Multi-target task determination method and device based on Pareto optimum and storage medium

Abstract

The invention provides a multi-target task determination method and device based on Pareto optimum and a storage medium, and belongs to the technical field of multi-target optimization. The determination method comprises the following steps: for a multi-target task solved by a multi-target optimization algorithm, selecting a plurality of performance indexes for measuring the multi-target task; calculating the performance of each multi-objective optimization algorithm in each performance index to form a multi-level Pareto leading edge; based on the multi-level Pareto leading edge, adopting at least one preset ranking algorithm to calculate the ranking of each multi-objective optimization algorithm; and determining a corresponding multi-target task according to the calculated ranking of each multi-target optimization algorithm. A plurality of performance indexes are considered, prejudice caused by introduction of a single performance index is reduced, and a multi-target task is solved more comprehensively; fairly and reasonably selecting the algorithm by using a non-dominated sorting algorithm; multiple ranking methods are configured for the algorithm; and the user can understand a plurality of algorithms for solving the multi-target task visually.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-objective optimization, and specifically relates to a method, apparatus and storage medium for determining a multi-objective task based on Pareto optimality. Background Art

[0002] With the increase in multi-objective optimization problems in practical problems, a large number of multi-objective optimization algorithms have been developed to solve these problems. In practice, these algorithms need to handle a set of conflicting objectives. Therefore, it may not be easy to find the optimal solution. To evaluate the quality of the solution set generated by a multi-objective algorithm, multiple performance metrics are usually required, but each performance metric may have its own advantages and limitations.

[0003] In the related art, relying on a single or a few performance metrics to evaluate an algorithm usually may introduce biases, resulting in a one-sided understanding of the algorithm's performance, making the comparison and ranking results of the algorithms less comprehensive; it is inconvenient to accommodate newly introduced performance metrics or newly added algorithms, with poor flexibility and scalability; moreover, it may also lead to contradictions between several performance metrics, making the overall ranking of the algorithms more complex; in addition, the ranking results of each algorithm cannot be visually and intuitively presented for users to understand. Summary of the Invention

[0004] The purpose of the embodiments of the present invention is to provide a method, apparatus and storage medium for determining a multi-objective task based on Pareto optimality, aiming to solve the problems in the prior art that relying on a single or a few performance metrics to evaluate an algorithm will introduce biases, have poor flexibility and scalability, the performance metrics are mutually contradictory, and the ranking results cannot be visually and intuitively presented.

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

[0006] Optionally, calculate the performance of each multi-objective optimization algorithm in each performance metric respectively to form a multi-level Pareto front, including: for each multi-objective optimization algorithm, calculate the performance scores of the multi-objective optimization algorithm corresponding to each performance metric multiple times to form a performance score matrix corresponding to the multi-objective optimization algorithm, where each row of the performance score matrix represents the performance scores of each performance metric, and each column represents the performance scores of each calculation under each performance metric; connect the performance score matrices of all multi-objective optimization algorithms to form a combined performance score matrix, where each row of the combined performance score matrix represents the performance score vector of all performance metrics 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 metric; use the non-dominated sorting algorithm to calculate all the performance scores in the combined performance score matrix to form a multi-level Pareto front. The first layer of the Pareto front includes the optimal performance scores among all the performance scores of each performance metric that are not dominated by any other performance scores. The second layer of the Pareto front refers to the performance scores that are dominated by the first layer of the Pareto front and remain dominant among the remaining performance scores. The subsequent layers of the Pareto front refer to the performance scores that are more sub-optimal with respect to the performance scores of the higher layers as each layer goes down.

[0007] Optionally, based on the multi-level Pareto front, use at least one preset ranking algorithm to calculate the ranking of each multi-objective optimization algorithm, including: calculate the contribution of each multi-objective optimization algorithm at each level of the Pareto front according to the performance scores 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 the at least one preset ranking algorithm, determine the ranking of each multi-objective optimization algorithm. The at least one preset ranking algorithm includes the Olympic method, the linear method, the exponential method, and the adaptive method.

[0008] Optionally, use the Olympic method to calculate the ranking of each multi-objective optimization algorithm, including: determine the ranking of each multi-objective optimization algorithm according to the contribution of each multi-objective optimization algorithm on the first layer of the Pareto front. The multi-objective optimization algorithm with a higher contribution has a higher ranking.

