Method for solving high-dimensional and constrained expensive combinatorial optimization problem
By using the method of random grouping parallel optimization in spacecraft cabin temperature monitoring and control, the problem of high-dimensional expensive combination optimization is solved, the appropriate number and location of measurement points are determined, the accuracy and reliability of temperature monitoring and control are improved, and the solution efficiency is improved.
Patent Information
- Application Number
- CN202510159230.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-13
- Publication Date
- 2025-07-18
AI Technical Summary
The prior art is difficult to effectively solve the problem of high-dimensional and constrained expensive combination optimization, especially in spacecraft cabin temperature monitoring and control, how to select the appropriate number and location of measurement points under resource limitations to ensure the accuracy and reliability of temperature monitoring and control.
By obtaining multiple solutions within and outside the constraint range of the decision space, random grouping is optimized in parallel, using the proxy model and initial population, the location and number of temperature sensor measurement points in the spacecraft cabin are determined, and the location and number of temperature sensor measurement points are decomposed into multiple sub-problems for independent optimization, and finally merged to obtain the optimal solution.
It realizes efficient and accurate determination of the measurement point position of the spacecraft cabin temperature monitoring and control under given constraints, improves the accuracy and reliability of temperature monitoring and control, and shortens the solution time.
Smart Images
Figure CN120337387A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of spacecraft, and particularly relates to a method for solving high-dimensional and constrained expensive combinatorial optimization problems. Background Art
[0002] In practical engineering applications, there are many optimization problems. Generally, an optimization problem contains three basic elements: decision variables, optimization objectives, and constraint conditions. Among numerous optimization problems, there is a class of complex optimization problems that are difficult to solve. Such problems usually have the following characteristics: the decision variables are binary 0 / 1 values; the dimension of the decision variables is very high, even reaching 10,000 dimensions; there are inequality constraints; the evaluation process of the optimization objective is very time-consuming or costly. Such problems are generally referred to as high-dimensional and constrained expensive combinatorial optimization problems, which are widespread in practical engineering, such as large-scale feature selection problems, circuit optimization problems, image recognition, etc.
[0003] For high-dimensional and constrained expensive combinatorial optimization problems, there is currently no method to solve such optimization problems. Existing methods can only solve high-dimensional expensive combinatorial optimization problems. Moreover, for high-dimensional expensive combinatorial optimization problems, currently, the method based on co-evolution is mainly adopted. The adoption of this method is divided into the idea of governance. The high-dimensional problem is decomposed into multiple low-dimensional sub-problems by random grouping, and then the sub-problems are solved in turn. Finally, the optimal solutions of the sub-problems are merged into the optimal solution of the original problem. However, when using random grouping to solve expensive high-dimensional optimization problems, since several or even dozens of surrogate models need to be constructed, there are problems of low operating efficiency and long solution time; moreover, affected by the prediction error of the surrogate model, the optimal value obtained by this method is not necessarily the true optimal value.
[0004] When the electronic components inside the spacecraft cabin panel are working, heat dissipation is inevitably generated, causing the temperature of the electronic components inside the cabin panel to rise. And due to the vacuum environment in space, the electronic components cannot dissipate heat outward through heat convection, and heat is more likely to accumulate, resulting in a rapid increase in the temperature of the electronic components, affecting their service life, safety, and reliability. In severe cases, it may even cause the electronic components to fail or be damaged. In order to make the electronic components inside the spacecraft cabin panel work within the allowable temperature range, it is necessary to monitor and control the temperature of the spacecraft cabin panel.
[0005] In order to achieve the temperature monitoring and control of the spacecraft cabin panel, usually multiple position points are selected inside the spacecraft cabin panel to arrange temperature sensors. The arranged multiple temperature sensors are used for on-orbit temperature monitoring of the spacecraft cabin panel. After converting the temperature monitoring data of the multiple temperature sensors into electrical signals, they are transmitted to the ground control center. The ground control center calculates the temperature field of the spacecraft cabin panel based on the obtained temperature monitoring data, and then realizes the temperature monitoring and control of the spacecraft cabin panel.
