CN112749495A - Multipoint-point-adding-based proxy model optimization method and device and computer equipment - Google Patents
Multipoint-point-adding-based proxy model optimization method and device and computer equipment Download PDFInfo
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Abstract
The application relates to a proxy model optimization method and device based on multipoint adding, computer equipment and a storage medium. The method comprises the following steps: parameter setting and initial sampling of an optimization model are carried out through time-consuming function information of an object to be optimized, a sample point set of the initial sampling and a corresponding response set are obtained, and a Gaussian process proxy model of a target function is established; the method comprises the steps of constructing a multi-target optimization subproblem of an efficient global optimization algorithm according to a Gaussian process proxy model, carrying out self-adaptive normalization processing on target items of the multi-target optimization subproblem, solving to obtain a multi-target optimal solution set comprising a plurality of candidate points, judging whether the optimization process meets set convergence criteria or not, if not, selecting a plurality of optimal points from the candidate points as new samples, carrying out parallel evaluation on the new samples through a time-consuming function to obtain new sample response values, updating the Gaussian process proxy model according to the updated sample point set and response set until the optimization process meets the convergence criteria, and finishing proxy model optimization.
Description
Technical Field
The present application relates to the field of engineering design technologies, and in particular, to a method and an apparatus for optimizing a proxy model based on multipoint adding, a computer device, and a storage medium.
Background
Time-consuming numerical simulations are usually required in engineering design, and optimization design problems based on these simulations are generally called time-consuming optimization problems, such as design of airfoils, design of external shapes of aircrafts, design of beam structures, and the like. Traditional gradient optimization algorithms and modern heuristic algorithms usually require a large number of function evaluations, and the efficiency of solving such problems is low. An optimization method based on a proxy model is one of the most effective methods for solving such engineering problems.
The agent model optimization method is a method for simulating an original high-precision model by using an approximate mathematical model and developing optimization design based on the mathematical model. The key to the proxy model optimization method is how to obtain sufficiently accurate results with minimal evaluation cost. The gaussian process model (also known as Kriging) is one of the most commonly used surrogate models, since it is possible to give both the predicted values and the predicted variances.
The most direct proxy model optimization method is to construct a proxy model by a small number of sample points and substitute the model into a mature optimization algorithm for optimization design. Although the principle is simple and easy to understand, it is difficult for this method to find a global optimum point. An efficient Global Optimization algorithm (EGO) updates a proxy model through an iterative dotting strategy and sequence, is an efficient proxy model Optimization method, can take both Global and local search performance into consideration, and is widely applied to solving various engineering problems.
Most of efficient global optimization algorithms only generate one candidate sample point in each iteration in the optimization process, the optimization convergence process cannot be accelerated by using a parallel computing environment, and an unknown region and a local optimal solution are difficult to explore in a design space at the same time. Therefore, the prior art has the problems of low optimization efficiency and large error.
Disclosure of Invention
In view of the foregoing, there is a need to provide a method, an apparatus, a computer device and a storage medium for optimizing a multi-point-adding-based proxy model, which can improve optimization efficiency and convergence accuracy.
A method for optimizing a proxy model based on multipoint adding, the method comprising:
acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of an efficient global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set of the initial sampling and a corresponding response set;
constructing a multi-objective optimization subproblem of an efficient global optimization algorithm according to the Gaussian process agent model; the multi-objective optimization subproblem takes two items of the maximum expected local mining and global exploration characteristics as two objective items;
performing adaptive normalization processing on the function of the target item, and solving the multi-target optimization subproblem after the adaptive normalization processing through a multi-target optimization algorithm to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points;
judging whether the optimization process meets the set convergence criterion, when the optimization process does not meet the convergence criterion, selecting a plurality of optimal points from the candidate points as new samples according to the information of the number of added points contained in the parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain response values of the new samples, updating the Gaussian process proxy model according to the new samples and the corresponding response values of the new samples, constructing a multi-target optimization subproblem, solving to obtain a plurality of candidate points until the optimization process meets the convergence criterion, and completing proxy model optimization.
In one embodiment, the method further comprises the following steps: acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of an efficient global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set of the initial sampling and a corresponding response set; the parameters in the parameter settings include: and designing the dimension of the variable, the maximum evaluation times of the time-consuming function, the number of the adding points and the number of initial sampling samples.
In one embodiment, the method further comprises the following steps: acquiring time-consuming function information of an original model of an object to be optimized, and setting parameters of an efficient global optimization algorithm according to the time-consuming function information;
acquiring initial sampling points in the whole design space by a Latin hypercube sampling method to obtain a sample point set of initial sampling, and evaluating the initial sampling points by the time-consuming function to obtain a response set of the initial sampling;
and establishing a Gaussian process proxy model of the target function according to the sample point set and the response set.
