Product recommendation method and system

Abstract

The present invention discloses a product recommendation method, including using a multi-objective optimization algorithm to obtain several types of product recommendation solutions; obtaining corresponding point set data according to several types of product recommendation solutions; using a hypervolume calculation method to calculate the hypervolume data corresponding to each product recommendation solution; selecting the product recommendation solution corresponding to the maximum hypervolume data value as the final product recommendation solution to complete the product recommendation. The present invention also discloses a system for implementing the product recommendation method. The present invention reasonably divides the complex hypervolume calculation problem into several simpler subsets of hypervolume calculation problems through the selection of optimal points, worst points and axis points. Therefore, the present invention can not only realize product recommendations based on hypervolume calculations, but also has higher reliability, better accuracy and higher efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of data signal processing, and in particular relates to a product recommendation method and system. Background Art

[0002] The multi-objective optimization algorithm is one of the optimization algorithms widely used at this stage; the multi-objective optimization algorithm can be applied to the field of product design optimization, and then comprehensively consider multiple objectives such as product cost, performance and reliability; in the field of resource allocation, the multi-objective optimization algorithm can be applied to project management, thereby optimizing multiple objectives such as time, cost and quality; the multi-objective optimization algorithm can also be applied to the fields of ecosystem management and financial portfolio optimization.

[0003] In the field of multi-objective optimization, the evaluation of multi-objective optimization algorithms has always been one of the research focuses of researchers. The performance evaluation of the solution set of a multi-objective optimization algorithm mainly includes the evaluation of the convergence of the solution set, the evaluation of the uniformity of the solution set, and the evaluation of the ductility of the solution set. Among the many evaluation indicators of multi-objective optimization algorithms, the hypervolume evaluation indicator is one of the indicators with the best comprehensive evaluation effect. Therefore, the calculation of the hypervolume corresponding to the solution set of the multi-objective optimization algorithm is particularly important.

[0004] According to current research results, in both three-dimensional and four-dimensional problems, the calculation process of hypervolume can be completed at a relatively low cost in time. However, the problem of hypervolume calculation is Therefore, the computation time of the hypervolume will increase exponentially with the number of objectives. At present, in multi-objective optimization problems with ten or more objectives, the precise computation process of the hypervolume is not only extremely complex, but also consumes a lot of time and space resources.

[0005] Correspondingly, the product recommendation method using the hypervolume index for evaluation also has the problem of complex solutions and occupying more time and space resources. Summary of the invention

[0006] One of the purposes of the present invention is to provide a product recommendation method with high reliability, good accuracy and high efficiency.

[0007] A second objective of the present invention is to provide a system for implementing the product recommendation method.

[0008] The product recommendation method provided by the present invention comprises the following steps:

[0009] A. Use multi-objective optimization algorithms to obtain recommendations for several types of products;

[0010] B. Obtain corresponding point set data based on the product recommendation solutions of several categories obtained in step A;

[0011] C. Use the hypervolume calculation method to calculate the hypervolume data corresponding to each product recommendation solution;

[0012] D. Select the product recommendation solution corresponding to the maximum value of the hypervolume data as the final product recommendation solution to complete the corresponding product recommendation;

[0013] The method for calculating the super volume described in step C comprises the following steps:

[0014] S1. Obtaining a solution set of a multi-objective optimization algorithm to be evaluated;

[0015] S2. performing a normalization operation on the point set obtained in step S1;

[0016] S3. Based on the normalized point set obtained in step S2, the optimal point and the worst point are selected according to the properties of the multi-objective optimization algorithm to be evaluated;

[0017] S4. Based on the current point set, select an axis point according to the relationship between the value of the element in the point set and the dimension of the point set;

[0018] S5. according to the selected pivot point, the elements in the current point set are divided into a number of subsets according to the magnitude relationship between the element values ​​of the current point set and the pivot point values;

[0019] S6. Determine the subsets obtained in step S5:

[0020] If the size of the subset is a set value, the hypervolume of the corresponding subset is directly calculated based on the selected optimal and worst points;

[0021] If the size of the subset is not the set value, the corresponding subset is used as the current point set, and the process returns to step S4 for the next round of iterative calculation;

[0022] S7. Based on the obtained hypervolumes of all subsets, the calculation of the hypervolume corresponding to the solution set of the multi-objective optimization algorithm to be evaluated is completed.

