CN119027221B - Product recommendation method and system - Google Patents
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Abstract
本发明公开了一种产品推荐方法，包括采用多目标优化算法获取若干类产品推荐方案；根据若干类产品推荐方案获取对应的点集数据；采用超体积计算方法计算得到各个产品推荐方案所对应的超体积数据；选择超体积数据值最大时所对应的产品推荐方案作为最终的产品推荐方案，完成产品推荐。本发明还公开了一种实现所述产品推荐方法的系统。本发明通过最优点、最劣点和轴点的选取，合理地将复杂的超体积计算问题循环划分为若干个较为简单的子集的超体积的计算问题，因此本发明不仅能够实现基于超体积计算的产品推荐，而且本发明的可靠性更高，精确性更好，效率也更高。
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 the 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
The invention belongs to the field of data signal processing, and particularly relates to a product recommendation method and system.
Background
The multi-objective optimization algorithm is one of optimization algorithms widely applied at the present stage, can be applied to the field of product design optimization, comprehensively considers a plurality of targets such as cost, performance and reliability of products, can be applied to the field of project management in the resource allocation field, and can be applied to the fields of optimizing time, cost, quality and the like, and the multi-objective optimization algorithm can also be applied to the fields of ecological system management field, financial investment combination optimization and the like.
In the field of multi-objective optimization, the evaluation problem of the multi-objective optimization algorithm is always one of the research focuses of researchers. The solution set performance evaluation of the multi-objective optimization algorithm mainly comprises the convergence evaluation of the solution set, the uniformity evaluation of the solution set and the ductility evaluation of the solution set. Among the multiple evaluation indexes of the multi-objective optimization algorithm, the super-volume evaluation index is one of indexes with the best comprehensive evaluation effect. Therefore, the method is particularly important for the super-volume calculation corresponding to the solution set of the multi-objective optimization algorithm.
From the research results at the present stage, in the three-dimensional and four-dimensional problems, the calculation process of the super volume can be completed with less time cost. However, the problem of the super-volume calculation is thatThe problem is that the calculation time of the super volume increases exponentially with the increase of the target number. In the present stage, in ten and more multi-objective optimization problems, the accurate calculation process of the super volume is extremely complex, and consumes extremely large time and space resources.
Correspondingly, the product recommendation method for evaluating the super-volume index also has the problems of complex scheme, and more occupied time and space resources.
Disclosure of Invention
One of the purposes of the invention is to provide a product recommendation method with high reliability, good accuracy and high efficiency.
The second object of the present invention is to provide a system for implementing the product recommendation method.
The product recommendation method provided by the invention comprises the following steps:
A. acquiring a plurality of product recommendation schemes by adopting a multi-objective optimization algorithm;
B. C, acquiring corresponding point set data according to the plurality of product recommendation schemes obtained in the step A;
C. adopting an ultra-volume calculation method to calculate and obtain ultra-volume data corresponding to each product recommendation scheme;
D. Selecting a product recommendation scheme corresponding to the maximum super-volume data value as a final product recommendation scheme to finish corresponding product recommendation;
The method for calculating the super volume in the step C comprises the following steps:
s1, acquiring a solution set of a multi-objective optimization algorithm to be evaluated;
S2, carrying out normalization operation on the point set obtained in the step S1;
S3, selecting an optimal point and a worst point according to the properties of the multi-objective optimization algorithm to be evaluated based on the normalized point set obtained in the step S2;
S4, selecting an axial point based on the current point set according to the relation between the element value in the point set and the dimension of the point set;
S5, dividing the elements in the current point set into a plurality of subsets according to the selected axis points and the size relation between the element values of the current point set and the axis point values;
s6, judging the subsets obtained in the step S5:
If the scale of the subset is a set value, directly calculating to obtain the supersvolume of the corresponding subset according to the selected optimal point and the selected worst point;
If the scale of the subset is not the set value, taking the corresponding subset as the current point set, and returning to the step S4 to perform the next round of iterative computation;
and S7, according to the obtained supersvolume of all the subsets, completing the calculation of the supersvolume corresponding to the solution set of the multi-objective optimization algorithm to be evaluated.
