## 1 Introduction
Its objective is to open the electricity supply business to social capital and empower customers' choice, thereby fostering a market structure of multiple buyers and sellers [2]. Over 6000 electricity retailers have applied for establishment in China, driving the thriving development of the country's electricity sale market [3]. Reference [9] introduced China's first personalized customization service platform, offering tailored packages to customers. The Kunming Electricity Trading Center, inspired by online e-commerce, launched the \"Laitao Electricity Platform\". However, considering the current landscape and experiences from domestic and international electricity market developments, compared to large customers directly engaging in the wholesale electricity market, small-to-medium industrial, commercial, and residential customers with independent choice rights generally prefer purchasing electricity through retailers. To secure market share and sustained profitability, electricity retailers must offer tailored sale packages to electricity consumers. Given the vast customer base in the electricity market, effectively recommending suitable electricity sale packages has emerged as a pressing challenge for electricity retailers. Existing electricity sale package recommendation methods can be broadly categorized into direct and indirect methods. Direct recommendation methods typically rely on straightforward weighted average calculations and are predominantly utilized on online recommendation platforms. These platforms, such as Select [6], Check24 [10], Power to Choose [11], Energy Made Easy [12], Entega [13], and Eprimo [14], recommend electricity sale packages with the lowest cost to customers based on their electricity consumption patterns. For instance, in Reference [15], a hierarchical clustering method for customers was proposed, utilizing differential feature extraction. Customers were clustered hierarchically according to their energy consumption levels and the variability of their electricity consumption behaviors, enabling targeted package recommendations to different customer segments. Additionally, a personalized electricity bill sale scheme recommendation system was introduced in Reference [16], leveraging customers' electricity bill consumption characteristics, evaluation information, and preferences, along with machine learning techniques for recommendations. While direct recommendation methods are straightforward and easy to implement, they have limitations. Specifically, they primarily focus on minimizing electricity bill costs, neglecting the diverse behavioral characteristics, preferences, and evaluation attributes of customers, such as value-added services and the proportion of renewable energy. On the other hand, indirect electricity sale package recommendation methods predominantly adopt a collaborative filtering (CF) framework, consisting of \"customer feature extraction--similar customer identification--package score prediction--electricity sale package recommendation\". For instance, in Reference [17], collaborative filtering and utility recommendation algorithms were employed, utilizing the electricity customer similarity matrix and the comprehensive utility of electricity price packages. Addressing scalability and high-dimensional data sparsity in the big data market, Reference [18] proposed a recommendation mode based on bidirectional clustering and the Spark framework. Furthermore, Reference [19] analyzed the influence of factors like pricing methods, time-of-use prices, average prices, and the proportion of green electricity on package selection, introducing a recommendation method based on implicit package scores and customer portraits. Other studies have refined the collaborative filtering approach. In Reference [20], a customer feature subset screening algorithm was designed using weighted increasing item coverage, and the collaborative filtering algorithm was applied to predict scores for electricity sale packages within the selected feature subset.