[0006] In order to ensure the accuracy and reliability of temperature monitoring and control of spacecraft cabin panels, the current practice is to select as many measuring points as possible to arrange temperature sensors to obtain as much temperature monitoring data as possible. However, since the number of measuring points and temperature sensors is directly related to the spacecraft platform's demand for hardware resources such as temperature monitoring sensor devices, measurement channels, and cables, if there are too many temperature monitoring points, it will inevitably lead to resource consumption, system weight increase, and an increase in development costs such as engineering implementation and testing. Therefore, in actual application, due to the limitations of conditions such as the weight and cost of the spacecraft, the number of measuring points that can be selected is limited and cannot exceed a certain threshold. Therefore, how to select the appropriate number of measuring points and measuring point locations to ensure the accuracy and reliability of temperature monitoring and control of spacecraft cabin panels based on the selected measuring points is a key technical problem that needs to be solved in the field of spacecraft thermal control. Summary of the invention
[0007] In order to solve part or all of the technical problems existing in the above-mentioned prior art, the present invention provides a method for solving a high-dimensional and constrained expensive combinatorial optimization problem.
[0008] The technical solution of the present invention is as follows:
[0009] A method for solving a high-dimensional and constrained expensive combinatorial optimization problem is provided, the method comprising:
[0010] According to the optimization problem to be solved, the decision variables, constraints, decision space and optimization objectives are determined. The optimization problem is the problem of selecting measurement points on the spacecraft cabin.
[0011] According to the decision space and the constraint conditions, a plurality of solutions outside the constraint range of the decision space and a plurality of solutions within the constraint range of the decision space are obtained, and a target value corresponding to each of the obtained solutions is calculated;
[0012] According to the optimization objective and target value, a preset number of solutions are selected from all the obtained solutions to form an initial population;
[0013] According to the dimension of decision variables, the decision variable set is randomly divided into multiple decision variable subsets, and the optimization problem is divided into multiple sub-problems, where the intersection of all decision variable subsets is empty and the union of all decision variable subsets is the decision variable set;
[0014] According to all the obtained solutions and the corresponding target values, decision variable subsets, initial populations and preset proxy models, each sub-problem is optimized respectively, the optimal solution corresponding to each sub-problem is determined, and the optimal solutions corresponding to all sub-problems are merged to obtain the optimal solution for the optimization problem.
[0015] In some alternative embodiments, the mathematical model of the optimization problem is as follows:
[0016]
[0017] Among them, f(X) represents the objective function, which is defined as the difference between the cabin plate temperature field data calculated based on the measurement point selection scheme X and the true temperature field data. X represents the measurement point selection scheme, X = (x1,…,x D )(x i ∈{0,1}, 1≤i≤D), xi i represents the i-th decision variable, which is used to indicate whether the i-th grid is selected as a measurement point. If xi i = 1, it means the i-th grid is selected; if xi i = 0, it means the i-th grid is not selected. D represents the number of grids divided on the spacecraft cabin plate. The dimension of the decision variable is D. g(X) represents the number of values equal to 1 in the measurement point selection scheme X. b represents the measurement point quantity threshold, and V represents the decision space.
[0018] In some alternative embodiments, according to the decision space and constraint conditions, obtaining multiple schemes located outside the constraint range of the decision space includes:
[0019] Randomly generate D random numbers between 0 and 1. For each random number, determine whether it is greater than p. If so, modify the random number to 1; if not, modify the random number to 0. Use the modified random numbers as decision variables to obtain a scheme including D decision variables. Repeat the random process multiple times until a preset number of schemes are obtained; where
[0020] In some alternative embodiments, according to the decision space and constraint conditions, obtaining multiple schemes located within the constraint range of the decision space includes:
[0021] Randomly sample in the decision space to obtain a scheme including D decision variables. Sum all the decision variables in the obtained scheme to determine whether the sum result c is greater than b. If so, select t decision variables with values equal to 1 in the obtained scheme and modify the values of the selected decision variables to 0 to repair the obtained scheme. Repeat the random sampling process until a preset number of schemes are obtained; where the value range of t is λ represents a random number sampled from the right side of the symmetry axis of N(0, 0.52), and N(0, 0.52) represents a normal distribution with a mean of 0 and a standard deviation of 0.5.
