# On Analyzing Routing Selection for Aerial Autonomous Vehicles Connected to Mobile Network
## 2 Related Work  
Routing selection in current networks requires multi-criteria selection algorithms, i.e., a selection based on optimization of a number of parameters. Multi-criteria optimization is achieved by defining a decision space that includes all the potential solutions that could result from the process of decision. Such potential solutions are called decision vectors. Each vector is \(m\)-dimensional, where \(m\) is the number of variables. Then, the decision space defines the feasible solutions of each one of the variables. The multi-criteria decision process aims to maximize or minimize a number (call \(k\)) of objective functions. All the \(k\) objective functions are called together the aggregate objective function.  
With the above definitions, a solution X dominates a solution Y when achieves better results in all the \(k\) objective functions (maximized or minimized). A solution X is called efficient if and only if there is not any other solution that dominates it. All the efficient solutions together are called Pareto Optimal and their outcome vectors are called the Pareto Frontier. If the Pareto Optimal contains only one solution, than the decision process is obvious, however, normally the Pareto optimal contains several efficient solutions and the multi-criteria decision process needs to provide some policy to take the final decision.  
Different policies may provide more information a priori, i.e., before analyzing the Pareto optimal, or a posteriori, i.e., the decision algorithm may introduce some information after the analysis of the Pareto optimal, such that the final Pareto optimal will contain one efficient solution [14]. For reducing the number of efficient solutions to one, a normal approach is to propose a function to reduce the multi-criteria problem to one unique variable. Such a function is named cost function [15]. One of the most common cost function is the Minkowski norm of order \(p\). Minkowski norm is non-linear, so the aggregation (the reduction of a number of efficient solutions to one) is also non-linear. A non-linear aggregation is able to come closer to the optimized solution subject to the fact that the algorithm has information about the order \(p\), otherwise non-liner aggregation may never reach optimized solution. In addition, it is not possible to know whether the solution specified by the algorithm is better or worse than other solutions, unless the Pareto Frontier is compared for all the Pareto optimal (which often is unworkable).  
There are other propositions to the cost function that aim to reduce the number of efficient solutions (the Pareto optimal). The decision algorithms with reference levels limit the number of solutions by defining two levels for each variable, one that should not be exceeded by any selected efficient solution (called reservation level) and one that once exceeded by an efficient solution, then any better value should not impact in the final decision (called aspiration level) [16; 17]. In [18], the authors adjust the reference levels to the decision space, such that the distance of the reference levels to the center of mass of the solutions is minimized. An extended approach of the decision algorithm with reference levels consists of using the Mahalanobis distance instead of the Euclidean distance [19].