Method and apparatus for multi-objective optimization method based on goal programming and objective space processing, and computer device

Abstract

Disclosed in the present application are a method and apparatus for multi-objective optimization based on goal programming and objective space processing, a computer device, and a storage medium. Specifically, disclosed in the present application is a multi-objective optimization method based on goal programming and objective space processing, the method comprising: establishing a multi-dimensional objective space according to a plurality of objectives, wherein the boundaries of the objective space are determined by the maximum and minimum values of the plurality of objectives; segmenting the multi-dimensional objective space into a plurality of sub-objective spaces; and solving for a plurality of target values for the plurality of sub-objective spaces to obtain an optimal solution set of the corresponding plurality of objectives. By means of the described method, the Pareto front of the plurality of target values can be accurately and directly obtained, thereby supporting various optimization scenarios.

Description

Methods, apparatus, and computer equipment for multi-objective optimization based on goal programming and goal space processing. Technical Field

[0001] This application relates to the field of optimization, and more specifically, to a method, apparatus, computer device, and storage medium for multi-objective optimization based on goal planning and goal space processing. Background Technology

[0002] In various decision-making scenarios, it is often necessary to weigh the optimization of multiple objectives.

[0003] For example, in operational optimization such as production planning, cost and service level are two typically conflicting key performance indicators (KPIs). In control optimization (such as auxiliary equipment group control), demand satisfaction, energy efficiency, and operational stability must be balanced. In product design optimization, technical, cost, and environmental performance must be considered simultaneously. In process optimization in discrete or process industries, quality, cost, and efficiency standards must be considered when adjusting process parameters.

[0004] In many cases, decision-making even requires collaboration among multiple entities. For example, in supply chain management, the purpose of Sales & Operations Planning (S&OP) is to find a point of consensus among multiple functional departments such as sales, planning, production, procurement, and finance, each of which has its own key performance indicators.

[0005] With the development of operations research (OR) algorithms, such as mathematical programming solvers, heuristics, and meta-heuristics, many single-objective decision problems can now be optimized, even with a huge number of decision variables and complex constraints. However, most (if not all) decision scenarios are inherently multi-objective, and current algorithms have limited ability to handle multi-objective problems; a gap still exists between the two.

[0006] This gap often leads to so-called usability problems between technology and business. No matter how optimized, if the solution provided by the algorithm does not conform to or reflect the user's expectations of the relationship between multiple objectives, the user will not consider the algorithm interpretable, reliable, or acceptable.

[0007] Summary of the Invention

[0008] This summary section is provided to introduce some selected concepts in a simplified form, which will be further described in the detailed description section below. This summary section is not intended to identify any key or essential features of the claimed subject matter, nor is it intended to help determine the scope of the claimed subject matter.

[0009] Based on this, this application discloses a multi-objective optimization method based on an objective space, which includes:

[0010] A multi-dimensional target space is established based on multiple target values, wherein the boundary of the target space is determined by the maximum and minimum values ​​of the targets;

[0011] The multi-dimensional target space is divided into multiple sub-target spaces;

[0012] The optimal solution set for each of the multiple sub-objective spaces is obtained by solving multiple objectives.

[0013] The Pareto front for multiple objectives can be obtained accurately and directly through the above methods, thus supporting various optimization scenarios.

[0014] Furthermore, the step of dividing the multi-dimensional target space into multiple sub-target spaces includes: dividing the multi-dimensional target space into multiple sub-target spaces based on the upper and lower boundary values ​​of the multiple targets.

[0015] Using the above method, the target space can be divided into multiple smaller sub-target spaces according to the requirements, and target programming can be used to transform the target space into a single-target solution.

[0016] Furthermore, the step of solving for multiple objectives in the multiple sub-objective spaces includes: traversing the target space in ascending order of the distances from the sub-objective spaces to the pseudo-origin.

[0017] Using the above method, we can start the solution from the pseudo-origin and quickly find the optimal solution.

[0018] Furthermore, the step of solving for multiple targets in the multiple sub-target spaces includes: receiving a reference point and traversing the target space according to the ray from the reference point.

