This paper proposes a new active learning method named as optimum-pursuing method (OPM) from the viewpoint of optimization theory, which aims to provide an effective tool for solving constrained optimization and reliability-based design optimization (RBDO) problems with low computation cost. It uses the cheap Kriging metamodel to replace the expensive physical response. The novelty of the proposed OPM primarily lies in two aspects. First, the OPM utilizes the advantage of the optimization theory rather than sampling technology. By using the augmented Lagrangian approach, it comprehensively considers the objective, constraints, and their relations, thereby automatic identification of important region in the vicinity of the optimum. Second, the accordingly optimum-pursuing function consists of three parts: Kriging mean, Kriging standard deviation, and merit function. Also, the target reliability surface is further considered to enhance the local accuracy of the reliability analysis. The performance of OPM is tested for both deterministic optimization and problems, in which two mathematical and three real-world engineering examples are selected to showcase the feasibility and validity. The results demonstrate that OPM is promising for solving both deterministic optimization and RBDO problems by comparing with the well-known active learning methods.

Recommendation systems powered by artificial intelligence (AI) are widely used to improve user experience. However, AI inevitably raises privacy leakage and other security issues due to the utilization of extensive user data. Addressing these challenges can protect users' personal information, benefit service providers, and foster service ecosystems. Presently, numerous techniques based on differential privacy have been proposed to solve this problem. However, existing solutions encounter issues such as inadequate data utilization and a tenuous trade-off between privacy protection and recommendation effectiveness. To enhance recommendation accuracy and protect users' private data, we propose ID-SR, a novel privacy-preserving social recommendation scheme for trustworthy AI based on the infinite divisibility of Laplace distribution. We first introduce a novel recommendation method adopted in ID-SR, which is established based on matrix factorization with a newly designed social regularization term for improving recommendation effectiveness. We then propose a differential privacy-preserving scheme tailored to the above method that leverages the Laplace distribution's characteristics to safeguard user data. Theoretical analysis and experimentation evaluation on two publicly available datasets demonstrate that our scheme achieves a superior balance between privacy protection and recommendation effectiveness, ultimately delivering an enhanced user experience.