A clustering method, system and device based on double-layer optimization

Abstract

The application discloses a clustering method, system and device based on double-layer optimization, and belongs to the technical field of information processing. The method comprises the following steps: obtaining product quality data, consumer category data and product promotion cost data in a database; obtaining probability data of consumers of various categories selecting various products according to the obtained data and based on position decision variables; constructing an upper-layer optimization model and a lower-layer optimization model to form a double-layer optimization model, obtaining a balanced strategy set through the double-layer optimization model, and linearizing the double-layer optimization model to obtain an optimal strategy set after solving. Compared with the prior art, the application has the advantages that, by comprehensively considering the behaviors of merchants, using a game theory method and a mathematical optimization technique, the accuracy of ranking data and results is significantly improved, and meanwhile, the efficiency of the ranking algorithm is greatly improved through algorithm optimization, and the ability of responding to market changes quickly is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of information processing, and more particularly, to a clustering method, system and device based on double-layer optimization. BACKGROUND

[0002] The rapid development of mobile Internet is due to the popularity of smart phones, tablet computers and other mobile devices, as well as the widespread application of high-speed network technology. These technologies enable people to access the Internet through mobile devices at any time and anywhere, and conduct information queries, social entertainment, online shopping and other activities. This convenience greatly promotes the online process of people's daily life. With the vigorous development of mobile Internet, people's daily life gradually shifts from offline to online, which greatly facilitates people's daily life, but at the same time brings obstacles to online consumption such as network virtuality and product diversity. Network virtuality is one of the main obstacles to online consumption. Unlike offline shopping, online shopping cannot allow consumers to directly touch and try the goods, and online shopping relies on product keyword search and virtual information such as pictures, text and videos to understand the goods. This information asymmetry easily leads consumers to have doubts about the quality and performance of the goods, thereby affecting the purchase decision. In addition, some merchants may also take advantage of the virtuality of the network to make false propaganda, exaggerate, and other behaviors, further exacerbating the consumers' distrust. Product diversity is an advantage of online shopping, but it is also an obstacle. Online platforms gather a large amount of product information, and consumers often feel overwhelmed and have no idea where to start when choosing. In addition, due to the variety of goods and uneven quality, consumers need to spend more time and effort to screen and compare goods. This not only increases the shopping cost of consumers, but also may cause problems such as returns and exchanges due to improper selection.

[0003] In the context of online shopping with a wide variety of products, platforms often rank and paginate related products to improve user experience and interface friendliness, helping consumers quickly filter out high-quality and popular products and improve shopping efficiency. Ranking is usually based on multiple factors such as sales, review rate, click rate, conversion rate, product weight (which may include store weight, product weight, brand weight, etc.), user behavior data (such as browsing time, collection amount, and add-to-cart amount), etc. The platform will calculate the comprehensive score of each product based on these indicators through complex algorithms and rank them accordingly. Consumers can view more products by paging, but usually only focus on the first few pages because products ranked higher are more likely to attract attention. This display method allows consumers to quickly find products that may interest them, but it also leads to some unfair competition among merchants. For example, merchants artificially inflate product sales and review rates through fake transactions, fake sales, and fake reviews. The practice of brushing sales seriously disrupts market order, harms consumers' interests, and affects the fairness and credibility of the platform. For example, merchants may offer cash or coupons to induce consumers to leave positive reviews. This practice undermines the fairness of the review system, making reviews less valuable and misleading other consumers' purchasing decisions. Therefore, to maintain market order and consumer rights, platforms usually take measures to address unfair competition by unscrupulous merchants.

[0004] The default ranking method on the current domestic mainstream platform generally considers multiple factors such as sales, price, and review count. However, this mechanism also faces some challenges and problems, particularly the impact of fake information and low-quality products on the ranking system, and the decline in ranking of high-quality products due to insufficient advertising investment. Despite the efforts of platforms in ranking mechanisms, it is still difficult to completely identify all fake information at this stage. Some low-quality product merchants may use fake information to improve their ranking and attract more consumer attention and purchases, thereby generating more profits; while high-quality products may decline in ranking due to low advertising investment by merchants or lack of sufficient exposure opportunities, leading to a decline in sales and profits, and falling into the "bad products expel good products" situation, which not only harms consumers' interests but also undermines the fair competition environment of the e-commerce market. Therefore, platforms need to strategically design their handling of product data to balance the interests of multiple parties, achieve a balance between consumer utility, merchant profits, and platform revenue, and build a healthier and sustainable e-commerce ecosystem.

[0005] In the related art, as provided in Chinese patent document CN114092172A, an e-commerce platform commodity sorting method, device, equipment and storage medium are provided, including a time estimation module for calculating estimated browsing time according to the average daily use time of the user; a browsing page estimation module for obtaining an estimated browsing page according to the estimated browsing time; and a heat ranking module for ranking commodities according to the sales and profits of commodities in the e-commerce platform. Although this scheme realizes a certain degree of personalized commodity sorting through the time estimation module, the browsing page estimation module and the heat ranking module, it has defects in the accuracy of ranking data and results and the efficiency of the ranking algorithm, especially it fails to effectively solve the influence of the unfair evaluation system caused by the business advertisement investment and false information when processing product data.

[0006] As can be seen from the above, the related art does not provide an effective solution to the problem of how to solve the influence of the unfair evaluation system caused by the business advertisement investment and false information when processing product data. SUMMARY

[0007] 1. Technical problem to be solved

[0008] In view of the problem of how to reduce the influence of false information on the data processing process in the prior art, the present application provides a clustering method, system and device based on double-layer optimization, which can build a double-layer optimization model, and then obtain a clustering method for product data based on double-layer optimization by solving examples, so as to obtain a globally optimal ranking strategy.

[0009] 2. Technical solution

[0010] The object of the present application is achieved by the following technical solution.

[0011] The content part of the present application is used to introduce the concepts in a simple form, which will be described in detail in the specific embodiment part. The content part of the present application is not intended to identify the key features or essential features of the claimed technical solution, nor is it intended to limit the scope of the claimed technical solution.

[0012] Some embodiments of the present application provide a clustering method, system and device based on double-layer optimization to solve the technical problems mentioned in the background part.

[0013] As a first aspect of this application, some embodiments of this application provide a clustering method based on bi-level optimization, including the following steps: obtaining product quality data, consumer category data, and product promotion cost data from a database; obtaining probability data of each category of consumers choosing each product based on the obtained data and location decision variables; constructing a bi-level optimization model by building an upper-level optimization model and a lower-level optimization model; obtaining a set of equilibrium strategies through the bi-level optimization model; and obtaining the optimal strategy set after solving by linearizing the bi-level optimization model.

