}\ =\ \frac{D}{1-packetlossrate},\]  
and  
\[D_{ij}=W_{q1_{j}}+D_{avg_{ij}}+\frac{1}{\mu},\]  
where \(W_{q1_{j}}\) is the queuing delay and \(\mu\) is the service time.