[0023] The step S2 specifically includes the following steps:

[0024] The point set obtained in step S1 is expressed as , where each point includes d dimensions; the i-th point Expressed as ;

[0025] Traverse the element values ​​of each dimension to get the maximum value on the kth dimension and the minimum value in the kth dimension ;

[0026] For each point ,right The values ​​of each dimension in are normalized using the following formula: In the formula is the value of the kth dimension of the i-th point after normalization; is the value of the kth dimension of the ith point before normalization.

[0027] The step S3 specifically includes the following steps:

[0028] If the solution set of the multi-objective optimization algorithm to be evaluated is a maximization problem, then the optimal point is selected. for , the worst point r is ;

[0029] If the solution set of the multi-objective optimization algorithm to be evaluated is a minimization problem, then the optimal point is selected. for , the worst point r is ;

[0030] The maximization problem is defined as the larger the value, the better the performance; the minimization problem is defined as the smaller the value, the better the performance. In the present invention, the main focus is on the maximization problem, so only the maximization problem will be considered later. It is worth emphasizing that the minimization problem can be easily converted into a maximization problem. Specifically, 1 is subtracted from each element value after normalization to obtain a new element value. This conversion is feasible because after normalization, the maximum value of all elements is 1.

[0031] The step S4 specifically comprises the following steps:

[0032] Set an empty set P;

[0033] For each point in the current point set , if point All dimensions of , then the point Put into the set P; among them, Representing a collection The element value is not greater than The number of elements in the set for ; To round up;

[0034] In the set P, choose The point with the largest value is used as the final axis point .

[0035] The step S5 specifically includes the following steps:

[0036] For each point in the current point set ,like The value in the kth dimension Greater than axis point The value in the kth dimension , then The point to be considered as the kth sub-problem;

[0037] Points to consider for the kth subproblem , the following rules are used for judgment and calculation:

[0038] when When The value of the jth dimension of The value is ;

[0039] when When The value of the jth dimension of The value is ;

[0040] when When The value of the jth dimension of The value is ;

[0041] Finally, the elements in the current point set are divided into several subsets.

[0042] The step S6 comprises the following steps:

[0043] If the size of the subset is 1, the hypervolume of the corresponding subset is calculated based on the selected optimal and worst points and the product of the points in the subset in each dimension;

[0044] If the size of the subset is 2, the hypervolume of the corresponding subset is calculated based on the selected optimal and worst points, the product of the points in the subset in each dimension, and the product of the dimensions corresponding to the smaller values ​​of the two points in each dimension;

[0045] If the size of the subset is greater than 2, the corresponding subset is used as the current point set, and the process returns to step S4 for the next round of iterative calculation.

[0046] The step S6 specifically includes the following steps:

[0047] If the size of the subset is 1:

[0048] The hypervolume of the subset is calculated using the following formula: : In the formula is the value of point a in the subset in the i-th dimension, is the value of the worst point r in the i-th dimension; in specific implementation, since the subset size is 1, point a is the only point in the S set, and the present invention mainly focuses on the maximization problem, so the worst point r is ;

[0049] If the size of the subset is 2:

[0050] Calculate the hypervolume of point a in the subset The hypervolume of point b in the and subset ;

[0051] For point a and point b in the subset, compare the values ​​of the two points in each dimension in turn, and take the smaller value of each dimension to form the worse point ; Expressed as ;

[0052] Poor calculation The hypervolume ;

[0053] Finally, the hypervolume of the subset is calculated for ;

[0054] If the size of the subset is greater than 2:

[0055] The corresponding subset is taken as the current point set, and the process returns to step S4 for the next round of iterative calculation.