In one embodiment, the method further comprises the following steps: and constructing a multi-objective optimization sub-problem of the efficient global optimization algorithm according to the Gaussian process agent model, wherein the multi-objective optimization sub-problem comprises the following steps:
wherein, EImopIndicating a multi-objective desired improvement; f. of1Representing a first target item in the multi-target optimization sub-problem; f. of2Representing a second target item in the multi-target optimization sub-problem; gminA minimum function value representing a time consuming function of sample points in the set of sample points; x represents an unknown observation point;
representing a function prediction value of the Gaussian process proxy model at an unknown observation point x;
representing the predicted variance of the Gaussian process proxy model at an unknown observation point x; phi (-) and phi (-) represent standard normal cumulative distribution functions and probability density functions;
optimizing a local mining objective function in the subproblem for the multiple objectives;
an objective function is explored for the global in the multi-objective optimization sub-problem.
In one embodiment, the method further comprises the following steps: performing adaptive normalization processing on the function of the target item, wherein the multi-target optimization sub-problem after the adaptive normalization processing is as follows:
therein, max' (EI)mop) Representing the multi-objective optimization sub-problem after the adaptive normalization processing; f. ofimin、fimax(i is 1,2) respectively representing the maximum value and the minimum value of the ith target item in the multi-target optimization process;
solving the multi-target optimization sub-problem after the self-adaptive normalization processing through a multi-target evolutionary algorithm based on decomposition to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points.
In one embodiment, the method further comprises the following steps: judging whether the expected improvement of the sampling points in the current sample point set is smaller than a preset threshold or not, or whether the times of simulation evaluation through the time-consuming function is larger than the preset maximum times or not;
when the expected improvement is larger than a preset threshold or the times of simulation evaluation through the time-consuming function are smaller than a preset maximum time, selecting a plurality of optimal points from the candidate points as new samples according to the information of the number of added points contained in parameter setting, carrying out parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, updating the Gaussian process proxy model according to the new samples and the response values corresponding to the new samples, constructing a multi-target optimization subproblem, solving to obtain a plurality of candidate points until the optimization process meets the convergence criterion, and finishing proxy model optimization.
In one embodiment, the method further comprises the following steps: acquiring point adding number information k contained in parameter setting;
deleting overlapped points in the candidate points and points which are repeated with the existing sampling points;
selecting the optimal point of the local mining objective function and the optimal point of the global exploration objective function from the candidate points as new samples;
when k is 3, selecting a candidate point corresponding to a point which is on the leading edge corresponding to the multi-target optimal solution set and has the maximum sum of the distances between the two selected points as a new sample;
when k is greater than 3, performing normalization processing on the leading edge, performing fuzzy clustering analysis on the remaining points in the candidate points according to the leading edge, dividing the remaining points into k-3 groups, and selecting the point with the largest prediction variance as a new sample in each group;
and carrying out parallel evaluation on the new sample through the time-consuming function to obtain a response value of the new sample.
An apparatus for multipoint-plus-point based proxy model optimization, the apparatus comprising:
the Gaussian process proxy model establishing module is used for acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of a high-efficiency global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set of the initial sampling and a corresponding response set;
the multi-objective optimization subproblem construction module is used for constructing a multi-objective optimization subproblem of the efficient global optimization algorithm according to the Gaussian process agent model; the multi-objective optimization subproblem takes two items of the maximum expected local excavation and global exploration characteristics as two objective items;
the candidate point acquisition module is used for carrying out self-adaptive normalization processing on the function of the target item and solving the multi-target optimization subproblem after the self-adaptive normalization processing through a multi-target optimization algorithm to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points;
and the proxy model optimization module is used for judging whether the set convergence criterion is met, deleting overlapped points in the candidate points and points repeated with the existing sampling points when the convergence criterion is not met, selecting a plurality of optimal points in the candidate points as new samples according to the information of the number of added points contained in the parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, and updating the Gaussian process proxy model according to the new samples and the corresponding response values until the convergence criterion is met to complete proxy model optimization.
A computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the following steps when executing the computer program:
acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of an efficient global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set of the initial sampling and a corresponding response set;
constructing a multi-objective optimization subproblem of an efficient global optimization algorithm according to the Gaussian process agent model; the multi-objective optimization subproblem takes two items of the maximum expected local mining and global exploration characteristics as two objective items;
performing adaptive normalization processing on the function of the target item, and solving the multi-target optimization subproblem after the adaptive normalization processing through a multi-target optimization algorithm to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points;
judging whether the optimization process meets a set convergence criterion, deleting overlapped points in the candidate points and points repeated with the existing sampling points when the optimization process does not meet the convergence criterion, selecting a plurality of optimal points in the candidate points as new samples according to the information of the number of added points contained in the parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, updating the Gaussian process proxy model according to the new samples and the response values corresponding to the new samples, constructing a multi-objective optimization subproblem, solving to obtain a plurality of candidate points until the optimization process meets the convergence criterion, and finishing proxy model optimization.