[0009] Optionally, use the linear method to calculate the ranking of each multi-objective optimization algorithm, including: assign weights to each level of the Pareto front in a linearly decreasing manner; use the weighted summation method to calculate the sum of the products of the contributions at each level of the Pareto front and the assigned weights as the total contribution; determine the ranking of each multi-objective optimization algorithm according to the total contribution of each multi-objective optimization algorithm.

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

[0011] Optionally, an adaptive method is adopted to calculate the ranking of each multi-objective optimization algorithm, including: dynamically assigning weights according to the cumulative total contribution at each level of the Pareto front; using the weighted summation method to calculate the sum of the products of the contributions at each level of the Pareto front and the assigned weights as the total contribution; determining the ranking of each multi-objective optimization algorithm according to the total contribution of each multi-objective optimization algorithm.

[0012] Optionally, based on the multi-level Pareto front, at least one preset ranking algorithm is adopted to calculate the ranking of each multi-objective optimization algorithm, and it further includes: using the 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 according to the complexity of the multi-objective task and the conflict degree of the performance indicators; using the 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 as the final contribution; determining the final ranking of each multi-objective optimization algorithm according to the final contribution of each multi-objective optimization algorithm.

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

[0014] In a third aspect, the present invention provides a readable storage medium, on which instructions are stored, and the instructions cause a machine to execute the method for determining a multi-objective task based on Pareto optimality as described in any one of the above in this application.

[0015] Through the above technical solutions, the method, apparatus, and storage medium for determining multi-objective tasks based on Pareto optimality provided by the embodiments of the present application can consider multiple performance indicators simultaneously based on the Pareto optimality method, reduce the bias introduced by a single performance indicator, and solve multi-objective tasks more comprehensively; by using the non-dominated sorting algorithm, conflicts generated by multiple performance indicators can be handled, and a fair and reasonable selection can be made for the algorithms to solve multi-objective tasks; new performance indicators can be added to the determination method without modifying the existing framework, and it can adapt to the increase in the number of algorithms, the types of performance indicators, and the number of algorithm runs, with good scalability; multiple ranking methods are equipped for the algorithms to solve multi-objective tasks, which can assist users in selecting appropriate algorithms to solve multi-objective tasks according to specific requirements, and can also combine multiple ranking methods to obtain robust and comprehensive ranking results for users to select algorithms to solve multi-objective tasks; through 2-D and 3-D RadViz visualization techniques, the distribution of each algorithm at different Pareto levels can be intuitively displayed, facilitating users to better understand and interpret 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 subsequent specific implementation part. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The drawings are used to provide a further understanding of the embodiments of the present invention, and constitute a part of the specification, and are used together with the following specific implementation to explain the embodiments of the present invention, but do not constitute a limitation to the embodiments of the present invention. In the drawings: Figure 1 is a flowchart of the determination method provided by an exemplary embodiment of the present application; Figure 2 is a flowchart of calculating the performance of each multi-objective optimization algorithm on each performance indicator in an exemplary embodiment of the present application; Figure 3 is a flowchart of calculating multi-level Pareto fronts using the non-dominated sorting algorithm in an exemplary embodiment of the present application; Figure 4 is a flowchart of the method for determining multi-objective tasks based on Pareto optimality provided by an exemplary embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] The following detailed description of the specific implementation of the embodiments of the present invention is provided in conjunction with the accompanying drawings. It should be understood that the specific implementation described herein is only used to illustrate and explain the embodiments of the present invention, and is not used to limit the embodiments of the present invention.

[0019] It should be noted that in the technical solution of this application, the acquisition, transmission, storage, use, processing, etc. of data all comply with the relevant provisions of national laws and regulations. In the embodiments of this application, some existing industry solutions such as certain software, components, models, etc. may be mentioned. They should be regarded as exemplary. The purpose is only to illustrate the feasibility in the implementation of the technical solution of this application, but it does not mean that the applicant has already or necessarily used this solution.

[0020] Before explaining the embodiments of this application in detail, the technical terms involved in this application are explained as shown in Table 1.

