When facing sparse user–item interaction data, recommendation systems often struggle to learn high-quality representations, which in turn affects the recommendation performance. To address this issue, this paper proposes a graph neural network-based recommendation algorithm with multi-scale attention and contrastive learning (GR-MC). First, a dedicated graph structure augmentation strategy based on user-focused edge dropout is designed to intentionally reduce the dominance of high-degree user nodes in neighbor aggregation, effectively alleviating degree bias and improving the model’s generalization ability. Second, a multi-scale attention embedding propagation mechanism is proposed to enhance the modeling of higher-order neighbor relationships. Finally, by treating node self-discrimination as a self-supervised task, contrastive learning is introduced to provide auxiliary signals for representation learning, thereby improving the discriminative ability of embeddings and the robustness of the model. Experimental results show that GR-MC outperforms existing methods on multiple public datasets, especially on the highly sparse Amazon-book dataset, where Recall@20 improves by 24.69%, fully demonstrating its effectiveness and robustness in sparse environments.

The Kepler optimization algorithm (KOA) is a metaheuristic algorithm based on Kepler’s laws of planetary motion and has demonstrated outstanding performance in multiple test sets and for various optimization issues. However, the KOA is hampered by the limitations of insufficient convergence accuracy, weak global search ability, and slow convergence speed. To address these deficiencies, this paper presents a multi-strategy fusion Kepler optimization algorithm (MKOA). Firstly, the algorithm initializes the population using Good Point Set, enhancing population diversity. Secondly, Dynamic Opposition-Based Learning is applied for population individuals to further improve its global exploration effectiveness. Furthermore, we introduce the Normal Cloud Model to perturb the best solution, improving its convergence rate and accuracy. Finally, a new position-update strategy is introduced to balance local and global search, helping KOA escape local optima. To test the performance of the MKOA, we uses the CEC2017 and CEC2019 test suites for testing. The data indicate that the MKOA has more advantages than other algorithms in terms of practicality and effectiveness. Aiming at the engineering issue, this study selected three classic engineering cases. The results reveal that the MKOA demonstrates strong applicability in engineering practice.

This paper introduces an enhanced Black-winged Kite Optimization Algorithm (SMBKA) to address the issues of slow convergence and poor accuracy in UAV route planning within three-dimensional complex environments. SMBKA enhances planning performance by incorporating sparrow-inspired behavior and multi-strategy optimization mechanisms. Specifically, the proposed method utilizes Latin hypercube sampling to generate the initial population, thereby improving its distribution uniformity and diversity. Furthermore, an adaptive weight factor is adopted to achieve a dynamic balance between exploration and exploitation. Meanwhile, a dynamic opposition-based learning strategy is integrated to effectively improve overall search performance and avoid premature convergence. Finally, the scout search mechanism from the sparrow search algorithm is incorporated to enhance the algorithm’s adaptability to complex environments. In terms of performance verification, SMBKA demonstrates superior performance on the CEC2017 test functions, achieving the best average accuracy in 16 out of 29 test functions. In the application of UAV route planning, the average flight path length is shortened by 7.2% to 18.68%, demonstrating the potential of this algorithm in practical applications.