The step S2 specifically comprises the following steps:
the point set acquired in step S1 is expressed as Wherein each point comprises d dimensions, the ith pointRepresented as;
Traversing the element value of each dimension to obtain the maximum value of the kth dimensionAnd a minimum in the kth dimension;
For each pointFor a pair ofThe values of each dimension in (c) are normalized using the following equation: In the middle of The value of the kth dimension of the ith point after normalization; is the value of the kth dimension of the ith point before normalization.
The step S3 specifically comprises the following steps:
If the solution set of the multi-objective optimization algorithm to be evaluated is the maximization problem, selecting the optimal point Is thatThe worst point r is;
If the solution set of the multi-objective optimization algorithm to be evaluated is the minimization problem, selecting the optimal pointIs thatThe worst point r is;
The maximization problem is defined as the better the performance as the value is larger, and the minimization problem is defined as the better the performance as the value is smaller. In the present invention, the focus is mainly on the maximization problem, so only the maximization problem will be considered later. It is worth emphasizing that minimizing problems can be easily translated into maximizing problems. Specifically, 1 is subtracted from each normalized element value to obtain a new element value. This conversion is possible because the maximum value of all elements is 1 after normalization.
The step S4 specifically comprises the following steps:
setting an empty set P;
for each point in the current set of points If it isAll dimensions of (1) satisfyWill be pointedPut into the collection P, wherein,Representing a collectionThe element value of the medium is not more thanElement number, collection of (2)Is that;Is rounded upwards;
In the set P, the selection is such that The point with the maximum value is taken as the final axis point。
The step S5 specifically comprises the following steps:
Each point in the current set of points If (if)Values in the kth dimensionGreater than the axis pointValues in the kth dimensionWill thenPoints to be considered as the kth sub-problem;
Points to consider for the kth sub-problem The following rules are used for determination and calculation:
When (when) When the dot is toThe value of the j-th dimension of (2)Take the value of;
When (when)When the dot is toThe value of the j-th dimension of (2)Take the value of;
When (when)When the dot is toThe value of the j-th dimension of (2)Take the value of;
Finally, the elements in the current point set are divided into subsets.
The step S6 comprises the following steps:
if the scale of the subset is 1, calculating to obtain the supersvolume of the corresponding subset according to the product of the selected optimal point and the selected worst point and the points in the subset in each dimension;
If the scale of the subset is 2, calculating to obtain the supersvolume of the corresponding subset according to the selected optimal point and the worst point, the product of the points in the subset in each dimension and the product of the points in the dimension corresponding to the smaller value in each dimension of the two points;
if the scale of the subset is larger than 2, the corresponding subset is used as the current point set, and the step S4 is returned to perform the next round of iterative computation.
The step S6 specifically comprises the following steps:
if the size of the subset is 1:
the supersolume of the subset is calculated using the following equation :In the middle ofFor the value of point a in the subset in the i-th dimension,In practice, point a is the only point of the S set because the subset size is 1, and the invention focuses mainly on maximizing the problem, so the worst point r is;
If the size of the subset is 2:
Computing the supersolume of point a in the sub-set And the supersvolume of point b in the subset;
Comparing the values of the points in each dimension with respect to the points a and b in the subset, and taking smaller values of each dimension to form worse points;Represented as;
Calculating the worse pointIs of an ultra-volume of (2);
Finally, calculating the super volume of the subsetIs that;
If the size of the subset is greater than 2:
and taking the corresponding subset as the current point set, and returning to the step S4 to perform the next round of iterative computation.
The step S7 specifically comprises the following steps:
And adding the obtained superscripts of all the subsets to obtain a final calculation result of the superscripts corresponding to the solution set of the multi-objective optimization algorithm to be evaluated.
