Method, system, device and medium for optimizing commodity recommendation based on three-branch decision

Abstract

The application provides a three-branch decision-based commodity recommendation optimization method, system, device and medium, relates to the technical field of recommendation system, and the method comprises the following steps: acquiring commodity income data on a commodity recommendation platform, a user's risk parameter, and historical scores and predicted scores of the user on commodities, introducing a cost constraint based on three-branch decision, and dividing commodities into a candidate set and a filtering set for different users; through an utility function and a preference probability function, the comprehensive value of different commodities for different users is quantified, and under the premise of meeting a recommendation accuracy threshold and the cost constraint, a revenue optimization function is constructed and solved to obtain an optimized platform total revenue and a corresponding commodity recommendation list, and the platform revenue is maximized under the premise of ensuring recommendation accuracy. By introducing the cost constraint based on three-branch decision, the platform revenue and user experience are comprehensively considered, low-relevance recommendation is effectively avoided, recommendation accuracy and adaptability are improved, and the risk of user loss is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of recommendation system, in particular to the technical field of commodity recommendation optimization. BACKGROUND

[0002] The recommendation system not only helps users quickly find content that meets their personal interests and needs from a large amount of information and commodities, improving user experience and satisfaction, but also brings significant commercial value to the platform. The existing technology mainly focuses on improving the accuracy and personalization of the recommendation system in the design of the recommendation system, such as content-based recommendation, collaborative filtering, hybrid recommendation system, and matrix decomposition-based methods, but they do not consider the important factor of decision cost. Even when using multi-objective genetic algorithm or artificial bee colony algorithm for profit-aware recommendation system design, only profit and accuracy are optimized, while the cost and risk in the recommendation process are ignored. These methods tend to have a high rate of incorrect recommendations while maximizing profits, especially when the personalized needs of users are not fully considered, which may lead to increased recommendation costs and user loss. SUMMARY

[0003] The present application provides a commodity recommendation optimization method, system, device and medium based on three decisions to solve one or more technical problems existing in the prior art and at least provide a beneficial choice or create conditions.

[0004] In one aspect, the present application provides a commodity recommendation optimization method based on three decisions, including the following steps: obtaining commodity revenue data on a commodity recommendation platform, a user's risk parameter, and his historical and predicted ratings of commodities;

[0005] Based on the cost constraint condition based on three decisions and the predicted rating, the commodities are divided into a candidate set or a filtered set corresponding to the user;

[0006] For the commodities in the candidate set, the user's preference probability value for the commodities is calculated by a utility function and a preference probability function according to the user's risk parameter and his predicted rating of commodities, and the comprehensive value of the commodities is calculated based on the preference probability value and the commodity revenue data;

[0007] According to the comprehensive value of the commodities, a revenue optimization function is constructed by combining a recommendation accuracy constraint condition and the cost constraint condition, and the function is solved to obtain an optimized total revenue of the platform and a corresponding commodity recommendation list.

[0008] Further, the cost constraint condition satisfies the following formula:

[0009] ;

[0010] wherein, represents a predicted score of a user for a commodity ; represents a preset score threshold; represents a sufficiently large positive number; is a binary decision variable, if , it indicates recommending the commodity to the user , if , it indicates filtering the commodity for the user .

[0011] Further, the utility function satisfies the following formula:

[0012] ;

[0013] wherein, represents a predicted score of a user for a commodity ; represents the utility function; represents a utility value of a user for a commodity ; represents a risk parameter of a user , used for controlling the curve shape of the utility function; if , it indicates that the user is risk-averse, and the utility function is an upward convex curve; if , it indicates that the user is risk-neutral, and the utility function is linear; if , it indicates that the user is risk-seeking, and the utility function is a downward concave curve; represents a minimum historical score of a user for a commodity, represents a maximum historical score of a user for a commodity; represents a lower limit of a score of a commodity, represents an upper limit of a score of a commodity.

[0014] Further, the preference probability function satisfies the following formula:

[0015] ;

[0016] wherein, represents a predicted score of a user for a commodity ; represents a user for the commodity ; representing a user for the commodity , , representing a user corresponding candidate set; is a binary decision variable, if , it indicates recommending the commodity to the user , if , it indicates filtering the commodity for the user .

[0017] Further, the revenue optimization function satisfies the following formula:

[0018] ;

[0019] wherein, represents the revenue optimization function; represents the number of users on the commodity recommendation platform; represents the corresponding revenue of the commodity ; represents the preference probability value of the user for the commodity , , representing a user corresponding candidate set; is a binary decision variable, if , it indicates recommending the commodity to the user , if , it indicates filtering the commodity for the user , , representing the number of commodities in the commodity recommendation list corresponding to the user ;

[0020] The revenue optimization function satisfies the cost constraint condition and the recommendation accuracy constraint condition;

[0021] The recommendation accuracy constraint condition satisfies the following formula:

[0022] ;

[0023] wherein, represents a preset recommendation accuracy threshold.

[0024] Further, the solving of the revenue optimization function obtains an optimized platform total revenue and a corresponding commodity recommendation list thereof, comprising:

[0025] reconstructing the revenue optimization function into a Lagrange relaxation function;

[0026] solving the Lagrange relaxation function using a Lagrange sub-gradient algorithm based on a greedy strategy to obtain the optimized platform total revenue and the corresponding commodity recommendation list thereof;

[0027] The Lagrange relaxation function satisfies the following formula:

[0028]

[0029] wherein, represents the Lagrange relaxation function, represents a Lagrange multiplier, .