[0022] In some alternative embodiments, among the multiple divided subsets of decision variables, except for the last subset of decision variables, the sizes of the remaining subsets of decision variables are equal.
[0023] In some alternative embodiments, optimizing each sub-problem according to all obtained solutions, the objective values corresponding to the solutions, the subsets of decision variables, the initial population, and the preset surrogate model respectively to determine the optimal solution corresponding to each sub-problem includes:
[0024] Taking a obtained solution and the objective value corresponding to the solution as an initial data respectively, and constructing a data set including multiple initial data;
[0025] According to the decision variables in the subset of decision variables corresponding to each sub-problem, selecting the corresponding decision variables and the corresponding objective values from each initial data respectively to construct a data subset corresponding to each sub-problem, wherein the data subset includes multiple sub-data, and the sub-data includes the decision variables selected from an initial data and the corresponding objective values;
[0026] Determining the initial sub-population corresponding to each sub-problem according to the initial population and the data subset;
[0027] Training the preset surrogate model corresponding to the sub-problem by using the data subset, optimizing the sub-problem by using the initial sub-population and the preset surrogate model, and determining the optimal solution corresponding to each sub-problem.
[0028] In some alternative embodiments, the method further includes:
[0029] Repeating the division processes of the subsets of decision variables and the sub-problems, as well as the optimization process of the sub-problems, and saving the optimal solution in a preset set each time the optimal solution of the optimization problem is obtained until a preset loop termination condition is reached.
[0030] In some alternative embodiments, the method further includes:
[0031] Randomly selecting one of the preset surrogate models corresponding to all trained sub-problems for saving each time the optimization process of the sub-problem is performed;
[0032] After the loop termination, combining all the saved preset surrogate models into an ensemble model, and re-evaluating all the optimal solutions saved in the preset set by using the ensemble model to determine the best-performing solution;
[0033] Taking the optimal solution obtained in the last loop or the determined best-performing solution as the final optimal solution of the optimization problem.
[0034] In some alternative embodiments, the method further includes:
[0035] Calculate the Hamming distance between the optimal solution obtained in the last iteration and the best-performing solution among all the obtained solutions, and the Hamming distance between the determined best-performing solution and the best-performing solution among all the obtained solutions. The solution corresponding to the shortest Hamming distance is taken as the final optimal solution of the optimization problem.
[0036] The main advantages of the technical solution of the present invention are as follows:
[0037] The method for solving high-dimensional and constrained expensive combinatorial optimization problems of the present invention can solve high-dimensional and constrained expensive combinatorial optimization problems by obtaining multiple solutions within and outside the constraint range of the decision space, and performing random grouping and parallel optimization of sub-problems based on the obtained solutions to obtain the optimal solution of the optimization problem. It can determine the number and positions of measurement points for arranging temperature sensors inside the spacecraft cabin panel under given constraint conditions to improve the accuracy and reliability of temperature monitoring and control of the spacecraft cabin panel, and has high optimization efficiency and solution accuracy, and the time required for the solution process is short. Description of the Drawings
[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0039] Figure 1 It is a flowchart of the method for solving high-dimensional and constrained expensive combinatorial optimization problems of the embodiments of the present invention. Detailed Embodiments
[0040] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions of the present invention in conjunction with the specific embodiments and corresponding drawings of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.
[0041] The following will detail the technical solutions provided by the embodiments of the present invention in conjunction with the drawings.