[0056] The step S7 specifically includes the following steps:

[0057] The hypervolumes of all the obtained subsets are added together to obtain the calculation result of the hypervolume corresponding to the solution set of the final multi-objective optimization algorithm to be evaluated.

[0058] The present invention also provides a system for implementing the product recommendation method, comprising a solution generation module, a point set acquisition module, a hypervolume calculation module and a product recommendation module; the solution generation module, the point set acquisition module, the hypervolume calculation module and the product recommendation module are connected in series in sequence; the solution generation module is used to adopt a multi-objective optimization algorithm to obtain several types of product recommendation solutions, and upload the data information to the point set acquisition module; the point set acquisition module is used to obtain corresponding point set data according to the received data information and the obtained several types of product recommendation solutions, and upload the data information to the hypervolume calculation module; the hypervolume calculation module is used to calculate the hypervolume data corresponding to each product recommendation solution according to the received data information and the hypervolume calculation method, and upload the data information to the product recommendation module; the product recommendation module is used to select the product recommendation solution corresponding to the maximum hypervolume data value according to the received data information as the final product recommendation solution to complete the corresponding product recommendation.

[0059] The product recommendation method and system provided by the present invention reasonably divides the complex hypervolume calculation problem into several simpler subsets of hypervolume calculation problems through the selection of the optimal point, the worst point and the axis point. Therefore, the present invention can not only realize product recommendation based on hypervolume calculation, but also has higher reliability, better accuracy and higher efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 A schematic diagram of a method flow chart of the product recommendation method of the present invention.

[0061] Figure 2 It is a schematic diagram of subset division of the hypervolume calculation method in the product recommendation method of the present invention.

[0062] Figure 3 This is a schematic diagram of the running time of the concave frontier surface of an embodiment of the hypervolume calculation method in the product recommendation method of the present invention; wherein, Figure 3 (a) is a schematic diagram of the running time of the 6-dimensional concave frontier. Figure 3 (b) is a schematic diagram of the running time of the 7-dimensional concave frontier. Figure 3 (c) is a schematic diagram of the running time of the 8-dimensional concave frontier. Figure 3 (d) Schematic diagram of the running time of the 9-dimensional concave frontier.

[0063] Figure 4 This is a schematic diagram of the running time of the uniformsphere frontier surface of an embodiment of the hypervolume calculation method in the product recommendation method of the present invention; wherein, Figure 4 (a) is a schematic diagram of the running time of the 6-dimensional uniformsphere frontier. Figure 4(b) is a schematic diagram of the running time of the 7-dimensional uniformsphere frontier. Figure 4 (c) is a schematic diagram of the running time of the 8-dimensional uniformsphere frontier. Figure 4 (d) Schematic diagram of the running time of the 9-dimensional uniformsphere frontier.

[0064] Figure 5 Schematic diagram of the functional modules of the system of the present invention. DETAILED DESCRIPTION

[0065] like Figure 1 The product recommendation method disclosed in the present invention comprises the following steps:

[0066] A. Use multi-objective optimization algorithms to obtain recommendations for several types of products;

[0067] B. Obtain corresponding point set data based on the product recommendation solutions of several categories obtained in step A;

[0068] C. Use the hypervolume calculation method to calculate the hypervolume data corresponding to each product recommendation solution;

[0069] D. Select the product recommendation solution corresponding to the maximum value of the hypervolume data as the final product recommendation solution to complete the corresponding product recommendation;

[0070] The method for calculating the super volume described in step C comprises the following steps:

[0071] S1. Obtaining a solution set of a multi-objective optimization algorithm to be evaluated;

[0072] In the specific implementation process, a solution set generated by the multi-objective optimization algorithm to be evaluated is obtained, and the solution set includes multiple d-dimensional solutions obtained by the algorithm; for the calculation of the hypervolume, each d-dimensional solution can be regarded as a point in the d-dimensional space, so it can also be called a point set;

