The omnichannel business has becomes a hot topic due to the fast development on e-commerce and the customers' acquaintance with multichannel shopping mode. Various business organizations have started to work on omnichannel business issue in order to satisfy the new trend of customer demand and tend to devote their efforts to both online and offline business. Thus, there is no doubt that understanding the shopping behavior for online customers is vital for the omnichannel business. The RFM (recency, frequency, monetary) model and the k-means clustering method are commonly used to extract customers' information and segment customers, respectively. To extend the RFM model, we divide the total frequency and monetary information into weekly level data, and as a consequence, the number of variables corresponding to one customer increases significantly, leading to the problem of high-dimensional analysis. To address this issue, in this paper we extend the regularized k-means clustering method with L ₁ -norm for independent case to the clustering method with elastic net penalty with a focus on correlated variables. Our simulation results show that the proposed method performs better than the standard k-means method by providing lower error rates and can select variables simultaneously under 4 different scenarios. A real example of an online retailer is presented to illustrate the use of the proposed method and highlight its high potential in clustering high-dimensional applications. In particular, the number of variables is reduced from 108 to 98 without any loss on clustering accuracy.

Due to the marked increase in the prevalence of overweight and obesity worldwide and an environment leading to a series of chronic diseases, physical exercise is an important way to prevent chronic diseases. Additionally, a good exercise smart bracelet can bring convenience to physical exercise. Quick and accurate evaluation of smart sports bracelets has become a hot topic and draws attention from both academic researchers and public society. In the literature, the analytic hierarchy process (AHP) and entropy weight method (EWM) were used to obtain the weights from both subjective and objective perspectives, which were integrated by the comprehensive weighting method, and furthermore the performance of sports smart bracelet was evaluated through fuzzy comprehensive evaluation. Also, to avoid complex weight calculations caused by the comprehensive weighting method, machine learning methods are used to model the structure and contribute to the comprehensive evaluation process. However, few studies have investigated all previous elements in the comprehensive evaluation process. In this study, we consider all previous parts when evaluating smart sports bracelets. In particular, we use the sparrow search algorithm (SSA) to optimize the backpropagation (BP) neural network for constructing the comprehensive score prediction model of the sports smart bracelet. Results show that the sparrow search algorithm-optimized backpropagation (SSA-BP) neural network model has good predictive ability and can quickly obtain evaluation results on the premise of effectively ensuring the accuracy of the evaluation results.

The implementation of PAFW is an important way to reduce food waste. Discussing how to more successfully implement PAFW to reduce food waste is of great significance in achieving sustainable development. Different from the previous literature, this paper uses evolutionary game theory to establish a strategic interaction income matrix between local governments and large supermarkets and analyzes the strategic interaction between local governments and large supermarkets by copying dynamic equations, revealing the strategic choice between the two parties evolution process. A simulation‐based approach is used to validate the theoretical results and analyze the influence of key parameters on the evolutionary trajectory. The study found the following: (1) to promote the system to an optimal evolutionarily stable strategy (ESS), it is necessary to strengthen policy publicity, increase the willingness of large supermarkets to implement the PAFW, and increase the enthusiasm of the public or third‐party organizations to monitor system; (2) stakeholders’ initial willingness will influence the evolutionary trajectory; and (3) it is important to strengthen the institutional development of local government regulators, improve the local government’s achievements, reduce the local government’s regulatory costs, improve policies to support large supermarkets’ implementation of the PAFW, and reduce the cost of implementing the PAFW for large supermarkets.

China produces the largest amount of CO₂ emissions since 2007 and is the second largest economy in the world since 2010, and the Yangtze River Delta (YRD) area plays a crucial role in promoting low-carbon development in China. Analyzing its evolutionary characteristics of spatial and temporal patterns and its decoupling effect is of great importance for the purpose of low-carbon development. However, this analysis relies on the estimation of CO₂ emissions. Recently, neural network-based models are widely used for CO₂ emission estimation. To improve the performance of neural network models, the Aquila Optimizer (AO) algorithm is introduced to optimize the hyper-parameter values in the back-propagation (BP) neural network model in this research due to the appealing searching capability of AO over traditional algorithms. Such a model is referred to as the AO-BP model, and this paper uses the AO-BP model to estimate carbon emissions, compiles a city-level CO₂ emission inventory for the YRD region, and analyzes the spatial dependence, spatial correlation characteristics, and decoupling status of carbon emissions. The results show that the CO₂ emissions in the YRD region show a spatial distribution pattern of “low in the west, high in the east, and developing towards the west”. There exists a spatial dependence of carbon emissions in the cities from 2001 to 2022, except for the year 2000, and the local spatial autocorrelation test shows that high-high is concentrated in Shanghai and Suzhou, and low-low is mainly centered in Anqing, Chizhou, and Huangshan in southern Anhui. Furthermore, there exist significant regional differences in the correlation levels of CO₂ emissions between cities, with a trend of low in the west and high in the east in location, and a decreasing and then increasing trend in time. From 2000 to 2022, the decoupling of carbon emissions and economic growth shows a steadily improving trend.