## 1 Introduction
These problems can be avoided by effectively routing flows while considering available network parameters and QoS requirements. The selection of paths in the routing process must evaluate the network conditions through the multiple available metrics, which can be  
Figure 1: Traditional routing. Metrics: delay (ms), packet loss (%), and bandwidth (Mbps). represented as objectives. The goals may conflict in this type of problem, and each purpose has a different solution. With more than one optimization criterion, this routing process is known as a multi-objective optimization problem (MOP) [12]. Discovering paths that provide QoS in a network according to different data flow requirements is a difficult problem, which is usually solved optimally using heuristic algorithms [13], especially those based on integer linear programming, game theory, and evolutionary algorithms (EA). Algorithms based on game theory and approximation are usually computationally intensive. Therefore, these two methods are usually not suitable for providing acceptable solutions. On the other hand, EAs search for global optima by developing an iterative search within a finite time. They have proven to provide high-quality solutions to the problem within a limited computation time [14]. Genetic algorithms (GA) are a family of models of EAs. They have emerged as a method for optimizing difficult search problems based on the principle of genetic selection, such as inheritance mutation, selection, and crossover. Their advantage is that they can handle large search spaces and generate multiple solutions in a single pass, which is suitable for this type of QoS routing optimization for SDN [15]. Our proposal (Figure 2) resides in the application plane and communicates with the SDN controller using the REST API provided by the Northbound interface. We use these SDN capabilities to create, query, and delete flow rules on OpenFlow (OF) switches, in order to forward data flow according to the path established by our path selection proposal or optimization criteria, based on a cellular genetic algorithm for multi-objective optimization (MOCell). The main contributions of our proposal are as follows:  
* An SDN strategy for routing data flows based on QoS that considers an inter-domain approach and compares its performance with traditional routing algorithms in the context of SDN. * Using MOCell, the routing strategy considers some of the most critical network parameters: available bandwidth, delay, and packet loss. The MOCell algorithm differs from conventional methods in evaluating multiple possible solutions from the first iteration. Its population is structured into small neighborhoods  
Figure 2: Routing architecture for SDN. that generate high-quality solutions. They are fed back with the non-dominant solutions stored in each iteration. This algorithm has shown better performance in extensive testing than the _NSGA-II_ and _SPEA2_ algorithms, which are widely recognized and used in practice [16]. Alongside this research, we set aside for future work the analysis of time complexity and computational delay. The fastest output results and least computational effort will likely be the result of [PERSON]'s algorithm, rather than the MOCell method. However, the network performance results of this work presented in Section 4 show how the MOCell method obtains better results than [PERSON]'s algorithm and the multi-objective evolutionary algorithm based on decomposition (MOEA/D). Additionally, the stationary state of the SDN network connection processes allows the implementation and evaluation of the MOCell method for a new inter-domain routing proposal. The rest of the article is organized as follows: Related work is presented in Section 2. Section 3 presents our proposed system and describes the experimental setup. In Section 4, the performance evolution is presented, and the results are discussed. Finally, Section 5 describes the conclusions of the work and future directions.