A computer-readable storage medium, having stored thereon a computer program which, when executed by a processor, performs the steps of:
acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of an efficient global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set of the initial sampling and a corresponding response set;
constructing a multi-objective optimization subproblem of an efficient global optimization algorithm according to the Gaussian process agent model; the multi-objective optimization subproblem takes two items of the maximum expected local mining and global exploration characteristics as two objective items;
performing adaptive normalization processing on the function of the target item, and solving the multi-target optimization subproblem after the adaptive normalization processing through a multi-target optimization algorithm to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points;
judging whether the optimization process meets a set convergence criterion, deleting overlapped points in the candidate points and points repeated with the existing sampling points when the optimization process does not meet the convergence criterion, selecting a plurality of optimal points in the candidate points as new samples according to the information of the number of added points contained in the parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, updating the Gaussian process proxy model according to the new samples and the response values corresponding to the new samples, constructing a multi-objective optimization subproblem, solving to obtain a plurality of candidate points until the optimization process meets the convergence criterion, and finishing proxy model optimization.
According to the multi-point and point-added proxy model optimization method, the multi-point and point-added proxy model optimization device, the computer equipment and the storage medium, parameter setting and initial sampling of the optimization model are carried out through time-consuming function information of an object to be optimized, a sample point set of the initial sampling and a corresponding response set are obtained, and a Gaussian process proxy model of a target function is established; constructing a multi-target optimization subproblem of an efficient global optimization algorithm according to a Gaussian process proxy model, solving to obtain a multi-target optimal solution set after adaptive normalization processing is performed on target items of the multi-target optimization subproblem, wherein the optimal solution set comprises a plurality of candidate points, the multi-target optimal solution set comprises the plurality of candidate points is obtained by solving, whether the optimization process meets the set convergence criterion is judged, if the optimization process does not meet the set convergence criterion, a plurality of optimal points are selected from the candidate points as new samples according to the number information of the added points contained in the parameter setting, the new samples are evaluated in parallel through a time-consuming function to obtain new sample response values, the sample point set is updated according to the new samples, the response set is updated according to the new sample response values, the Gaussian process proxy model is updated according to the updated sample point set and response set until the optimization process meets the convergence criterion, and finishing the optimization of the proxy model. According to the method, the whole multi-target optimal solution set with better uniformity and higher point selection quality can be obtained by constructing the multi-target optimization sub-problem and normalizing the target items, the number of optimization iterations can be greatly reduced, the convergence precision can be improved, and therefore the contradiction between the optimization speed and the convergence precision is solved.
Drawings
FIG. 1 is a schematic flow chart diagram illustrating a method for multi-point-plus-point-based proxy model optimization according to an embodiment;
FIG. 2 is a diagram illustrating an embodiment of an optimization of a two-dimensional test function Six-hump camel-back;
FIG. 3 is a graph of the optimization of a two-dimensional test function Branin in another embodiment;
FIG. 4 is a result of an optimization of a two-dimensional test function Goldstein-Price in another embodiment;
FIG. 5 is a flowchart illustrating a multi-point-plus-point-based proxy model optimization method in another embodiment;
FIG. 6 is a block diagram of an apparatus for multi-point-plus-point based proxy model optimization according to an embodiment;
FIG. 7 is a diagram illustrating an internal structure of a computer device according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The multi-point and point-adding-based proxy model optimization method can be applied to the following application environments. Parameter setting and initial sampling of an optimization model are carried out through time-consuming function information of an object to be optimized, a sample point set of the initial sampling and a corresponding response set are obtained, and a Gaussian process proxy model of a target function is established; the method comprises the steps of constructing a multi-target optimization subproblem of an efficient global optimization algorithm according to a Gaussian process proxy model, solving to obtain a multi-target optimal solution set comprising a plurality of candidate points, judging whether the optimization process meets a set convergence criterion, deleting overlapped points in the candidate points and points repeated with existing sampling points when the optimization process does not meet the set convergence criterion, selecting a plurality of optimal points from the candidate points as new samples according to the number information of added points contained in parameter setting, carrying out parallel evaluation on the new samples through a time-consuming function to obtain new sample response values, updating the sample point set according to the new samples, updating the response set according to the new sample response values, updating the Gaussian process proxy model according to the updated sample point set and response set until the optimization process meets the convergence criterion, and finishing proxy model optimization.
In one embodiment, as shown in fig. 1, a method for optimizing a proxy model based on multipoint adding is provided, which includes the following steps:
102, acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of an efficient global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set and a corresponding response set of the initial sampling.
The object to be optimized is a design problem which needs time-consuming simulation in engineering design, such as design of wing profiles, appearance design of aircrafts, design of beam structures and the like. An optimization method based on a proxy model is one of the most effective methods for solving such engineering design problems.
