The key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxation-based evolutionary algorithm (ACREA) for CMOPs. ACREA adaptively relaxes the constraints according to the iteration information of population, whose purpose is to induce infeasible solutions to transform into feasible ones and thus improve the ability to explore the unknown regions. Completely ignoring constraints can cause the population to waste significant resources searching for infeasible solutions, while excessively satisfying constraints can trap the population in local optima. Therefore, balancing constraints and objectives is a crucial approach to improving algorithm performance. By appropriately relaxing the constraints, it induces infeasible solutions to be transformed into feasible ones, thus obtaining more information from infeasible solutions. At the same time, it also establishes an archive for the storage and update of solutions. In the archive update process, a diversity-based ranking is proposed to improve the convergence speed of the algorithm. In the selection process of the mating pool, common density selection metrics are incorporated to enable the algorithm to obtain higher-quality solutions. The experimental results show that the proposed ACREA algorithm not only achieved the best Inverse Generation Distance (IGD) value in 54.6% of the 44 benchmark test problems and the best Hyper Volume (HV) value in 50% of them, but also obtained the best results in seven out of nine real-world problems. Clearly, CP-TSEA outperforms its competitors.

Traditional single image super-resolution (SISR) methods, which focus on integer scale super-resolution, often require separate training for each scale factor, leading to increased computational resource consumption. In this paper, we propose MambaSR, a novel arbitrary-scale super-resolution approach integrating Mamba with Fast Fourier Convolution Blocks. MambaSR leverages the strengths of the Mamba state-space model to extract long-range dependencies. In addition, Fast Fourier Convolution Blocks are proposed to capture the global information in the frequency domain. The experimental results demonstrate that MambaSR achieves superior performance compared to different methods across various benchmark datasets. Specifically, on the Urban100 dataset, MambaSR outperforms MetaSR by 0.93 dB in PSNR and 0.0203 dB in SSIM, and on the Manga109 dataset, it achieves an average PSNR improvement of 1.00 dB and an SSIM improvement of 0.0093 dB. These results highlight the efficacy of MambaSR in enhancing image quality for arbitrary-scale super-resolution.

With the advancement of deep learning, its application in financial market forecasting has become a research hotspot. This paper proposes an innovative Multi-Scale TsMixer model for predicting stock index futures in the A-share market, covering SSE50, CSI300, and CSI500. By integrating Multi-Scale time-series features across the short, medium, and long term, the model effectively captures market fluctuations and trends. Moreover, since stock index futures reflect the collective movement of their constituent stocks, we introduce a novel approach: predicting individual constituent stocks and merging their forecasts using three fusion strategies (average fusion, weighted fusion, and weighted decay fusion). Experimental results demonstrate that the weighted decay fusion method significantly improves the prediction accuracy and stability, validating the effectiveness of Multi-Scale TsMixer.

Accurate stock price prediction requires the integration of heterogeneous data streams, yet conventional techniques struggle to simultaneously leverage fine-grained micro-stock features and broader macroeconomic indicators. To address this gap, we propose MambaLLM, a novel framework that fuses macro-index and micro-stock inputs through the synergistic use of state-space models (SSMs) and large language models (LLMs). Our two-branch architecture comprises (i) Micro-Stock Encoder, a Mamba-based temporal encoder for processing granular stock-level data (prices, volumes, and technical indicators), and (ii) Macro-Index Analyzer, an LLM module—employing DeepSeek R1 7B distillation—capable of interpreting market-level index trends (e.g., S&P 500) to produce textual summaries. These summaries are then distilled into compact embeddings via FinBERT. By merging these multi-scale representations through a concatenation mechanism and subsequently refining them with multi-layer perceptrons (MLPs), MambaLLM dynamically captures both asset-specific price behavior and systemic market fluctuations. Extensive experiments on six major U.S. stocks (AAPL, AMZN, MSFT, TSLA, GOOGL, and META) reveal that MambaLLM delivers up to a 28.50% reduction in RMSE compared with suboptimal models, surpassing traditional recurrent neural networks and MAMBA-based baselines under volatile market conditions. This marked performance gain highlights the framework’s unique ability to merge structured financial time series with semantically rich macroeconomic narratives. Altogether, our findings underscore the scalability and adaptability of MambaLLM, offering a powerful, next-generation tool for financial forecasting and risk management.