In this paper, we propose a novel phase unwrapping method termed the square root cubature Kalman filter phase unwrapping (SCKFPU) method. Specifically, as the system model of the interferometric synthetic aperture (InSAR) phase unwrapping can be formulated as the discrete Markovian jump system (MJS) for tracking a maneuvering target, a phase unwrapping method is proposed by combining the SCKF algorithm with a phase gradient estimator. Moreover, we design a phase quality estimate function and present an optimal path-following strategy. The strategy ensures that the SCKFPU method simultaneously performs noise suppression and unwraps InSAR images along the pixels with high-reliance to the pixels with low-reliance. Simulation results based on synthetic data, true InSAR data and measured (real) InSAR data show that the proposed InSAR phase unwrapping method can achieve better performance compared with other existing phase unwrapping methods.

In this article, we design a robo-advisor which has a bi-level framework. The framework enables it to handle a large amount of assets using fast algorithms in the lower level. The proposed robo-advisor can utilize the closed-form solutions for investors’ risk preferences based on corresponding portfolio choices. A dynamic weight is applied to update investors’ risk preferences. Numerical results based on real data in Chinese stock market show that our proposed robo-advisor can accurately estimate the risk preferences of investors and outperform the benchmark formed by market indexes.

When constructing an investment portfolio, it is important to maximize returns while minimizing risks. This portfolio optimization can be considered as a multi-objective optimization problem that is solved by means of multi-objective evolutionary algorithms. The use of multi-objective evolutionary algorithms (MOEAs) provides an effective approach for dealing with the complex data involved in multi-objective optimization problems. However, current MOEAs often rely on a single strategy to obtain optimal solutions, leading to premature convergence and an insufficient population diversity. In this paper, a new MOEA called the Synergistic MOEA with Diffusion Population Generation (DPG-SMOEA) is proposed to address these limitations by integrating MOEAs with diffusion models. To train the diffusion model, a mixed memory pool strategy is optimized, which collects improved solutions from the MOEA/D-AEE, an optimized MOEA, as training samples. The trained model is then used to generate offspring. Considering the cold-start mechanism of the diffusion model, particularly during the training phase where it is not suitable for generating initial offspring, this paper adjusts and optimizes the collaborative strategy to enhance the synergy between the diffusion model and MOEA/D-AEE. Experimental validation of the DPG-SMOEA demonstrates the advantages of using diffusion models in low-dimensional and relatively continuous data analysis. The results show that the DPG-SMOEA performs well on the low-dimensional Hang Seng Index test dataset, while achieving average performance on other high-dimensional datasets, consistent with theoretical predictions. Overall, the DPG-SMOEA achieves better results compared to MOEA/D-AEE and other multi-objective optimization algorithms.