[0030] Further, for any Lagrange multiplier , the Lagrange relaxation function provides an upper bound for the target value of the revenue optimization function, i.e., satisfies ;

[0031] a tight upper bound for the target value of the revenue optimization function is obtained by solving a Lagrange dual problem function; the Lagrange dual problem function satisfies the following formula:

[0032]

[0033] wherein, represents the Lagrange dual problem function; the Lagrange multiplier is iteratively updated by a Lagrange sub-gradient algorithm until a preset convergence condition is satisfied.

[0034] In another aspect, the application provides a commodity recommendation optimization system based on three-way decision, comprising a data acquisition module, a three-way decision module, a preference probability module, and a revenue optimization module;

[0035] The data acquisition module is configured to acquire commodity revenue data on a commodity recommendation platform, a user's risk parameter, and a historical score and a predicted score of the user on a commodity;

[0036] The three-way decision module is configured to divide the commodity into a candidate set or a filtered set corresponding to the user in combination with a cost constraint condition based on three-way decision and the predicted score;

[0037] ​​The preference probability module is configured to calculate, for each item in the candidate set, a preference probability value of the item for the user according to the risk parameter of the user and the predicted score of the item for the user by using a utility function and a preference probability function, and calculate a comprehensive value of the item based on the preference probability value and the item revenue data.

[0038] The revenue optimization module is configured to construct a revenue optimization function according to the comprehensive value of the item, in combination with a recommendation accuracy constraint condition and the cost constraint condition, and solve the revenue optimization function to obtain an optimized total revenue of the platform and a corresponding item recommendation list.

[0039] In another aspect, the present application provides a three-way decision-based item recommendation optimization apparatus, comprising a processor and a memory; the memory is configured to store a program; when the program is executed by the processor, the processor implements the three-way decision-based item recommendation optimization method as described above.

[0040] In another aspect, the present application provides a computer medium storing a processor-executable program, which, when executed by a processor, is configured to implement the three-way decision-based item recommendation optimization method as described above.

[0041] The present application has the following beneficial effects: the present application provides a three-way decision-based item recommendation optimization method, obtains item revenue data on an item recommendation platform, a risk parameter of a user and historical scores and predicted scores of the user for items, and introduces a cost constraint based on three-way decision, divides items into a candidate set and a filter set for different users; quantifies comprehensive values of different items for different users by using a utility function and a preference probability function, and constructs a revenue optimization function and solves the function under the premise of meeting a recommendation accuracy threshold and a cost constraint to obtain an optimized total revenue of the platform and a corresponding item recommendation list, thereby ensuring maximization of platform revenue. By introducing a three-way decision-based cost constraint, the present application comprehensively considers platform revenue and user experience, effectively avoids low-relevance recommendation, improves recommendation accuracy and adaptability, and reduces user churn risk. The present application also provides corresponding apparatuses, systems and media, which have similar beneficial effects as the method, and thus will not be described here.

[0042] Other features and advantages of the present application will be set forth in the following description, and in part will become apparent to those skilled in the art from the description, or can be learned by practice of the present application. The objects and other advantages of the present application will be realized and attained by the structure particularly pointed out in the written description and claims hereof, together with the appended drawings. BRIEF DESCRIPTION OF DRAWINGS

[0043] The accompanying drawings are used to provide a further understanding of the technical solutions of the present application, constitute a part of the specification, and are used to explain the technical solutions of the present application together with the embodiments of the present application, and do not constitute a limitation on the technical solutions of the present application.

[0044] Figure 1 is a flowchart of the commodity recommendation optimization method based on three-branch decision provided by the present application;

[0045] Figure 2 is a schematic diagram of the utility function provided by the present application;

[0046] Figure 3 is a structural diagram of the commodity recommendation optimization system based on three-branch decision provided by the present application;

[0047] Figure 4 is a structural diagram of the commodity recommendation optimization device based on three-branch decision provided by the present application. DETAILED DESCRIPTION

[0048] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0049] The present application will be further described below with reference to the drawings and specific embodiments. The described embodiments should not be regarded as limiting the present application, and all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0050] In the following description, "some embodiments" are related to a subset of all possible embodiments, but it can be understood that "some embodiments" can be the same subset or different subsets of all possible embodiments, and can be combined with each other without conflict.

[0051] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs. The terms used herein are only for the purpose of describing the embodiments of the present application, and are not intended to limit the present application.

[0052] In the information overload era, a recommendation system provides users with possible interesting content by analyzing the historical behavior data of the users, which has become an indispensable part in many fields such as e-commerce, social media, etc. The combination of intelligent recommendation and business practice not only improves the user experience, but also brings considerable economic benefits to enterprises, and has become one of the research hotspots in the field of recommendation system. The ultimate goal of the recommendation system is to help users efficiently find valuable information or commodities, and at the same time, create more sales opportunities for enterprises.

[0053] Existing technologies in recommender system design primarily focus on improving the accuracy and personalization of recommendations, such as content-based recommendations, collaborative filtering, hybrid recommender systems, and matrix factorization-based methods. However, these methods generally neglect the crucial factor of decision-making costs. This means that when optimizing recommendation performance, they often fail to fully consider the potential losses and risks caused by erroneous recommendations, potentially leading to a high erroneous recommendation rate, impacting user experience, and increasing unnecessary operational costs.