[0042] See Figure 1 , the embodiments of the present invention provide a method for solving high-dimensional and constrained expensive combinatorial optimization problems, and the method includes the following steps:
[0043] S1. According to the optimization problem to be solved, determine the decision variables, constraints, decision space, and optimization objective. The optimization problem is the problem of selecting measurement points on the spacecraft cabin panel;
[0044] S2. According to the decision space and constraints, obtain multiple solutions outside the constraint range of the decision space and multiple solutions within the constraint range of the decision space, and calculate the objective value corresponding to each obtained solution;
[0045] S3. According to the optimization objective and objective values, select a preset number of solutions from all the obtained solutions to form an initial population;
[0046] S4. According to the dimension of the decision variables, randomly divide the set of decision variables into multiple subsets of decision variables, and divide the optimization problem into multiple sub-problems. Among them, the intersection of all subsets of decision variables is empty, and the union of all subsets of decision variables is the set of decision variables;
[0047] S5. Optimize each sub-problem according to all the obtained solutions, the objective values corresponding to the solutions, the subsets of decision variables, the initial population, and the preset surrogate model respectively, determine the optimal solution corresponding to each sub-problem, and merge the optimal solutions corresponding to all sub-problems to obtain the optimal solution of the optimization problem.
[0048] The method for solving high-dimensional and constrained expensive combinatorial optimization problems provided by the embodiments of the present invention can obtain multiple solutions within and outside the constraint range of the decision space, and perform random grouping and parallel optimization of sub-problems based on the obtained solutions to obtain the optimal solution of the optimization problem. It can solve high-dimensional and constrained expensive combinatorial optimization problems, determine the number and positions of measurement points for arranging temperature sensors inside the spacecraft cabin panel under given constraints to improve the accuracy and reliability of temperature monitoring and control of the spacecraft cabin panel, and has high optimization efficiency and solution accuracy, and the time required for the solution process is short.
[0049] The following specifically illustrates the steps and principles of the method for solving high-dimensional and constrained expensive combinatorial optimization problems provided by the embodiments of the present invention through specific examples.
[0050] Step S1. According to the optimization problem to be solved, determine the decision variables, decision space, constraints, and optimization objective.
[0051] In the embodiments of the present invention, the optimization problem is the problem of selecting measurement points on the spacecraft cabin panel.
[0052] Specifically, in the embodiments of the present invention, for the problem of selecting measurement points on the spacecraft cabin panel, the spacecraft cabin panel is evenly divided into multiple grids, each grid can be used to arrange a temperature sensor, and at most one temperature sensor can be arranged in each grid.
[0053] Based on the above settings, for the problem of measuring point selection on the spacecraft cabin panel, the decision variables are expressed as:
[0054] X = (x1, …, x D )(x i ∈ {0, 1}, 1 ≤ i ≤ D);
[0055] where X represents a set of decision variables, that is, a measuring point selection scheme, and x i represents the i-th decision variable, which is used to indicate whether the i-th grid is selected as a measuring point. If x i = 1, it means the i-th grid is selected; if x i = 0, it means the i-th grid is not selected. D represents the number of grids divided on the spacecraft cabin panel, and D represents the dimension of the decision variables.
[0056] Based on the above settings, for the problem of measuring point selection on the spacecraft cabin panel, the constraint conditions are expressed as:
[0057] g(X) ≤ b;
[0058] where g(X) represents the number of values equal to 1 in the measuring point selection scheme X, and b represents the threshold of the number of measuring points.
[0059] Based on the above settings, the decision space is specifically set according to the actual situation. For example, it consists of all optional measuring point selection schemes whose number of values equal to 1 does not exceed a certain set value.
[0060] Based on the above settings, the optimization objective is to minimize the difference between the cabin panel temperature field data calculated based on the measuring point selection scheme and the true temperature field data.
[0061] Furthermore, based on the above analysis, for the problem of measuring point selection on the spacecraft cabin panel, the mathematical model of this optimization problem can be expressed as:
[0062]
[0063] where f(X) represents the objective function, which is defined as the difference between the cabin panel temperature field data calculated based on the measuring point selection scheme X and the true temperature field data, and V represents the decision space.
[0064] Step S2: According to the decision space and constraint conditions, obtain multiple schemes outside the constraint range of the decision space and multiple schemes within the constraint range of the decision space, and calculate the objective values corresponding to each obtained scheme.
[0065] Before using a surrogate model to assist in solving expensive optimization problems, a certain amount of training data needs to be collected to fit and train the surrogate model. Due to the constraints in the decision space, when the optimal solution of the optimization problem is distributed near the constraints, if only sampling is performed within the constraint range of the decision space to obtain data, it will lead to extremely poor prediction performance of the surrogate model in the area near the constraints, and may cause the actual optimal solution not to be found when solving the optimization problem.