[0014] Furthermore, after obtaining the product keywords, the database is traversed to output n product information items and their corresponding n display location information items, where n is a natural number; the location decision variable X ijl The set X to which it belongs is represented as:

[0015] X = {X ijl |i,j∈[n]}∈{0,1} n×n ;

[0016] Where i represents the product number, which is a natural number; j represents the display position number, which is a natural number; and l represents the merchant type number, which is a natural number.

[0017] Furthermore, when the display position number of product with sequence number i is j, the position decision variable X ijl =1; When the display position number of product with sequence number i is not equal to j, the position decision variable X = 1; ijl =0.

[0018] Furthermore, when considering the effect of location, the initial utility u ilα lnθ occurs j The offset; considering the position effect, the initial utility is expressed as: u ilα +lnθ j ;

[0019] Among them, u ilα Let θ represent the initial utility of a consumer of type α for product number i. j Indicates the visibility of the display position with index j; lnθ j Represents the base θ j The natural logarithm;

[0020] Initial utility in the product selection phase when considering the impact of advertising investment Represented as:

[0021]

[0022] Where, r il This represents the product rating for serial number i, s ilrepresents the sales volume of product i, n il represents the number of reviews of product i, L represents the total number of merchant types; ∈ i represents the random utility of the consumer affected by the environment in the product selection stage, which is subject to a normal distribution with a mean of 0 and a variance of ∈ 2 represents the product selection stage, cpc represents the CPC unit price set by the platform, P cpa represents the CPA unit price set by the platform, represents the number of times of CPC investment of the l-type merchant to product i, represents the number of times of CPA investment of the l-type merchant to product i.

[0023] Further, the evaluation utility of product i in the utility evaluation stage is represented as:

[0024]

[0025] where δ i is the random utility of the consumer affected by the environment in the utility evaluation stage, which is subject to a normal distribution with a mean of 0 and a variance of δ 2 ; f il represents the number of fake reviews invested, represents the probability that the α-type consumer identifies the fake positive reviews of the l-type merchant to product i;

[0026] When evaluating the utility of all products, the expected utility E ijlα of the product is represented as:

[0027]

[0028] where z ilα represents the evaluation cost paid each time.

[0029] Further, the position decision variable X ijl is introduced, and the preference weight of product i is represented as:

[0030]

[0031] where e represents the base of the natural logarithm; represents the probability that the α-type consumer selects the product under the influence of the position decision variable,

[0032] Based on the position decision variable, in the set S={(i,j)|X ijl =1} of the combination of product serial number and its corresponding display position serial number, when , the expected utility of product i is represented as: ​

[0033] Let

[0034] The probability of selecting the product with the serial number i is represented as:

[0035]

[0036] Further, the maximum platform expected revenue is obtained by the upper optimization model, and the maximum merchant expected profit is obtained by the lower optimization model; wherein the objective function max F1 of the upper optimization model is represented as:

[0037] max F1=E c +E a ;

[0038] max represents maximizing the function behind it, F1 represents the revenue in the platform cycle, E c represents the platform commission income, E a represents the platform advertising investment.

[0039] Further, the objective function max F2 of the lower optimization model is represented as:

[0040] max F2=E s -C c -C a -C m -C r -C f ;

[0041] Wherein, F2 represents the profit in the merchant cycle, E s represents the income of the merchant selling products, C c represents the commission taken by the platform from the sales amount of the merchant, C a represents the advertising investment cost of the merchant, C m represents the product purchase cost of the merchant, C r represents the product return cost of the merchant, C f represents the false comment investment cost of the merchant.

[0042] As a second aspect of the present application, some embodiments of the present application provide a clustering system based on double-layer optimization, comprising: a data acquisition module for acquiring product quality data, consumer category data and product promotion cost data in a database; a data processing module for obtaining probability data of each type of consumer selecting each product according to the acquired data and based on location decision variables; a double-layer optimization model composed of an upper optimization model and a lower optimization model is constructed, a balanced strategy set is obtained through the double-layer optimization model, and the optimal strategy set after solving is obtained by linearizing the double-layer optimization model.

[0043] As a third aspect of the present application, some embodiments of the present application provide a clustering device based on double-layer optimization, comprising one or more processors and a memory, the memory storing a program and being configured to be executed by the one or more processors to perform the following steps: obtaining product quality data, consumer category data and product promotion cost data in a database; obtaining probability data of each category of consumers selecting each product according to the obtained data and based on location decision variables; obtaining a set of equilibrium strategies through a double-layer optimization model composed of an upper-layer optimization model and a lower-layer optimization model, and obtaining an optimal strategy set after solving by linearizing the double-layer optimization model.

[0044] 3. Beneficial effects

[0045] Compared with the prior art, the present application has the following advantages:

[0046] (1) The present scheme constructs an e-commerce platform double-layer optimization dynamic ranking model, expands and enriches the ranking optimization application, and the proposed product ranking method considers the influence of merchant advertising investment and false information, balances the interests of merchants and the platform; by simulating the dynamic interaction process between the e-commerce platform and the merchants, the false information and advertising investment level of different types of merchants are deeply explored, and a reasonable promotion scheme is formulated for the merchants; it can design a more scientific and reasonable product ranking in the situation where the platform cannot identify all the influences of false information, which is conducive to establishing good stickiness and interaction with consumers and merchants, and realizing the maximization of platform revenue under the principle of mutual benefit and win-win with merchants;

[0047] (2) The present technical scheme comprehensively considers the behavior of merchants, uses advanced game theory methods and mathematical optimization techniques, not only significantly improves the accuracy of ranking data and results, making them more close to the real market situation, but also greatly improves the efficiency of the ranking algorithm through algorithm optimization, realizes the ability to quickly respond to market changes, and compared with the prior art, it shows obvious advantages in both accuracy and efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 FIG. 1 is a flowchart of a double-layer optimization-based clustering method in an embodiment of the present application;

[0049] Figure 2 FIG. 2 is a consumer two-stage sequential selection model diagram in an embodiment of the present application;

[0050] Figure 3 FIG. 3 is a logic structure diagram of a product ranking method based on double-layer optimization in an embodiment of the present application;

[0051] Figure 4 FIG. 4 is a flowchart of solving a double-layer optimization problem based on KKT conditions in an embodiment of the present application. DETAILED DESCRIPTION

[0052] The application will be described in greater detail with reference to the accompanying drawings and specific embodiments.

[0053] According to Figures 1 to 4 As shown in the figure, a clustering method based on double-layer optimization of the application includes the following steps:

[0054] Collect product quality data, consumer category data and product promotion cost data from the database;

[0055] According to the obtained data and based on the location decision variable, obtain the probability data of each category of consumers selecting each product; by constructing an upper-layer optimization model and a lower-layer optimization model to form a double-layer optimization model.