[0073] S2. Perform a normalization operation on the point set obtained in step S1; specifically, the steps include:

[0074] The point set obtained in step S1 is expressed as , where each point includes d dimensions; the i-th point Expressed as ;

[0075] Traverse the element values ​​of each dimension to get the maximum value on the kth dimension and the minimum value in the kth dimension ;

[0076] For each point ,right The values ​​of each dimension in are normalized using the following formula: In the formula is the value of the kth dimension of the i-th point after normalization; is the value of the kth dimension of the ith point before normalization;

[0077] By normalizing, we ensure The value of is in the range of 0 to 1;

[0078] S3. Based on the normalized point set obtained in step S2, the optimal point and the worst point are selected according to the properties of the multi-objective optimization algorithm to be evaluated; specifically, the steps include:

[0079] If the solution set of the multi-objective optimization algorithm to be evaluated is a maximization problem, then the optimal point is selected. for , the worst point r is ;

[0080] If the solution set of the multi-objective optimization algorithm to be evaluated is a minimization problem, then the optimal point is selected. for , the worst point r is ;

[0081] The maximization problem is defined as the problem that the larger the value, the better the performance. For example, in portfolio optimization, the higher the return on investment, the better the investment performance. The minimization problem is defined as the problem that the smaller the value, the better the performance. For example, in engineering design, the lower the cost of materials, the better the economy.

[0082] In the present invention, the main focus is on the maximization problem, so only the maximization problem will be considered in the following. At the same time, the minimization problem can be easily converted into the maximization problem, that is, 1 is subtracted from each element value after normalization to obtain a new element value. This conversion is feasible because after normalization, the maximum value of all elements is 1.

[0083] S4. Based on the current point set, select an axis point according to the relationship between the value of the element in the point set and the dimension of the point set; specifically, the steps include:

[0084] Set an empty set P;

[0085] For each point in the current point set , if point All dimensions of , then the point Put into the set P; among them, Representing a collection The element value is not greater than The number of elements in the set for ; To round up;

[0086] In the set P, choose The point with the largest value is used as the final axis point ;

[0087] S5. According to the selected pivot point, the elements in the current point set are divided into a number of subsets according to the size relationship between the element value of the current point set and the pivot point value; specifically, the steps include:

[0088] For each point in the current point set ,like The value in the kth dimension Greater than axis point The value in the kth dimension , then The point to be considered as the kth sub-problem;

[0089] Points to consider for the kth subproblem , the following rules are used for judgment and calculation:

[0090] when When The value of the jth dimension of The value is ;

[0091] when When The value of the jth dimension of The value is ;

[0092] when When The value of the jth dimension of The value is ;

[0093] Finally, the elements in the current point set are divided into several subsets;

[0094] S6. Determine the subsets obtained in step S5:

[0095] If the size of the subset is a set value, the hypervolume of the corresponding subset is directly calculated based on the selected optimal and worst points;

[0096] If the size of the subset is not the set value, the corresponding subset is used as the current point set, and the process returns to step S4 for the next round of iterative calculation;

[0097] The specific implementation includes the following steps:

[0098] exist In the d-dimensional space, given two points and , if and only if for every , all exist and , it is described as "x dominates y" and is expressed as ;

[0099] Given a set of points and reference point , the hypervolume of the point set S relative to r is defined as In the formula is the Lebesgue measure of the set, and , is the characteristic function, when hour ,when hour ;

[0100] If the size of the subset is 1, the hypervolume of the corresponding subset is calculated based on the selected optimal and worst points and the product of the points in the subset in each dimension; specifically, the hypervolume of the subset is calculated using the following formula: : In the formula is the value of point a in the subset in the i-th dimension, is the value of the worst point r in the i-th dimension; in specific implementation, since the subset size is 1, point a is the only point in the S set, and the present invention mainly focuses on the maximization problem, so the worst point r is ;

[0101] If the size of the subset is 2, the hypervolume of the corresponding subset is calculated based on the selected optimal and worst points, the product of the points in the subset in each dimension, and the product of the dimensions corresponding to the smaller values ​​of the two points in each dimension;