[0021] Table 1

[0022] Please refer to Figure 1 and Figure 4 Examples, which are embodiments of the present invention. This embodiment provides a method for determining a multi-objective task based on Pareto optimality. The determination method may include the following steps: Step S110: For a multi-objective task solved by a multi-objective optimization algorithm, select multiple performance indicators for measuring the performance of the multi-objective task.

[0023] In the embodiments of this application, first, M performance indicators for evaluating the performance of the multi-objective optimization algorithm are selected. The performance indicators may be Hypervolume, Inverted Generational Distance, Generational Distance, etc. Considering multiple performance indicators can reduce the bias introduced by a single performance indicator and solve the multi-objective task more comprehensively.

[0024] For example, the embodiments of this application may select the logistics distribution path as the multi-objective task, select path planning algorithms A, B, and C as the multi-objective optimization algorithms for solving the logistics distribution path, and select the shortest delivery time (minutes), the lowest fuel cost (yuan), and the shortest driving distance (kilometers) as the multiple performance indicators for measuring the logistics distribution path.

[0025] Step S120: Calculate the performance of each multi-objective optimization algorithm in each performance indicator respectively to form a multi-level Pareto front.

[0026] Among them, the Pareto front refers to the set of Pareto-optimal performance scores corresponding to multiple performance metrics. In a two-dimensional performance metric space, the Pareto front can be represented as a curve, and in a three-dimensional performance metric space, it can form a surface or a scatter distribution, which facilitates the intuitive display of the distribution of each algorithm at different Pareto levels through 2-D and 3-D RadViz visualization techniques, making it easier for users to better understand and interpret multiple algorithms for solving multi-objective tasks.

[0027] Please refer to Figure 2 the example. In a preferred embodiment of the present application, when calculating the performance of each multi-objective optimization algorithm for each performance metric, steps S1201 - S1204 may be included.

[0028] Step S1201: For each multi-objective optimization algorithm, calculate the performance scores corresponding to each performance metric multiple times to form a performance score matrix corresponding to the multi-objective optimization algorithm.

[0029] Among them, each row of the performance score matrix represents the performance scores of each performance metric, and each column represents the performance scores of each calculation under each performance metric.

[0030] For example, path planning algorithms A, B, and C can be independently run multiple times. After each run, calculate the shortest delivery time (in minutes), the lowest fuel cost (in yuan), and the shortest driving distance (in kilometers) corresponding to path planning algorithms A, B, and C, and present multiple sets of shortest delivery times (in minutes), lowest fuel costs (in yuan), and shortest driving distances (in kilometers) in the form of a matrix.

[0031] Among them, each row of the matrix represents the shortest delivery time (in minutes), the lowest fuel cost (in yuan), and the shortest driving distance (in kilometers) obtained after each run of path planning algorithms A, B, and C; the first column of the matrix represents the shortest delivery time (in minutes) obtained after each run of path planning algorithms A, B, and C, the second column represents the lowest fuel cost (in yuan) obtained after each run of path planning algorithms A, B, and C, and the third column represents the shortest driving distance (in kilometers) obtained after each run of path planning algorithms A, B, and C.

[0032] Step S1202: Concatenate 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 metrics 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 metric.

[0033] For example, multiple performance score matrices of path planning algorithms A, B, and C are concatenated to form a combined performance score matrix.

[0034] Among them, the first row of the combined performance score matrix represents multiple groups of shortest delivery times (in minutes), lowest fuel costs (in yuan), and shortest driving distances (in kilometers) vectors obtained after each run of path planning algorithm A; the second row represents multiple groups of shortest delivery times (in minutes), lowest fuel costs (in yuan), and shortest driving distances (in kilometers) vectors obtained after each run of path planning algorithm B; the third row represents multiple groups of shortest delivery times (in minutes), lowest fuel costs (in yuan), and shortest driving distances (in kilometers) vectors obtained after each run of path planning algorithm C; the first column of the combined performance score matrix represents multiple groups of shortest delivery times (in minutes) vectors obtained after each run of path planning algorithms A, B, and C; the second column represents multiple groups of lowest fuel costs (in yuan) vectors obtained after each run of path planning algorithms A, B, and C; the third column represents multiple groups of shortest driving distances (in kilometers) vectors obtained after each run of path planning algorithms A, B, and C.

