Large-scale overlapping problems are prevalent in practical engineering applications， and the optimization challenge is significantly amplified due to the existence of shared variables. Decomposition-based Cooperative Co-evolution （CC） algorithms have demonstrated promising performance in addressing large-scale overlapping problems. However， certain novel CC frameworks designed for overlapping problems rely on grouping methods for the identification of overlapping problem structures and the current grouping methods for large-scale overlapping problems fail to consider both accuracy and efficiency simultaneously. To address the above problems， a Two-Stage Differential Grouping （TSDG） method for large-scale overlapping problems was proposed， which achieves accurate grouping while significantly reducing computational resource consumption. In the first stage， a grouping method based on the finite difference principle was employed to efficiently identify all subcomponents and shared variables. To enhance both stability and accuracy in grouping， a grouping refinement method was proposed in the second stage to examine the information of the subcomponents and shared variables obtained in the previous stage and correct inaccurate grouping results. Based on the synergy of the two stages， TSDG achieves efficient and accurate decomposition of large-scale overlapping problems. Extensive experimental results demonstrate that TSDG is capable of accurately grouping large-scale overlapping problems while consuming fewer computational resources. In the optimization experiment， TSDG exhibits superior performance compared to state-of-the-art algorithms for large-scale overlapping problems.

According to the characteristics of traditional multivariate linear regression method for long processing time and limited memory, a parallel multivariate linear regression forecasting model was designed based on MapReduce for the time-series sample data. The model was composed of three MapReduce processes which were used to solve the eigenvector and standard orthogonal vector of cross product matrix composed by historical data, to forecast the future parameter of the eigenvalues and eigenvectors matrix, and to estimate the regression parameters in the next moment respectively. Experiments were designed and implemented to the validity effectiveness of the proposed parallel multivariate linear regression forecasting model. The experimental results show multivariate linear regression prediction model based on MapReduce has good speedup and scaleup, and suits for analysis and forecasting of large data.

To keep the trade-off of time complexity and accuracy of community detection in complex networks, Community Detection Algorithm based on Clustering Granulation (CGCDA) was proposed in this paper. The granules were regarded as communities so that the granulation for a network was actually the community partition of a network. Firstly, each node in the network was regarded as an original granule, then the granule set was obtained by the initial granulation operation. Secondly, granules in this set which satisfied granulation coefficient were merged by clustering granulation operation. The process was finished until granulation coefficient was not satisfied in the granule set. Finally, overlapping nodes among some granules were regard as isolated points, and they were merged into corresponding granules based on neighbor nodes voting algorithm to realize the community partition of complex network. Newman Fast Algorithm (NFA), Label Propagation Algorithm (LPA), CGCDA were realized on four benchmark datasets. The experimental results show that CGCDA can achieve modularity 7.6% higher than LPA and time 96% less than NFA averagely. CGCDA has lower time complexity and higher modularity. The balance between time complexity and accuracy of community detection is achieved. Compared with NFA and LPA, the whole performance of CGCDA is better.

Graph theory was utilized to improve image segmentation of traditional Fuzzy C-Means (FCM). The proposed algorithm used weighting of graph theory to calculate the distance of FCM, compared with Euclid distance, the proposed algorithm not only considered the distance of every sample, but also considered the Grayscale difference of every sample, and gained fuzzy membership function which was suitable for image segmentation. Based on the experimental result, probability of error and index of evaluation through comparing with image segmentation based traditional FCM and image segmentation based graph theory. The improved FCM in this paper is proved to be an appropriate method which is suitable for image segmentation.

In the field of Natural Language Processing （NLP）， as an efficient method for sentence representation learning， contrastive learning mitigates the anisotropy of Transformer-based pre-trained language models effectively and enhances the quality of sentence representations significantly. However， the existing research focuses on English conditions， especially under supervised settings. Due to the lack of labeled data， it is difficult to utilize contrastive learning effectively to obtain high-quality sentence representations in most non-English languages. To address this issue， a cross-lingual knowledge transfer method for contrastive learning models was proposed， transferring knowledge across languages by aligning the structures of different language representation spaces. Based on this， a simple and effective cross-lingual knowledge transfer framework， TransCSE， was developed to transfer the knowledge from supervised English contrastive learning models to non-English models. Through knowledge transfer experiments from English to six directions， including French， Arabic， Spanish， Turkish， and Chinese， knowledge was transferred successfully from the supervised contrastive learning model SimCSE （Simple contrastive learning of sentence embeddings） to the multilingual pre-trained language model mBERT （Multilingual Bidirectional Encoder Representations from Transformers） by TransCSE. Experimental results show that model trained using the TransCSE framework achieves accuracy improvements of 17.95 and 43.27 percentage points on XNLI （Cross-lingual Natural Language Inference） and STS （Semantic Textual Similarity） 2017 benchmark datasets， respectively， compared to the original mBERT， proving the effectiveness of TransCSE. Moreover， compared to cross-lingual knowledge transfer methods based on shared parameters and representation alignment， TransCSE has the best performance on both XNLI and STS 2017 benchmark datasets.

Concerning the limitations of Chain-of-Thought （CoT） prompting technology， such as insufficient integration of human strategies and poorly performance for small-scale Large Language Models （LLMs）， a CoT prompting framework based on the 6W2H （Why， What， Which， When， Where， Who， How， How much） problem decomposition strategy， WH-CoT （6W2H Chain-of-Thought）， was proposed. Firstly， the task dataset was clustered， sampled and divided into training and test datasets by using the Sentence-BERT model. Then， in the training dataset， all samples were subjected to element extraction， problem decomposition， answer paragraph construction， and answer generation to form the CoT， thereby constructing a task-specific corpus. Finally， during the reasoning stage， demonstration samples were extracted adaptively from the corpus and added to the prompts， allowing the model to combine the prompts to generate answers to test questions. For the Qwen-turbo model， on arithmetic reasoning task， the average accuracy of WH-CoT is improved by 3.35 and 4.27 percentage points respectively compared with those of the mainstream Zero-Shot-CoT and Manual-CoT； on multi-hop reasoning task， compared with Zero-Shot-CoT and Manual-CoT， WH-CoT has the total performance improvement ratio on EM （Exact Matching ratio） increased by 36 and 111 percentage points respectively. In addition， for the Qwen-14B-Chat and Qwen-7B-Chat models， the total performance improvement ratios of WH-CoT are higher than those of Zero-Shot-CoT and Manual-CoT on both EM and F1. It can be seen that by further integrating human strategies with machine intelligence， WH-CoT can improve the reasoning performance of LLMs of different sizes effectively on both arithmetic reasoning and multi-hop reasoning tasks.