Method, apparatus, and storage medium for determining Pareto-optimal multi-objective tasks

Abstract

This invention provides a method, apparatus, and storage medium for determining multi-objective tasks based on Pareto optimality, belonging to the field of multi-objective optimization technology. The determination method includes: for a multi-objective task solved by a multi-objective optimization algorithm, selecting multiple performance metrics to measure the multi-objective task; calculating the performance of each multi-objective optimization algorithm on each performance metric to form a multi-level Pareto front; based on the multi-level Pareto front, using at least one preset ranking algorithm, calculating the ranking of each multi-objective optimization algorithm; and determining the corresponding multi-objective task based on the calculated ranking of each multi-objective optimization algorithm. It considers multiple performance metrics, reducing bias introduced by a single performance metric, and provides a more comprehensive solution to multi-objective tasks; it utilizes a non-dominated ranking algorithm for fair and reasonable algorithm selection; it equips algorithms with multiple ranking methods; and it allows users to intuitively and visually understand multiple algorithms for solving multi-objective tasks.

Description

Technical Field

[0001] This invention relates to the field of multi-objective optimization technology, and more specifically to a method, apparatus, and storage medium for determining multi-objective tasks based on Pareto optimality. Background Technology

[0002] With the increasing prevalence of multi-objective optimization problems in real-world applications, numerous multi-objective optimization algorithms have been developed to address these issues. In practice, these algorithms need to handle a set of conflicting objectives, making it challenging to find the optimal solution. To evaluate the quality of the solution set generated by multi-objective algorithms, multiple performance metrics are typically used, but each metric may have its advantages and limitations.

[0003] In related technologies, algorithms are usually evaluated based on a single or a few performance metrics, which may introduce bias and lead to a one-sided understanding of the algorithm's performance, resulting in an incomplete ranking of algorithms. It is also inconvenient to accommodate newly introduced performance metrics or newly added algorithms, resulting in poor flexibility and scalability. Furthermore, it may lead to contradictions between several performance metrics, making the overall ranking of algorithms more complex. In addition, the ranking results of each algorithm cannot be presented intuitively and visually for easy user understanding. Summary of the Invention

[0004] The purpose of this invention is to provide a method, apparatus, and storage medium for determining multi-objective tasks based on Pareto optimality. This aims to solve the problems of existing technologies that rely on a single or a few performance indicators to evaluate algorithms, which introduce bias, lack flexibility and scalability, have contradictory performance indicators, and cannot intuitively visualize ranking results.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for determining a multi-objective task based on Pareto optimality. The method includes: for a multi-objective task solved by a multi-objective optimization algorithm, selecting multiple performance metrics to measure the multi-objective task; calculating the performance of each multi-objective optimization algorithm on each performance metric to form a multi-level Pareto front, where the Pareto front refers to the set of Pareto optimal performance scores corresponding to the multiple performance metrics; based on the multi-level Pareto front, using at least one preset ranking algorithm to calculate the ranking of each multi-objective optimization algorithm; and determining the corresponding multi-objective task based on the calculated ranking of each multi-objective optimization algorithm.

[0006] Optionally, the step of calculating the performance of each multi-objective optimization algorithm for each performance metric to form a multi-level Pareto front includes: for each multi-objective optimization algorithm, calculating the performance score of the algorithm for each performance metric multiple times to form a performance score matrix for that multi-objective optimization algorithm, wherein each row of the performance score matrix represents the performance score for each performance metric, and each column represents the performance score calculated for each performance metric each time; concatenating the performance score matrices of all multi-objective optimization algorithms to form a combined performance score matrix, wherein each row of the combined performance score matrix represents the performance score vector of all performance metrics for each multi-objective optimization algorithm, and the combined performance... Each column of the score matrix represents the performance score vector of all multi-objective optimization algorithms for each performance metric. Using a non-dominated sorting algorithm, all performance scores in the combined performance score matrix are calculated to form a multi-level Pareto front. The first layer of the Pareto front includes the best performance score among all performance scores for each performance metric that is not dominated by any other performance score. The second layer of the Pareto front refers to the second-best performance score that is dominated by the first layer of the Pareto front and maintains its advantage among the remaining performance scores. Subsequent layers of the Pareto front refer to performance scores that are even more suboptimal relative to the performance scores of higher layers.