[0035] Step S1203: Each performance metric can be individually standardized to ensure that all performance metrics are treated as minimization problems. Reverse the performance scores of some performance metrics, that is, if the performance score of a certain performance metric is better the higher it is, take its reciprocal or negative number to unify it into a minimization problem, so as to eliminate the influence of different performance metric dimensions.

[0036] Step S1204: Use the non-dominated sorting algorithm to calculate all the performance scores in the combined performance score matrix to form a multi-level Pareto front.

[0037] Among them, the first layer of the Pareto front includes the optimal performance scores that are not dominated by any other performance scores among all the performance scores of each performance metric. The second layer of the Pareto front refers to the performance scores that are dominated by the first layer of the Pareto front and remain dominant among the remaining performance scores. The subsequent layers of the Pareto front refer to the performance scores that are more sub-optimal for each lower layer compared to the performance scores of the higher layers. In this way, the conflicts generated by multiple performance metrics can be handled, and a fair and reasonable selection can be made for the algorithms to solve multi-objective tasks.

[0038] Please refer to Figure 3 Example. In a preferred embodiment of the present application, step S1204 may include steps S12041 - S12043.

[0039] Step S12041: Calculate the dominance relationship of performance scores through fast non-dominated sorting. Compare all performance scores pairwise to determine how many other performance scores each performance score is dominated by and the set of performance scores it dominates.

[0040] Step S12042: Extract performance scores hierarchically. The first layer of the Pareto front is the set of all performance scores that are not dominated by any other performance scores. Extract from the remaining performance scores the set of performance scores that are dominated by all performance scores in the previous layer but not dominated by the current layer or lower layers to form the second layer and subsequent layers of the Pareto front. Repeat this process until all performance scores are hierarchically divided. Performance scores in higher layers generally represent better trade-offs, but performance scores in lower layers may have local advantages in certain performance metrics.

[0041] Step S12043: Integrate the set of performance scores to generate a multi-level Pareto front.

[0042] For example, by processing the combined performance score matrix of path planning algorithm A, path planning algorithm B, and path planning algorithm C through the non-dominated sorting algorithm, a three-layer Pareto front can be obtained. The first layer represents the optimal performance scores for each performance metric, the second layer represents the sub-optimal performance scores for each performance metric, and the third layer represents the remaining performance scores for each performance metric, as shown in Table 2.

[0043] Table 2

[0044] 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.

[0045] In a preferred embodiment of the present application, according to the performance scores of each multi-objective optimization algorithm at each level of the Pareto front, calculate the contribution 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.

[0046] For example, referring to the example in Table 2, the contribution of path planning algorithm A at the first layer of the Pareto front is 1 point, the contribution at the second layer is 1 point, and the contribution at the third layer is 0 points; the contribution of path planning algorithm B at the first layer of the Pareto front is 1 point, and the contribution at the second layer is 1 point; the contribution of path planning algorithm C at the first layer of the Pareto front is 1 point.

[0047] In a preferred embodiment of the present application, based on the contributions 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 at least one preset ranking algorithm may include the Olympic method, the linear method, the exponential method, the adaptive method, etc. This can assist users in selecting a suitable algorithm for solving multi-objective tasks according to specific requirements, and can also combine multiple ranking methods to obtain a robust and comprehensive ranking result for users to select an algorithm for solving multi-objective tasks.

[0048] Further, using the Olympic method to calculate the ranking of each multi-objective optimization algorithm may include: determining the ranking of each multi-objective optimization algorithm according to the contribution of each multi-objective optimization algorithm on the first layer of the Pareto front. The multi-objective optimization algorithm with a higher contribution has a higher ranking. If there is a tie, the contributions on the second layer and the third layer are compared in turn.

[0049] In a preferred embodiment of the present application, the Olympic method can be represented by the following formula:

[0050] Wherein, is the contribution of the multi-objective optimization algorithm on the th layer of the Pareto front, is the index of the multi-objective optimization algorithm, that is, it represents the th algorithm.

[0051] For example, the contributions of path planning algorithm A, path planning algorithm B, and path planning algorithm C on the first layer of the Pareto front are all 1. The contributions of path planning algorithm A and path planning algorithm B on the second layer of the Pareto front are both 1, and path planning algorithm C has no contribution on the second layer of the Pareto front. Path planning algorithm A, path planning algorithm B, and path planning algorithm C have no contribution on the third layer of the Pareto front. Therefore, path planning algorithm A and path planning algorithm B are tied for first, and it is impossible to distinguish the advantages and disadvantages of the two.