[0056] Specifically, the present scheme performs clustering analysis on user behavior data, and this clustering analysis is not only based on static data, but also considers dynamic user behavior data; the user behavior data includes consumer behavior data and merchant behavior data. In addition, the merchant behavior data is one of the important inputs in the double-layer optimization model of the present scheme, and by analyzing these data, the cost-effectiveness of different promotion strategies can be evaluated. The present scheme comprehensively considers user behavior data through the double-layer optimization model, deeply analyzes user behavior data and merchant behavior data, and realizes accurate grasp of user demand and optimization of marketing strategies.

[0057] Among them, the double-layer optimization model involves two levels of decision makers, namely merchants and platforms, who have independent objective functions and decision variables. In this case, it is very difficult to directly find a global optimal strategy set because different levels of decision makers may make conflicting decisions in pursuit of their own optimal interests. Therefore, the double-layer optimization model adopts a more realistic and feasible method, i.e. finding an equilibrium strategy set. The equilibrium strategy set refers to the mutually coordinated decision-making schemes accepted and implemented by each level of decision maker under given conditions. These schemes may not be globally optimal, but they achieve a certain degree of balance among different decision makers, so that there is no motivation to change the strategy because changing will not bring additional benefits. This equilibrium state provides a stable and predictable decision-making framework in a complex decision-making environment, which helps to reduce decision-making risks and improve decision-making efficiency.

[0058] In addition, the equilibrium strategy set also considers the mutual influence and constraint relationship between decision makers at different levels. In the two-level optimization model, the decision of the upper-level decision maker will affect the behavior and goal realization of the lower-level decision maker, and the reaction of the lower-level decision maker will also affect the decision of the upper-level decision maker. This mutual influence and constraint relationship makes the equilibrium strategy set more in line with the actual situation, because in the actual decision-making process, each decision maker often needs to consider the reaction and interests of other decision makers.

[0059] Since the game process between the merchant and the platform is dynamic, there is a certain time difference in giving strategies by both parties. The state of the merchant getting a temporary "maximum benefit" (greater than the benefit of the equilibrium strategy) is unstable, because the platform strategy will change, and the merchant's benefit will be affected. When solving the model, this scheme considers the final equilibrium strategy, so the optimal strategy mentioned in this scheme is equivalent to the equilibrium strategy.

[0060] In a specific embodiment, the specific steps of the two-level optimization-based clustering method are as follows:

[0061] S1, acquire and process data:

[0062] The process of acquiring and processing data is that the platform collects product quality data and consumer category data from the database, and the merchant acquires product promotion cost data from the platform, and finally obtains the probability of different categories of consumers selecting each product.

[0063] Specifically, the process of acquiring and processing data focuses on the deep description of the interactive behavior of the platform, the merchant and the consumer in the transaction process and their mutual relationship, and at the same time, it analyzes the two-stage selection behavior mode of the consumer in detail. Given the position advantage effect implied in the ranking, the consumer's attention is often focused on the products ranked at the top, and the limited time and patience resources make the probability of selecting the top products significantly increase. The platform sets the advertising unit price and product ranking mechanism to increase its advertising revenue and the commission income extracted from the sales of the merchant, aiming to optimize the advertising revenue and the sales commission structure. In this scheme, the commission income extracted from the sales of the merchant is simply referred to as commission. At the merchant level, the merchant will choose to invest in advertising and false information to improve the display position ranking of the product, and then increase the product selection rate and sales revenue, that is, according to the ranking mechanism of the platform, the merchant will strategically invest in advertising or take information beautification means to improve the ranking of the product, and then promote the probability of the product being selected and the growth of sales revenue.

[0064] In this game scenario, the platform plays the role of the leader, aiming to maximize its expected revenue; while merchants, as followers, strive to maximize their own expected profits. The interaction between the two parties follows the logic of a master-servant game, reflecting the dynamic process of "bargaining." Analyzing consumers' two-stage choice behavior requires recognizing the unique characteristics of consumer choice behavior in the e-commerce environment. This uniqueness manifests in two stages: the product selection stage and the utility evaluation stage.

[0065] like Figure 2 As shown, during the product selection phase, consumers browse products according to their ranking on the platform. At this stage, they only view the basic attributes of the products displayed on the page, representing a quick browse based on these basic attributes. When a product matches a consumer's preferences, it generates initial utility and is added to the shopping cart. At this stage, consumers incur search costs related to the product's display position to decide whether to continue browsing. Consumers weigh the cost of continued browsing (related to the product's display position) against potential benefits. Once the total utility of the product combination in the shopping cart reaches their expectations, the browsing behavior stops, and all products in the cart constitute a consideration set. It is worth noting that while the platform has a general understanding of consumer type distribution (influenced by factors such as gender, age, and purchase history, which determine consumers' expected utility for different products), it lacks information on the specific type of each individual. Therefore, the platform needs to design a reasonable product ranking strategy to improve consumers' expected utility and purchase intention, ultimately promoting mutual revenue growth for both merchants and the platform.

[0066] In a specific embodiment, the process of acquiring and processing data is as follows:

[0067] Assuming that after a consumer enters product keywords, the platform displays a total of n products, that is, n products correspond to n display positions, where n is a natural number;

[0068] Let X ijl Let X be the location decision variable. ijl This indicates whether a product with serial number i from merchant type l is placed in display position j, where i represents the product serial number (a natural number); j represents the display position number (a natural number); and l represents the merchant type serial number (a natural number).

[0069] At this point, the location decision variable X ijl The set X to which it belongs is then represented as:

[0070] X = {X ijl |i,j∈[n]}∈{0,1} n×n ;

[0071] According to the expression, the display position of the product is judged and the value of the position decision variable is obtained:

[0072] When the display position corresponding to the product with serial number i = j, the position decision variable X ijl = 1; when the display position corresponding to the product with serial number i ≠ j, the position decision variable X ijl = 0.

[0073] Based on the position decision variable, the set S represents the set of combinations of product serial numbers and corresponding display position serial numbers, that is, the set S contains the ranking mode of all products. Each element in the set S is a combination of product serial number and corresponding display position serial number (i, j), that is, S = {(i, j) | X ijl = 1}.

[0074] Since different types of consumers have different preferences for the same product, it is assumed that there are K types of consumers, K is a natural number; β α represents the proportion of α type consumers, then β α ∈ [0, 1]; Let u ilα represent the initial utility of the product i for the α type consumer. Specifically, the initial utility refers to the preliminary attraction or value that the product produces to the consumer to consider adding the product to the shopping cart based on the basic attributes of the product when the product meets the consumer's preferences in the product selection stage.