[0054] The paper "Devising a profit-aware recommender system using multi-objective GA" proposes a profit-aware recommender system designed based on a multi-objective genetic algorithm. This system aims to simultaneously optimize both profit and accuracy. Experimental results show that this method outperforms traditional collaborative filtering algorithms in improving accuracy and increasing profit. However, while this method improves recommendation quality to some extent, its focus remains limited to profit and accuracy, failing to adequately consider other factors influencing recommendation performance, such as user risk preferences and personalized needs.

[0055] The paper "A multi-objective artificial bee colony approach for profit-aware recommender systems" employs a multi-objective artificial bee colony algorithm, aiming to simultaneously increase the probability of user preferences and platform profits in each iteration. By introducing novel intelligent operators, experimental results on a movie dataset show that this method outperforms collaborative filtering and multi-objective genetic algorithms in recommendation performance. However, this method also has limitations: it focuses too much on profit maximization while neglecting a deeper understanding of personalized user needs and consideration of decision-making costs.

[0056] While both studies attempted to optimize recommender systems from different perspectives, they share a common problem: a singular focus on accuracy and profit as the two basic objectives, without introducing other metrics to comprehensively evaluate and control recommendation quality. This singular goal orientation leads to erroneous recommendations in practical applications and makes it difficult to meet the personalized needs of different users, thus limiting further improvements in the overall performance and user experience of the recommender system.

[0057] To address the problems existing in related technologies, embodiments of this application provide a product recommendation optimization method, system, apparatus, and medium based on three-way decision-making. The aim is to maximize sales revenue while ensuring the accuracy of recommendation results by considering decision-making costs. This method not only focuses on improving the accuracy of recommendations but also emphasizes the importance of controlling costs during the recommendation process to generate a product recommendation list that meets both user needs and platform interests.

[0058] This application introduces a cost constraint based on three-way decision-making as a key constraint. For different users, products are divided into candidate sets and filter sets, effectively reducing the possibility of erroneous recommendations during the recommendation process. By employing utility functions and preference probability functions, the comprehensive value of different products to different users is quantified, effectively filtering out truly valuable recommendations, thereby reducing cost losses due to erroneous recommendations and further improving the overall efficiency of the recommendation process.

[0059] This application's embodiments, by constructing a revenue optimization function and designing a corresponding solution algorithm, enable the product recommendation platform to recommend products that better match users' interests and needs. Simultaneously, it can recommend products that generate higher revenue for the platform, reducing recommendation costs while improving user retention. Because the recommended content is more personalized and of higher quality, users can more easily find products that interest them. This not only increases user satisfaction but also promotes continued user engagement and loyalty, bringing long-term value growth to the platform.

[0060] Therefore, the product recommendation optimization method, system, apparatus, and medium based on three-way decision-making provided in this application have broad application prospects. They are not only applicable to various types of shopping platforms but can also be extended to multiple fields such as movie recommendations and social media. Whether in e-commerce environments or digital content consumption scenarios, they can provide effective solutions to help different platforms improve operational efficiency and service quality.

[0061] First, the product recommendation optimization method based on three-way decision-making provided in the embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0062] Reference Figure 1 The implementation process of the product recommendation optimization method based on three-way decision-making provided in this application embodiment includes, but is not limited to, the following steps. Step 101: Obtain product revenue data, user risk parameters, and their historical and predicted ratings for products from the product recommendation platform.

[0063] In step 101, key information from the product recommendation platform is collected, including product revenue data, user risk parameters, and their historical and predicted product ratings. Product revenue data reflects the economic benefits of selling different products and is one of the important indicators for measuring recommendation effectiveness. User risk parameters reflect users' attitudes towards recommendations, such as risk preference, risk neutrality, or risk aversion, which is crucial for personalized recommendations. Historical ratings show users' past preferences, while predicted ratings predict users' future preferences based on existing models. These data together provide the necessary input for subsequent steps, ensuring that the recommendation results both align with user interests and consider economic benefits.

[0064] Step 102: Combining the cost constraints and predicted scores based on the three-way decision-making process, the products are divided into candidate sets or filter sets corresponding to the users.

[0065] In step 102, by combining cost constraints based on three-way decision-making with predicted scores, products are categorized into candidate sets or filter sets for different users. Cost constraints help identify potentially incorrectly recommended products, preventing negative user experiences or platform losses due to inappropriate recommendations. This method effectively filters out products most likely to be accepted by users into the candidate set, while excluding products that do not meet user needs from the filter set, thereby improving the relevance and accuracy of recommendations.

[0066] Step 103: For the products in the candidate set, based on the user's risk parameters and their predicted rating of the products, the user's preference probability value for the products is calculated through the utility function and preference probability function. Based on the preference probability value and product revenue data, the comprehensive value of the products is calculated.

[0067] In step 103, for each product in the candidate set, the user's preference probability value for each product is calculated using a utility function and a preference probability function, based on the user's risk parameters and their predicted ratings for the products. This step considers not only the user's personal preferences but also their attitude towards risk, making the recommendations more personalized. Next, based on the calculated preference probability values ​​and product revenue data, the comprehensive value of the products is further calculated. This process comprehensively considers the economic value of the products and the user's level of interest in them, ensuring that the final recommendation list both meets user needs and maximizes platform revenue.

[0068] Step 104: Based on the comprehensive value of the products, combined with the recommendation accuracy constraints and cost constraints, construct a revenue optimization function, solve for it, and obtain the optimized total platform revenue and its corresponding product recommendation list.