[0007] Optionally, the step of calculating the ranking of each multi-objective optimization algorithm based on the multi-level Pareto front using at least one preset ranking algorithm includes: calculating the contribution of each multi-objective optimization algorithm at each level of the Pareto front based on the performance score of each multi-objective optimization algorithm at each level of the Pareto front; and determining the ranking of each multi-objective optimization algorithm based on the calculated contribution of each multi-objective optimization algorithm at each level of the Pareto front using the at least one preset ranking algorithm, wherein the at least one preset ranking algorithm includes the Olympic method, the linear method, the exponential method, and the adaptive method.

[0008] Optionally, the Olympic method is used to calculate the ranking of each multi-objective optimization algorithm, including: determining the ranking of each multi-objective optimization algorithm based on its contribution to the first layer of the Pareto front, with the multi-objective optimization algorithm with higher contribution having a higher ranking.

[0009] Optionally, a linear method is used to calculate the ranking of each multi-objective optimization algorithm, including: assigning weights to each level of the Pareto front in a linear decreasing manner; using a weighted summation method to calculate the sum of the products of the contribution at each level of the Pareto front and the assigned weights as the total contribution; and determining the ranking of each multi-objective optimization algorithm based on the total contribution of each multi-objective optimization algorithm.

[0010] Optionally, an exponential method is used to calculate the ranking of each multi-objective optimization algorithm, including: assigning weights to each level of the Pareto front in an exponentially decreasing manner; using a weighted summation method to calculate the sum of the products of the contribution at each level of the Pareto front and the assigned weights as the total contribution; and determining the ranking of each multi-objective optimization algorithm based on the total contribution of each multi-objective optimization algorithm.

[0011] Optionally, an adaptive method is used to calculate the ranking of each multi-objective optimization algorithm, including: dynamically allocating weights based on the total contribution accumulated at each level of the Pareto front; using a weighted summation method to calculate the sum of the products of the contribution at each level of the Pareto front and the allocated weights as the total contribution; and determining the ranking of each multi-objective optimization algorithm based on the total contribution of each multi-objective optimization algorithm.

[0012] Optionally, the step of calculating the ranking of each multi-objective optimization algorithm based on the multi-level Pareto front and using at least one preset ranking algorithm further includes: calculating the total contribution of each multi-objective optimization algorithm using the at least one preset ranking algorithm; dynamically allocating weights to the at least one preset ranking algorithm according to the complexity of the multi-objective task and the degree of conflict of performance indicators; calculating the sum of the products of the total contribution of each multi-objective optimization algorithm and the dynamically allocated weights using a weighted summation method, as the final contribution; and determining the final ranking of each multi-objective optimization algorithm based on the final contribution of each multi-objective optimization algorithm.

[0013] In a second aspect, the present invention provides a control device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for determining a multi-objective task based on Pareto optimality as described in any of the preceding claims.

[0014] Thirdly, the present invention provides a readable storage medium storing instructions that cause a machine to execute the Pareto-optimal multi-objective task determination method described in any of the preceding claims of this application.

[0015] Through the above technical solutions, the Pareto-optimal method, apparatus, and storage medium for determining multi-objective tasks provided in this application can simultaneously consider multiple performance indicators, reduce bias introduced by a single performance indicator, and more comprehensively solve multi-objective tasks. Utilizing a non-dominated ranking algorithm, it can handle conflicts arising from multiple performance indicators, ensuring a fair and reasonable selection of algorithms for solving multi-objective tasks. New performance indicators can be added to the determination method without modifying the existing framework, adapting to increases in the number of algorithms, performance indicator types, and algorithm execution times, exhibiting good scalability. Multiple ranking methods are provided for algorithms solving multi-objective tasks, assisting users in selecting appropriate algorithms based on specific needs. Furthermore, combining multiple ranking methods yields robust and comprehensive ranking results for users to choose from. Through 2-D and 3-D RadViz visualization technology, the distribution of each algorithm at different Pareto levels can be intuitively displayed, facilitating users' better understanding and interpretation of multiple algorithms for solving multi-objective tasks.

