In recent years, Wireless Sensor Networks with a Mobile Sink (WSN-MS) have been an active research topic due to the widespread use of mobile devices. However, how to get the balance between data delivery latency and energy consumption becomes a key issue of WSN-MS. In this paper, we study the clustering approach by jointly considering the Route planning for mobile sink and Clustering Problem (RCP) for static sensor nodes. We solve the RCP problem by using the minimum travel route clustering approach, which applies the minimum travel route of the mobile sink to guide the clustering process. We formulate the RCP problem as an Integer Non-Linear Programming (INLP) problem to shorten the travel route of the mobile sink under three constraints: the communication hops constraint, the travel route constraint and the loop avoidance constraint. We then propose an Imprecise Induction Algorithm (IIA) based on the property that the solution with a small hop count is more feasible than that with a large hop count. The IIA algorithm includes three processes: initializing travel route planning with a Traveling Salesman Problem (TSP) algorithm, transforming the cluster head to a cluster member and transforming the cluster member to a cluster head. Extensive experimental results show that the IIA algorithm could automatically adjust cluster heads according to the maximum hops parameter and plan a shorter travel route for the mobile sink. Compared with the Shortest Path Tree-based Data-Gathering Algorithm (SPT-DGA), the IIA algorithm has the characteristics of shorter route length, smaller cluster head count and faster convergence rate.

To improve classification performance, feature selection is usually employed to reduce data dimensionality, eliminate irrelevant features, and decrease computational cost. Among various classifiers, the K-Nearest Neighbors (KNN) algorithm is widely used because of its simplicity and robustness. However, KNN performance is highly sensitive to interdependent parameters. Simultaneously optimizing these parameters is challenging due to the high-dimensional search space. A multi-objective feature selection method is proposed to address these challenges, which is based on an improved Kepler Optimization Algorithm (IKOAfs). The proposed algorithm employs tent mapping, Lévy flight, and self-perturbation to improve search performance, and uses a multi-objective fitness function to jointly optimize classification accuracy, feature selection, and KNN parameters. The reliability of IKOAfs was evaluated in CEC2022 and eight representative public benchmark datasets. The results demonstrate that IKOAfs achieves superior performance compared to six well-known swarm intelligence algorithms in terms of classification accuracy, feature reduction rate, and generalization stability, particularly on high-dimensional datasets.