[0075] In a specific embodiment, when it is mentioned that the consumer will look down the product in the given ranking order, this is a specific embodiment of the position effect, which describes the different effects of products or information on consumers due to different display positions. Since the display position of the product will have an effect on the selection behavior of the consumer, the position effect in this scheme is represented by the degree of difficulty of the position visibility that the product is in, that is, the position visibility, which is represented by θ j here to represent the visibility of the display position j.

[0076] When only considering the influence of the position effect on the selection behavior of the consumer, the initial utility obtained by the consumer selecting the product with serial number i of the l type merchant on the display position with serial number j is offset by lnθ j ; wherein, lnθ j represents the natural logarithm of the base θ j , therefore, the initial utility considering the position effect is u ilα + lnθ j .

[0077] Position visibility is related to the level of investment of business advertisements and fake reviews. In considering the relationship between position visibility and business advertisement investment, the present scheme analyzes from two types of pricing advertisements, CPC and CPA. Among them, CPC (cost per click) refers to charging per single click; CPA (cost per action) refers to charging per specified action, and CPA usually refers to the cost of payment when a consumer makes a purchase.

[0078] In a specific embodiment, when considering the influence of advertisement investment, the initial utility of the α type consumer in the product selection stage can be expressed as:

[0079]

[0080] wherein r il represents the product rating of the product with the serial number i, s il represents the sales volume of the product with the serial number i, n il represents the number of product reviews of the product with the serial number i, and L represents the total number of business types.

[0081] ∈ i represents the random utility of the consumer affected by the environment in the product selection stage, which is subject to a normal distribution with a mean of 0 and a variance of ∈ 2 ;

[0082] P cpc represents the CPC unit price set by the platform, P cpa represents the CPA unit price set by the platform, represents the number of CPC investments of the l type business on the product i, represents the number of CPA investments of the l type business on the product with the serial number i.

[0083] Specifically, since the consumer browses the products in the order of product ranking, a certain browsing cost v jα is required each time. The browsing cost v jα is only related to the type of consumer and the display position of the product, and the browsing cost v jα increases with the decrease of position visibility. The consumer usually has a psychological expectation minimum threshold τ α for the product that he or she may purchase. When the difference between the initial utility obtained by the consumer in browsing the product and the browsing cost paid is greater than the set threshold τ αIf the total initial utility of the product and the total browsing cost is less than the total initial utility of the current product and the total browsing cost, the consumer stops browsing down, and all the products in the set form a consideration set.

[0084] In the utility evaluation stage, the consumer further evaluates the utility of the products in the consideration set by viewing the ratings, sales, online reviews, and other information of the products, and selects the product with the maximum utility or does not select any product in the consideration set based on the MNL model. The MNL model is a classic discrete choice model based on consumer utility. In the MNL model, the consumer's choice is divided into two categories: purchasing a product and not purchasing any product. The consumer's choice of not purchasing any product is equivalent to selecting product "0", i.e., purchasing a non-existent product.

[0085] In a specific embodiment, the perceived quality of the product by the consumer is affected by the ratings, sales, and number of online reviews. In the utility evaluation stage, the evaluation utility of the product i by the consumer can be represented as:

[0086]

[0087] where δ i is the random utility of the consumer in the utility evaluation stage affected by the environment, which is subject to a normal distribution with a mean of 0 and a variance of v 2 ;

[0088] where f il represents the number of fake reviews, represents the probability that an α-type consumer identifies that an l-type merchant has invested in fake positive reviews for product i.

[0089] Since the consumer will evaluate the utility of all products in the consideration set, each evaluation will require a certain evaluation cost z ilα . The evaluation cost z ilα is related to the type of consumer, the online reviews of the product, and the size of the consideration set, and the evaluation cost increases with the increase of the consideration set and the number of online reviews. Further, the expected utility E ijlα of the α-type consumer for the product i of the l-type merchant can be represented as:

[0090]

[0091] Specifically, the preference weight w ijlα of the α-type consumer for the product i of the l-type merchant can be represented as:​

[0092]

[0093] Introducing location decision variable X ijl Indicates product ranking, X ijl =1 indicates that product i from merchant l is displayed at position j, and e represents the base of the natural logarithm. In this case, the preference weight of type α consumers for product i from merchant l is... It can be represented as:

[0094]

[0095] Since there are cases where consumers browse products but do not click on any, this scheme uses w0 to represent the preference weight in this case. Without loss of generality, assuming the expected utility of a consumer not clicking on any product is 0, then w0 = e 0 =1 indicates that the consumer has the same level of preference for all products.

[0096] In one specific embodiment, using This represents the probability that, given a product ranking on the platform, an α-type consumer will choose to display the product of type l merchant with index j at the display position. like but

[0097] To simplify the formula, let

[0098] Furthermore, based on the MNL model, the probability that an α-type consumer will choose product number i is... It can be represented as:

[0099]

[0100] By acquiring data in step S1, the probability of different categories of consumers choosing each product can be obtained. Based on the obtained selection probability, the expected revenue that merchants can obtain from consumers purchasing products can be characterized, and the platform's commission revenue can be obtained, thus laying the foundation for building a two-layer optimization model.

[0101] S2. Construct a two-layer optimization model:

[0102] like Figure 3 As shown, this solution uses a two-layer optimization model to deeply depict the complex and dynamic game between the platform and merchants regarding product ranking. The two-layer optimization model consists of two parts: constructing an upper-layer optimization model and constructing a lower-layer optimization model.

[0103] The upper-layer optimization model is constructed to describe the expected income of the upper-layer platform, and the lower-layer optimization model is constructed to describe the expected profit of the lower-layer merchant.

[0104] First, the upper-layer optimization model is constructed from the perspective of the platform. The process of constructing the upper-layer optimization model includes constructing an objective function of the upper-layer optimization model and constructing a constraint condition of the upper-layer optimization model.

[0105] In a specific embodiment, the process of constructing the upper-layer optimization model is specifically as follows:

[0106] First, the objective function of the upper-layer optimization model is constructed. The upper-layer optimization model is used to maximize the expected revenue of the platform, and the expected revenue of the platform includes platform commission income and platform advertising investment. Therefore, the objective function of the upper-layer optimization model is represented as:

[0107] max F1=E c +E a (7)

[0108] Wherein, max represents maximizing the function behind it, F1 represents the revenue in the platform period, E c represents the platform commission income, and E a represents the platform advertising investment.