[0066] To this end, in the embodiments of the present invention, according to the decision space and constraint conditions, multiple solutions located outside the constraint range of the decision space are obtained, and at the same time, multiple solutions located within the constraint range of the decision space are also obtained.
[0067] Specifically, for the specifically set problem of selecting measurement points on the spacecraft cabin panel, that is, the constraint condition is g(X) ≤ b and the dimension of the decision variables in the solution is D, obtaining multiple solutions located outside the constraint range of the decision space includes the following steps:
[0068] Randomly generate D random numbers between 0 and 1. For each random number, determine whether it is greater than p. If so, modify the random number to 1. If not, modify the random number to 0. Use the modified random numbers as decision variables to obtain a solution including D decision variables. Repeat the random process multiple times until the preset number of solutions is obtained; where
[0069] The number of decision variables equal to 1 in the solutions obtained through the above steps is basically greater than b. The solutions obtained above can be used as solutions located outside the constraint range of the decision space.
[0070] Further, for the specifically set problem of selecting measurement points on the spacecraft cabin panel, that is, the constraint condition is g(X) ≤ b and the dimension of the decision variables in the solution is D, obtaining multiple solutions located within the constraint range of the decision space includes the following steps:
[0071] Randomly sample in the decision space to obtain a solution including D decision variables. Sum all the decision variables in the obtained solution and determine whether the sum result c is greater than b. If so, select t decision variables with a value of 1 in the obtained solution and modify the values of the selected decision variables to 0 to repair the obtained solution. Repeat the random sampling process until the preset number of solutions is obtained; where the value range of t is λ represents a random number sampled from the right side of the axis of symmetry of N(0, 0.52), and N(0, 0.52) represents a normal distribution with a mean of 0 and a standard deviation of 0.5.
[0072] In an embodiment of the present invention, when obtaining a solution within the constraint range of the decision space, random sampling is first performed in the decision space, and then corresponding processing is performed based on the sampled solution. If the sampled solution is not within the constraint range, the solution is repaired to be within the constraint range.
[0073] Specifically, for the above-mentioned specific spacecraft cabin measurement point selection problem, the constraint of this optimization problem is that the number of decision variables that are 1 in the scheme does not exceed b. Since the value of the decision variable is 0 or 1, the number of decision variables that are 1 in scheme X can be determined by summing all decision variables in scheme X. The summation result of scheme X is represented by g(X). If g(X)>b, it means that the number of decision variables that are 1 in scheme X exceeds b, and the scheme does not meet the constraint. If the scheme is to be repaired to meet the constraint, it is only necessary to set g(X)≤b. The most direct method is to modify at least g(X)-b decision variables to make their values equal to 0, that is, it is necessary to select at least g(X)-b decision variables that are equal to 1 from X for modification. However, in the repair process, it is also necessary to consider that within the constraint range, the larger the value of g(X), the more individuals are sampled and modified. In the embodiment of the present invention, in order to achieve the above functions, a random number that obeys a normal distribution with a mean of 0 and a standard deviation of 0.5 is used to control the repair process of the solution that does not meet the constraints.
[0074] Furthermore, after the scheme is acquired, all the acquired schemes are merged into a whole, each scheme is evaluated through simulation experiments or real experiments, and the target value corresponding to each acquired scheme is calculated. In an embodiment of the present invention, the target value corresponding to the scheme is the difference between the cabin temperature field data calculated based on the temperature data at the measuring point position selected in the scheme and the actual temperature field data. Among them, the experimental conditions corresponding to each scheme are the same. Among them, when calculating the cabin temperature field data based on the temperature data at the measuring point position, it can be calculated using the existing finite element calculation method or neural network proxy model.
[0075] Step S3, selecting a preset number of solutions from all the obtained solutions to form an initial population according to the optimization target and the target value.
[0076] In the embodiment of the present invention, all the schemes are sorted according to the target values corresponding to all the schemes, and a preset number of schemes with the best performance are selected to form an initial population.