The embodiment adopts a gaussian process agent model (Kriging) and an Efficient Global Optimization (EGO). The Kriging agent model can give a predicted value and a predicted variance at the same time, and is one of the most commonly used agent models. The EGO algorithm updates the proxy model through an iteration point adding strategy and a sequence, is an efficient proxy model optimization method, can give consideration to global and local search performance, and is widely applied to solving various engineering problems.
The EGO algorithm is based on a Kriging agent model, firstly, the hyper-parameters of the Kriging agent model need to be trained, then, the position of the next sampling point is obtained by solving the maximum expected improvement, and the idea of the EGO algorithm is to add the iteration sampling point at the position with the maximum expected improvement.
In this embodiment, the parameters in the parameter setting include the dimension d of the design variable, and the maximum evaluation times N of the time-consuming functionmaxThe number of points added is k, the number of initial sampling samples is N, d, NmaxThe values of k and n are positive integers, and the number of initial sampling points is preferably 8 × d. The sample data includes a sample point and a sample point response value.
And 104, constructing a multi-objective optimization sub-problem of the efficient global optimization algorithm according to the Gaussian process agent model.
The multi-objective optimization subproblem takes two items of the maximum expected local mining and global exploration characteristics as two objective items; when the maximum expected improvement is calculated by a classical EGO algorithm, multi-target optimization is converted into a single-target problem through non-negative weighted summation, a candidate sample point is obtained through one iteration, and in fact, global exploration and local excavation are balanced in a weighted mode. According to the method, a plurality of candidate sample points can be obtained through a multi-objective optimization algorithm by constructing a multi-objective optimization subproblem of an efficient global optimization algorithm.
106, performing adaptive normalization processing on a function of the target item, and solving a multi-target optimization subproblem subjected to the adaptive normalization processing through a multi-target optimization algorithm to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points;
the multi-target optimal solution set PS (pareto set) and the front edge PF (pareto front) can be obtained through a multi-target optimization algorithm, and the uniformity of the PS can be improved and the point selection quality can be improved by normalizing the target items of the multi-target optimization subproblems. Through multi-objective optimization, multiple candidate points can be generated in one iteration, and the candidate points are points on the front edge of the multi-objective optimization problem.
And 108, judging whether the optimization process meets the set convergence criterion, when the optimization process does not meet the convergence criterion, selecting a plurality of optimal points from the candidate points as new samples according to the point adding number information contained in the parameter setting, performing parallel evaluation on the new samples through a time-consuming function to obtain response values of the new samples, updating the Gaussian process proxy model according to the new samples and the corresponding response values of the new samples until the optimization process meets the convergence criterion, and finishing proxy model optimization.
And selecting a plurality of optimal points from the candidate points as new samples, wherein the selected points have the characteristics of global search, local mining and expected improvement, and the accuracy and the efficiency can be better considered. And updating the sample point set according to the new sample, updating the response set according to the response value of the new sample, and updating the Gaussian process proxy model according to the updated sample point set and response set until the optimization process meets the convergence criterion, thereby completing the proxy model optimization.
And screening a plurality of sample points by using a point adding strategy according to the candidate points, performing multi-point adding in a point adding stage of the EGO algorithm, and performing iterative cycle, thereby greatly improving the precision and efficiency of the multi-point adding agent-based optimization method under the condition of meeting the stop criterion.
In the multi-point and point-added proxy model optimization method, parameter setting and initial sampling of an optimization model are performed through time-consuming function information of an object to be optimized, so that a sample point set of the initial sampling and a corresponding response set are obtained, and a Gaussian process proxy model of a target function is established; the method comprises the steps of constructing a multi-target optimization subproblem of an efficient global optimization algorithm according to a Gaussian process proxy model, carrying out self-adaptive normalization processing on target items of the multi-target optimization subproblem, solving to obtain a multi-target optimal solution set comprising a plurality of candidate points, judging whether the optimization process meets set convergence criteria or not, when the optimization process does not meet the set convergence criteria, selecting a plurality of optimal points from the candidate points as new samples according to point adding number information contained in parameter setting, carrying out parallel evaluation on the new samples through a time-consuming function to obtain new sample response values, updating the sample point set according to the new samples, updating the response set according to the new sample response values, updating the Gaussian process proxy model according to the updated sample point set and response set until the optimization process meets the convergence criteria, and finishing proxy model optimization. According to the method, by constructing the multi-target optimization subproblem and normalizing the target items, the whole multi-target optimal solution set with better uniformity and higher point selection quality can be obtained, the number of optimization iterations can be greatly reduced, the convergence precision can be improved, and the spear of optimization speed and convergence precision is solved.