[0109] Specifically, the platform commission income E c can be represented as:

[0110]

[0111] Wherein, n ic is the total number of consumers who have demand for the product with serial number i on the platform; p il is the price of the product with serial number i of the l-type merchant; e il is the proportion of the commission of the platform to the product with serial number i of the l-type merchant, p il e il is the commission of the platform from the product transaction amount for each product sold. It is worth noting that if the consumer has a return behavior, the platform will not refund the commission paid by the merchant.

[0112] Different types of merchants are divided based on the quality of the product. The platform knows the distribution of the types of merchants, but does not know the specific types. The probability of the product with serial number i of the l-type merchant being selected by the a-type consumer is

[0113] Specifically, the platform advertising revenue E a can be represented as:

[0114]

[0115] The advertising input refers to the advertising fee paid by the merchant to the platform, is a fixed income and is not affected by whether the product is purchased; and is paid only when the consumer actually purchases.

[0116] Specifically, the constraint conditions of the upper optimization model include product position constraints and factual integer constraints, and the specific process of constructing the constraint conditions is as follows:

[0117] Constructing product position constraints: the product position constraints include that there is at most one product on each display position and that each product is placed on at most one display position; wherein the product position constraint that there is at most one product on each display position can be expressed as: The product position constraint that each product is placed on at most one display position can be expressed as: Therefore, the product position constraint is expressed as:

[0118]

[0119] Constructing factual integer constraints: the factual integer constraints include that X ijl is a variable with a value of 0-1; and there are n products and their corresponding ranking display positions. Wherein, X ijl is a variable with a value of 0-1, which is expressed as X ijl ∈{0,1}; there are n products expressed as: 1≤i≤n,i∈Z; the corresponding ranking display positions of the n products are expressed as: 1≤j≤n,j∈Z; therefore, the factual integer constraint is expressed as:

[0120] X ijl ∈{0,1}(12)

[0121] 1≤i≤n,i∈Z(13)

[0122] 1≤j≤n,j∈Z(14)

[0123] Thus, the upper optimization model of the platform perspective in the double-layer optimization model is obtained, and the constructed upper optimization model is as follows:

[0124]

[0125] Through the above steps, the upper optimization model of the platform perspective in the double-layer optimization model is obtained, and the lower optimization model is constructed from the perspective of the merchant. The process of constructing the lower optimization model includes constructing the objective function of the lower optimization model and constructing the constraint conditions of the lower optimization model.

[0126] In one specific embodiment, the process of constructing the lower optimization model is as follows:

[0127] First, we construct the objective function of the lower-level optimization model. The lower-level optimization model aims to maximize the merchant's expected profit, which includes both revenue and expenditure. The objective function, max F², is expressed as:

[0128] max F2=E s -C c -C a -C m -C r -C f (16)

[0129] Where F2 represents the merchant's profit during the period, E s C represents the revenue generated by the merchant from the sale of products. c This refers to the commission that the platform takes from the merchant's sales revenue, C. a C represents the advertising investment cost of the business. m C represents the merchant's product purchase cost. r C represents the merchant's product return cost. f This indicates the cost that merchants invest in creating fake positive reviews.

[0130] Specifically, merchant sales revenue E s Represented as:

[0131]

[0132] in, This refers to the probability that an α-type consumer will choose product i from a l-type merchant.

[0133] Commission C c Represented as:

[0134]

[0135] Merchant advertising cost C a Represented as:

[0136]

[0137] CPC type advertising cost Product costs and fake positive reviews are fixed expenses, unaffected by whether the product is ultimately purchased, while CPA (Cost Per Action) advertising costs... It is only spent when a consumer makes an actual purchase.

[0138] Product purchase cost C m Represented as:

[0139]

[0140] wherein c il represents the cost of the product of the merchant of type l with serial number i.

[0141] the cost of false praise C f is expressed as:

[0142]

[0143] wherein F il represents the number of false praises input by the product of the merchant of type l with serial number i, f il is the cost of a single false praise of the product of the merchant of type l with serial number i.

[0144] the cost of product return C r is expressed as:

[0145]

[0146] wherein represents the probability of return after purchase of the product i by the consumer of type a.

[0147] In a specific embodiment, the constraint conditions of the lower layer optimization model include factual constraint conditions, consumer selection constraint conditions and merchant promotion constraint conditions, and the specific process of constructing the constraint conditions of the upper layer optimization model is as follows:

[0148] Specifically, the factual constraint conditions include: the number of advertisement inputs of the merchant to the product with serial number i is a non-negative integer; the product rating is a 5-point system; the number of false praises of the product is not more than the total number of product reviews; there are n products and the product corresponding ranking display positions; the product price of the merchant is not lower than the total cost input to the product.

[0149] wherein the number of advertisement inputs of the merchant to the product with serial number i is a non-negative integer is expressed as: and the product rating is a 5-point system is expressed as: s il ∈[0,5]; the number of false praises of the product is not more than the total number of product reviews is expressed as: F il ≤n il ∈Z; there are n products is expressed as: 1≤i≤n, i∈Z; the n products corresponding ranking display positions are expressed as: 1≤j≤n, j∈Z; the product price of the merchant is not lower than the total cost input to the product is expressed as:

[0150] Therefore, the factual constraint conditions are expressed as:

[0151]

[0152] s il ∈[0,5](25)

[0153] F il ≤n il ∈Z (26)

[0154] 1≤i≤n,i∈Z (27)

[0155] 1≤j≤n,j∈Z (28)

[0156]

[0157] Specifically, the consumer selection constraint condition includes: a threshold condition of product joining the consideration set; and a termination condition of consumer browsing behavior.

[0158] The threshold condition of product joining the consideration set is expressed as: The termination condition of consumer browsing behavior is expressed as:

[0159]

[0160] Therefore, the consumer selection constraint condition is expressed as:

[0161]

[0162] Specifically, the merchant promotion constraint condition includes: the merchant can obtain higher revenue through advertising investment and false comment investment, wherein, P (i) represents the probability of consumer purchasing the product when the merchant does not perform any advertising and false comment investment. The merchant promotion constraint condition is expressed as:

[0163]

[0164]

[0165] Thus, the lower optimization model in the constructed double-layer optimization model is as follows:

[0166]

[0167] The lower optimization model of the merchant perspective in the double-layer optimization model is constructed through the above steps, and the double-layer optimization model is composed of the upper optimization model of the platform perspective and the lower optimization model of the merchant perspective.

[0168] S3, verifying Stackelberg equilibrium

[0169] For the double-layer optimization model constructed in step S2, this step will verify whether the double-layer optimization model has a Stackelberg equilibrium. The Stackelberg equilibrium refers to the fact that the merchant and the platform involved in the present application need to reach a consensus decision, and any party will not improve the overall decision-making effect of the game by changing the strategy unilaterally.