[0019] Using the methods described above, the system can iterate through the data based on user experience or external recommendations, and thus quickly find the optimal solution.

[0020] Furthermore, the step of dividing the multi-dimensional target space into multiple sub-target spaces includes: adjusting the upper and lower boundary values ​​of the multiple targets based on the center point of the sub-target spaces as reference points.

[0021] By using the above method, the values ​​of the upper and lower boundaries can be adjusted according to the center position, thereby defining the size of the sub-target space, which makes it easier to find the optimal solution.

[0022] Furthermore, the step of solving for multiple objectives in the multiple sub-objective spaces includes: solving for multiple objectives in the sub-objective spaces based on time constraints, distance constraints, and a warm-start mechanism.

[0023] By using the above methods, the solution strategy can be adjusted according to actual needs, making it easier to quickly find the optimal solution.

[0024] Furthermore, this application discloses a multi-objective optimization device based on objective planning and objective space processing, comprising:

[0025] A space establishment module is used to establish a multi-dimensional target space based on multiple objectives, wherein the boundary of the target space is determined by the maximum and minimum values ​​of the multiple objectives;

[0026] The spatial segmentation module is used to segment the multi-dimensional target space into multiple sub-target spaces;

[0027] The spatial solution module is used to solve multiple objectives in the multiple sub-objective spaces to obtain the optimal solution set for the corresponding multiple objectives.

[0028] This application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described method.

[0029] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method.

[0030] This application also provides a computer program product tangibly stored on a computer-readable medium and comprising computer-executable instructions that, when executed, cause at least one processor to perform the methods described above. Attached Figure Description

[0031] Implementations of this disclosure are illustrated in the accompanying drawings by way of example rather than limitation, and similar reference numerals in the drawings denote the same or similar parts.

[0032] Figure 1 is a schematic flowchart of a multi-objective optimization method based on goal planning and goal space processing according to an embodiment of this application.

[0033] Figure 2 is a schematic diagram of a multi-objective optimization apparatus based on target planning and target space processing according to an embodiment of this application.

[0034] Figure 3 is a schematic diagram of a computer device for multi-objective optimization based on goal planning and goal space processing according to an embodiment of this application.

[0035] Figure 4 is a schematic diagram of a target space for multi-objective optimization based on target planning and target space processing according to an embodiment of this application.

[0036] Figure 5 is a schematic diagram of solving a multi-objective optimization based on goal planning and goal space processing according to an embodiment of this application.

[0037] Figure 6 is a schematic diagram of solving a multi-objective optimization based on goal planning and goal space processing according to an embodiment of this application.

[0038] Figure 7 is a schematic diagram of solving a multi-objective optimization based on goal planning and goal space processing according to an embodiment of this application.

[0039] The reference numerals in the accompanying drawings are as follows: S101-S103 Step 200: Device 201: Module 202: Module 203: Module 204: Module 300: Computer device 302: Processor 304: Memory Detailed Implementation

[0040] In the following description, numerous specific details are set forth for illustrative purposes. However, it will be understood that the invention can be implemented without these specific details. In other instances, well-known circuits, structures, and techniques have not been shown in detail so as not to affect the understanding of the description.

[0041] Throughout the specification, references to "an implementation," "implementation," "exemplary implementation," "some implementations," "various implementations," etc., indicate that the implementation of the invention described may include specific features, structures, or characteristics. However, it is not implied that every implementation must include these specific features, structures, or characteristics. Furthermore, some implementations may have some, all, or none of the features described for other implementations.

[0042] In general, multi-objective optimization problems can be formulated as follows:

[0043] st

[0044] Here, x is a multidimensional vector of decision variables, f(x) are the m constraints to be followed, and z(x) are the n objective functions to be optimized. When n=1, the multi-objective optimization problem simplifies to a single-objective problem.

[0045] Currently, there are several methods for handling multi-objective tasks in OR optimization algorithms.