[0016] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0017] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0018] Figure 1 This is a flowchart illustrating the determination method provided in an exemplary embodiment of this application;

[0019] Figure 2 This is a flowchart illustrating the calculation of the performance of each multi-objective optimization algorithm for each performance metric in an exemplary embodiment of this application.

[0020] Figure 3 This is a schematic diagram of the process for calculating a multi-level Pareto front using a non-dominated sorting algorithm, as exemplified in this application.

[0021] Figure 4 This is a flowchart of a method for determining multi-objective tasks based on Pareto optimization, provided in an exemplary embodiment of this application. Detailed Implementation

[0022] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0023] It should be noted that the acquisition, transmission, storage, use, and processing of data in the technical solution of this application all comply with the relevant provisions of national laws and regulations. In the embodiments of this application, certain existing industry solutions such as software, components, and models may be mentioned. These should be considered exemplary, intended only to illustrate the feasibility of implementing the technical solution of this application, and do not imply that the applicant has already used or necessarily used such solutions.

[0024] Before explaining the embodiments of this application in detail, the technical terms involved in this application will be explained as shown in Table 1.

[0025] Table 1

[0026]

[0027] Please refer to Figure 1 and Figure 4 For example, as an embodiment of the present invention, this embodiment provides a method for determining a multi-objective task based on Pareto optimality. This method may include the following steps:

[0028] Step S110: For a multi-objective task solved by a multi-objective optimization algorithm, select multiple performance metrics to measure the multi-objective task.

[0029] In this embodiment of the application, M performance metrics are first selected to evaluate the multi-objective optimization algorithm. These performance metrics can be Hypervolume, Inverted Generational Distance, Generational Distance, etc. Considering multiple performance metrics can reduce the bias introduced by a single performance metric and solve multi-objective tasks more comprehensively.

[0030] For example, in this application embodiment, a logistics delivery route can be selected as a multi-objective task, and route planning algorithm A, route planning algorithm B and route planning algorithm C can be selected as multi-objective optimization algorithms for solving the logistics delivery route. The shortest delivery time (minutes), the lowest fuel cost (yuan) and the shortest driving distance (kilometers) can be selected as multiple performance indicators for measuring the logistics delivery route.

[0031] Step S120: Calculate the performance of each multi-objective optimization algorithm for each performance metric to form a multi-level Pareto front.

[0032] The Pareto front refers to the set of Pareto optimal performance scores corresponding to multiple performance metrics. In the two-dimensional performance metric space, the Pareto front can be represented as a curve, while in the three-dimensional performance metric space, it can form a surface or a scatter distribution. This allows for the intuitive display of the distribution of each algorithm at different Pareto levels through 2-D and 3-D RadViz visualization technology, making it easier for users to better understand and explain multiple algorithms for solving multi-objective tasks.

[0033] Please refer to Figure 2 For example, in a preferred embodiment of this application, calculating the performance of each multi-objective optimization algorithm for each performance metric may include steps S1201-S1204.

[0034] Step S1201: For each multi-objective optimization algorithm, calculate the performance score of the multi-objective optimization algorithm for each performance index multiple times to form the performance score matrix corresponding to the multi-objective optimization algorithm.

[0035] In this matrix, each row represents the performance score for each performance metric, and each column represents the performance score calculated for each performance metric in each instance.

[0036] For example, route planning algorithms A, B, and C can be run independently multiple times. After each run, the shortest delivery time (minutes), lowest fuel cost (yuan), and shortest driving distance (kilometers) corresponding to route planning algorithms A, B, and C can be calculated, and multiple sets of shortest delivery time (minutes), lowest fuel cost (yuan), and shortest driving distance (kilometers) can be represented in matrix form.