[0170] When the merchant makes an optimal response according to the product ranking and advertisement pricing given by the platform, and the platform also accepts this result, the game reaches a Stackelberg equilibrium, assuming and is the equilibrium solution of the master-slave game model proposed in the present solution, then and satisfy the following conditions:

[0171]

[0172] Before the Stackelberg equilibrium solution is obtained, the existence and uniqueness of the Stackelberg equilibrium solution need to be verified, which requires the following three conditions to be met:

[0173] The set of all feasible strategies of the leader and the follower is a non-empty compact convex set, that is, the strategy is a non-empty convex set and a compact set;

[0174] When the strategy of the leader is given, the follower has a unique optimal solution;

[0175] When the strategy of the follower is given, the leader has a unique optimal solution.

[0176] In the present solution, the platform is the leader and the merchant is the follower, and the strategies of the platform and the merchant are the decision variables in the above steps. In the double-layer optimization model in the present solution, the decision variable of the platform is the position decision variable X ijl , the set advertisement unit price variable is P cpc and P cpa , and the decision variable of the merchant is the number of fake good review variables F il and the number of advertisement investment variables and The process of proving the existence and uniqueness of the equilibrium solution is as follows:

[0177] Firstly, the constraints of the platform decision variables are expressed in (10)-(14), and the constraints of the merchant decision variables are expressed in (23)-(33), both of which are non-empty and convex sets; secondly, the first-order derivatives of the upper optimization model objective function and the lower optimization model objective function are calculated. Since at any time, the position decision variables of the platform and the advertising unit price, the advertising and fake review input times are all non-negative integers, the first-order partial derivatives of the upper optimization model objective function and the lower optimization model objective function are always greater than zero and subject to strategy interval constraints, so the upper optimization model and the lower optimization model both have a unique optimal solution. Therefore, the double-layer optimization model proposed in the present scheme has a unique Stackelberg equilibrium solution.

[0178] S4, transforming the linearization model and solving

[0179] The upper optimization model objective function and the lower optimization model objective function of the double-layer optimization model established in the present scheme are coupled, which is difficult to solve directly. As shown in Figure 4 Through model analysis, it is found that the upper and lower target functions of the double-layer optimization model are convex functions, and their respective constraints are convex sets. Therefore, the lower optimization model is transformed into an additional condition of the upper optimization model by KKT condition transformation, so that the model established in the present scheme is transformed into a single objective model. In addition, considering that the display position visibility of product ranking makes the target functions of the upper optimization model and the lower optimization model both have nonlinear terms, according to the duality theorem, the nonlinear terms in the respective target functions can be transformed into linear terms. The KKT (Karush Kuhn Tucher) condition is a set of nonlinear equations, which is widely used in solving optimization problems with inequality constraints. The complementary slackness condition in the KKT condition is a nonlinear constraint, which can be converted into a linear constraint by introducing a sufficiently large number and a variable with a value of 0-1, that is, the model can be transformed into a mixed integer linear programming MILP (Mixed-integer linear programming) problem, and then the MILP problem can be solved in the Python program by calling the Gurobi solver. The Gurobi solver is a mathematical programming optimizer that can be used to quickly and efficiently solve large-scale optimization problems.

[0180] The prior art focuses on ranking products by comprehensive indicators, but does not consider the influence of merchant behavior on product ranking. To this end, the present scheme builds a double-layer optimization model, wherein the upper-layer optimization model is to maximize the expected revenue of the platform, including the product commission of the merchant and the advertising input amount; the lower-layer optimization model is to maximize the expected profit of the merchant, and the merchant income refers to the price income of selling products, and the merchant expenditure includes the return cost, the advertising input cost and the false comment input cost. Both the platform and the merchant pursue their own profit maximization, and use master-slave game to describe the bargaining process of both sides. It is proved by theoretical derivation that the proposed model has a unique Stackelberg equilibrium solution, and the double-layer model is converted into a mixed integer quadratic programming problem by applying the KKT optimal condition and the duality theorem; finally, by solving the example, the global optimal product ranking strategy is obtained.

[0181] In combination Figures 1 to 4 A clustering system based on double-layer optimization, comprising:

[0182] A data acquisition module for acquiring product quality data, consumer category data and product promotion cost data from a database;

[0183] A data processing module for obtaining probability data of each category of consumers selecting each product based on the acquired data and based on position decision variables; and a double-layer optimization model composed of an upper-layer optimization model and a lower-layer optimization model.

[0184] For the clustering device based on double-layer optimization, it can be a hardware device comprising one or more processors and a memory, the memory storing a program and being configured to be executed by the one or more processors to perform the following steps:

[0185] Acquiring product quality data, consumer category data and product promotion cost data from a database;

[0186] Obtaining probability data of each category of consumers selecting each product based on the acquired data and based on position decision variables; and a double-layer optimization model composed of an upper-layer optimization model and a lower-layer optimization model.

[0187] In the prior art, the ranking of products is mainly based on comprehensive indicators such as sales, ratings, prices, etc. These indicators often ignore the impact of merchant behavior on the actual value of products and user satisfaction. For example, some merchants may use false reviews, excessive marketing, etc. to improve the comprehensive indicators in the short term, resulting in a ranking result that does not match the actual product quality and user feedback. The present scheme uses a double-layer optimization model that not only considers direct indicators of products but also analyzes the impact of merchant behavior (such as return cost, advertising investment, and false review investment) on ranking, thus more accurately reflecting the real market performance and user demand of products. Moreover, through theoretical derivation, it is proved that the model has a unique Stackelberg equilibrium solution, ensuring that the strategy selection of the platform and the merchant in the game process reaches the optimal balance, reducing the ranking deviation caused by information asymmetry or strategic misleading.

[0188] The double-layer optimization model of the present scheme can dynamically adjust the ranking strategy and respond to real-time changes in merchant behavior, making the ranking result more close to the actual market and improving the timeliness and accuracy of the data.

[0189] Traditional ranking algorithms are often based on complex rules and a large amount of data processing, which is computationally intensive and slow to respond, making it difficult to quickly adapt to market changes and rapid iteration of user demand. The advantage of the present scheme is that it considers mixed integer quadratic programming transformation, global optimal solution solving, and modularity and scalability. Specifically, by applying the KKT optimality condition and duality theorem, the present scheme successfully transforms the double-layer optimization model into a mixed integer quadratic programming problem. This transformation not only simplifies the computational complexity but also preserves the core optimization objective of the model, significantly improving the execution efficiency of the algorithm. Moreover, through solving examples, the present scheme can directly obtain the globally optimal product ranking strategy, avoiding the trap of local optimal solutions and ensuring the effectiveness and efficiency of the algorithm. In addition, the model design of the present scheme has modular characteristics, making it easy to quickly adjust algorithm parameters or introduce new variables according to new market trends or regulatory requirements, enhancing the flexibility and scalability of the system. In the long run, this is beneficial to continuously optimize the ranking algorithm and maintain its efficient operation.