The invention further provides a system for realizing the product recommendation method, which comprises a scheme generation module, a point set acquisition module, a super-volume calculation module and a product recommendation module, wherein the scheme generation module, the point set acquisition module, the super-volume calculation module and the product recommendation module are sequentially connected in series, the scheme generation module is used for acquiring a plurality of types of product recommendation schemes by adopting a multi-objective optimization algorithm and uploading data information to the point set acquisition module, the point set acquisition module is used for acquiring corresponding point set data according to the received data information and the obtained plurality of types of product recommendation schemes and uploading the data information to the super-volume calculation module, the super-volume calculation module is used for calculating super-volume data corresponding to each product recommendation scheme according to the received data information and uploading the data information to the product recommendation module, and the product recommendation module is used for selecting the product recommendation scheme corresponding to the maximum super-volume data value as the final product recommendation scheme so as to finish the corresponding product recommendation.
According to the product recommendation method and system provided by the invention, the complex hypervolume calculation problem is reasonably circularly divided into the hypervolume calculation problems of a plurality of simpler subsets through the selection of the optimal point, the worst point and the axis point, so that the product recommendation method and system based on the hypervolume calculation not only can realize the product recommendation based on the hypervolume calculation, but also has higher reliability, better accuracy and higher efficiency
Drawings
Fig. 1 is a schematic flow chart of a product recommendation method according to the present invention.
Fig. 2 is a schematic view of a subset division of the super-volume calculation method in the product recommendation method of the present invention.
FIG. 3 is a schematic diagram of the run time of the concave front of an embodiment of the super volume computing method in the product recommendation method of the present invention, wherein FIG. 3 (a) is a schematic diagram of the run time of the 6-dimensional concave front, FIG. 3 (b) is a schematic diagram of the run time of the 7-dimensional concave front, FIG. 3 (c) is a schematic diagram of the run time of the 8-dimensional concave front, and FIG. 3 (d) is a schematic diagram of the run time of the 9-dimensional concave front.
Fig. 4 is a schematic diagram of the run time of the uniformsphere front of the embodiment of the super-volume computing method in the product recommendation method according to the present invention, in which fig. 4 (a) is a schematic diagram of the run time of the 6-dimensional uniformsphere front, fig. 4 (b) is a schematic diagram of the run time of the 7-dimensional uniformsphere front, fig. 4 (c) is a schematic diagram of the run time of the 8-dimensional uniformsphere front, and fig. 4 (d) is a schematic diagram of the run time of the 9-dimensional uniformsphere front.
FIG. 5 is a schematic diagram of functional modules of the system of the present invention.
Detailed Description
The method for recommending the product disclosed by the invention comprises the following steps:
A. acquiring a plurality of product recommendation schemes by adopting a multi-objective optimization algorithm;
B. C, acquiring corresponding point set data according to the plurality of product recommendation schemes obtained in the step A;
C. adopting an ultra-volume calculation method to calculate and obtain ultra-volume data corresponding to each product recommendation scheme;
D. Selecting a product recommendation scheme corresponding to the maximum super-volume data value as a final product recommendation scheme to finish corresponding product recommendation;
The method for calculating the super volume in the step C comprises the following steps:
s1, acquiring a solution set of a multi-objective optimization algorithm to be evaluated;
in the specific implementation process, a solution set generated by a multi-objective optimization algorithm to be evaluated is obtained, wherein the solution set comprises a plurality of d-dimensional solutions obtained by the algorithm, and for the calculation of the super volume, each d-dimensional solution can be regarded as a point in a d-dimensional space, so that the solution set can also be called as a point set;
s2, carrying out normalization operation on the point set obtained in the step S1, wherein the method specifically comprises the following steps:
the point set acquired in step S1 is expressed as Wherein each point comprises d dimensions, the ith pointRepresented as;
Traversing the element value of each dimension to obtain the maximum value of the kth dimensionAnd a minimum in the kth dimension;
For each pointFor a pair ofThe values of each dimension in (c) are normalized using the following equation: In the middle of The value of the kth dimension of the ith point after normalization; A value of a kth dimension that is an ith point before normalization;
By normalization, ensure The value of (2) is in the range of 0-1;
S3, selecting the optimal point and the worst point according to the property of the multi-objective optimization algorithm to be evaluated based on the normalized point set obtained in the step S2, wherein the method specifically comprises the following steps:
If the solution set of the multi-objective optimization algorithm to be evaluated is the maximization problem, selecting the optimal point Is thatThe worst point r is;
If the solution set of the multi-objective optimization algorithm to be evaluated is the minimization problem, selecting the optimal pointIs thatThe worst point r is;
The maximization problem is defined as a problem that the larger the value is, the better the performance is, for example, in investment portfolio optimization, the higher the return on investment is, the better the investment performance is; the minimization problem is defined as a problem that the smaller the value is, the better the performance is, for example, in engineering design, the lower the cost of materials is, the better the economy is;
In the invention, the maximization problem is mainly focused, so that only the maximization problem is considered later, and meanwhile, the minimization problem can be conveniently converted into the maximization problem, namely, 1 is subtracted from each normalized element value to obtain a new element value, and the conversion is feasible because the maximum value of all elements is 1 after normalization treatment;
s4, selecting an axis point based on the relation between the size of element values in the point set and the dimension of the point set, wherein the method specifically comprises the following steps:
setting an empty set P;
for each point in the current set of points If it isAll dimensions of (1) satisfyWill be pointedPut into the collection P, wherein,Representing a collectionThe element value of the medium is not more thanElement number, collection of (2)Is that;Is rounded upwards;
In the set P, the selection is such that The point with the maximum value is taken as the final axis point;
S5, dividing the elements in the current point set into a plurality of subsets according to the selected axis points and the size relation between the element values of the current point set and the axis point values, wherein the method specifically comprises the following steps:
Each point in the current set of points If (if)Values in the kth dimensionGreater than the axis pointValues in the kth dimensionWill thenPoints to be considered as the kth sub-problem;
Points to consider for the kth sub-problem The following rules are used for determination and calculation:
When (when) When the dot is toThe value of the j-th dimension of (2)Take the value of;
When (when)When the dot is toThe value of the j-th dimension of (2)Take the value of;
When (when)When the dot is toThe value of the j-th dimension of (2)Take the value of;
Finally, dividing the elements in the current point set into a plurality of subsets;
s6, judging the subsets obtained in the step S5:
If the scale of the subset is a set value, directly calculating to obtain the supersvolume of the corresponding subset according to the selected optimal point and the selected worst point;
If the scale of the subset is not the set value, taking the corresponding subset as the current point set, and returning to the step S4 to perform the next round of iterative computation;
The specific implementation method comprises the following steps:
At the position of In d-dimensional space of (2), two points are givenAndIf and only if for eachAre all provided withAnd is also provided withThen described as "x dominates y" and denoted as;
Given point setAnd reference pointThe supersvolume of the point set S relative to r is defined asIn the middle ofIs a set of Leberg measures, and,As a characteristic function whenTime of dayWhen (when)Time of day;
If the scale of the subset is 1, the supersvolume of the corresponding subset is calculated according to the products of the selected optimal point and the worst point and the points in the subset in each dimension, specifically, the supersvolume of the subset is calculated by adopting the following formula:In the middle ofFor the value of point a in the subset in the i-th dimension,In practice, point a is the only point of the S set because the subset size is 1, and the invention focuses mainly on maximizing the problem, so the worst point r is;
If the scale of the subset is 2, calculating to obtain the supersvolume of the corresponding subset according to the selected optimal point and the worst point, the product of the points in the subset in each dimension and the product of the points in the dimension corresponding to the smaller value in each dimension of the two points;
the method comprises the following steps:
Computing the supersolume of point a in the sub-set And the supersvolume of point b in the subset;
Comparing the values of the points in each dimension with respect to the points a and b in the subset, and taking smaller values of each dimension to form worse points;Represented as;
Calculating the worse pointIs of an ultra-volume of (2);
Finally, calculating the super volume of the subsetIs that;
If the scale of the subset is larger than 2, the corresponding subset is used as the current point set, and the step S4 is returned to carry out the next round of iterative computation;
as shown in FIG. 2, a schematic diagram of the result of the division of the subsets is a set of points After division, two new points are generatedAndAnd finally three new subsets are formed、And;
S7, according to the obtained supersvolume of all the subsets, completing the calculation of the supersvolume corresponding to the solution set of the multi-objective optimization algorithm to be evaluated, wherein the method specifically comprises the following steps:
And adding the obtained superscripts of all the subsets to obtain a final calculation result of the superscripts corresponding to the solution set of the multi-objective optimization algorithm to be evaluated.