[0046] The most common approach is to normalize multiple objectives across different dimensions, allowing single-objective optimization algorithms (solvers, heuristics, etc.) to be used based on the surrogate objective. There are two methods to achieve this.

[0047] (1) Weighted sum: Substitute a single objective into min:∑ j∈{1,…,n} ω j ·z j (x), where ω j It is the weight of the j-th objective.

[0048] (2) Hierarchical: Objectives are ranked according to importance, and then any two solutions are compared. For example, if the priority is z1>z1>z3, and the solutions x1 and x2 have z1(x1) = z1(x2) and z2(x1) respectively.<z2(x2),z3(x1)> If z3(x2), then x1 is better than x2. This is actually an extreme simplification of the weighted sum; for example, setting ω1 >> ω2 >> ω3 would reflect the preference in the example above.

[0049] From a technical perspective, this normalization method is very straightforward. For example, in Advanced Planning and Scheduling (APS) software such as Preactor, users can adjust the weights of multiple objectives; in solvers such as Cplex, users can specify hierarchical preferences among multiple objectives. However, the usability of the resulting solution is limited because it simplifies the original multiple objectives into a single surrogate objective.

[0050] (1) The impact of weights on the solution is indirect. By setting weight values, users cannot predict or control the performance of the solution in different target directions. In the worst case, even if all weight combinations are enumerated, users may still get the same unwanted solution.

[0051] (2) For the same reason, the algorithm cannot improve the user experience by taking into account the user’s expectations of the target value (if they exist, whether they are feasible or not, whether they are based on experience or guesswork, whether they are based on first impressions or interaction process).

[0052] Another approach is evolutionary multi-objective optimization (EMO), a population-based metaheuristic algorithm, such as NSGA-II, NSGA-III, and R-NSGA-III. The search-evaluation iterative mechanism of evolutionary algorithms can be naturally used to construct Pareto fronts, which consist of non-dominated solutions distributed within the multi-objective space or around a reference direction. However, it still has limitations.

[0053] (1) As a heuristic algorithm, EMO cannot guarantee or even evaluate the optimality of its solution. In other words, the constructed Pareto front may be far from the true front, or the multiple Pareto solutions found may be easily dominated by a single solution found by the solver.

[0054] (2) Unlike solvers, the return on investment (the ratio of solution quality to computational cost) of EMO decreases significantly as the problem size and complexity increase. To achieve an acceptable balance between performance and efficiency, it is often necessary to adjust various hyperparameters and design custom encoding-decoding schemes.

[0055] (3) In the multi-objective aspect, the forward logic of the first search then evaluate mechanism, and the potentially customizable encoding-decoding scheme, still have an indirect impact on the solution. Similar to the normalization method, this will limit the diversity and density of Pareto solutions, especially for combinatorial optimizations where the solution space is usually discrete and has a hyperplane.

[0056] This application proposes a multi-objective optimization method based on goal programming and objective space processing. This application fully leverages the advantages of current solvers in single-objective optimization while ensuring the diversity and intensification of Pareto solutions.

[0057] Based on this, this application discloses a multi-objective optimization method based on goal programming and goal space processing, which includes:

[0058] S101, Based on multiple objectives, establish a multi-dimensional objective space, wherein the boundary of the objective space is determined by the maximum and minimum values ​​of the multiple objectives.

[0059] In some embodiments, the effective objective space is first determined. Specifically:

[0060] First, calibrate the n-dimensional target space, that is, determine the minimum and maximum range of each target j. Among them, the as well as This represents the maximum or minimum value of multiple objectives. The specific steps are as follows:

[0061] (1) For each objective k∈{1,...,n}, solve its single-objective optimization problem.

[0062] [SO k min:z k (x)

[0063] st

[0064] Given the solution x k Its evaluation value on each objective j is z. j (x k )

[0065] (2) For each target j, Based on the aforementioned multi-objective maximum and minimum values, a multi-dimensional objective space is further constructed. In some embodiments, this multi-dimensional objective space may be referred to as a hypercube. It is the boundary of the effective objective space. It is easy to prove that any solution for any objective value outside the hypercube cannot be at the Pareto front, because it will be affected by the objective value at some x-axis on the surface of the hypercube. k dominated.