In one embodiment, the method further comprises the following steps: acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of an efficient global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set and a corresponding response set of the initial sampling; the parameters in the parameter setting include: the dimension of the design variable, the maximum number of evaluations of the time-consuming function, the number of plus points and the number of initial sampling samples.
In one embodiment, taking a two-dimensional test function Branin as an example of the time-consuming function, since Branin is a two-dimensional function, the dimension d of the design variable is 2, and the maximum evaluation time N of the time-consuming function is obtainedmaxThe number k of the adding points is equal to 3, and the number n of the initial sampling samples is equal to 16, 80.
In one embodiment, the method further comprises the following steps: acquiring time-consuming function information of an original model of an object to be optimized, and setting parameters of an efficient global optimization algorithm according to the time-consuming function information; obtaining initial sampling points in the whole design space by a Latin hypercube sampling method to obtain a sample point set of initial sampling, and evaluating the initial sampling points by a time-consuming function to obtain a response set of the initial sampling; and establishing a Gaussian process proxy model of the target function according to the sample point set and the response set.
Latin hypercube sampling is a method for approximate random sampling from multivariate parameter distribution, belongs to a layered sampling technology, and is commonly used for computer experiments or Monte Carlo integration and the like.
In one embodiment, the method further comprises the following steps: the multi-objective optimization sub-problem of the efficient global optimization algorithm is constructed according to the Gaussian process agent model and comprises the following steps:
wherein, EImopIndicating a multi-objective desired improvement; f. of1Representing a first target item in the multi-target optimization sub-problem; f. of2Representing a second target item in the multi-target optimization sub-problem; gminA minimum function value representing a time consuming function of sample points in the set of sample points; x represents an unknown observation point;
representing a function prediction value of the Gaussian process proxy model at an unknown observation point x;
representing the predicted variance of the Gaussian process proxy model at an unknown observation point x; phi (-) and phi (-) represent standard normal cumulative distribution functions and probability density functions;
optimizing a local mining objective function in the subproblem for the multiple objectives; 
an objective function is explored for the global in the multi-objective optimization sub-problem.
In one embodiment, the method further comprises the following steps: performing self-adaptive normalization processing on the function of the target item, wherein the multi-target optimization sub-problem after the self-adaptive normalization processing is as follows:
therein, max' (EI)mop) Representing a multi-objective optimization sub-problem after adaptive normalization processing; f. ofimin、fimax(i is 1,2) respectively representing the maximum value and the minimum value of the ith target item in the multi-target optimization process; solving the multi-target optimization subproblem after the self-adaptive normalization processing through a multi-target evolutionary algorithm based on decomposition to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points.
By normalizing the target items, the whole multi-target optimal solution set with better uniformity and higher point selection quality can be obtained, the optimization iteration times are greatly reduced, and the convergence precision is improved.
In one embodiment, the method further comprises the following steps: judging whether the expected improvement of the sampling points in the current sample point set is smaller than a preset threshold or not, or whether the times of simulation evaluation through a time-consuming function is larger than the preset maximum times or not; when the expected improvement is larger than a preset threshold or the simulation evaluation times through a time-consuming function are smaller than the preset maximum times, selecting a plurality of optimal points from candidate points as new samples according to point adding number information contained in parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, updating the sample point set according to the new samples, updating the response set according to the new sample response values, updating the Gaussian process proxy model according to the updated sample point set and the response set until the optimization process meets the convergence criterion, and completing proxy model optimization.
In this embodiment, the threshold for the desired improvement of the termination criteria is 0.001.
In one embodiment, the method further comprises the following steps: acquiring point adding number information k contained in parameter setting; deleting overlapped points in the candidate points and points which are repeated with the existing sampling points; selecting an optimal point of a local mining objective function and an optimal point of a global exploration objective function from the candidate points as new samples; when k is 3, selecting a candidate point corresponding to a point which is located on the front edge corresponding to the multi-target optimal solution set and has the maximum sum of the distances between the two selected points as a new sample; when k is greater than 3, the leading edge is subjected to normalization processing, fuzzy clustering analysis is carried out on the residual points in the candidate points according to the leading edge, the residual points are divided into k-3 groups, and the point with the largest prediction variance is selected from each group to serve as a new sample; and carrying out parallel evaluation on the new sample through a time-consuming function to obtain a response value of the new sample.
And selecting a plurality of optimal points from the candidate points as new samples, wherein the selected points have the characteristics of global search, local mining and expected improvement, and the accuracy and the efficiency can be better considered. The repeated point with the existing sampling point is the point with the Euclidean distance less than 1 multiplied by 10 from the existing sampling point-6D, overlapping points, meaning Euclidean distances less than 1 × 10-6D, when two dots overlap, preferentially deleting the dot with the smaller prediction standard root mean square error.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in a strict order unless explicitly stated herein, and may be performed in other orders. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
Specifically, the optimization results of the invention on three two-dimensional test functions, Six-hump camel-back, Branin and Goldstein-Price are shown in FIG. 2, FIG. 3 and FIG. 4, respectively. The abscissa and ordinate in the figure represent two elements of the two-dimensional design variable, respectively, "+" represents an initial sampling point, "Δ" represents a newly added sample point, and "∘" represents an optimal design point. As can be seen from fig. 2, 3 and 4, the method of the present invention can find a design point close enough to the global optimal solution within a given time-consuming function evaluation number.