The product recommendation method has the core content of the related content of the super-volume calculation method, has the advantages of high reliability, good accuracy and higher efficiency, and is also based on the super-volume calculation method, so that the effect of the super-volume calculation method in the product recommendation method is further described by combining an embodiment:
The tested objects are convex test examples proposed in paper A box decomposition algorithm to compute the hypervolume indicator in 2017 by Lacour and examples which are generated by Jaszkiewicz and are uniformly distributed on the multi-dimensional sphere, the target number of the objects can be up to 10, and the number of the points can be up to 1000.
The super-volume calculation method in the scheme of the invention is adopted to perform super-volume calculation on the class 2 data set, and the common performance evaluation indexes, namely the running time (Times) and the branch number (Numberofoperations), are used for comparing and describing the performance of the method with other existing schemes.
The performance comparison diagrams are shown in fig. 3 and 4, wherein oQHV is a scheme proposed by Russo in 2014 in paper "Quick hypervolume", QHV2 is a scheme proposed by Jaszkiewicz in 2018 in paper "Improved quick hypervolume algorithm", and qhv2_r is an over-volume calculation scheme in the scheme of the invention;
The test data are shown in tables 1,2,3 and 4:
TABLE 1 schematic table of branch number experiment results for dataset sizes of 100-500 under concave datasets
TABLE 2 schematic Table of branch number experiment results for datasets with dataset sizes of 600-1000 under concave datasets
TABLE 3 Branch number Experimental results schematic Table for data set sizes of 100-500 under the unitorm_sphere data set
TABLE 4 Branch number Experimental results schematic Table for data set sizes of 600-1000 under the unitorm_sphere data set
In tables 1 to 4, the data in the middle of the tables is the number of sub-problems, and the physical meaning of the data is the number of the sub-problems generated in the operation process of the super-volume calculation method in the scheme of the invention.
As can be seen from FIGS. 3,4 and tables 1-4, the super-volume calculation scheme in the scheme of the present invention has an increasingly superior performance as the number of target dimensions and the number of target solutions increases. The method is characterized in that the super-volume calculation scheme in the scheme combines the constrained axis point selection and the uniform space division strategy, so that the reasonable number of sub-instances can be ensured, the size balance of the sub-instances can be effectively maintained, and the calculation efficiency is improved. This advantage is particularly pronounced in high-dimensional datasets. The super-volume calculation scheme in the scheme of the invention has lower running time and high calculation capability and is obviously superior to other comparison methods. Particularly when processing high-dimensional data, the low running time of the super-volume calculation scheme in the scheme of the invention makes the super-volume calculation method an effective super-volume calculation method. These results further demonstrate the applicability and superiority of the super-volume computing scheme in the scheme of the invention in a high-dimensional environment, and provide powerful support for popularization in practical application.
The system for realizing the product recommendation method comprises a scheme generating module, a point set acquiring module, a super-volume calculating module and a product recommendation module, wherein the scheme generating module, the point set acquiring module, the super-volume calculating module and the product recommendation module are sequentially connected in series, the scheme generating module is used for acquiring a plurality of types of product recommendation schemes by adopting a multi-objective optimization algorithm and uploading data information to the point set acquiring module, the point set acquiring module is used for acquiring corresponding point set data according to the received data information and the obtained plurality of types of product recommendation schemes and uploading the data information to the super-volume calculating module, the super-volume calculating module is used for calculating super-volume data corresponding to each product recommendation scheme according to the received data information and uploading the data information to the product recommendation module, and the product recommendation module is used for selecting the product recommendation scheme corresponding to the maximum super-volume data value as a final product recommendation scheme according to the received data information so as to complete the corresponding product recommendation.
In addition, the super-volume calculation scheme in the scheme of the invention can be applied to other scenes:
Scenario 1 Multi-objective optimization in engineering design
Taking the automotive design as an example, automotive engineers need to trade-off between multiple performance metrics, such as:
fuel efficiency-the vehicle should use fuel as efficiently as possible.
Safety-the safety of the vehicle in the event of a collision should be protected.
Cost-manufacturing costs should be as low as possible in order to maintain price advantage in a strong market competition.