[0190] Specifically, how to implement the device is realized in the prior art, and again, no specific elaboration is made, and the following explains the possibility of corresponding implementation from the principle.

[0191] In the 1990s, an improvement in technology can be clearly distinguished as an improvement in hardware (e.g., improvement in circuit structures such as diodes, transistors, switches, etc.) or an improvement in software (e.g., improvement in method processes). However, as technology has developed, many improvements in method processes today can be considered as direct improvements in hardware circuit structures.

[0192] Designers almost always obtain the corresponding hardware circuit structure by programming the improved method flow into hardware circuit. Therefore, it cannot be said that the improvement of a method flow cannot be implemented by hardware entity modules. For example, a Programmable Logic Device (PLD) such as a Field Programmable Gate Array (FPGA) is an integrated circuit whose logic function is determined by the user programming the device. A designer himself programs a digital system "integrated" on a PLD without having to ask a chip manufacturer to design and manufacture a dedicated integrated circuit chip. Moreover, instead of manually manufacturing integrated circuit chips, this programming is now mostly implemented using "logic compiler" software similar to the software compiler used when developing programs, and the original code to be compiled is written in a specific programming language, called a Hardware Description Language (HDL), of which there are many, such as Verilog. The person skilled in the art will also be aware that it is sufficient to simply logically program the method flow in one of the above-mentioned hardware description languages and program it into an integrated circuit to easily obtain a hardware circuit implementing the logical method flow.

[0193] The controller can be implemented in any suitable manner, for example, the controller can take the form of a microprocessor or processor and a computer readable medium storing computer readable program code (e.g. software or firmware) executable by the (micro)processor, logic gates, switches, Application Specific Integrated Circuits (ASICs), programmable logic controllers and embedded microcontrollers, examples of controllers include but are not limited to the following microcontrollers: ATMEL AT89S52, microchip pic 16c57 The memory controller can also be implemented as part of the control logic of the memory. The person skilled in the art will also be aware that, in addition to implementing the controller in pure computer readable program code, it is also possible to implement the controller in the form of logic gates, switches, ASICs, programmable logic controllers and embedded microcontrollers by logically programming the method steps to perform the same functions. Such a controller can therefore be considered a hardware component, and the means included therein for performing various functions can be considered structures within the hardware component. Alternatively, or even, the means for performing various functions can be considered both a software module implementing a method and a structure within a hardware component.

[0194] The systems, apparatuses, modules, or units disclosed in the above embodiments can be specifically implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, the computer can be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices. For the convenience of description, the above apparatuses are described in functions as various units for description. Of course, the functions of the units can be implemented in one or more software and / or hardware in the implementation of the present specification.

[0195] Those skilled in the art should understand that embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage, etc.) containing computer-usable program code. The present application is described with reference to flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and combinations of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions that are executed by the processor of the computer or other programmable data processing apparatus generate an apparatus that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that implements the functions specified in the flowcharts and / or block diagrams.

[0196] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable data processing apparatus to produce a computer-implemented process such that the instructions executed by the computer or other programmable data processing apparatus provide the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1The steps of a method, process, or algorithm described in connection with the present disclosure can be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module can reside in RAM, flash memory, ROM, or any other form of non- volatile storage. Further, the software module can include, but is not limited to, routines, programs, objects, components, data structures, and the like that perform particular tasks or implement particular abstract data types. The software module can also be implemented in a centralized or distributed fashion, in which case they are located in one or more general purpose computers.

[0197] Computer-readable media includes permanent and non-permanent, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disc read-only memory (CD-ROM), digital versatile disc (DVD), or other optical storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible to a computing device. According to the definition herein, computer-readable media does not include transitory media such as modulated data signals and carriers.

[0198] It should also be noted that the terms "comprising," "including," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements recited, but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element preceded by "comprises a" does not, without more constraints, foreclose the existence of additional identical elements in the process, method, article, or apparatus that includes the recited element.

[0199] Those skilled in the art will appreciate that embodiments of the present specification can be provided as methods, systems or computer program products. Accordingly, the present specification can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the specification can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, magnetic disks, CD-ROMs, optical storage media, etc.) embodying computer usable program code.

[0200] The specification can be described in the general context of computer- executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The specification can also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules can be located in both local and remote computer storage media including memory storage devices.