[0037] In this matrix, each row represents the shortest delivery time (minutes), lowest fuel cost (yuan), and shortest driving distance (kilometers) obtained after each run of path planning algorithms A, B, and C; the first column of the matrix represents the shortest delivery time (minutes) obtained after each run of path planning algorithms A, B, and C; the second column represents the lowest fuel cost (yuan) obtained after each run of path planning algorithms A, B, and C; and the third column represents the shortest driving distance (kilometers) obtained after each run of path planning algorithms A, B, and C.

[0038] Step S1202: Connect the performance score matrices of all multi-objective optimization algorithms to form a combined performance score matrix. Each row of the combined performance score matrix represents the performance score vector of all performance indicators of each multi-objective optimization algorithm, and each column of the combined performance score matrix represents the performance score vector of all multi-objective optimization algorithms under each performance indicator.

[0039] For example, multiple performance score matrices of path planning algorithm A, path planning algorithm B, and path planning algorithm C can be concatenated to form a combined performance score matrix.

[0040] The combined performance score matrix consists of the following columns: the first row represents multiple vectors of shortest delivery time (minutes), lowest fuel cost (yuan), and shortest driving distance (km) obtained after each run of path planning algorithm A; the second row represents multiple vectors of shortest delivery time (minutes), lowest fuel cost (yuan), and shortest driving distance (km) obtained after each run of path planning algorithm B; the third row represents multiple vectors of shortest delivery time (minutes), lowest fuel cost (yuan), and shortest driving distance (km) obtained after each run of path planning algorithm C; the first column represents multiple vectors of shortest delivery time (minutes) obtained after each run of path planning algorithms A, B, and C; the second column represents multiple vectors of lowest fuel cost (yuan) obtained after each run of path planning algorithms A, B, and C; and the third column represents multiple vectors of shortest driving distance (km) obtained after each run of path planning algorithms A, B, and C.

[0041] Step S1203: Each performance index can be standardized individually to ensure that all performance indexes are considered as minimization problems. The performance scores of some performance indexes can be reversed. That is, if the performance score of a certain performance index is higher, it is better. Then take its reciprocal or negative number to unify it as a minimization problem. This can eliminate the influence of different performance index dimensions.

[0042] Step S1204: Calculate all performance scores in the combined performance score matrix using a non-dominated sorting algorithm to form a multi-level Pareto front.

[0043] The first layer of the Pareto front includes the best performance score among all performance scores of each performance metric that is not dominated by any other performance score. The second layer of the Pareto front refers to the second-best performance score that is dominated by the first layer of the Pareto front and maintains its advantage among the remaining performance scores. The subsequent layers of the Pareto front refer to performance scores that are even more suboptimal relative to the performance scores of higher layers. This can handle conflicts arising from multiple performance metrics and make a fair and reasonable selection of algorithms for solving multi-objective tasks.

[0044] Please refer to Figure 3 For example, in a preferred embodiment of this application, step S1204 may include steps S12041-S12043.

[0045] Step S12041: The fast non-dominated sort calculates the dominance relationships of performance scores, compares all performance scores pairwise, and determines how many other performance scores dominate each performance score and the set of performance scores it dominates.

[0046] Step S12042: Extract performance scores in layers. The first layer of the Pareto front is the set of all performance scores that are not dominated by any other performance scores. Extract the set of performance scores that are dominated by all performance scores in the previous layer but not by the current layer or lower layers from the remaining performance scores to form the second layer and subsequent layers of the Pareto front. Repeat this process until all performance scores are layered. The performance scores in higher layers usually represent a better trade-off, but the performance scores in lower layers may have a local advantage on certain performance metrics.

[0047] Step S12043: Integrate the performance score set to generate a multi-level Pareto frontier.