For the above three 2-dimensional test functions, the 3-dimensional test function Hartman3 and the 6-dimensional test function Hartman6, the results of comparing the optimal solution precision and the function iteration times by using the proxy model optimization algorithm based on the multi-point addition criterion and the classical EGO algorithm are shown in table 1. The result shows that the proxy model optimization algorithm (EGO-MO) based on the multi-point and point criterion can obtain a better global approximate optimal solution, which is specifically represented by smaller average error, smaller maximum error, smaller average iteration number and smaller maximum iteration number.
TABLE 1 comparison of EGO-MO with classical EGO Algorithm for iteration number and near optimal solution precision
In an embodiment, as shown in fig. 5, a multi-point-adding-based surrogate model optimization method is provided, after an initial sample is generated, a response value of the sample is calculated, an objective function Kriging surrogate model is established according to a current sample and a corresponding response value, a multi-target optimization sub-problem is established on the basis of the objective function Kriging surrogate model and optimization calculation is performed to obtain candidate sample points, when an optimization process does not meet a convergence criterion, k update points are selected from the candidate sample points as new samples, a time-consuming function is used to calculate a response value of the new sample, the new sample is added into a sample library, the objective function Kriging surrogate model is updated until the optimization process meets the convergence criterion, and optimization of the surrogate model is completed.
In one embodiment, as shown in fig. 6, there is provided a multipoint-plus-point-based proxy model optimization apparatus, including: a gaussian process agent model building module 602, a multi-objective optimization sub-problem building module 604, a candidate point obtaining module 606 and an agent model optimization module 608, wherein:
a gaussian process proxy model establishing module 602, configured to obtain time-consuming function information of an original model of an object to be optimized, perform parameter setting of an efficient global optimization algorithm according to the time-consuming function information, perform initial sampling, and establish a gaussian process proxy model of a target function according to a sample point set of the initial sampling and a corresponding response set;
a multi-objective optimization sub-problem construction module 604, configured to construct a multi-objective optimization sub-problem of the efficient global optimization algorithm according to the gaussian process proxy model; the multi-objective optimization subproblem takes two items of the maximum expected local mining and the overall exploration characteristics as two objective items;
a candidate point obtaining module 606, configured to perform adaptive normalization on a function of a target item, and solve the multi-target optimization sub-problem after the adaptive normalization through a multi-target optimization algorithm to obtain a multi-target optimal solution set, where the optimal solution set includes multiple candidate points;
and the proxy model optimization module 608 is configured to determine whether the set convergence criterion is met, select a plurality of optimal points from the candidate points as new samples according to the information about the number of added points included in the parameter setting when the convergence criterion is not met, perform parallel evaluation on the new samples by using a time-consuming function to obtain response values of the new samples, update the sample point set according to the new samples, update the response set according to the response values of the new samples, and update the gaussian process proxy model according to the updated sample point set and the response set until the convergence criterion is met, thereby completing proxy model optimization.
The gaussian process proxy model establishing module 602 is further configured to obtain time-consuming function information of the original model of the object to be optimized, and perform parameter setting of the efficient global optimization algorithm according to the time-consuming function information; obtaining initial sampling points in the whole design space by a Latin super-stereo sampling method to obtain a sample point set of the initial sampling, and evaluating the initial sampling points by a time-consuming function to obtain a response set of the initial sampling; and establishing a Gaussian process proxy model of the target function according to the sample point set and the response set.
The multi-objective optimization sub-problem construction module 604 is further configured to construct a multi-objective optimization sub-problem of the efficient global optimization algorithm according to the gaussian process agent model as follows:
wherein, EImopIndicating a multi-objective desired improvement; f. of1Representing a first target item in the multi-target optimization sub-problem; f. of2Representing a second target item in the multi-target optimization sub-problem; gminA minimum function value representing a time consuming function of sample points in the set of sample points; x represents an unknown observation point;
representing a function prediction value of the Gaussian process proxy model at an unknown observation point x;
representing the predicted variance of the Gaussian process proxy model at an unknown observation point x; phi (-) and phi (-) represent standard normal cumulative distribution functions and probability density functions;
optimizing a local mining objective function in the subproblem for the multiple objectives;
The candidate point obtaining module 606 is further configured to perform adaptive normalization processing on the function of the target item, where the multi-target optimization sub-problem after the adaptive normalization processing is:
therein, max' (EI)mop) Representing a multi-objective optimization sub-problem after adaptive normalization processing; f. ofimin、 fimax(i is 1,2) respectively representing the maximum value and the minimum value of the ith target item in the multi-target optimization process; solving the multi-target optimization subproblem after the self-adaptive normalization processing through a multi-target evolutionary algorithm based on decomposition to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points.