[0052] Further, using the 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 the weighted summation method to calculate the sum of the products of the contributions on each level of the Pareto front and the assigned weights as the total contribution. The higher the weight of the layer, the greater the impact on the total contribution. The ranking of each multi-objective optimization algorithm is determined according to the total contribution of each multi-objective optimization algorithm.

[0053] In a preferred embodiment of the present application, the linear method can be represented by the following formula:

[0054] Among them, is the contribution of the multi-objective optimization algorithm to the Pareto front at the -th layer, is the total number of layers of the Pareto front, is the index of the multi-objective optimization algorithm, which represents the -th algorithm.

[0055] For example, the total number of layers of the Pareto front can be 3, and the weights of each layer of the Pareto front decrease in turn, that is, the weights of the first layer, the second layer, and the third layer can be 3 points, 2 points, and 1 point respectively. Then the 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, which is consistent with the ranking result of the Olympic method, and it is still impossible to distinguish the advantages and disadvantages of path planning algorithm A and path planning algorithm B.

[0056] Furthermore, by using the exponential method, the ranking of each multi-objective optimization algorithm can be calculated, which can include: allocating weights to each layer of the Pareto front according to the exponentially decreasing form, ensuring that the contribution of the higher layers has a significant impact on the total contribution, but the contribution of the lower layers still has a certain contribution. Using the weighted summation method, calculate the sum of the products of the contribution on each layer of the Pareto front and the allocated weights as the total contribution, and determine the ranking of each multi-objective optimization algorithm according to the total contribution of each multi-objective optimization algorithm.

[0057] In the preferred embodiment of the present application, the exponential method can be represented by the following formula:

[0058] Among them, is the contribution of the multi-objective optimization algorithm to the Pareto front at the -th layer, is the weight of the -th layer, is the index of the multi-objective optimization algorithm, which represents the -th algorithm.

[0059] For example, the total number of layers of the Pareto front can be 3, and the weights of each layer of the Pareto front decrease exponentially, that is, the weights of the first layer, the second layer, and the third layer 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 algorithms A and B are tied for first place, which is consistent with the ranking results of the Olympic method and the linear method. It is still impossible to distinguish the advantages and disadvantages of path planning algorithms A and B, but the weight decay is steeper.

[0060] Furthermore, by adopting an adaptive method, the ranking of each multi-objective optimization algorithm can be calculated, which may include: dynamically allocating weights according to the total contribution accumulated at each level of the Pareto front, comprehensively considering the contributions of the multi-objective optimization algorithms at each level. If the total contribution of a certain level is relatively high, it may indicate that this level is more important for the multi-objective task, and the weight of this level is increased accordingly. Using the weighted summation method, calculate the sum of the products of the contributions at each level of the Pareto front and the allocated weights as the total contribution, and determine the ranking of each multi-objective optimization algorithm according to the total contribution of each multi-objective optimization algorithm.

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

[0062] wherein, is the contribution of the th multi-objective optimization algorithm at the th level, is the total contribution of all multi-objective optimization algorithms at the th level, is the weight of the k th level dynamically calculated based on the total contribution of the th level or the complexity of the multi-objective task, is the index of the multi-objective optimization algorithm, that is, it represents the nd algorithm.

[0063] For example, the total number of levels of the Pareto front can be 3. The total contribution of the first level of the Pareto front can be the total contribution accumulated by path planning algorithms A, B, and C, that is, the total contribution of the first level of the Pareto front , the weight , and so on. The total contribution of the second level of the Pareto front , the weight , the total contribution of the third level of the Pareto front , the weight .

[0064] The 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 tie for first place, which is consistent with the ranking results of the Olympic method, the linear method, and the exponential method. It is still impossible to distinguish the advantages and disadvantages of path planning algorithm A and path planning algorithm B, but the allocation of weights depends more on the inter-layer competition situation.