[0048] For example, by processing the combined performance score matrix of path planning algorithms A, B, and C using a non-dominated sorting algorithm, a three-layer Pareto front can be obtained. The first layer represents the optimal performance score for each performance metric, the second layer represents the suboptimal performance score for each performance metric, and the third layer represents the remaining performance scores for each performance metric, as shown in Table 2.

[0049] Table 2

[0050]

[0051] Step S130: Based on the multi-level Pareto front, use at least one preset ranking algorithm to calculate the ranking of each multi-objective optimization algorithm.

[0052] In a preferred embodiment of this application, the contribution of each multi-objective optimization algorithm at each level of the Pareto front is calculated based on the performance score of each multi-objective optimization algorithm at each level of the Pareto front. The contribution is the number of points of each multi-objective optimization algorithm at each level of the Pareto front.

[0053] For example, referring to the examples in Table 2, path planning algorithm A contributes 1 point to the first layer of the Pareto front, 1 point to the second layer, and 0 points to the third layer; path planning algorithm B contributes 1 point to the first layer of the Pareto front and 1 point to the second layer; path planning algorithm C contributes 1 point to the first layer of the Pareto front.

[0054] In a preferred embodiment of this application, based on the calculated contribution of each multi-objective optimization algorithm at each level of the Pareto front, and using at least one preset ranking algorithm, the ranking of each multi-objective optimization algorithm is determined. The preset at least one ranking algorithm may include the Olympic method, linear method, exponential method, and adaptive method, etc., which can assist users in selecting appropriate algorithms for solving multi-objective tasks according to specific needs. Furthermore, multiple ranking methods can be combined to obtain robust and comprehensive ranking results for users to select algorithms for solving multi-objective tasks.

[0055] Furthermore, the ranking of each multi-objective optimization algorithm is calculated using the Olympic method. This can include: determining the ranking of each multi-objective optimization algorithm based on its contribution to the first layer of the Pareto front, with the algorithm contributing more ranking higher; and comparing the contributions to the second and third layers in turn if there is a tie.

[0056] In a preferred embodiment of this application, the Olympic method can be represented by the following formula:

[0057]

[0058] in, It is a multi-objective optimization algorithm in the first Contributions to the Pareto frontier, It is the index of the multi-objective optimization algorithm, that is, it represents the first... Algorithms.

[0059] For example, path planning algorithms A, B, and C all contribute 1 to the first layer of the Pareto front. Algorithms A and B both contribute 1 to the second layer, while algorithm C contributes nothing. Algorithms A, B, and C all contribute nothing to the third layer. Therefore, algorithm A and B are tied for first place, and it's impossible to distinguish their relative merits.

[0060] Furthermore, using a linear method to calculate the ranking of each multi-objective optimization algorithm may include: assigning weights to each level of the Pareto front in a linearly decreasing manner; using a weighted summation method to calculate the sum of the products of the contribution at each level of the Pareto front and the assigned weights, which is taken as the total contribution. The higher the weight of the level, the greater its influence on the total contribution. The ranking of each multi-objective optimization algorithm is determined based on the total contribution of each multi-objective optimization algorithm.

[0061] In a preferred embodiment of this application, the linear method can be represented by the following formula:

[0062]

[0063] in, It is a multi-objective optimization algorithm in the first The contributions of the Pareto frontier, It is the total number of layers in the Pareto front. It is the index of the multi-objective optimization algorithm, that is, it represents the first... Algorithms.

[0064] For example, the total number of Pareto front layers can be 3, and the weights of each layer of the Pareto front decrease sequentially. That is, the weights of the 1st, 2nd, and 3rd layers can be 3, 2, and 1 respectively. Then the total contribution of path planning algorithm A is... Total contribution of path planning algorithm B Total contribution of path planning algorithm C Therefore, path planning algorithm A and path planning algorithm B are tied for first place, consistent with the ranking results of the Olympic method, and it is still impossible to distinguish the superiority or inferiority of path planning algorithm A and path planning algorithm B.