[0102] Specifically:

[0103] Calculate the hypervolume of point a in the subset The hypervolume of point b in the and subset ;

[0104] For point a and point b in the subset, compare the values ​​of the two points in each dimension in turn, and take the smaller value of each dimension to form the worse point ; Expressed as ;

[0105] Poor calculation The hypervolume ;

[0106] Finally, the hypervolume of the subset is calculated for ;

[0107] If the size of the subset is greater than 2, the corresponding subset is used as the current point set, and the process returns to step S4 for the next round of iterative calculation;

[0108] like Figure 2 As shown, this is a schematic diagram of the result of subset partitioning: point set , after division, two new points are generated and ; Finally, three new subsets were formed , and ;

[0109] S7. According to the obtained hypervolumes of all subsets, the calculation of the hypervolume corresponding to the solution set of the multi-objective optimization algorithm to be evaluated is completed; specifically comprising the following steps:

[0110] The hypervolumes of all the obtained subsets are added together to obtain the calculation result of the hypervolume corresponding to the solution set of the final multi-objective optimization algorithm to be evaluated.

[0111] Since the core content of the product recommendation method of the present invention lies in the related content of the super volume calculation method, the advantages of high reliability, good accuracy and high efficiency of the product recommendation method of the present invention are also brought about by the super volume calculation method; therefore, the effect of the super volume calculation method in the product recommendation method of the present invention is further described below in conjunction with an embodiment:

[0112] The objects tested are the convex test instances proposed by Lacour in the paper "A box decomposition algorithm to compute the hypervolume indicator" in 2017, and the instances generated by Jaszkiewicz and uniformly distributed on the multidimensional sphere; the number of targets of the objects can be up to 10, and the number of points can be up to 1000.

[0113] The hypervolume calculation method in the solution of the present invention is used to perform hypervolume calculation on the above two types of data sets, and the commonly used performance evaluation indicators: running time (Times) and number of branches (Number of operations) are used to compare and illustrate the performance of the method of the present invention with other existing solutions.

[0114] Performance comparison chart Figure 3 and 4As shown, the oQHV scheme is the scheme proposed by Russo in the paper “Quickhypervolume” in 2014, the QHV2 scheme is the scheme proposed by Jaszkiewicz in the paper “Improved quickhypervolume algorithm” in 2018, and the QHV2_R scheme is the hypervolume calculation scheme in the scheme of the present invention;

[0115] The test data are shown in Table 1, Table 2, Table 3 and Table 4:

[0116] Table 1 Schematic diagram of experimental results of branch number when the dataset size is 100~500 in concave dataset

[0117]

[0118] Table 2 Schematic diagram of experimental results of branch number when the dataset size is 600~1000 under concave dataset

[0119]

[0120] Table 3 Schematic diagram of experimental results of branch number when the dataset size is 100~500 in uniform_sphere dataset

[0121]

[0122] Table 4 Schematic diagram of experimental results of branch number when the dataset size is 600~1000 under uniform_sphere dataset

[0123]

[0124] In Tables 1 to 4, the unit of the data in the middle of the tables is the number of sub-problems, and its physical meaning is the number of sub-problems generated during the operation of the hypervolume calculation method in the solution of the present invention.

[0125] pass Figure 3 , Figure 4It can be seen from Tables 1 to 4 that the performance of the hypervolume calculation scheme in the scheme of the present invention becomes increasingly superior as the number of target dimensions and the number of target solutions increase. This is because the hypervolume calculation scheme in the scheme of the present invention combines constrained axis point selection and a uniform space division strategy, so it can not only ensure a reasonable number of sub-instances, but also effectively maintain the size balance of the sub-instances, thereby improving the computational efficiency. This superiority is particularly evident in high-dimensional data sets. The hypervolume calculation scheme in the scheme of the present invention exhibits lower running time and efficient computing power, which is significantly better than other comparison methods. Especially when processing high-dimensional data, the low running time of the hypervolume calculation scheme in the scheme of the present invention makes it an effective hypervolume calculation method. These results further demonstrate the applicability and superiority of the hypervolume calculation scheme in the scheme of the present invention in a high-dimensional environment, and provide strong support for its promotion in practical applications.

