## 7 Ground-Segment Optimization Aspects
### Applicable Optimization Methods for Ground Segment
#### 7.2.2 Long Short-Term Memory (LSTM)
If we define the path cost from the current node to node \(n\) as \(g(n)\), then the decision function \(f(n)\) can be written as in Equation (44) for Algorithm 6. Table 2.9

To employ the A* Search instead of Dijkstra, this decision function must be modified, as seen in Equation (45), where \(h(n)\) is some heuristic function, for example, a state value function, or a greedy function. Figure 8:0

The general advantage of A* over Dijkstra is that as it uses a heuristic to select the nodes to explore, it is significantly faster than Dijkstra, which results in a more optimal overhead. However, as a result, its ability to find the global optimum is dependent on the heuristic function's ability to represent the real network. ### Method Comparisons for the User Segment

Finally, we compare the discussed optimization methods throughout this section in Table 11, similar to the way we did in Sections 6 and 7. Note that the traditional and search methods entries are generalization terms that do not refer to the individual performance of the methods but to our interpretation of the overall performance of similar methods that utilize the same type of approach with varying success. ## 9 Design Recommendations

In this section, we compile our comparisons of the methods from Tables 9-11 in order to provide general recommendations for the optimization problems related to each LEO segment when having the application class of autonomous vehicles in mind. Our design recommendation can serve as a basis for the future design of LEO-based networks to meet the stringent requirements for autonomous transportation, as listed in Figure 8:1

Regarding the space segment, the current studies show that the best trade-off between various performance metrics can be achieved with the evolutionary algorithm variants (such as MOGA and MOPSO), as well as with ML-based approaches, such as constructing an DNN for the optimization problem, given a good dataset that represents the system high dynamics. However, specifically for the space segment, ML-based approaches seem to be a scarce case in the literature, which we attribute to the lack of available quality data regarding constellation optimization. As a result, we recommend focusing on the evolutionary algorithms, where the dominated methods are between GA and PSO variants that make use of smart modifications to guide the methods through the search space. In terms of the ground-segment optimization, our literature review has shown that LSTM typically provides the best solution for the majority of applicable cases, followed by NSGA-II. Regarding the drawbacks of LSTM, as with most other data-driven approaches, its performance highly depends on the availability of a good training dataset that is able to reflect the main characteristics of the optimization problem at hand. In reality, such a quality dataset might not be easy or feasible to acquire. Therefore, our design recommendation for ground-segment optimization is to use NSGA-II optimization engines, providing a good tradeoff between different performance metrics. Indeed, in terms of performance, NSGA-II is not far behind LSTM, but since it does not depend on available training data, its application range is wider than the one of LSTM, and it is, in our opinion, more suitable for the application areas relying on stringent requirements, such as those from autonomous transportation. That being said, NSGA-II performance is heavily affected by the choice of the algorithm criteria, such as the probability models related to genetic operators, but fairly accurate models can be found in the literature and are relatively common. As for the user segment, it is difficult to provide meaningful generic design recommendations, as this is the segment with the most amount of challenges and possible applications, as well as the segment most heavily affected by the nature of the above-mentioned problems or applications.