[0065] Furthermore, the ranking of each multi-objective optimization algorithm is calculated using an exponential method. This can include: assigning weights to each level of the Pareto front in an exponentially decreasing manner to ensure that the contributions of higher levels have a significant impact on the total contribution, while the contributions of lower levels still have a certain contribution; using a weighted summation method to calculate the sum of the products of the contribution at each level of the Pareto front and the assigned weights, which is taken as the total contribution; and determining the ranking of each multi-objective optimization algorithm based on its total contribution.

[0066] In a preferred embodiment of this application, the exponential method can be represented by the following formula:

[0067]

[0068] in, It is a multi-objective optimization algorithm in the first The contributions of the Pareto frontier, It is the first Layer weights, It is the index of the multi-objective optimization algorithm, that is, it represents the first... Algorithms.

[0069] For example, the total number of Pareto fronts can be 3, and the weights of each Pareto front layer decrease exponentially, meaning the weights of layers 1, 2, and 3 can be... , and Then the total contribution of path planning algorithm A Then the total contribution of path planning algorithm B Then the total contribution of path planning algorithm C Therefore, path planning algorithm A and path planning algorithm B are tied for first place, consistent with the ranking results of the Olympic method and the linear method. It is still impossible to distinguish the superiority or inferiority of path planning algorithm A and path planning algorithm B, but the weight decay is steeper.

[0070] Furthermore, an adaptive method is used to calculate the ranking of each multi-objective optimization algorithm. This can include: dynamically allocating weights based on the total contribution accumulated at each level of the Pareto front; comprehensively considering the contribution of the multi-objective optimization algorithm at each level; if the total contribution of a certain level is high, it may indicate that the level is more important to the multi-objective task, and the weight of the level is increased accordingly; using a weighted summation method, the sum of the products of the contribution at each level of the Pareto front and the allocated weights is calculated as the total contribution; and the ranking of each multi-objective optimization algorithm is determined based on the total contribution of each multi-objective optimization algorithm.

[0071] In a preferred embodiment of this application, the adaptive method can be represented by the following formula:

[0072]

[0073] in, It is the first The multi-objective optimization algorithm in the first... The contribution of the layer It is the first of all multi-objective optimization algorithms. Total contribution of the layer Based on the k The total contribution of the layer or the complexity of a multi-objective task is dynamically calculated. Layer weights, It is the index of the multi-objective optimization algorithm, that is, it represents the first... Algorithms.

[0074] For example, the total number of layers in a Pareto front can be 3. The total contribution of the first layer of the Pareto front can be the cumulative contribution of path planning algorithm A, path planning algorithm B, and path planning algorithm C, i.e., the total contribution of the first layer of the Pareto front. Weight And so on, the total contribution of the second layer of the Pareto front Weight Total contribution of Pareto front layer 3 Weight .

[0075] Total contribution of path planning algorithm A The total contribution of path planning algorithm B The total contribution of path planning algorithm C Therefore, path planning algorithm A and path planning algorithm B are tied for first place, consistent with the ranking results of the Olympic method, linear method and exponential method. It is still impossible to distinguish the superiority or inferiority of path planning algorithm A and path planning algorithm B, but the allocation of weights depends more on the inter-layer competition.

[0076] In the preferred embodiments of this application, although various ranking methods have their own characteristics, their independent use may lead to inconsistent results due to the complexity of multi-task objectives or the contradiction of performance indicators. Therefore, the ranking results of various ranking methods can be combined through weighted average or voting mechanism to ensure that the extreme results of a single ranking method are corrected by other ranking methods. Before calculating the final ranking, the multi-objective optimization algorithm is required to reach a certain baseline performance in the multi-level Pareto front; otherwise, the ranking will be downgraded.

[0077] In a preferred embodiment of this application, based on the multi-level Pareto front, at least one preset ranking algorithm is used to calculate the ranking of each multi-objective optimization algorithm. The method may further include: using at least one preset ranking algorithm to calculate the total contribution of each multi-objective optimization algorithm; dynamically assigning weights to the at least one preset ranking algorithm based on the complexity of the multi-objective task and the degree of conflict of performance indicators; using a weighted summation method to calculate the sum of the products of the total contribution of each multi-objective optimization algorithm and the dynamically assigned weights, which is taken as the final contribution; and determining the final ranking of each multi-objective optimization algorithm based on its final contribution.