[0126] like Figure 5 The figure shows a schematic diagram of the functional modules of the system of the present invention: the system for implementing the product recommendation method disclosed in the present invention comprises a solution generation module, a point set acquisition module, a hypervolume calculation module and a product recommendation module; the solution generation module, the point set acquisition module, the hypervolume calculation module and the product recommendation module are connected in series in sequence; the solution generation module is used to adopt a multi-objective optimization algorithm to obtain several types of product recommendation solutions, and upload the data information to the point set acquisition module; the point set acquisition module is used to obtain corresponding point set data according to the received data information and the obtained several types of product recommendation solutions, and upload the data information to the hypervolume calculation module; the hypervolume calculation module is used to calculate the hypervolume data corresponding to each product recommendation solution according to the received data information by adopting the hypervolume calculation method, and upload the data information to the product recommendation module; the product recommendation module is used to select the product recommendation solution corresponding to the maximum hypervolume data value according to the received data information as the final product recommendation solution to complete the corresponding product recommendation.

[0127] In addition, the hypervolume calculation solution in the solution of the present invention can also be applied to other scenarios:

[0128] Scenario 1: Multi-objective optimization in engineering design

[0129] Taking automobile design as an example, automotive engineers need to make trade-offs between multiple performance indicators, such as:

[0130] Fuel efficiency: Vehicles should use fuel as efficiently as possible.

[0131] Safety: The vehicle should protect the safety of its occupants in a collision.

[0132] Cost: Manufacturing cost should be as low as possible in order to maintain price advantage in the fierce market competition.

[0133] Performance: The vehicle's acceleration and handling should meet expectations.

[0134] In this application, engineers can use multi-objective optimization algorithms such as NSGA-II or SPEA2 to explore the design space. During the design process, hypervolume is used to measure the quality of the solution set found.

[0135] (1) Suppose that engineers have obtained several design solutions through optimization algorithms. These solutions have different performances in terms of fuel efficiency, safety, and cost.

[0136] (2) By calculating the hypervolume of these solutions in the target space, engineers can derive a number that represents the effective area of ​​the target space covered by these solutions.

[0137] (3) A larger hypervolume means that the design set has more valid solutions for all objectives. Conversely, a smaller hypervolume means that the design is concentrated on a few solutions and lacks diversity.

[0138] For example, if a design optimization algorithm ends up with three different design solutions, they form a region in the three-dimensional objective space. If the calculated hypervolume is larger than the hypervolumes of the other solutions, it can be concluded that the algorithm is more successful in finding diverse solutions that perform well on multiple objectives. Ultimately, this will guide engineers to choose the best design solution and balance different design requirements.

[0139] This example shows the usefulness of hypervolume in multi-objective optimization processes, helping engineers identify and select better solutions in complex design decisions.

[0140] Scenario 2: Advertising

[0141] In advertising, multi-objective optimization often involves multiple performance indicators, such as:

[0142] Click-through rate (CTR): How often your ad is clicked.

[0143] Conversion rate (CR): The proportion of users who actually make a purchase or other target behavior after clicking.

[0144] Cost per click (CPC or CPM): The cost of your ad per click or per thousand impressions.

[0145] User coverage: The range of audiences reached by the advertisement.

[0146] In such situations, advertisers need to balance multiple goals, such as increasing click-through rate and conversion rate while minimizing costs.

[0147] (1) Multi-objective optimization problem setting: Suppose a company is running digital advertising and its goal is to optimize the three indicators of click-through rate, conversion rate, and advertising cost. The setting of advertising strategy can significantly affect the performance of these indicators.

[0148] (2) Generate solution sets of different strategies: By using multi-objective optimization algorithms (such as genetic algorithms, particle swarm optimization, etc.), a variety of different advertising delivery strategies can be generated. These strategies may perform differently in different situations.

