CN112231915A - Physical planning algorithm based on projection ranging - Google Patents
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Abstract
The invention relates to the technical field of electricians, in particular to a physical planning algorithm based on projection ranging, which searches an optimal value corresponding to a single target through a scalar taboo optimization algorithm and determines a problem anchor point; determining ideal line segments of an optimization problem by anchor pointsLOr ideal spaceΩ，To be provided withndThe central point of the sub-region is the vertex, and the construction is carried outndA pseudo preference area; judging whether all sampling points are outside the pseudo preference area, calculating an aggregation target function set based on all the pseudo preference areas, dynamically reducing the search range, and updating an external fileARecording the optimal solution of each pseudo preference area, comparing the optimal solution with the current optimal solution, and storing the better into an external fileA(ii) a Judging the number of iterations isIf the maximum value is reached, when the number of iterations isi>(N D +N I ) Then, output the external fileAAs a result, a plurality of Pareto solutions can be obtained by one operation in the invention; the Pareto frontier searched in the invention has good distributivity; compared with the original physical planning algorithm, the method has the advantage of fast convergence.
Description
Technical Field
The invention relates to the technical field of electricians, in particular to a physical planning algorithm based on projection ranging.
Background
In recent years, with the continuous progress of scientific technology and the increasing level of manufacturing technology, and the increasingly strong market competition, people have higher and higher requirements on electric and electronic products. Therefore, the electromagnetic field inverse problem of the comprehensive design of electric and electronic products based on the numerical analysis and calculation of electromagnetic fields and other physical fields is generated and enters a vigorous development stage. At present, the problem of electromagnetic field reversal becomes a research hotspot of computational electromagnetism, and the electromagnetic field reversal problem is listed as a subject and an important development direction of a conference in famous electromagnetic field numerical computation academic conferences at home and abroad. In view of the complexity of the inverse problem of the electromagnetic field, the analysis and calculation of the inverse problem of the electromagnetic field are generally decomposed into a series of positive problems, and then solved by an iterative method with the help of an optimization algorithm. Therefore, the optimization algorithm and the numerical calculation method of the electromagnetic field positive problem become two main research aspects of the analysis and calculation of the electromagnetic field inverse problem. Since the analysis and calculation of each step in the iterative process requires numerical analysis of the electromagnetic field, the analysis and calculation of the inverse problem requires huge computational resources compared to the positive problem of the electromagnetic field. In addition, the inverse problem of the electromagnetic field generally has the problems of equation ill-condition, non-uniqueness of solution, multiple targets, multiple extreme points and the like. Efficient and reliable multi-objective optimization algorithm is always a main pursuit target of electromagnetic field inverse problem research.
Disclosure of Invention
1. Technical problem to be solved
The purpose of the invention is: the method is characterized in that a physical planning algorithm based on projection ranging is provided, the physical planning algorithm is high in solving efficiency, the convergence speed of solving the multi-target electromagnetic field inverse problem is high, and Pareto solution distribution is uniform.
2. Technical scheme
In order to solve the above problems, the present invention adopts the following technical solutions.
The physical planning algorithm based on the projection ranging specifically comprises the following steps,
step 1: determining an objective function;
step 2: searching an optimal value corresponding to the single target through a scalar tabu optimization algorithm, and determining a problem anchor point;
and step 3: determining an ideal line segment L or an ideal space omega of an optimization problem through an anchor point, and dividing the ideal line segment L or the ideal space omega into nd uniformly-distributed sub-areas according to the number nd of Pareto solutions in an optimal solution set, which is required to be obtained by a designer;
and 4, step 4: taking the center point of the nd sub-regions as a vertex, and constructing nd pseudo preference regions;
and 5: defining a number N of diversified search iterationsDAnd number of search iterations NIInitializing an iteration time indication variable i to be 0, and generating N initial sampling points by using super-volume sampling;
step 6: calculating an objective function value and a pseudo preference area to which the objective function value belongs, projecting a sampling point to an ideal line segment L or an ideal space omega, determining a projection point position corresponding to the sampling point and a sub-area to which the sampling point belongs, and calculating the distance between the projection point and the sampling point to serve as a subsequent evolution basis;
and 7: judging whether all sampling points are outside the pseudo preference area, if no one point of the current sampling points belongs to the pseudo preference area, namely the sampling points belonging to all the pseudo preference areas are empty, correcting the pseudo preference offset vector, executing the step 6, and if the current sampling points are not outside the pseudo preference area, executing the step 8;
and 8: calculating an aggregation target function set based on all the pseudo preference areas, dynamically reducing the search range, updating an external file A, recording the optimal solution of each pseudo preference area, comparing the optimal solution with the current optimal solution, and storing the better of the optimal solution into the external file A;
and step 9: when the iteration number i is less than or equal to NDThen, the algorithm is in a diversified searching stage, and next iterative sampling points are generated by using the optimal solution; when the number of iterations (N)D+NI)≥i>NDThen, the algorithm is in an enhanced search stage, and a next iteration sampling point is generated by using the current optimal solution;
step 10: judging whether the iteration times reach the maximum value, and when the iteration times i reach the maximum value>(ND+NI) Outputting the result of the external file A, entering step 11, and when the iteration times i is less than or equal to (N)D+NI) If yes, returning to the step 6;
step 11: the flow ends.