[0078] In a preferred embodiment of this application, the combined ranking of multiple methods can be expressed by the following formula:

[0079]

[0080] in, It is the index of the multi-objective optimization algorithm, that is, it represents the first... One algorithm, The weights are those of the Olympic method. These are the weights of the linear method. These are the weights of the exponential method. These are the weights of the adaptive method. .

[0081] Accordingly, the present invention provides a method for determining a multi-objective task based on Pareto optimality. The method includes: for a multi-objective task solved by a multi-objective optimization algorithm, selecting multiple performance indicators to measure the multi-objective task; calculating the performance of each multi-objective optimization algorithm on each performance indicator to form a multi-level Pareto front, wherein the Pareto front refers to the set of Pareto optimal performance scores corresponding to multiple performance indicators; based on the multi-level Pareto front, using at least one preset ranking algorithm to calculate the ranking of each multi-objective optimization algorithm; and determining the corresponding multi-objective task based on the calculated ranking of each multi-objective optimization algorithm.

[0082] Pareto-optimal methods can consider multiple performance metrics simultaneously, reducing biases introduced by a single performance metric and providing a more comprehensive solution to multi-objective tasks. Utilizing non-dominated ranking algorithms, conflicts arising from multiple performance metrics can be handled, ensuring a fair and reasonable selection of algorithms for multi-objective tasks. New performance metrics can be added to the deterministic method without modifying the existing framework, adapting to increases in the number of algorithms, performance metrics, and algorithm runs, demonstrating good scalability. Multiple ranking methods are provided for algorithms solving multi-objective tasks, assisting users in selecting appropriate algorithms based on specific needs. Furthermore, combining multiple ranking methods yields robust and comprehensive ranking results for user selection. Through 2-D and 3-D RadViz visualization techniques, the distribution of each algorithm at different Pareto levels can be intuitively displayed, facilitating better understanding and interpretation of multiple algorithms for solving multi-objective tasks.

[0083] This invention provides a control device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the computer program to implement the determination method described above.

[0084] This invention provides a readable storage medium storing instructions that cause a machine to execute the determination method described above.

[0085] This invention provides a device including a processor, a memory, and a program stored in the memory and executable on the processor. The processor executes a Pareto-optimal multi-objective task determination method. The device described herein can be a server, PC, PAD, mobile phone, etc.

[0086] This application also provides a computer program product that, when executed on a data processing device, is suitable for performing a method for determining a Pareto-optimal multi-objective task.

[0087] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0088] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0089] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0090] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0091] In a typical configuration, a computing device includes one or more processors (CPUs), input / output interfaces, network interfaces, and memory.

[0092] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0093] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, 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 technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0094] It should also be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, commodity, or apparatus that includes a series of elements includes not only those elements but also other elements not explicitly listed, or includes elements inherent to such process, method, commodity, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, commodity, or apparatus that includes the element.

[0095] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for determining multi-objective tasks based on Pareto optimality, characterized in that, The determination method includes: For a multi-objective task solved by a multi-objective optimization algorithm, select multiple performance metrics to measure the multi-objective task. The performance of each multi-objective optimization algorithm on each performance metric is calculated to form a multi-level Pareto front, where the Pareto front refers to the set of Pareto optimal performance scores corresponding to multiple performance metrics. Based on the multi-level Pareto front, at least one pre-defined ranking algorithm is used to calculate the ranking of each multi-objective optimization algorithm; and Based on the ranking of each multi-objective optimization algorithm calculated, the corresponding multi-objective task is determined; An adaptive method is used to calculate the ranking of each multi-objective optimization algorithm, including: Weights are dynamically allocated based on the total cumulative contribution at each level of the Pareto frontier. Using a weighted summation method, the sum of the products of the contribution at each level of the Pareto front and the assigned weights is calculated as the total contribution. The ranking of each multi-objective optimization algorithm is determined based on its total contribution.