Claims

1. A clustering method based on double-layer optimization, comprising the following steps, obtaining product quality data, consumer category data and product promotion cost data in a database; According to the obtained data and based on a location decision variable, probability data of selection of each product by each category of consumer is obtained; the location decision variable is , is a product serial number, is a display location serial number, is a serial number of a merchant type; when the serial number is , the product display location serial number is , , otherwise ; The probability data is represented as: ； For the consumer category, , , For the product rating, For the product sales volume, For the product number of comments, For the initial utility, For the browsing cost, For the evaluation cost, For the number of fake reviews, For Type consumer identification merchant The probability of investing fake positive reviews for the product , And CPC and CPA prices set by the platform respectively, And The number of times the merchant CPC and CPA investment times for the product , The total number of merchant types; building a double-layer optimization model by constructing an upper-layer optimization model and a lower-layer optimization model, obtaining maximum platform expected revenue through the upper-layer optimization model, and obtaining maximum merchant expected profit through the lower-layer optimization model; wherein The objective function of the upper optimization model is represented as: ； revenue for the platform period, revenue for the platform, advertising spend for the platform; wherein, ； ； is the total number of consumers on the platform who have a demand for the product ; is the merchant ; is the price of the product ; is the percentage of the product ; is the commission taken by the platform from the transaction amount of the product sold; The objective function of the lower layer optimization model is represented as: ； a profit of the merchant in a period, a revenue of the merchant from selling a product, a commission of the platform from a sales amount of the merchant, an advertising input cost of the merchant, a product purchase cost of the merchant, a product return cost of the merchant, a false comment input cost of the merchant; wherein, ； ； ； ； ； ； pointing to a consumer selecting a merchant product probability of a product; cost of a product of a merchant cost of a product number of fake reviews of a product of a merchant number of fake reviews of a product cost of a single fake review of a product of a merchant cost of a single fake review of a product probability of a product being returned by a consumer after purchase transforming the double-layer optimization model into a mixed integer quadratic programming problem through KKT condition and duality theorem, and solving the problem to obtain an equilibrium strategy set and an optimal strategy set. 2.The clustering method based on double-layer optimization according to claim 1, wherein, After obtaining the product keyword, traverse the database to output product information and corresponding display position information, is a natural number; Position decision variable Set in which the position decision variable is located is represented as: ； wherein, represents a serial number of a product, is a natural number; represents a serial number of a display position, is a natural number; represents a serial number of a merchant type, is a natural number. 3.The clustering method based on double-layer optimization according to claim 2, wherein, Considering the effect of position effect, the initial utility occurs a shift; the initial utility considering the effect of position effect is expressed as: ; wherein, represents the initial utility of a type consumer to a product with serial number , represents the visibility of a display location with serial number ; represents the natural logarithm of a base number . Considering the impact of advertising investment, the initial utility of the product selection stage is represented as: ； wherein, represents the product score of the product with the serial number , represents the product sales volume of the product with the serial number , represents the product comment number of the product with the serial number , represents the total number of the merchant type; represents the random utility of the consumer affected by the environment in the product selection stage, which is subject to a normal distribution with a mean of and a variance of ; represents the CPC unit price set by the platform, represents the CPA unit price set by the platform, represents the number of times of CPC investment of the type merchant on the product , represents the number of times of CPA investment of the type merchant on the product . 4.The clustering method based on double-layer optimization according to claim 3, wherein, The utility evaluation phase evaluates the utility of the product with serial number is represented as: ​ ； in, For consumers, random utility influenced by the environment during the utility evaluation phase follows a mean of . The variance is The normal distribution; This indicates the number of fake comments submitted. express Type consumer identification Type of merchant for products The probability of submitting fake positive reviews; when utility is assessed for all products, the expected utility of a product is represented as: wherein, represents the cost of browsing, represents the cost of evaluation paid each time of evaluation. 5.The clustering method based on double-layer optimization according to claim 4, wherein, Introducing position decision variables , the preference weight of the product with serial number is expressed as:​ ； where e represents the base of the natural logarithm; represents the probability that a type consumer chooses a product given a change in location decision, ; based on the location decision variable, a set of combinations of product serial numbers and their corresponding display location serial numbers When , ​ Let , ; The probability of selecting a product with serial number is represented as: ​ 。 6. A clustering system based on double-layer optimization, characterized in that, comprising, a data acquisition module for obtaining product quality data, consumer category data and product promotion cost data in a database; a data processing module for obtaining probability data of consumers of each category selecting each product based on position decision variables according to the obtained data; Wherein, the position decision variable is , is a product serial number, is a display position serial number, is a merchant type serial number; when the serial number is , the product display position serial number is , , otherwise ; The probability data is represented as: ； For the consumer category, , , For the rating of the product , For the sales volume of the product , For the number of comments on the product , For the initial utility, For the browsing cost, For the evaluation cost, For the number of fake comments invested, For Type of consumer to identify the merchant The probability of investing fake positive comments on the product , And CPC and CPA prices set by the platform respectively, And The number of times the merchant Invests in CPC and CPA for the product , The total number of merchant types; building a double-layer optimization model by constructing an upper-layer optimization model and a lower-layer optimization model, obtaining maximum platform expected revenue through the upper-layer optimization model, and obtaining maximum merchant expected profit through the lower-layer optimization model; In the formula, the objective function of the upper-layer optimization model is is represented as: ； revenue for the platform period, revenue for the platform, advertising spend for the platform; wherein, ； ； is the total number of consumers on the platform who have a demand for the product ; is the merchant ; is the price of the product ; is the percentage of the product ; is the commission taken by the platform from the transaction amount of the product sold; The objective function of the lower layer optimization model is represented as: ； a profit of the merchant in a period, a revenue of the merchant from selling a product, a commission of the platform from a sales amount of the merchant, an advertising input cost of the merchant, a product purchase cost of the merchant, a product return cost of the merchant, a fake review input cost of the merchant; wherein, ； ； ； ； ； ； pointing to a consumer selecting a merchant product probability; cost of a product of a merchant cost of a product number of fake reviews of a product of a merchant number of fake reviews of a product cost of a single fake review of a product of a merchant cost of a single fake review of a product probability of a consumer returning a product after purchasing it transforming the double-layer optimization model into a mixed integer quadratic programming problem through KKT condition and duality theorem, and solving the problem to obtain an equilibrium strategy set and an optimal strategy set.

7. A clustering apparatus based on double-layer optimization, characterized in that, comprising one or more processors and a memory, the memory storing a program and being configured to be executed by the one or more processors to perform the following steps: obtaining product quality data, consumer category data and product promotion cost data in a database; obtaining probability data of consumers of each category selecting each product based on position decision variables according to the obtained data; wherein the position decision variable is , is a product serial number, is a display position serial number, is a serial number of a merchant type; when the serial number is the product display position serial number is , , otherwise ; The probability data is represented as: ； For the consumer category, , , For the rating of the product , For the sales volume of the product , For the number of comments on the product , For the initial utility, For the browsing cost, For the evaluation cost, For the number of fake comments invested, For The type of consumer identifies the merchant The probability of investing fake positive comments on the product , And The CPC unit price and the CPA unit price set by the platform respectively, And The number of times of CPC investment and the number of times of CPA investment of the merchant On the product , The total number of merchant types; building a double-layer optimization model by constructing an upper-layer optimization model and a lower-layer optimization model, obtaining maximum platform expected revenue through the upper-layer optimization model, and obtaining maximum merchant expected profit through the lower-layer optimization model; In the formula, the objective function of the upper-layer optimization model is is represented as: ； revenue for the platform period, revenue for platform commission, revenue for platform advertising; wherein, ； ； is the total number of consumers on the platform who have a demand for the product ; is the merchant ; is the price of the product ; is the percentage of the product ; is the commission taken by the platform from the transaction amount of the product sold; The objective function of the lower layer optimization model is represented as: ； a profit of the merchant in a period, a revenue of the merchant from selling a product, a commission of the platform from a sales amount of the merchant, an advertising input cost of the merchant, a product purchase cost of the merchant, a product return cost of the merchant, a false comment input cost of the merchant; wherein, ； ； ； ； ； ； Consumers Select Merchant Products The probability of; It is a merchant Products The cost; It is a merchant Products Fake positive reviews It is a merchant Products The cost of a single fake positive review; Consumers Purchase products The probability of returns; transforming the double-layer optimization model into a mixed integer quadratic programming problem through KKT condition and duality theorem, and solving the problem to obtain an equilibrium strategy set and an optimal strategy set.

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