[0149] (3) Calculate the hypervolume: After evaluating all generated strategies in the multidimensional target space, calculate the hypervolume of each strategy. The size of the hypervolume can represent the area that can be covered by the optimization solution within the set target range.

[0150] (4) Select the best strategy: A larger hypervolume indicates that the advertising strategy is more competitive in terms of all objectives (such as high click-through rate, high conversion rate, and low cost). Advertisers can choose the best delivery strategy based on this hypervolume indicator.

[0151] In this way, advertisers can not only evaluate the effectiveness of different advertising strategies, but also discover new delivery combinations to optimize the overall performance of the campaign. This application effectively integrates the concept of hypervolume into the decision-making process of advertising delivery, achieving scientific decision-making in a multi-objective environment.

[0152] In addition, the calculation process of hypervolume can also be used in the following fields:

[0153] Algorithm comparison and selection: In evolutionary algorithms and other optimization algorithms, hypervolume is used as a performance metric to compare the effects of different algorithms in multi-objective optimization tasks;

[0154] Engineering design and optimization: For example, in the fields of automotive design and aerospace engineering, hypervolume is used to measure the advantages and balance of different design schemes in terms of performance indicators;

[0155] Environmental Science and Ecology: In biodiversity assessment and ecosystem research, quantitative evaluation of ecological complexity and diversity by calculating the supervolume of species traits;

[0156] Finance and Economics: In portfolio optimization, hypervolume is used to assess the trade-off between risk and return, helping investors develop better investment strategies;

[0157] Computational geometry and graphics: In the field of computational geometry, hypervolumes are used to calculate the volume of high-dimensional shapes. Related research can be applied to graphics rendering, path planning, and robot motion planning.

[0158] Advertisement delivery optimization: In digital marketing, hyper-volume is used to evaluate the performance of different advertising strategies in terms of multiple objectives such as click-through rate, conversion rate, and cost, so as to make more effective delivery decisions.

[0159] Correspondingly, these application scenarios also illustrate the importance of hypervolume in the analysis and decision support of complex problems in multiple fields, enabling decision makers to find the best solutions in multi-objective environments.

Claims

1. A product recommendation method, characterized in that The steps include: A. Use multi-objective optimization algorithms to obtain recommendations for several types of products; B. Obtain corresponding point set data based on the product recommendation solutions of several categories obtained in step A; C. Use the hypervolume calculation method to calculate the hypervolume data corresponding to each product recommendation solution; D. Select the product recommendation solution corresponding to the maximum value of the hypervolume data as the final product recommendation solution to complete the corresponding product recommendation; The method for calculating the super volume described in step C comprises the following steps: S1. Obtaining a point set of a multi-objective optimization algorithm to be evaluated; S2. performing a normalization operation on the point set obtained in step S1; S3. Based on the normalized point set obtained in step S2, the optimal point and the worst point are selected according to the properties of the multi-objective optimization algorithm to be evaluated; S4. Based on the current point set, select an axis point according to the relationship between the value of the element in the point set and the dimension of the point set; S5. according to the selected pivot point, the elements in the current point set are divided into a number of subsets according to the magnitude relationship between the element values ​​of the current point set and the pivot point values; S6. Determine the subsets obtained in step S5: If the size of the subset is a set value, the hypervolume of the corresponding subset is directly calculated based on the selected optimal and worst points; If the size of the subset is not the set value, the corresponding subset is used as the current point set, and the process returns to step S4 for the next round of iterative calculation; S7. Based on the obtained hypervolumes of all subsets, the calculation of the hypervolume corresponding to the point set of the multi-objective optimization algorithm to be evaluated is completed.