Performance-acceleration and handling properties of the vehicle should be expected.
In this application, engineers may use multi-objective optimization algorithms (such as NSGA-II or SPEA 2) to explore the design space. In the design process, the supersvolume is used to measure the quality of the found solution set.
(1) It is assumed that engineers are deriving several designs through optimization algorithms that behave differently in three dimensions of fuel efficiency, safety, and cost.
(2) By calculating the supersvolume of these schemes in the target space, the engineer can derive a number that indicates that these schemes cover the active area of the target space.
(3) A larger supersvolume means that the design set has more effective solutions on all targets, whereas a design comparison is concentrated on a few solutions, lacking diversity.
For example, if a design optimization algorithm ultimately yields three different designs, they form a region in three-dimensional object space. If the calculated supersvolume is larger than that of other schemes, it can be concluded that the algorithm is more successful in finding a variety of solutions, and that these solutions perform well on multiple targets. Ultimately, this will guide engineers in choosing the best design, balancing the different design requirements.
By way of this example, the utility of supersvolume in a multi-objective optimization process can be seen, helping engineers identify and select a better solution in complex design decisions.
Scene 2 advertisement delivery
In advertising, multi-objective optimization often involves multiple performance metrics, such as:
click Through Rate (CTR), the frequency with which advertisements are clicked.
Conversion Rate (CR) is the proportion of users who actually make purchases or other target actions after clicking.
The cost of delivery (CPC or CPM) is the cost of showing an advertisement per click or thousands of times.
User coverage is the audience range reached by the advertisement contact.
In such cases, advertisers need to trade-off between goals, such as increasing click-through and conversion rates while minimizing costs.
(1) The multi-objective optimization problem is set by assuming that a company is carrying out digital advertisement delivery, and the objective is to optimize three indexes of click rate, conversion rate and advertisement cost. The setting of the advertisement placement strategy can significantly affect the performance of these metrics.
(2) A solution set of different strategies is generated-by using a multi-objective optimization algorithm (e.g., genetic algorithm, particle swarm optimization, etc.), a plurality of different advertising strategies may be generated. These strategies may behave differently in different situations.
(3) And calculating the supersvolume, namely, after all the generated strategies are evaluated in the multidimensional target space, calculating the supersvolume of each strategy. The size of the supersolume may represent the area that can be covered by the optimization scheme within a set target range.
(4) The selection of the best strategy, a larger supersvolume, indicates that the advertisement placement strategy is more competitive on all targets (e.g., high click-through rate, high conversion rate, and low cost). The advertiser may select an optimal placement strategy based on this supersvolume indicator.
In this way, advertisers can not only evaluate the effectiveness of different advertising strategies, but also discover new impression combinations, thereby optimizing the overall performance of the advertising campaign. The application effectively integrates the concept of super volume into the decision process of advertisement delivery, and realizes scientific decision in a multi-target environment.
In addition, the calculation process of the super volume can be used in the following fields:
Algorithm comparison and selection, wherein in an evolutionary algorithm and other optimization algorithms, the supersvolume is used as a performance index for comparing the effects of different algorithms in a multi-objective optimization task;
Engineering design and optimization, such as automobile design, aerospace engineering and other fields, the super volume is used for measuring the advantages and balance of different design schemes on performance indexes;
Environmental science and ecology, in the evaluation of biological diversity and the study of an ecological system, the ecological complexity and diversity are quantitatively evaluated by calculating the supersvolume of species characteristics;
Finance and economics-in investment portfolio optimization, supersvolume is used to evaluate trade-off between risk and return, helping investors to formulate better investment strategies;
in the field of calculation geometry, the super volume is used for calculating the volume of a high-dimensional shape, and related research can be applied to graphic rendering, path planning and robot motion planning;
Advertisement delivery optimization in digital marketing, the performance of different advertisement strategies on multiple targets such as click rate, conversion rate, cost and the like is evaluated through super volume so as to make more effective delivery decisions.
Correspondingly, these application scenarios also illustrate the importance of supersolume in multiple fields for analysis and decision support of complex problems, enabling a decision maker to find an optimal solution in a multi-objective environment.
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