[0069] In step 104, based on the comprehensive value of the products and considering the constraints of recommendation accuracy and cost, a revenue optimization function is constructed. This function is then solved to obtain the optimal total platform revenue and the corresponding product recommendation list. This step maximizes platform revenue while maintaining high recommendation accuracy by globally optimizing all candidate products. Furthermore, it considers potential costs during the recommendation process, striving to reduce unnecessary expenses. The resulting product recommendation list not only enhances user experience, increases user satisfaction and retention rates, but also effectively improves the platform's overall operational efficiency and profitability.

[0070] In some embodiments of this application, the cost constraint satisfies the following formula (1):

[0071] (1);

[0072] In formula (1), Indicates user For goods Predicted score; This indicates the preset scoring threshold; Represent a sufficiently large positive number; Given a binary decision variable, if This means to the user Recommended products ,like This indicates the user. Filtered products .

[0073] The main function of this formula is to introduce a cost control mechanism into the recommendation process. This is achieved by setting appropriate scoring thresholds. and using a sufficiently large positive number This effectively filters out products with ratings above a threshold, reducing the risk of incorrect recommendations. The preset rating threshold distinguishes between products a user might be interested in (high-rated products) and products they are unlikely to be interested in (low-rated products). By setting this threshold, the system can determine which products should be recommended to the user and which should not.

[0074] This formula uses the "Big-M Method" to transform the logical condition (whether to recommend a product) into a linear constraint. If... , ;like , .because Represent a sufficiently large positive number, regardless of The constraint holds true regardless of the threshold value, allowing filtering of products with low user ratings. In other words, it mandates that the predicted rating of recommended products must not be lower than the threshold, ensuring recommendation quality.

[0075] This mechanism helps optimize the performance of recommendation systems, improving recommendation accuracy, reducing the risk of user churn due to unsuitable product recommendations, and lowering platform operating costs to some extent by reducing unnecessary resource waste (e.g., display and promotion costs for low-interest products). Therefore, this formula is of great significance for building efficient, accurate, and cost-effective recommendation systems.

[0076] Suppose an e-commerce platform sets (User rating out of 5) For goods The predicted score is ,like and cost constraints Contradictory, therefore mandatory For users Filtered products Recommended.

[0077] In some embodiments of this application, the predicted ratings of products by users are typically estimated using various methods based on users' past behavior, preferences, and other relevant information. Common methods include collaborative filtering, which predicts ratings by analyzing similar users or products; content-based recommendation, which mainly matches similar products based on product features and users' historical preferences; matrix factorization techniques, which mainly learn the latent factor representations of users and products to predict ratings; deep learning methods, which mainly utilize neural networks to capture complex user-product relationships; hybrid recommendation systems, which combine the advantages of multiple methods; graph-based learning methods, which mainly enhance recommendation performance through relationships between nodes; and context-aware recommendation, which mainly considers the influence of different contextual factors. These methods each leverage their strengths to improve the accuracy and personalization level of the recommendation system.

[0078] In some embodiments of this application, the utility function satisfies the following formula (2):

[0079] (2);

[0080] In formula (2), Indicates user For goods The predicted score. Represents the utility function. Indicates user For goods The utility value indicates the user's stronger preference for the product. Indicates user The risk parameter is used to control the shape of the utility function curve. If... This indicates that the user For risk-averse individuals, their utility function exhibits an upward-convex curve. If... This indicates that the user For risk-neutral applications, the utility function is linear. If This indicates that the user For risk-seeking individuals, the utility function exhibits a concave curve. Indicates user Minimum historical rating for the product. Indicates user The highest historical rating for a product. This indicates the lower limit of the product's rating. This indicates the maximum possible rating for a product.

[0081] The utility function provided in this application, through segmented design and dynamic adjustment of risk parameters, effectively improves the personalization and accuracy of the recommendation system. Specifically, the utility function is divided into three intervals based on the user's predicted rating.

[0082] When the predicted rating is lower than the user's minimum historical rating for the product And not lower than the lower limit of the score Time (i.e.) A utility value of 0 indicates that the user has almost no interest in products within this rating range, thus filtering out low-scoring products and avoiding invalid recommendations.

[0083] When the rating falls within the user's historical rating range (i.e.) The utility value is calculated using a piecewise function whose form depends on the user's risk parameters. The utility value is dynamically adjusted according to the user's risk preference, accurately matching personalized needs.

[0084] When the rating is higher than the user's highest historical rating for the product And not exceeding the rating limit Time (i.e.) A utility value of 1 means that users have the highest preference for these highly rated products, so the platform is forced to recommend high-rated products to ensure its revenue.

[0085] In addition, risk parameters Used to adjust the shape of the utility function, reflecting the user's attitude towards uncertainty. If If the user is considered risk-averse, the utility function will exhibit an upward-convex curve, indicating that the increase in user satisfaction from improved ratings gradually diminishes. If If the user is risk-neutral, their utility function exhibits linear growth; that is, for every point increase in rating, user satisfaction increases proportionally. If If the user is risk-seeking, then the utility function will show a concave curve, indicating that the user's interest in highly rated products increases rapidly as the rating increases.

[0086] This utility function aims to capture more precisely the changes in users' interest in products with different rating levels, while also taking into account individual differences in risk attitudes among users. In this way, the recommendation system can generate recommendation lists that better match individual user preferences, considering not only predicted product ratings but also user risk preference characteristics, thereby improving the accuracy and personalization of recommendations. Furthermore, this strategy helps optimize platform revenue because it can adjust recommendation strategies based on different users' risk attitudes, ensuring that recommendations both meet user needs and maximize the platform's economic benefits.