[0066] S102, the multi-dimensional target space is divided into multiple sub-target spaces.

[0067] Furthermore, the step of dividing the multi-dimensional target space into multiple sub-target spaces includes: dividing the multi-dimensional target space into multiple sub-target spaces based on the upper and lower boundary values ​​of the target value.

[0068] Using the above method, the target space can be divided into multiple small sub-target spaces according to the requirements, and target programming can be used to transform the target space into a single-target solution.

[0069] Specifically, this means determining the diversification search. The details are as follows:

[0070] Based on the aforementioned hypercube, spatial slicing and goal programming are applied to construct the Pareto frontier and perform diversified searches. The specific process is as follows:

[0071] (1) By dividing the effective range of each target direction into slots, which can be uniform or non-uniform, the hypercube is cut into a grid, which can be called a sub-target space. Each grid g can be written as:

[0072] in, Indicates the lower boundary value. This represents the upper boundary value.

[0073] S103, solve for the multi-objective values ​​in the multiple sub-objective spaces to obtain the optimal solution set of the corresponding multi-objective values.

[0074] Furthermore, for each grid g, a modified single-objective optimization problem is solved.

[0075] [MSO g min:∑ j∈{1,…,n} z j (x)

[0076] st

[0077] The weighted sum of multiple objectives (each objective has a weight of 1) finds the optimal z-value within the grid range (i.e., the last constraint). j The solution x is the value g Of course, MSO g It may also be unfeasible.

[0078] Specifically, the grid is enumerated, and the solutions to the MSO problems are collected. In this embodiment, not every MSO needs to be solved; that is, some grids can be skipped quickly, thanks to the direct influence of goal programming on the solution.

[0079] The above method can accurately and directly obtain the optimal solution set for multiple objective values, which facilitates the rapid construction of the Pareto front.

[0080] Furthermore, the step of solving for the multi-objective value for the multiple sub-objective spaces includes: traversing the target space in ascending order of the distance from the sub-objective space to the pseudo-origin.

[0081] Specifically, it can be:

[0082] a. The mesh is aligned to the pseudo-origin of the hypercube. The grids are traversed in ascending order of their distance to the pseudo-original point of the hyper-cube. ).

[0083] b. Collected MSO solution set S MSO Originally for The algorithm is updated every time the MSO of the mesh is solved.

[0084] c. For each grid g, if there exists a solution-dominant grid g among the previously solved grids, i.e. Then the MSO of grid g can be skipped. g Please provide a solution.

[0085] Using the above method, we can start solving from the vicinity of the pseudo-origin and quickly find the optimal solution.

[0086] Furthermore, the step of solving for multiple objective values ​​in the multiple sub-objective spaces includes: solving for multiple objective values ​​in the sub-objective spaces based on time constraints, distance constraints, and a warm-start mechanism. Specifically, as follows:

[0087] a. When solving MSOs using a solver, early termination conditions can be set, such as time limits or distance limits. Although solution quality is sacrificed for solution speed, optimality can still be measured. Furthermore, a warm start mechanism can be utilized, where solutions from nearby meshes can help quickly start the solution for the current mesh.

[0088] b. Because the MSOs of the grid are relatively independent, multiprocessing can be applied to facilitate parallel computing. The grid can be pre-grouped or dynamically load-balanced.

[0089] By using the above methods, the solution strategy can be adjusted according to actual needs, making it easier to quickly find the optimal solution.

[0090] Furthermore, the step of solving for multiple target values ​​in the multiple sub-target spaces includes: receiving a reference point and traversing the target space according to the ray from the reference point.

[0091] Specifically, this can include intensification search. Details are as follows:

[0092] When users provide some reference points in the target space, such as through subjective judgment or through analysis of the Pareto front, the diversified search can be further extended into a reinforced search, that is, to delve deeper into possible Pareto solutions around the reference direction. The specific process is as follows.

