The Preponderance of literature has established that most of the metaheuristic algorithms were associated with identified challenges in solving the Controller Placement Problem in SD-WAN. This study proposed a Stochastic Computational Graph Model with an Ensemble Learning (SCGMEL) approach to address the scalability, intelligence, and high computational complexity challenges experienced by the existing metaheuristic algorithms. The proposed SCGMEL used stochastic gradient descent with momentum and learning rate decay, a computational graph model, and the eXtreme Gradient Boosted Trees (XGBoost) algorithm as the optimization and machine learning approaches. The proposed solution was tested using datasets from Internet Zoo topology with six objective functions: load balancing, maximum controller failure, average controller-to-controller latency, average switch-to-controller latency, and maximum controller-to-controller latency. The XGBoost outperformed other regression models, in predicting the number of controllers, with mean absolute error of versus , , and for the random forest, logistic regression, and K-nearest neighbor, respectively. Furthermore, the execution time, average and total CPU usages of the algorithms demonstrated the computational efficiency of the proposed SCGMEL over ANSGA-III, NSGA-II, and MOPSO with percentage decreases of , , and , respectively. Consequently, the proposed SCGMEL was recommended for controller placement in SD-WAN, subject to the usage conditions.

中文翻译：

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具有集成学习模型的随机计算图用于解决软件定义的广域网中的控制器放置问题

大量文献表明，大多数元启发式算法都与解决 SD-WAN 中控制器放置问题的已识别挑战相关。本研究提出了一种采用集成学习（SCGMEL）方法的随机计算图模型，以解决现有元启发式算法所遇到的可扩展性、智能性和高计算复杂性挑战。所提出的 SCGMEL 使用具有动量和学习率衰减的随机梯度下降、计算图模型和 eXtreme Gradient Boosted Trees (XGBoost) 算法作为优化和机器学习方法。使用来自 Internet Zoo 拓扑的数据集对所提出的解决方案进行了测试，该数据集具有六个目标函数：负载平衡、最大控制器故障、平均控制器到控制器延迟、平均交换机到控制器延迟和最大控制器到控制器延迟。 XGBoost 在预测控制器数量方面优于其他回归模型，随机森林、逻辑回归和 K 最近邻的平均绝对误差分别为 、 和 。此外，算法的执行时间、平均和总 CPU 使用率证明了所提出的 SCGMEL 相对于 ANSGA-III、NSGA-II 和 MOPSO 的计算效率，百分比分别降低了 、 和 。因此，建议根据使用条件将提议的 SCGMEL 用于 SD-WAN 中的控制器放置。