[0087] In some embodiments of this application, reference is made to Figure 2 , Figure 2 This is a schematic diagram of the utility function provided in the embodiments of this application. Figure 2 In the middle, the horizontal axis corresponds to the user. For goods Predicted score The vertical axis corresponds to the predicted score. Corresponding utility value ;curve Risk parameters The curve corresponding to the utility function at time , A convex curve indicates that the increase in user satisfaction with improved ratings gradually decreases; at this point, the user is considered risk-averse. Risk parameters The curve corresponding to the utility function at time , It exhibits linear growth, meaning that for every point increase in rating, user satisfaction increases proportionally; the curve... Risk parameters The curve corresponding to the utility function at time , The concave curve indicates that users' interest in highly rated products increases rapidly as the rating increases, suggesting that these users are risk-seeking.

[0088] When users For goods Predicted score The rating is lower than the minimum historical rating given by users for the product. And not lower than the lower limit of the score Time (i.e.) The utility value is 0 when the rating is higher than the user's highest historical rating for the product. And not exceeding the rating limit Time (i.e.) ), with a utility value of 1.

[0089] When users For goods Predicted score Within the range of the user's historical ratings (i.e.) ), based on risk parameters To adjust the shape of the utility function. For the same predicted score ,curve The corresponding utility value is ,curve The corresponding utility value is ,curve The corresponding utility value is It can be seen that... That is, for the same predicted score Risk-averse users have the highest utility value, while risk-seeking users have the lowest.

[0090] By leveraging differences in utility values, the system dynamically adapts to users' risk attitudes. For example, risk-averse users, even when faced with the same rated product, have a higher utility value than other user types, resulting in more conservative recommendations. For high-risk users (such as those with a preference for risky products), high-utility products (such as highly rated luxury goods) are prioritized to increase average order value. For low-risk users (such as those with aversion to risk), stable product recommendations reduce return rates. If the predicted rating is within the historical range but close to the lower limit, risk-averse users still have a relatively high utility value and may be recommended products; while risk-seeking users have a low utility value and may be filtered out to avoid exposure to low-quality products.

[0091] In summary, by adjusting risk parameters to optimize the form of the utility function, this method achieves the following core values: First, precise preference mapping enables the same predicted score to generate differentiated utility values ​​based on users' different risk attitudes, thereby significantly improving the personalization level of recommendations. Second, dynamic strategy adaptation can identify and satisfy the needs of risk-averse users for stable goods and the interest of risk-seeking users in high-potential goods, ensuring that the recommendation strategy matches users' psychological expectations. Furthermore, risk controllability, by setting utility value thresholds to filter out inefficient goods, not only helps reduce platform operational risks but also reduces the probability of user churn due to unsatisfactory recommendations. In conclusion, this design represents a key technological breakthrough for recommendation systems in achieving personalized services, optimizing revenue, and strengthening risk management.

[0092] In some embodiments of this application, the preference probability function satisfies the following formula (3):

[0093] (3);

[0094] In formula (3), Indicates user For goods The predicted score. Indicates user For goods The utility value. Indicates user For goods The preference probability value, , Indicates user The corresponding candidate set. Given a binary decision variable, if This means to the user Recommended products ,like This indicates the user. Filtered products .

[0095] This preference probability function accurately calculates the probability of a user's preference for each product by combining the user's predicted rating, utility value, and recommendation decision, thus achieving highly personalized recommendations. It not only improves the accuracy and effectiveness of recommendations but also ensures that recommended products better reflect the user's actual needs and interests, thereby increasing user satisfaction and retention rates. Simultaneously, this method allows platforms to balance recommendation quality and commercial benefits while optimizing user experience; for example, prioritizing recommendations that both match user preferences and generate higher profits, promoting sales growth and enhancing the platform's market competitiveness. In summary, this formula is of great significance for improving the personalization level of recommendation systems, optimizing user experience, and supporting business goals.

[0096] In some embodiments of this application, the profit optimization function satisfies the following formula (4):

[0097] (4);

[0098] In formula (4), This represents the profit optimization function, which aims to maximize the profit of the entire recommendation system. This indicates the number of users on the product recommendation platform; Indicates goods The corresponding revenue, that is, the economic benefits that can be obtained from selling the product; Indicates user For goods The preference probability value reflects the degree of interest of users in a particular product; , Indicates user The corresponding candidate set, that is, the set of all products that may be recommended to the user; Given a binary decision variable, if This means to the user Recommended products ,like This indicates the user. Filtered products , , Indicates user The number of products in the corresponding product recommendation list.

[0099] The revenue optimization function satisfies both cost and recommendation accuracy constraints. The recommendation accuracy constraint ensures the quality of the recommendations and satisfies the following formula (5):

[0100] (5);

[0101] In formula (5), This represents the preset recommendation accuracy threshold, which is used to measure the minimum standard that the average score of the recommendation results must reach.

[0102] The core of the revenue optimization function lies in maximizing overall revenue by maximizing the weighted revenue of each user's preference probability for items in their candidate set. Specifically: by considering the probability of user preference for different items, the system can make personalized recommendations based on user interests and needs, thereby increasing the likelihood of user acceptance and satisfaction; by combining the revenue of items with the user's preference probability, the system ensures that while satisfying user preferences, it selects items that bring higher economic returns for recommendation, thus improving the platform's overall revenue. Furthermore, utilizing binary decision variables, the system can make optimal choices among numerous candidate items, avoiding the recommendation of inefficient or irrelevant items and improving the effectiveness and relevance of recommendations.