[0077] Further, for the problem of selecting measurement points on the spacecraft cabin panel set above, since the optimization objective is to minimize the difference between the cabin panel temperature field data calculated based on the measurement point selection scheme and the real temperature field data, the smaller the objective value corresponding to the scheme, the better the performance of the scheme. Therefore, in the embodiments of the present invention, according to the objective values corresponding to all the schemes, all the schemes are sorted in ascending order of the objective values, and the preset number of schemes in the front is selected to form the initial population, that is, the preset number of schemes with the best performance form the initial population.
[0078] Step S4, according to the dimension of the decision variables, the set of decision variables is randomly divided into multiple subsets of decision variables, and the optimization problem is divided into multiple sub-problems, where the intersection of all subsets of decision variables is empty, and the union of all subsets of decision variables is the set of decision variables.
[0079] To solve the optimization problem, after the scheme sampling is completed, it is necessary to construct and train the corresponding surrogate model according to the sampled schemes, and then use the surrogate model to solve the optimization problem. However, in high-dimensional and constrained expensive combinatorial optimization problems, the dimension of the decision variables is extremely high, and it is difficult to directly construct an efficient surrogate model.
[0080] To solve the above problems, in the embodiments of the present invention, according to the dimension of the decision variables, the set of decision variables is divided into multiple subsets of decision variables, that is, the high-dimensional set of decision variables is divided into multiple low-dimensional subsets, and then according to the divided decision variables, the optimization problem is also divided into corresponding multiple sub-problems, and the optimization problem is solved by independently optimizing and solving each sub-problem.
[0081] By grouping the decision variables and the optimization problem to solve the optimization problem, there is no need to construct a surrogate model for processing high-dimensional data, which can significantly improve the solution efficiency of the optimization problem.
[0082] In the embodiments of the present invention, when grouping the decision variables, a random grouping method is adopted, that is, the set of decision variables is randomly divided into multiple subsets of decision variables, and the intersection of all subsets of decision variables is empty, and the union of all subsets of decision variables is the set of decision variables.
[0083] Adopting the above grouping method of decision variables, there is no need to perform the real evaluation process of the objective function, which can further improve the optimization solution efficiency.
[0084] Optionally, among the multiple subsets of decision variables divided, except for the last subset of decision variables, the sizes of the remaining subsets of decision variables are equal.
[0085] Step S5: Optimize each sub-problem respectively according to all the obtained solutions, the corresponding objective values, decision variable subsets, initial populations, and preset surrogate models, determine the optimal solution corresponding to each sub-problem, and merge the optimal solutions corresponding to all sub-problems to obtain the optimal solution of the optimization problem.
[0086] Specifically, in the embodiments of the present invention, optimizing each sub-problem respectively according to all the obtained solutions, the corresponding objective values, decision variable subsets, initial populations, and preset surrogate models, and determining the optimal solution corresponding to each sub-problem includes the following steps:
[0087] S51: Respectively use an obtained solution and the corresponding objective value as an initial data, and construct a data set including multiple initial data.
[0088] S52: According to the decision variables in the decision variable subset corresponding to each sub-problem, respectively select the corresponding decision variables and the corresponding objective values from each initial data to construct the data subset corresponding to each sub-problem. Wherein, the data subset includes multiple sub-data, and the sub-data includes the decision variables selected from one initial data and the corresponding objective values.
[0089] S53: Determine the initial sub-population corresponding to each sub-problem according to the initial population and the data subset.
[0090] S54: Use the data subset to train the preset surrogate model corresponding to the sub-problem, and use the initial sub-population and the preset surrogate model to optimize the sub-problem to determine the optimal solution corresponding to each sub-problem.
[0091] According to the divided decision variable subsets and sub-problems, as well as the sampled solutions, adopting the above method for optimizing and solving sub-problems can achieve parallel optimization of sub-problems and improve the optimization and solving efficiency.
[0092] Since the mutual relationship between decision variables is not considered when randomly grouping decision variables, in order to increase the probability that relevant decision variables are grouped into the same group, in the embodiments of the present invention, the method may further include:
[0093] Repeat the processes of dividing decision variable subsets and sub-problems, as well as the optimization process of sub-problems for multiple times, and after obtaining the optimal solution of the optimization problem each time, save the optimal solution in a preset set until the preset loop termination condition is reached.