[0093] (1) For the reference point Its corresponding reference direction is from p o to p r The ray reflects the user's implicit preference for different targets. A point along the reference direction can be written as p. λ =λp r +(1-λ)p o ,λ≥0

[0094] (2) With appropriate precision, the closest approximation to p can be found along the reference direction. o Feasibility points.

[0095] a. Iterate at a certain step size, increasing λ until the point is reached. In p λ Build a grid around it, that is

[0096] Then try to solve the corresponding MSO. λ .

[0097] [MSO λ min:∑ j∈{1,…,n} z j (x)

[0098] st

[0099] b. Once MSO λ Once the solution is found, the iteration will stop. For the obtained solution x... t Its point in the target space is p. t =(z1(x) t ),…,z n (x t )). p t It can be approximated as the intersection of the reference direction and the Pareto front.

[0100] Using the methods described above, the system can iterate through the data based on user experience or external recommendations, and thus quickly find the optimal solution.

[0101] Furthermore, the step of dividing the multi-dimensional target space into multiple sub-target spaces includes: adjusting the upper and lower boundary values ​​of the target value based on the center point of the sub-target space as a reference point.

[0102] For example, construct a pt The local hypercube centered on

[0103] The aforementioned diversification search is then applied within this local hypercube. The resulting Pareto front is a local front around the reference direction. The local hypercube can then be progressively enlarged, and the above steps repeated until a satisfactory Pareto solution is obtained. In some embodiments, Figure 6 illustrates the above process, where n is set to 2 for clarity.

[0104] In some embodiments, a Pareto front can be easily constructed based on the MSO solutions collected from the grid. Pareto solution diversity can be achieved, for example, by dividing and conquering the entire effective objective space. The granularity of the grid division can adjust the search accuracy, while the objective planning of each grid ensures direct control over the performance of the solution in different objective directions.

[0105] By using the above method, the values ​​of the upper and lower boundaries can be adjusted according to the center position and other factors, thereby defining the size of the sub-target space, which makes it easier to find the optimal solution.

[0106] In some embodiments, Figure 4 shows an example of a sliced ​​hypercube and a mesh for solving the MSO. For visual clarity, n is set to 3. Note that the hypercube and each mesh do not necessarily need to be square, and the segments on each axis do not necessarily need to be uniform.

[0107] In some embodiments, Figure 5 illustrates the Pareto frontier obtained using the method described above. The multi-objective optimization problem to be solved is a Service and Operations (S&OP) based on experience providing services to a Chinese automaker. The three most important key performance indicators for the company are demand fulfillment rate, production cost, and procurement workload. The multi-objectives are demand fulfillment rate, production cost, and procurement workload.

[0108] After calibrating the target space, the resulting hypercube was divided into 1000 (10*10*10) grids, of which only 98 MSOs needed to be solved, while the other 902 MSOs were quickly skipped. Of the 98 solutions, 45 were non-dominated and the remaining 53 were dominated. These 45 Pareto solutions help users make trade-offs and decisions, not only because they provide a sufficient number of choices, but also because they are widely distributed throughout the target space, even though the target space is sparse and irregular.

[0109] In contrast, this application attempted a normalization method. Unsurprisingly, due to the indirect effect of the weights on the solution, after enumerating 1000 combinations of (ω1,ω2,ω3) values, only 5 Pareto solutions were obtained, and they were all very close to each other. Furthermore, there was no opportunity to quickly skip over any solutions.

[0110] As for EMO, since S&OP has over 900 decision variables, it's impossible to directly use EMO to solve the problem. Note that in practice, combinatorial optimization problems can have over 10,000 decision variables. That is, the optimal solution consists of parameters with over 10,000 dimensions.