[0103] The recommendation accuracy constraint ensures that the average predicted rating of recommended products is not lower than a preset recommendation accuracy threshold, which is crucial for guaranteeing the quality and effectiveness of the recommendation system. First, by setting a minimum recommendation accuracy standard, it ensures that most recommended products meet user expectations, thereby increasing user trust and satisfaction, and promoting long-term retention. Second, high-quality recommendations help attract new users and enhance the loyalty of existing users, helping the platform build a positive brand image and improve market competitiveness. Furthermore, although the system's primary goal is to maximize economic benefits, the introduction of recommendation accuracy constraints allows for a balance between increasing revenue and maintaining a focus on user experience, achieving a equilibrium between economic benefits and user experience.

[0104] Since the profit optimization function needs to satisfy cost constraints and recommendation accuracy constraints, it is a nonlinear 0-1 integer programming model. and When the value of is large enough, it evolves into a large-scale nonlinear 0-1 integer programming model, which poses a significant challenge to solving because it is extremely difficult to solve directly using commercial solvers or existing algorithms.

[0105] In some embodiments of this application, solving the revenue optimization function to obtain the optimized total platform revenue and its corresponding product recommendation list includes: reconstructing the revenue optimization function into a Lagrange relaxation function, and using a Lagrange subgradient algorithm based on a greedy strategy to solve the Lagrange relaxation function to obtain the optimized total platform revenue and its corresponding product recommendation list.

[0106] First, the original profit optimization function is transformed into a Lagrange relaxation form. This process involves introducing Lagrange multipliers to handle constraints, thus converting the original problem into an unconstrained optimization problem. This not only simplifies the solution process but also allows for the use of more efficient algorithms to find the optimal solution. Specifically, the Lagrange relaxation method allows complex constraints such as cost and recommendation accuracy to be incorporated into the objective function, balancing the impact of these constraints by adjusting the Lagrange multipliers.

[0107] Next, a Lagrange subgradient algorithm based on a greedy strategy is used to solve for the reconstructed Lagrange relaxation function. This algorithm uses a greedy strategy to gradually approach the optimal solution, selecting the best or near-optimal solution in each iteration. This method is particularly suitable for large-scale datasets and complex optimization problems because it can effectively reduce computation time and resource consumption. Furthermore, the Lagrange subgradient algorithm can dynamically adjust the Lagrange multipliers, ensuring that a globally optimal or near-optimal solution is found while satisfying all constraints.

[0108] Finally, by solving the Lagrange relaxation function, the optimized total platform revenue and the corresponding product recommendation list can be obtained. The result of this step directly determines which products will be recommended to users, thus directly affecting user experience and platform revenue. Through the optimization process described above, the system not only maximizes overall revenue but also ensures that the quality of recommendations meets preset standards, such as recommendation accuracy thresholds. This not only improves user satisfaction and retention rates but also brings higher economic benefits and market competitiveness to the platform. The final product recommendation list is the result of precise calculation and optimization, aiming to achieve the best balance between user experience and commercial interests.

[0109] In some embodiments of this application, the Lagrange relaxation function satisfies the following formula (6):

[0110] (6);

[0111] In formula (6), Let represent the Lagrange relaxation function, and let represent the optimization objective after relaxing the recommendation accuracy constraint; Represents the Lagrange multipliers. The numerator is used to weigh the degree to which profit maximization is satisfied against the constraint of recommendation accuracy; the numerator is used to combine the product's profit. Recommendation decision variables and utility value , represents the revenue contribution of the high-utility goods; the denominator term is used to normalize the utility values ​​within the candidate set to ensure the reasonableness of the preference probability; the slack term is used to penalize the degree of violation of the recommendation accuracy constraint.

[0112] In some embodiments of this application, for any Lagrange multiplier The Lagrange relaxation function provides an upper bound on the objective value of the profit optimization function, i.e., it satisfies... By relaxing complex constraints on the profit optimization function (such as recommendation accuracy constraints), an upper bound is provided for the optimal value of the profit optimization function, which helps to evaluate the quality of the solution. Moreover, through constraint relaxation, constraints that are difficult to handle directly (such as nonlinear or integer constraints) are transformed into penalty terms in the objective function, simplifying the solution process.

[0113] By solving the Lagrange dual problem function, the tight upper bound of the objective value of the payoff optimization function is obtained. The Lagrange dual problem function satisfies the following formula (7):

[0114] (7);

[0115] In formula (7), Let represent the Lagrange dual problem function. This is achieved by minimizing all possible functions. Find the closest The upper bound (i.e., the tightest upper bound) of the optimal value is used to narrow the duality gap between the profit optimization function and the Lagrange relaxation function. This is under the condition that strong duality holds (such as in convex optimization problems). equal The optimal value is obtained; otherwise, an approximate solution is provided. Finally, the Lagrange multipliers are iteratively updated using the Lagrange subgradient algorithm until the preset convergence condition is met.

[0116] In summary, the Lagrange relaxation method simplifies the original optimization problem and reduces the difficulty of solving it by introducing Lagrange multipliers to integrate complex constraints into the objective function. This method not only provides an upper bound on the optimal value of the original problem, ensuring the reliability and theoretical feasibility of the solution, but also balances the relationship between maximizing revenue and satisfying specific constraints (such as recommendation accuracy) by adjusting the influence of different constraints, thus effectively improving system performance and recommendation quality. Furthermore, iterative solving using the Lagrange subgradient algorithm improves the solution efficiency and allows for flexible adjustments based on specific problem characteristics, making this method valuable and flexible in practical applications such as resource allocation and product recommendation. In conclusion, this method ensures recommendation accuracy while dynamically adjusting to maximize revenue, thereby optimizing user experience and platform economic benefits.