2. The determination method according to claim 1, characterized in that, The calculation of the performance of each multi-objective optimization algorithm on each performance metric to form a multi-level Pareto front includes: For each multi-objective optimization algorithm, the performance score of the multi-objective optimization algorithm for each performance index is calculated multiple times to form a performance score matrix for the multi-objective optimization algorithm. Each row of the performance score matrix represents the performance score of each performance index, and each column represents the performance score calculated for each performance index each time. The performance score matrices of all multi-objective optimization algorithms are concatenated to form a combined performance score matrix. Each row of the combined performance score matrix represents the performance score vector of all performance indicators of each multi-objective optimization algorithm, and each column of the combined performance score matrix represents the performance score vector of all multi-objective optimization algorithms under each performance indicator. Using a non-dominated sorting algorithm, all performance scores in the combined performance score matrix are calculated to form a multi-level Pareto front. The first level of the Pareto front includes the best performance score among all performance scores of each performance metric that is not dominated by any other performance score. The second level of the Pareto front refers to the second-best performance score that is dominated by the first level of the Pareto front and maintains its advantage among the remaining performance scores. Subsequent levels of the Pareto front refer to performance scores that are less than the best performance scores of higher levels.

3. The determination method according to claim 1, characterized in that, The method based on the multi-level Pareto front employs at least one pre-defined ranking algorithm to calculate the ranking of each multi-objective optimization algorithm, including: The contribution of each multi-objective optimization algorithm at each level of the Pareto front is calculated based on the performance score of each multi-objective optimization algorithm at each level of the Pareto front. Based on the calculated contribution of each multi-objective optimization algorithm at each level of the Pareto front, and using at least one preset ranking algorithm, the ranking of each multi-objective optimization algorithm is determined. The preset ranking algorithm includes at least one method such as the Olympic method, the linear method, the exponential method, and the adaptive method.

4. The determination method according to claim 3, characterized in that, The ranking of each multi-objective optimization algorithm is calculated using the Olympic method, including: The ranking of each multi-objective optimization algorithm is determined based on its contribution to the first layer of the Pareto front; the multi-objective optimization algorithm with a higher contribution has a higher ranking.

5. The determination method according to claim 3, characterized in that, A linear method is used to calculate the ranking of each multi-objective optimization algorithm, including: Weights are assigned to each level of the Pareto front in a linearly decreasing manner. Using a weighted summation method, the sum of the products of the contribution at each level of the Pareto front and the assigned weights is calculated as the total contribution. The ranking of each multi-objective optimization algorithm is determined based on its total contribution.

6. The determining method according to claim 3, characterized in that, The ranking of each multi-objective optimization algorithm is calculated using an exponential method, including: Weights are assigned to each level of the Pareto front in an exponentially decreasing manner. Using a weighted summation method, the sum of the products of the contribution at each level of the Pareto front and the assigned weights is calculated as the total contribution. The ranking of each multi-objective optimization algorithm is determined based on its total contribution.

7. The determination method according to claim 3, characterized in that, The method of calculating the ranking of each multi-objective optimization algorithm based on the multi-level Pareto front, using at least one preset ranking algorithm, further includes: The total contribution of each multi-objective optimization algorithm is calculated using at least one of the preset ranking algorithms. Based on the complexity of the multi-objective task and the degree of conflict of performance indicators, weights are dynamically assigned to at least one preset ranking algorithm. Using a weighted summation method, the sum of the total contribution of each multi-objective optimization algorithm and the product of the dynamically assigned weights is calculated as the final contribution; The final ranking of each multi-objective optimization algorithm is determined based on its final contribution.

8. A control device, characterized in that, The control device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the determination method according to any one of claims 1-7.

9. A readable storage medium, characterized in that, The readable storage medium stores instructions that cause a machine to perform the determination method according to any one of claims 1-7.

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