The agent model optimization module 608 is further configured to determine whether an expected improvement of the sampling points in the current sample point set is smaller than a preset threshold, or whether the number of times of simulation evaluation performed by the time-consuming function is greater than a preset maximum number of times; when the expected improvement is larger than a preset threshold or the times of simulation evaluation through a time-consuming function are smaller than the preset maximum times, deleting overlapped points and points repeated with the existing sampling points in the candidate points, selecting a plurality of optimal points from the candidate points as new samples according to the point adding number information contained in the parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, updating the sample point sets according to the new samples, updating the response sets according to the new sample response values, updating the Gaussian process proxy model according to the updated sample point sets and response sets until the optimization process meets the convergence criterion, and finishing proxy model optimization.
The agent model optimization module 608 is further configured to obtain the adding point number information k included in the parameter setting; deleting overlapped points in the candidate points and points which are repeated with the existing sampling points; selecting an optimal point of a local mining target function and an optimal point of a global exploration target function from the candidate points as new samples; when k is 3, selecting a candidate point corresponding to a point which is on the front edge corresponding to the multi-target optimal solution set and has the maximum sum of the distances between the two selected points as a new sample; when k is greater than 3, performing fuzzy clustering analysis on the remaining points in the candidate points, dividing the remaining points into k-3 groups, and selecting the point with the largest prediction variance in each group as a new sample; and carrying out parallel evaluation on the new sample through a time-consuming function to obtain a response value of the new sample.
For the specific definition of the proxy model optimization device, reference may be made to the above definition of the proxy model optimization method based on multipoint and point, and details are not described here. The modules in the proxy model optimization device can be wholly or partially implemented by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent of a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a terminal, the internal structure of which may be as shown in fig. 7. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a multipoint-plus-point based proxy model optimization method. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on the shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.
Those skilled in the art will appreciate that the architecture shown in fig. 7 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In an embodiment, a computer device is provided, comprising a memory storing a computer program and a processor implementing the steps in the above-described method embodiments when executing the computer program.
In an embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which computer program, when being executed by a processor, carries out the steps of the above-mentioned method embodiments.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware related to instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above examples only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A proxy model optimization method based on multipoint adding is characterized by comprising the following steps:
acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of an efficient global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set and a corresponding response set of the initial sampling;
constructing a multi-objective optimization subproblem of an efficient global optimization algorithm according to the Gaussian process agent model; the multi-objective optimization subproblem takes two items of the maximum expected local mining and global exploration characteristics as two objective items;
performing adaptive normalization processing on the function of the target item, and solving the multi-target optimization subproblem after the adaptive normalization processing through a multi-target optimization algorithm to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points;
judging whether the optimization process meets the set convergence criterion, when the optimization process does not meet the convergence criterion, selecting a plurality of optimal points from the candidate points as new samples according to the point adding number information contained in the parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, updating the Gaussian process proxy model according to the new samples and the corresponding response values until the optimization process meets the convergence criterion, and finishing proxy model optimization.
2. The method according to claim 1, wherein the obtaining time-consuming function information of an original model of an object to be optimized, setting parameters of a high-efficiency global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a gaussian process proxy model of an objective function according to a sample point set of the initial sampling and a corresponding response set comprises:
acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of an efficient global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set and a corresponding response set of the initial sampling; the parameters in the parameter setting include: and designing the dimension of the variable, the maximum evaluation times of the time-consuming function, the number of the adding points and the number of initial sampling samples.
3. The method according to claim 2, wherein the obtaining time-consuming function information of an original model of an object to be optimized, setting parameters of a high-efficiency global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a gaussian process proxy model of an objective function according to a sample point set of the initial sampling and a corresponding response set comprises:
acquiring time-consuming function information of an original model of an object to be optimized, and setting parameters of an efficient global optimization algorithm according to the time-consuming function information;
acquiring initial sampling points in the whole design space by a Latin hypercube sampling method to obtain a sample point set of initial sampling, and evaluating the initial sampling points by the time-consuming function to obtain a response set of the initial sampling;
and establishing a Gaussian process proxy model of the target function according to the sample point set and the response set.