[0117] In summary, the product recommendation optimization method based on three-way decision-making provided in this application has the following technical effects.

[0118] This application's embodiments model personalized user needs using dynamic utility functions and risk preference parameters. Combined with three decision rules, it accurately divides the candidate set, filter set, and delayed decision set, effectively improving the accuracy and adaptability of the recommendation system. The utility function adjusts the rating sensitivity based on the user's risk attitude (aversion, neutrality, preference), ensuring that high-risk users prefer stable products, while low-risk users explore high-potential products. The delayed decision mechanism optimizes the exposure of boundary products through dynamic thresholds. Simultaneously, the revenue optimization model integrates product revenue and preference probability, balancing recommendation quality and business objectives under the drive of the Lagrange relaxation algorithm to maximize the platform's total revenue. For example, high-return products may still be recommended even if their ratings are close to the threshold, while low-quality products are strictly filtered, ensuring both user experience and improved conversion rates.

[0119] Furthermore, by combining the cost constraints of the three-way decision-making process with the Lagrange subgradient algorithm, the risk of erroneous recommendations is significantly reduced, thus decreasing user churn. Its core advantage lies in efficiently handling large-scale, complex constraint problems—the relaxed optimization model adapts to tens of millions of user and product data points, while subgradient iteration ensures real-time response to demands and improves average computational efficiency. The Lagrange subgradient algorithm only requires first-order gradient information to converge quickly, making it suitable for handling optimization problems in large-scale datasets and high-dimensional spaces, effectively improving computational efficiency. This technical solution not only improves user satisfaction and retention rates but also brings higher commercial value and social benefits to product recommendation platforms. Through a close integration of theory and practice, this application provides a new approach and tool for solving complex and ever-changing product recommendation problems, offering strong support for achieving precision marketing.

[0120] Secondly, refer to Figure 3This application provides a product recommendation optimization system based on three-way decision-making, including a data acquisition module, a three-way decision-making module, a preference probability module, and a revenue optimization module.

[0121] The data acquisition module is used to acquire product revenue data, user risk parameters, and their historical and predicted ratings for products from the product recommendation platform.

[0122] The three-way decision module combines cost constraints and predicted scores based on three-way decision-making to divide products into candidate sets or filter sets corresponding to users.

[0123] The preference probability module is used to calculate the user's preference probability value for a product in the candidate set based on the user's risk parameters and their predicted rating of the product, using a utility function and a preference probability function. Based on the preference probability value and product revenue data, the module calculates the comprehensive value of the product.

[0124] The revenue optimization module is used to construct a revenue optimization function based on the comprehensive value of the products, combined with the constraints of recommendation accuracy and cost, and solve the function to obtain the optimized total platform revenue and its corresponding product recommendation list.

[0125] Furthermore, refer to Figure 4 This application provides a product recommendation optimization apparatus based on three-way decision-making, including a processor and a memory. The memory stores a program. When the program is executed by the processor, the processor implements the aforementioned product recommendation optimization method based on three-way decision-making.

[0126] Furthermore, embodiments of this application provide a computer medium storing a processor-executable program, which, when executed by a processor, is used to implement the aforementioned product recommendation optimization method based on three-way decision-making.

[0127] Similarly, the content of the above method embodiments is applicable to system embodiments, device embodiments, and medium embodiments. The specific functions implemented by system embodiments, device embodiments, and medium embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0128] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this application are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0129] Furthermore, although this application is described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding this application. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of ordinary skill of an engineer. Therefore, those skilled in the art can implement the application set forth in the claims using ordinary skill. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of this application, which is determined by the full scope of the appended claims and their equivalents.

[0130] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several programs to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0131] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequential list of executable programs for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, a program execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can retrieve and execute a program from or in conjunction with such a program execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can mean any means that can contain, store, communicate, propagate, or transmit a program for use by or in conjunction with a program execution system, apparatus, or device.

[0132] More specific examples (a non-exhaustive list) of computer-readable media include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which programs can be printed, because programs can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpreting, or, if necessary, processing in a suitable manner, and then stored in computer memory.

[0133] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable program execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0134] In the foregoing description of this specification, the reference to terms such as "one embodiment / implementation," "another embodiment / implementation," or "certain embodiments / implementations," etc., indicates that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in an embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0135] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0136] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of the present invention.