[0111] In some embodiments, Figure 7 illustrates a portion of the Pareto front of the aforementioned S&OP. In Figure 7, the global Pareto solution, reference point, and local Pareto solutions are labeled with a cross, a triangle, and a dot, respectively. Different reference points correspond to different local Pareto solutions. Indeed, the local Pareto solutions all lie on the global Pareto front and are located around the reference direction. In Figure 7, for a single reference point where z1 is near 82000, z2 is near 0, and z3 is near 0, only one local Pareto solution can be found because the discrete Pareto front along this reference direction is relatively sparse. In this case, the application can progressively expand the local hypercube to find more Pareto solutions, although these solutions will be farther from the reference direction.

[0112] In this application, the above methods are illustrated one by one by examples. The solution procedures or processes discussed can be executed using a mathematical programming solver, and relevant user configuration initialization is performed. Furthermore, the proposed methods are configurable in many aspects, including: for the effective target space, the user can directly specify... Values; for diversified searches, the granularity of spatial partitioning can be adjusted to achieve a balance between accuracy and speed; in reinforced searches, the source point of the reference direction can also be specified by the user instead of using p. o In p t The precision of the surrounding search and assessment can also be adjusted, for example, by increasing the step size of λ or σ. λ and δ j The values, the granularity of cutting the local hypercube, and the step size of expanding the local hypercube, etc.

[0113] Under the same diversified search and reinforcement search approach, various variations are possible, as shown in the two examples in Figure 6(a) and (b). Of course, the above steps can be freely combined to facilitate an interactive decision-making process.

[0114] The beneficial effects of this application include: the proposed solution effectively combines the advantages of existing solutions while overcoming their disadvantages, thereby solving the usability problem. Specifically, this includes:

[0115] Compared to normalization and EMO, users can predict and control the performance of the solution in different target directions. This results in a high degree of diversity in the obtained Pareto solutions, and the user's expected value can be fully considered by the algorithm.

[0116] Compared to EMO, using a solver ensures that the constructed Pareto front is of good quality and measurable. It also offers a higher return on investment during the algorithm design, development, and computation phases, especially for large-scale and complex combinatorial optimization problems.

[0117] The methods for detecting whether the methods described in this application are used may include the following:

[0118] (1) If the method for multi-objective optimization is based on the proposed idea, it should be clearly derived from the description / instruction of the method used.

[0119] (2) Infer from the interface specifications / user interface functions / system workflow if the implicit method is based on the proposed idea.

[0120] (3) If there are keywords such as target planning or target space processing, they are implied in the introduction / promotion information.

[0121] It should be understood that although the steps in the flowchart of Figure 1 are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in Figure 1 may include multiple steps or multiple stages, which are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages in other steps.

[0122] Figure 2 provides a multi-objective optimization device 200 based on goal planning and goal space processing. It includes:

[0123] The space establishment module 201 is used to establish a multi-dimensional target space based on multiple targets, wherein the boundary of the target space is determined by the maximum and minimum values ​​of the targets;

[0124] The spatial segmentation module 202 is used to segment the multi-dimensional target space into multiple sub-target spaces;

[0125] The spatial solution module 203 is used to solve multiple objectives in the multiple sub-objective spaces to obtain the optimal solution set of the corresponding multiple objectives.

[0126] It should be noted that the device may contain more or fewer modules to implement the described functions. For example, at least one module in FIG2 may be further divided into a plurality of different sub-modules, each sub-module being used to perform at least a portion of the operations described herein in conjunction with the corresponding module. Furthermore, in some examples, device 200 may also include additional modules for performing other operations already described in the specification. Moreover, those skilled in the art will understand that the exemplary device 200 may be implemented using software, hardware, firmware, or any combination thereof.

[0127] Figure 3 provides a computer device. According to one embodiment, the computer device 300 may include a processor 302 that executes a computer program stored in a memory 304. When executed by the processor, the computer program implements the method described above.

[0128] Those skilled in the art will understand that the structure shown in Figure 3 is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or may combine certain components, or may have different component arrangements.

[0129] Those skilled in the art will understand that all or part of the processes in the methods described above can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0130] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the above steps.

[0131] This application also provides a computer program product tangibly stored on a computer-readable medium and including computer-executable instructions that, when executed, cause at least one processor to perform the methods described above.