[0065] In a preferred embodiment of the present application, although various ranking methods have their own characteristics, using them independently may lead to inconsistent results due to the complexity of multi-task objectives or conflicts in performance indicators. Therefore, the ranking results of various ranking methods can be integrated through weighted averaging or a voting mechanism to ensure that extreme results of a single ranking method are corrected by other ranking methods. Before calculating the final ranking, it is required that the multi-objective optimization algorithm achieve a certain baseline performance in the multi-layer Pareto front; otherwise, the ranking will be downgraded.

[0066] In a preferred embodiment of the present application, based on the multi-layer Pareto front, at least one preset ranking algorithm is used to calculate the ranking of each multi-objective optimization algorithm. It may also include: using at least one preset ranking algorithm to calculate the total contribution of each multi-objective optimization 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 in performance indicators, and using the weighted summation method to calculate the sum of the products of the total contribution of each multi-objective optimization algorithm and the dynamically allocated weights as the final contribution, and determining the final ranking of each multi-objective optimization algorithm according to the final contribution of each multi-objective optimization algorithm.

[0067] In a preferred embodiment of the present application, the comprehensive ranking of multiple methods can be represented by the following formula:

[0068] where is the index of the multi-objective optimization algorithm, that is, it represents the th algorithm, is the weight of the Olympic method, is the weight of the linear method, is the weight of the exponential method, is the weight of the adaptive method, .

[0069] Accordingly, the present invention provides a method for determining a multi-objective task based on Pareto optimality. The determination method includes: for a multi-objective task solved by a multi-objective optimization algorithm, selecting multiple performance indicators for measuring the multi-objective task; calculating the performance of each multi-objective optimization algorithm in each performance indicator respectively to form a multi-level Pareto front, where the Pareto front refers to a 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 according to the calculated ranking of each multi-objective optimization algorithm.

[0070] The method based on Pareto optimality can consider multiple performance indicators simultaneously, reduce the bias introduced by a single performance indicator, and solve multi-objective tasks more comprehensively; using the non-dominated sorting algorithm, it can handle the conflicts generated by multiple performance indicators and make a fair and reasonable selection of the algorithms for solving multi-objective tasks; new performance indicators can be added to the determination method without modifying the existing framework, and it can adapt to the increase in the number of algorithms, the types of performance indicators, and the number of algorithm runs, with good scalability; equipping multiple ranking methods for the algorithms for solving multi-objective tasks can assist users in selecting appropriate algorithms for solving multi-objective tasks according to specific requirements, and can also combine multiple ranking methods to obtain a robust and comprehensive ranking result for users to select algorithms for solving multi-objective tasks; through 2-D and 3-D RadViz visualization techniques, the distribution of each algorithm at different Pareto levels can be intuitively displayed, facilitating users to better understand and interpret multiple algorithms for solving multi-objective tasks.

[0071] An embodiment of the present invention provides a control device, which includes: a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor executes the computer program to implement the above determination method.

[0072] An embodiment of the present invention provides a readable storage medium, on which instructions are stored, and the instructions cause a machine to execute the above determination method.

[0073] An embodiment of the present invention provides a device, which includes a processor, a memory, and a program stored on the memory and executable on the processor. The processor executes the method for determining a multi-objective task based on Pareto optimality. The device herein can be a server, a PC, a PAD, a mobile phone, etc.

[0074] The present application also provides a computer program product, which is suitable for executing the method for determining a multi-objective task based on Pareto optimality when executed on a data processing device.

[0075] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) that contain computer-usable program code.

[0076] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0077] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including instruction means, and the instruction means implements the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0078] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0079] In a typical configuration, a computing device includes one or more processors (CPUs), an input / output interface, a network interface, and memory.

[0080] The memory may include non-permanent memory in the computer-readable medium, in the form of random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.

[0081] A computer-readable medium includes permanent and non-permanent, removable and non-removable media that can implement information storage by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic disk storage or other magnetic storage devices, or any other non-transitory medium that can be used to store information accessible by a computing device. As defined herein, a computer-readable medium does not include transitory computer-readable media such as modulated data signals and carrier waves.

[0082] It should also be noted that the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or apparatus comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or apparatus. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or apparatus comprising the element.

[0083] The above are only embodiments of the present application and are not used to limit the present application. For those skilled in the art, various changes and modifications can be made to the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included within the scope of the claims of the present application.