Further, the step 6 specifically calculates the classification method of the pseudo preference to which the sampling point belongs; projecting all sampling points to an ideal line segment L or an ideal space omega, and recording projection coordinates of each sampling point; defining the distance between the center point of the nd sub-areas and the projection coordinates as the projection distance of the sampling point; and determining the attribution preference of the sampling points according to the projection distance and the boundary of the nd sub-area.
A pseudo-preferred region aggregation target is calculated. And calculating an aggregation objective function value of the sampling point based on the pseudo preference, and constructing an aggregation function value matrix G of the sampling point calculated based on all the pseudo preferences. And classifying and sequencing the data in the matrix G to obtain an optimal solution set in the pseudo-preference, and carrying out contract evolution on the optimal solution set, thereby realizing one-time operation to obtain the whole Pareto solution set.
Wherein, gjkIs the aggregate function value calculated at the kth sample point based on the jth pseudo-preference region.
Further, the step 8 specifically includes a method for dynamically narrowing the search range: since the position of the Pareto solution of the physical planning algorithm is closely related to the pseudo preference position and the size, the pseudo preference which is uniformly distributed often cannot obtain the Pareto solution set which is uniformly distributed. Therefore, the present invention provides a method for dynamically narrowing the search range. With the increase of the iteration times, the range of the pseudo preference area is dynamically reduced, so that the search direction is more definite, and the Pareto front edge with uniform distribution is obtained. The angle correction variable α is evolved according to the following formula:
α＝αu+(αl-αu)e-Ni/τ
wherein alpha isu，αlIs the upper and lower limit values corresponding to the angle correction variable alpha; n number of sampling points in the pseudo preference area; i is the current iteration number; τ is the time constant.
Further, the step 7 specifically includes a method for correcting the pseudo preference offset vector: due to the randomness of the initial sampling points and the complexity of the multi-objective optimization algorithm, at the early stage of algorithm evolution, all the current sampling points are probably out of the pseudo-preference range. This results in the algorithm not being able to continue to evolve. To solve this problem, the present invention proposes a method of correcting the pseudo preference offset vector. The pseudo preference offset vector is one of the key factors in deciding the pseudo preference position. And gradually correcting the pseudo preference offset vector, and further changing the pseudo preference position until at least one sampling point is in the current pseudo preference frame. The pseudo-preference offset vector is modified as follows:
wherein the content of the first and second substances,
is a pseudo preference offset vector; t is the current movement times of the pseudo preference offset vector; a isjIs the target space size; k is a scaling factor related to the search direction.
3. Advantageous effects
Compared with the prior art, the invention has the advantages that:
firstly, a new technical idea of a physical planning algorithm based on projection ranging is provided;
secondly, a plurality of Pareto solutions can be obtained by one-time operation in the invention;
thirdly, the Pareto frontier searched in the invention has good distributivity;
and fourthly, compared with the original physical planning algorithm, the method has the advantage of fast convergence.
Drawings
FIG. 1 is a flow chart of the program architecture of the present invention;
FIG. 2 is a schematic diagram of a method for dynamically narrowing a search range according to the present invention;
FIG. 3 is a geometric distribution diagram of the antenna array of the present invention;
FIG. 4 is a Pareto solution set of an antenna array according to a physical planning algorithm based on projection ranging of the present invention.