[0132] Furthermore, the computer program can be stored and run in the cloud to execute the method. Furthermore, the components of the program can be deployed on multiple devices or in the cloud; for example, corresponding steps can be deployed and run on a local computer, or run on different cloud devices, transmitting signals via communication connections, or they can also be deployed and run on a local computer. This application does not limit the described approach or method; corresponding technologies can be flexibly deployed and fully utilized to execute and complete the method using cloud computing, big data, supercomputing capabilities, and other equipment and technologies.

[0133] Some implementations of this disclosure may include an article of writing. The article of writing may include a storage medium for storing logic. Examples of storage media may include one or more types of computer-readable storage media capable of storing electronic data, including volatile or non-volatile memory, removable or non-removable memory, erasable or non-erasable memory, writable or rewritable memory, and so on. Examples of logic may include various software units, such as software components, programs, applications, computer programs, application programs, system programs, machine programs, operating system software, middleware, firmware, software modules, routines, subroutines, functions, methods, procedures, software interfaces, application programming interfaces (APIs), instruction sets, computational code, computer code, code segments, computer code segments, words, values, symbols, or any combination thereof. In some implementations, for example, the article of writing may store executable computer program instructions that, when executed by a processor, cause the processor to perform the methods and / or operations described herein. Executable computer program instructions may include any suitable type of code, such as source code, compiled code, interpreted code, executable code, static code, dynamic code, and so on. Executable computer program instructions can be implemented according to a predefined computer language, method, or syntax used to command the computer to perform specific functions. These instructions can be implemented using any suitable high-level, low-level, object-oriented, visual, compiled, and / or interpreted programming language.

[0134] The examples described above include those of the disclosed architecture. It is certainly impossible to describe every conceivable combination of components and / or methods, but those skilled in the art will understand that many other combinations and arrangements are also possible. Therefore, this novel architecture is intended to cover all such alternatives, modifications, and variations that fall within the spirit and scope of the appended claims.

Claims

1. A multi-objective optimization method based on goal programming and goal space processing, wherein, include: Based on multiple objectives, a multi-dimensional objective space is established, wherein the boundary of the objective space is determined by the maximum and minimum values ​​of the multiple objectives; The multi-dimensional target space is divided into multiple sub-target spaces; The optimal solution set for each of the multiple sub-objective spaces is obtained by solving multiple objectives.

2. The method according to claim 1, wherein, The segmentation of the multi-dimensional target space into multiple sub-target spaces includes: Based on the upper and lower boundary values ​​of the multiple targets, the multi-dimensional target space is divided into multiple sub-target spaces.

3. The method according to claim 1, wherein, The multi-objective solution for the multiple sub-objective spaces includes: The target space is traversed in ascending order of distance from the sub-target space to the pseudo-origin.

4. The method according to claim 1, wherein, The multi-objective solution for the multiple sub-objective spaces includes: Receive a reference point and traverse the target space using a ray from the reference point.

5. The method according to claim 2, wherein, The segmentation of the multi-dimensional target space into multiple sub-target spaces includes: The upper and lower boundary values ​​of the multi-target are adjusted based on the center point of the sub-target space as a reference point.

6. The method according to claim 1, wherein, The multi-objective solution for the multiple sub-objective spaces includes: Based on time constraints, distance constraints, and a warm-start mechanism, the sub-objective space is solved for multiple objectives.

7. A multi-objective optimization device based on target space, wherein, include: A space establishment module is used to establish a multi-dimensional target space based on multiple objectives, wherein the boundary of the target space is determined by the maximum and minimum values ​​of the multiple objectives; The spatial segmentation module is used to segment the multi-dimensional target space into multiple sub-target spaces; The spatial solution module is used to solve multiple objectives in the multiple sub-objective spaces to obtain the optimal solution set for the corresponding multiple objectives.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, wherein, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

10. A computer program product tangibly stored on a computer-readable medium and comprising computer-executable instructions that, when executed, cause at least one processor to perform the method according to any one of claims 1 to 6.

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