Claims

1. A determination method for 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 for measuring the performance of the multi-objective task; Calculate the performance of each multi-objective optimization algorithm in each performance metric respectively 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, use at least one preset ranking algorithm to calculate the ranking of each multi-objective optimization algorithm; and Determine the corresponding multi-objective task according to the calculated ranking of each multi-objective optimization algorithm.

2. The determination method according to claim 1, wherein The calculating the performance of each multi-objective optimization algorithm in each performance metric respectively to form a multi-level Pareto front includes: For each multi-objective optimization algorithm, calculate the performance scores corresponding to each performance metric multiple times to form a performance score matrix corresponding to the multi-objective optimization algorithm, where each row of the performance score matrix represents the performance scores of each performance metric, and each column represents the performance scores of each calculation under each performance metric; Connect the performance score matrices of all multi-objective optimization algorithms to form a combined performance score matrix, where each row of the combined performance score matrix represents the performance score vector of all performance metrics 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 metric; Use the non-dominated sorting algorithm to calculate all the performance scores in the combined performance score matrix to form a multi-level Pareto front. The first layer of the Pareto front includes the optimal performance scores among all the performance scores of each performance metric that are not dominated by any other performance scores. The second layer of the Pareto front refers to the performance scores that are dominated by the first layer of the Pareto front and remain dominant among the remaining performance scores. The subsequent layers of the Pareto front refer to the performance scores that are more sub-optimal with respect to the performance scores of the higher layers as each layer goes down.

3. The determination method according to claim 1, characterized in that, The calculating the ranking of each multi-objective optimization algorithm based on the multi-level Pareto front and using at least one preset ranking algorithm includes: Calculate the contribution of each multi-objective optimization algorithm at each level of the Pareto front according to the performance scores 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 the at least one preset ranking algorithm, determine the ranking of each multi-objective optimization algorithm; The at least one preset ranking algorithm includes the Olympic method, the linear method, the exponential method, and the adaptive method.

4. The determination method according to claim 3, wherein Using the Olympic method to calculate the ranking of each multi-objective optimization algorithm includes: Determine the ranking of each multi-objective optimization algorithm according to the contribution of each multi-objective optimization algorithm on 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 Using the linear method to calculate the ranking of each multi-objective optimization algorithm includes: Assign weights to each level of the Pareto front according to a linearly decreasing manner; Using the weighted summation method, calculate the sum of the products of the contributions at each level of the Pareto front and the assigned weights as the total contribution; Determine the ranking of each multi-objective optimization algorithm according to the total contribution of each multi-objective optimization algorithm.

6. The determination method according to claim 3, characterized in that, Adopt an exponential method to calculate the ranking of each multi-objective optimization algorithm, including: Assign weights to each level of the Pareto front according to an exponentially decreasing manner; Using the weighted summation method, calculate the sum of the products of the contributions at each level of the Pareto front and the assigned weights as the total contribution; Determine the ranking of each multi-objective optimization algorithm according to the total contribution of each multi-objective optimization algorithm.

7. The determination method according to claim 3, characterized in that, Adopt an adaptive method to calculate the ranking of each multi-objective optimization algorithm, including: Dynamically assign weights according to the cumulative total contribution at each level of the Pareto front; Using the weighted summation method, calculate the sum of the products of the contributions at each level of the Pareto front and the assigned weights as the total contribution; Determine the ranking of each multi-objective optimization algorithm according to the total contribution of each multi-objective optimization algorithm.

8. The determination method according to claim 3, wherein Based on the multi-level Pareto front, using at least one preset ranking algorithm to calculate the ranking of each multi-objective optimization algorithm, further includes: Using the at least one preset ranking algorithm to calculate the total contribution of each multi-objective optimization algorithm; Dynamically assign weights to the at least one preset ranking algorithm according to the complexity of the multi-objective task and the degree of conflict of the performance indicators; Using the weighted summation method, calculate the sum of the products of the total contribution of each multi-objective optimization algorithm and the dynamically assigned weights as the final contribution; Determine the final ranking of each multi-objective optimization algorithm according to the final contribution of each multi-objective optimization algorithm.

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

10. A readable storage medium, characterized in that, Instructions are stored on the readable storage medium, and the instructions cause the machine to execute the determination method according to any one of claims 1-8.

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