[0094] Among them, the preset loop termination condition can be set according to the actual situation. For example, it can be set as: the number of loops reaches a preset threshold.
[0095] Considering different random grouping methods, different optimal solutions may be generated. When a parallel optimization of a sub-problem is completed, if random grouping and parallel optimization still need to be performed, since the grouping method has changed, the optimal solution obtained this time may be overwritten. Therefore, in the embodiments of the present invention, after combining the optimal solutions of each sub-problem into the optimal solution of the original optimization problem, the current optimal solution of the original optimization problem is saved in an independent preset set, so that the optimal solutions under different grouping methods can be recorded by using the preset set.
[0096] Further, in the embodiments of the present invention, the method may further include:
[0097] When optimizing each sub-problem each time, randomly select one from all the trained preset proxy models corresponding to the sub-problems for saving;
[0098] After the loop terminates, combine all the saved preset proxy models into an ensemble model, and use the ensemble model to re-evaluate all the optimal solutions saved in the preset set to determine the best-performing solution;
[0099] Take the optimal solution obtained in the last loop or the best-performing solution determined as the final optimal solution of the optimization problem.
[0100] Since after completing the division process of multiple decision variable subsets and sub-problems, as well as the optimization process of the sub-problems, the solutions saved in the preset set all come from different optimization processes, and the proxy models corresponding to each solution are also different, it is impossible to directly determine which solution in the preset set performs the best. In the embodiments of the present invention, by randomly selecting a proxy model for saving during each random grouping and parallel optimization, and after the loop ends, combining all the saved proxy models into an ensemble model and using the ensemble model to re-evaluate each solution, the solution that may perform the best in the preset set can be determined.
[0101] Further, considering that the proxy models combined into the ensemble model are randomly selected, in order to determine the actual optimal solution of the optimization problem as much as possible, in the embodiments of the present invention, the method may further include:
[0102] Calculate the Hamming distance between the optimal solution obtained in the last loop and the best-performing solution among all the obtained solutions, and the Hamming distance between the best-performing solution determined and the best-performing solution among all the obtained solutions respectively, and take the solution corresponding to the shortest Hamming distance as the final optimal solution of the optimization problem.
[0103] It should be noted that in this text, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. In addition, in this text, "front", "rear", "left", "right", "upper" and "lower" are all referenced with respect to the placement state shown in the drawings.
[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for solving high-dimensional and constrained expensive combinatorial optimization problems, characterized in that, Including: According to the optimization problem to be solved, determine the decision variables, constraints, decision space, and optimization objective. The optimization problem is the problem of selecting measurement points on the spacecraft cabin panel. According to the decision space and constraints, obtain multiple solutions outside the constraint range of the decision space and multiple solutions within the constraint range of the decision space, and calculate the objective value corresponding to each obtained solution. According to the optimization objective and objective values, select a preset number of solutions from all the obtained solutions to form an initial population. According to the dimension of the decision variables, randomly divide the set of decision variables into multiple subsets of decision variables, and divide the optimization problem into multiple sub-problems. Among them, the intersection of all subsets of decision variables is empty, and the union of all subsets of decision variables is the set of decision variables. According to all the obtained solutions, the objective values corresponding to the solutions, the subsets of decision variables, the initial population, and the preset surrogate model, optimize each sub-problem respectively to determine the optimal solution corresponding to each sub-problem, and merge the optimal solutions corresponding to all sub-problems to obtain the optimal solution of the optimization problem.
2. The method for solving high-dimensional and constrained expensive combinatorial optimization problems according to claim 1, characterized in that The mathematical model of the optimization problem is: Among them, f(X) represents the objective function, which is defined as the difference between the cabin plate temperature field data calculated based on the measurement point selection scheme X and the true temperature field data. X represents the measurement point selection scheme, X = (x1, …, D )( i ∈ {0, 1}, 1 ≤ i ≤ D), where xi i represents the i-th decision variable, which is used to indicate whether the i-th grid is selected as a measurement point. If xi i = 1, it means that the i-th grid is selected. If xi i = 0, it means that the i-th grid is not selected. D represents the number of grids divided on the spacecraft cabin plate. The dimension of the decision variable is D. g(X) represents the number of values equal to 1 in the measurement point selection scheme X. b represents the measurement point quantity threshold, and V represents the decision space.