2. The product recommendation method according to claim 1, characterized in that The step S2 specifically includes the following steps: The point set obtained in step S1 is expressed as , where each point includes d dimensions; the i-th point Expressed as ; Traverse the element values ​​of each dimension to get the maximum value on the kth dimension and the minimum value in the kth dimension ; For each point ,right The values ​​of each dimension in are normalized using the following formula: In the formula is the value of the kth dimension of the i-th point after normalization; is the value of the kth dimension of the ith point before normalization.

3. The product recommendation method according to claim 2, characterized in that The step S3 specifically includes the following steps: If the point set of the multi-objective optimization algorithm to be evaluated is a maximization problem, then select the optimal point for , the worst point r is ; If the point set of the multi-objective optimization algorithm to be evaluated is a minimization problem, then select the optimal point for , the worst point r is ; The maximization problem is defined as the larger the value, the better the performance; the minimization problem is defined as the smaller the value, the better the performance.

4. The product recommendation method according to claim 3, characterized in that The step S4 specifically comprises the following steps: Set an empty set P; For each point in the current point set , if point All dimensions of , then the point Put into the set P; among them, Representing a collection The element value is not greater than The number of elements in the set for ; To round up; In the set P, choose The point with the largest value is used as the final axis point .

5. The product recommendation method according to claim 4, characterized in that The step S5 specifically includes the following steps: For each point in the current point set ,like The value in the kth dimension Greater than axis point The value in the kth dimension , then The point to be considered as the kth sub-problem; Points to consider for the kth subproblem , the following rules are used for judgment and calculation: when When The value of the jth dimension of The value is ; when When The value of the jth dimension of The value is ; when When The value of the jth dimension of The value is ; Finally, the elements in the current point set are divided into several subsets.

6. The product recommendation method according to claim 5, characterized in that The step S6 comprises the following steps: If the size of the subset is 1, the hypervolume of the corresponding subset is calculated based on the selected optimal and worst points and the product of the points in the subset in each dimension; If the size of the subset is 2, the hypervolume of the corresponding subset is calculated based on the selected optimal and worst points, the product of the points in the subset in each dimension, and the product of the dimensions corresponding to the smaller values ​​of the two points in each dimension; If the size of the subset is greater than 2, the corresponding subset is used as the current point set, and the process returns to step S4 for the next round of iterative calculation; The specific implementation includes the following steps: If the size of the subset is 1: The hypervolume of the subset is calculated using the following formula: : In the formula is the value of point a in the subset in the i-th dimension, is the value of the worst point r in the i-th dimension; If the size of the subset is 2: Calculate the hypervolume of point a in the subset The hypervolume of point b in the and subset ; For point a and point b in the subset, compare the values ​​of the two points in each dimension in turn, and take the smaller value of each dimension to form the worse point ; Expressed as ; Poor calculation The hypervolume ; Finally, the hypervolume of the subset is calculated for ; If the size of the subset is greater than 2: The corresponding subset is taken as the current point set, and the process returns to step S4 for the next round of iterative calculation.

7. The product recommendation method according to claim 6, characterized in that The step S7 specifically includes the following steps: The hypervolumes of all the obtained subsets are added together to obtain the calculation result of the hypervolume corresponding to the final point set of the multi-objective optimization algorithm to be evaluated.

8. A system for implementing the product recommendation method according to any one of claims 1 to 7, characterized in that It includes a solution generation module, a point set acquisition module, a hypervolume calculation module and a product recommendation module; the solution generation module, the point set acquisition module, the hypervolume calculation module and the product recommendation module are connected in series in sequence; the solution generation module is used to adopt a multi-objective optimization algorithm to obtain a number of product recommendation solutions, and upload the data information to the point set acquisition module; the point set acquisition module is used to obtain the corresponding point set data according to the received data information and the obtained product recommendation solutions, and upload the data information to the hypervolume calculation module; The hypervolume calculation module is used to calculate the hypervolume data corresponding to each product recommendation solution based on the received data information using the hypervolume calculation method, and upload the data information to the product recommendation module; The product recommendation module is used to select the product recommendation solution corresponding to the maximum value of the hypervolume data according to the received data information as the final product recommendation solution to complete the corresponding product recommendation.

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