Claims

1. A product recommendation optimization method based on three-way decision-making, characterized in that, The steps include: obtaining product revenue data, user risk parameters, and their historical and predicted ratings for products from the product recommendation platform; Combining the cost constraints based on three-way decision-making with the predicted score, the products are divided into a candidate set or a filter set corresponding to the user; The cost constraint satisfies the following formula: ； in, Indicates user For goods Predicted score; This indicates the preset scoring threshold; Represent a sufficiently large positive number; Given a binary decision variable, if This means to the user Recommended products ,like This indicates the user. Filtered products ; For each item in the candidate set, based on the user's risk parameters and their predicted rating of the item, the user's preference probability value for the item is calculated using a utility function and a preference probability function. Based on the preference probability value and the item's revenue data, the comprehensive value of the item is calculated. The utility function satisfies the following formula: ； in, Indicates user For goods Predicted score; Represents the utility function; Indicates user For goods The utility value; Indicates user The risk parameter is used to control the curve shape of the utility function; if This indicates that the user For risk-averse individuals, the utility function exhibits an upward-convex curve; if This indicates that the user For risk-neutral applications, the utility function is linear; if This indicates that the user For risk-seeking individuals, the utility function exhibits a concave curve. Indicates user Minimum historical rating for the product. Indicates user Maximum historical rating for the product; This indicates the lower limit of the product's rating. Indicates the maximum possible rating for a product; Based on the comprehensive value of the products, combined with the recommendation accuracy constraint and the cost constraint, a revenue optimization function is constructed and solved to obtain the optimized total platform revenue and its corresponding product recommendation list. The profit optimization function satisfies the following formula: ； in, Denotes the profit optimization function; This indicates the number of users on the product recommendation platform; Indicates goods The corresponding benefits; Indicates user For goods The preference probability value, , Indicates user The corresponding candidate set; Given a binary decision variable, if This means to the user Recommended products ,like This indicates the user. Filtered products , , Indicates user The number of products in the corresponding product recommendation list; The revenue optimization function satisfies the cost constraint and the recommendation accuracy constraint. The recommendation accuracy constraint satisfies the following formula: ； in, This indicates the preset recommendation accuracy threshold.

2. The product recommendation optimization method based on three-way decision-making according to claim 1, characterized in that, The preference probability function satisfies the following formula: ； in, Indicates user For goods Predicted score; Indicates user For goods The utility value; Indicates user For goods The preference probability value, , Indicates user The corresponding candidate set; Given a binary decision variable, if This means to the user Recommended products ,like This indicates the user. Filtered products .

3. The product recommendation optimization method based on three-way decision-making according to claim 1, characterized in that, Solving the revenue optimization function yields the optimized total platform revenue and its corresponding product recommendation list, including: The profit optimization function is reconstructed into a Lagrange relaxation function; The Lagrange subgradient algorithm based on a greedy strategy is used to solve the Lagrange relaxation function to obtain the optimized total platform revenue and its corresponding product recommendation list. The Lagrange relaxation function satisfies the following formula: ； in, Denotes the Lagrange relaxation function, Represents the Lagrange multipliers. .

4. The product recommendation optimization method based on three-way decision-making according to claim 3, characterized in that, For any of the Lagrange multipliers The Lagrange relaxation function provides an upper bound for the objective value of the profit optimization function, i.e., satisfies the following: By solving the Lagrange dual problem function, the tight upper bound of the objective value of the profit optimization function is obtained; the Lagrange dual problem function satisfies the following formula: ； in, Let represent the Lagrange dual problem function; the Lagrange multipliers are iteratively updated using the Lagrange subgradient algorithm until the preset convergence condition is met.

5. A product recommendation optimization system based on three-way decision-making, characterized in that, It includes a data acquisition module, a three-way decision-making module, a preference probability module, and a profit optimization module; The data acquisition module is used to acquire product revenue data, user risk parameters, and their historical and predicted ratings for products on the product recommendation platform. The three-way decision module is used to combine the cost constraints based on the three-way decision and the predicted score to divide the product into a candidate set or a filter set corresponding to the user. The cost constraint satisfies the following formula: ； in, Indicates user For goods Predicted score; This indicates the preset scoring threshold; Represent a sufficiently large positive number; Given a binary decision variable, if This means to the user Recommended products ,like This indicates the user. Filtered products ; The preference probability module is used to calculate the user's preference probability value for the product in the candidate set based on the user's risk parameters and the user's predicted rating of the product, using a utility function and a preference probability function, and to calculate the comprehensive value of the product based on the preference probability value and the product's revenue data. The utility function satisfies the following formula: ； in, Indicates user For goods Predicted score; Represents the utility function; Indicates user For goods The utility value; Indicates user The risk parameter is used to control the curve shape of the utility function; if This indicates that the user For risk-averse individuals, the utility function exhibits an upward-convex curve; if This indicates that the user For risk-neutral applications, the utility function is linear; if This indicates that the user For risk-seeking individuals, the utility function exhibits a concave curve. Indicates user Minimum historical rating for the product. Indicates user Maximum historical rating for the product; This indicates the lower limit of the product's rating. Indicates the maximum possible rating for a product; The revenue optimization module is used to construct a revenue optimization function based on the comprehensive value of the product, combined with the recommendation accuracy constraint and the cost constraint, and solve it to obtain the optimized total platform revenue and its corresponding product recommendation list. The profit optimization function satisfies the following formula: ； in, Denotes the profit optimization function; This indicates the number of users on the product recommendation platform; Indicates goods The corresponding benefits; Indicates user For goods The preference probability value, , Indicates user The corresponding candidate set; Given a binary decision variable, if This means to the user Recommended products ,like This indicates the user. Filtered products , , Indicates user The number of products in the corresponding product recommendation list; The revenue optimization function satisfies the cost constraint and the recommendation accuracy constraint. The recommendation accuracy constraint satisfies the following formula: ； in, This indicates the preset recommendation accuracy threshold.

6. A product recommendation optimization device based on three-way decision-making, characterized in that, include: Processor and memory; The memory is used to store a program; when the program is executed by the processor, the processor implements the product recommendation optimization method based on three-way decision-making as described in any one of claims 1 to 4.

7. A computer medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to implement the product recommendation optimization method based on three-way decision-making as described in any one of claims 1 to 4.

Images