3. The method for solving a high-dimensional and constrained expensive combinatorial optimization problem according to claim 2, wherein According to the decision space and constraints, obtain multiple solutions outside the constraint range of the decision space, including: Randomly generate D random numbers between 0 and 1. For each random number, determine whether it is greater than p. If so, modify the random number to 1; if not, modify the random number to 0. Use the modified random numbers as decision variables to obtain a solution including D decision variables. Repeat the random process multiple times until the preset number of solutions is obtained; among them, 4. The method for solving high-dimensional and constrained expensive combinatorial optimization problems according to claim 2, characterized in that According to the decision space and constraints, obtain multiple solutions within the constraint range of the decision space, including: Randomly sample in the decision space to obtain a solution including D decision variables. Sum all the decision variables in the obtained solution, and determine whether the sum result c is greater than b. If so, select t decision variables with a value of 1 from the obtained solution, and modify the values of the selected decision variables to 0 to repair the obtained solution. Repeat the random sampling process until a preset number of solutions are obtained; where the value range of t is λ represents a random number sampled from the right side of the axis of symmetry of N(0, 0.5 2 ), and N(0, 0.5 2 ) represents a normal distribution with a mean of 0 and a standard deviation of 0.
5.
5. The method for solving a high-dimensional and constrained expensive combinatorial optimization problem according to claim 1, wherein Among the multiple subsets of decision variables divided, except for the last subset of decision variables, the sizes of the remaining subsets of decision variables are equal.
6. The method for solving a high-dimensional and constrained expensive combinatorial optimization problem according to any one of claims 1 to 5, characterized in that, The step of optimizing each sub-problem respectively according to all the obtained solutions, the objective values corresponding to the solutions, the subsets of decision variables, the initial population, and the preset surrogate model to determine the optimal solution corresponding to each sub-problem includes: Respectively take an obtained solution and the objective value corresponding to the solution as an initial data, and construct a data set including multiple initial data. According to the decision variables in the subset of decision variables corresponding to each sub-problem, respectively select the corresponding decision variables and the corresponding objective values from each initial data to construct a data subset corresponding to each sub-problem. Among them, the data subset includes multiple sub-data, and the sub-data includes the decision variables selected from an initial data and the corresponding objective values. According to the initial population and the data subset, determine the initial sub-population corresponding to each sub-problem. Use the data subset to train the preset surrogate model corresponding to the sub-problem, and use the initial sub-population and the preset surrogate model to optimize the sub-problem to determine the optimal solution corresponding to each sub-problem.
7. The method for solving a high-dimensional and constrained expensive combinatorial optimization problem according to claim 6, wherein The method further includes: Repeat the process of dividing the subsets of decision variables and sub-problems, and the optimization process of sub-problems multiple times. And after obtaining the optimal solution of the optimization problem each time, save the optimal solution in a preset set until the preset loop termination condition is reached.
8. The method for solving a high-dimensional and constrained expensive combinatorial optimization problem according to claim 7, wherein The method further includes: When performing the optimization process of each sub-problem each time, randomly select one of the trained preset surrogate models corresponding to all sub-problems for saving. After the loop terminates, combine all the saved preset surrogate models into an ensemble model, and use the ensemble model to re-evaluate all the optimal solutions saved in the preset set to determine the best-performing solution. Take the optimal solution obtained in the last iteration or the best-performing solution determined as the final optimal solution to the optimization problem.
9. The method for solving high-dimensional and constrained expensive combinatorial optimization problems according to claim 8, characterized in that The method further includes: Calculate the Hamming distances between the optimal solution obtained in the last iteration and the best-performing solution among all the obtained solutions, and between the best-performing solution determined and the best-performing solution among all the obtained solutions, respectively. Take the solution corresponding to the shortest Hamming distance as the final optimal solution to the optimization problem.