4. The method of claim 1, wherein the constructing a multi-objective optimization subproblem of an efficient global optimization algorithm according to the gaussian process proxy model comprises:
and constructing a multi-objective optimization sub-problem of the efficient global optimization algorithm according to the Gaussian process agent model, wherein the multi-objective optimization sub-problem comprises the following steps:
wherein, EImopIndicating a multi-objective desired improvement; f. of1Representing a first target item in the multi-target optimization sub-problem; f. of2Representing a second target item in the multi-target optimization sub-problem; gminA minimum function value representing a time consuming function of sample points in the set of sample points; x represents an unknown observation point;
representing a function prediction value of the Gaussian process proxy model at an unknown observation point x;
representing a predicted variance of the Gaussian process proxy model at an unknown observation point x; phi (-) and phi (-) represent standard normal cumulative distribution functions and probability density functions;
optimizing a local mining objective function in the subproblem for the multiple objectives;
an objective function is explored for the global in the multi-objective optimization sub-problem.
5. The method of claim 1, wherein the performing adaptive normalization on the function of the target item, and solving the multi-objective optimization sub-problem after the adaptive normalization through a multi-objective optimization algorithm, obtain a multi-objective optimal solution set, wherein the optimal solution set includes a plurality of candidate points, includes:
performing adaptive normalization processing on the function of the target item, wherein the multi-target optimization sub-problem after the adaptive normalization processing is as follows:
therein, max' (EI)mop) Representing the multi-objective optimization sub-problem after the adaptive normalization processing; f. ofimin、fimax(i is 1,2) respectively representing the maximum value and the minimum value of the ith target item in the multi-target optimization process;
solving the multi-target optimization sub-problem after the self-adaptive normalization processing through a multi-target evolutionary algorithm based on decomposition to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points.
6. The method according to claim 5, wherein the determining whether the optimization process meets a set convergence criterion, and when the convergence criterion is not met, selecting a plurality of optimal points from the candidate points as new samples according to the information on the number of points added included in the parameter setting, and performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, updating the Gaussian process proxy model according to the new samples and the response values corresponding thereto, and constructing a multi-objective optimization subproblem to solve to obtain a plurality of candidate points until the optimization process meets the convergence criterion, thereby completing the proxy model optimization, includes:
judging whether the expected improvement of the sampling points in the current sample point set is smaller than a preset threshold or not, or whether the times of simulation evaluation through the time-consuming function are larger than the preset maximum times or not;
when the expected improvement is larger than a preset threshold or the times of simulation evaluation through the time-consuming function are smaller than a preset maximum time, selecting a plurality of optimal points from the candidate points as new samples according to point adding number information contained in parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, updating the Gaussian process proxy model according to the new samples and the response values corresponding to the new samples until the optimization process meets the convergence criterion, and completing proxy model optimization.
7. The method according to claim 6, wherein the selecting a plurality of optimal points from the candidate points as new samples according to the adding point number information included in the parameter setting, and performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values comprises:
acquiring point adding number information k contained in parameter setting;
deleting overlapped points in the candidate points and points which are repeated with the existing sampling points;
selecting the optimal point of the local mining objective function and the optimal point of the global exploration objective function from the candidate points as new samples;
when k is 3, selecting a candidate point corresponding to a point which is on the leading edge corresponding to the multi-target optimal solution set and has the maximum sum of the distances between the two selected points as a new sample;
when k is greater than 3, performing normalization processing on the leading edge, performing fuzzy clustering analysis on the remaining points in the candidate points according to the leading edge, dividing the remaining points into k-3 groups, and selecting the point with the largest prediction variance as a new sample in each group;
and carrying out parallel evaluation on the new sample through the time-consuming function to obtain a response value of the new sample.
8. A multipoint-plus-point based proxy model optimization apparatus, the apparatus comprising:
the Gaussian process proxy model establishing module is used for acquiring time-consuming function information of an original model of an object to be optimized, setting parameters of a high-efficiency global optimization algorithm according to the time-consuming function information, initially sampling, and establishing a Gaussian process proxy model of a target function according to a sample point set of the initial sampling and a corresponding response set;
the multi-objective optimization sub-problem construction module is used for constructing a multi-objective optimization sub-problem of an efficient global optimization algorithm according to the Gaussian process agent model; the multi-objective optimization subproblem takes two items of the maximum expected local mining and global exploration characteristics as two objective items;
the candidate point acquisition module is used for carrying out self-adaptive normalization processing on the function of the target item, solving the multi-target optimization subproblem after the self-adaptive normalization processing through a multi-target optimization algorithm to obtain a multi-target optimal solution set, wherein the optimal solution set comprises a plurality of candidate points;
and the proxy model optimization module is used for judging whether the set convergence criterion is met, when the convergence criterion is not met, selecting a plurality of optimal points from the candidate points as new samples according to the point adding number information contained in the parameter setting, performing parallel evaluation on the new samples through the time-consuming function to obtain new sample response values, and updating the Gaussian process proxy model according to the new samples and the response values corresponding to the new samples until the convergence criterion is met to complete proxy model optimization.
9. A computer device comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the steps of the method of any one of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 7.
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