From the perspective of network attackers, finding attack sequences that can cause significant damage to network controllability is an important task, which also helps defenders improve robustness during network constructions. Therefore, developing effective attack strategies is a key aspect of research on network controllability and its robustness. In this paper, we propose a Leaf Node Neighbor-based Attack (LNNA) strategy that can effectively disrupt the controllability of undirected networks. The LNNA strategy targets the neighbors of leaf nodes, and when there are no leaf nodes in the network, the strategy attacks the neighbors of nodes with a higher degree to produce the leaf nodes. Results from simulations on synthetic and real-world networks demonstrate the effectiveness of the proposed method. In particular, our findings suggest that removing neighbors of low-degree nodes (i.e., nodes with degree 1 or 2) can significantly reduce the controllability robustness of networks. Thus, protecting such low-degree nodes and their neighbors during network construction can lead to networks with improved controllability robustness.

The No Free Lunch Theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. This paper introduces an innovative algorithm selection approach called the CNN-HT, which is a two-stage algorithm selection framework. In the first stage, a Convolutional Neural Network (CNN) is employed to classify problems. In the second stage, the Hypothesis Testing (HT) technique is used to suggest the best-performing algorithm based on the statistical analysis of the performance metric of algorithms that address various problem categories. The two-stage approach can adapt to different algorithm combinations without the need to retrain the entire model, and modifications can be made in the second stage only, which is an improvement of one-stage approaches. To provide a more general structure for the classification model, we adopt Exploratory Landscape Analysis (ELA) features of the problem as input and utilize feature selection techniques to reduce the redundant ones. In problem classification, the average accuracy of classifying problems using CNN is 96%, which demonstrates the advantages of CNN compared to Random Forest and Support Vector Machines. After feature selection, the accuracy increases to 98.8%, further improving the classification performance while reducing the computational cost. This demonstrates the effectiveness of the first stage of the CNN-HT method, which provides a basis for algorithm selection. In the experiments, CNN-HT shows the advantages of the second stage algorithm as well as good performance with better average rankings in different algorithm combinations compared to the individual algorithms and another algorithm combination approach.

The No Free Lunch theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. In this paper, an innovative algorithm selection approach called the CNN-HT two-stage algorithm selection framework is introduced. In the first stage, a Convolutional Neural Network (CNN) is employed to classify problems. In the second stage, the Hypothesis Testing (HT) technique is used to suggest the best-performing algorithm based on the statistical analysis of the performance metric of algorithms that address various problem categories. To provide a more general structure for the classification model, we adopt Exploratory Landscape Analysis (ELA) features of the problem as the input and utilize feature selection techniques to reduce the redundant ones. In problem classification, our proposed algorithm selection framework achieves an average accuracy of 96% for the classification of unknown black-box problems, and it improves to 98.8% after feature selection. This shows that our proposed classification method can accurately classify BBOB problems into 24 classes of problems and thus can correctly recommend algorithms accordingly. The performance of CNN-HT is compared with a single optimization algorithm on a continuous black-box optimization problem set, and the average ranking of CNN-HT is superior, demonstrating its effectiveness.

From the perspective of network attackers, finding attack sequences that can make significant damage on network controllability is an important task, which also helps defenders improve the robustness during network constructions. Therefore, developing effective attack strategies is a key aspect of research on network controllability and its robustness. In this paper, we propose a Leaf Node Neighbor-based Attack (LNNA) strategy that can effectively disrupt the controllability of undirected networks. The LNNA strategy targets the neighbors of leaf nodes, and when there are no leaf nodes in the network, the strategy attacks the neighbors of nodes with a higher degree to produce the leaf nodes. Results from simulations on synthetic and real-world networks demonstrate the effectiveness of the proposed method. In particular, our findings suggest that removing neighbors of low-degree nodes (i.e., nodes with degree 1 or 2) can significantly reduce the controllability robustness of networks. Thus, protecting such low-degree nodes and their neighbors during network construction can lead to networks with improved controllability robustness.