Detailed Description
As shown in fig. 1, the projection ranging-based physical planning algorithm includes the following steps,
step 1: determining an objective function;
step 2: searching an optimal value corresponding to the single target through a scalar tabu optimization algorithm, and determining a problem anchor point;
and step 3: determining an ideal line segment L or an ideal space omega of an optimization problem through an anchor point, and dividing the ideal line segment L or the ideal space omega into nd uniformly-distributed sub-areas according to the number nd of Pareto solutions in an optimal solution set, which is required to be obtained by a designer;
and 4, step 4: taking the center point of the nd sub-regions as a vertex, and constructing nd pseudo preference regions;
and 5: defining a number N of diversified search iterationsDAnd number of search iterations NIInitializing an iteration time indication variable i to be 0, and generating N initial sampling points by using super-volume sampling;
step 6: calculating an objective function value and a pseudo preference area to which the objective function value belongs, projecting a sampling point to an ideal line segment L or an ideal space omega, determining a projection point position corresponding to the sampling point and a sub-area to which the sampling point belongs, and calculating the distance between the projection point and the sampling point to serve as a subsequent evolution basis;
and 7: judging whether all sampling points are outside the pseudo preference area, if no one point of the current sampling points belongs to the pseudo preference area, namely the sampling points belonging to all the pseudo preference areas are empty, correcting the pseudo preference offset vector, executing the step 6, and if the current sampling points are not outside the pseudo preference area, executing the step 8;
and 8: calculating an aggregation target function set based on all the pseudo preference areas, dynamically reducing the search range, updating an external file A, recording the optimal solution of each pseudo preference area, comparing the optimal solution with the current optimal solution, and storing the better of the optimal solution into the external file A;
and step 9: when the iteration number i is less than or equal to NDThen, the algorithm is in a diversified searching stage, and next iterative sampling points are generated by using the optimal solution; when the number of iterations (N)D+NI)≥i>NDThe algorithm is in the enhanced search stage, and benefitGenerating a next iteration sampling point by using the current optimal solution;
step 10: judging whether the iteration times reach the maximum value, and when the iteration times i reach the maximum value>(ND+NI) Outputting the result of the external file A, entering step 11, and when the iteration times i is less than or equal to (N)D+NI) If yes, returning to the step 6;
step 11: the flow ends.
Step 6, specifically calculating a classification method of the pseudo preference to which the sampling point belongs; projecting all sampling points to an ideal line segment L or an ideal space omega, and recording projection coordinates of each sampling point; defining the distance between the center point of the nd sub-areas and the projection coordinates as the projection distance of the sampling point; and determining the attribution preference of the sampling points according to the projection distance and the boundary of the nd sub-area.
A pseudo-preferred region aggregation target is calculated. And calculating an aggregation objective function value of the sampling point based on the pseudo preference, and constructing an aggregation function value matrix G of the sampling point calculated based on all the pseudo preferences. And classifying and sequencing the data in the matrix G to obtain an optimal solution set in the pseudo-preference, and carrying out contract evolution on the optimal solution set, thereby realizing one-time operation to obtain the whole Pareto solution set.
Wherein, gjkIs the aggregate function value calculated at the kth sample point based on the jth pseudo-preference region.
The step 8 specifically includes a method for dynamically narrowing the search range: since the position of the Pareto solution of the physical planning algorithm is closely related to the pseudo preference position and the size, as shown in fig. 2, the pseudo preference which is often uniformly distributed cannot obtain a uniformly distributed Pareto solution set. Therefore, the present invention provides a method for dynamically narrowing the search range. With the increase of the iteration times, the range of the pseudo preference area is dynamically reduced, so that the search direction is more definite, and the Pareto front edge with uniform distribution is obtained. The angle correction variable α is evolved according to the following formula:
α＝αu+(αl-αu)e-Ni/τ
wherein alpha isu，αlIs the upper and lower limit values corresponding to the angle correction variable alpha; n number of sampling points in the pseudo preference area; i is the current iteration number; τ is the time constant.
The step 7 specifically includes a method of correcting the pseudo preference offset vector: due to the randomness of the initial sampling points and the complexity of the multi-objective optimization algorithm, at the early stage of algorithm evolution, all the current sampling points are probably out of the pseudo-preference range. This results in the algorithm not being able to continue to evolve. To solve this problem, the present invention proposes a method of correcting the pseudo preference offset vector. The pseudo preference offset vector is one of the key factors in deciding the pseudo preference position. And gradually correcting the pseudo preference offset vector, and further changing the pseudo preference position until at least one sampling point is in the current pseudo preference frame. The pseudo-preference offset vector is modified as follows:
wherein the content of the first and second substances,
is a pseudo preference offset vector; t is the current movement times of the pseudo preference offset vector; a isjIs the target space size; k is a scaling factor related to the search direction.
The optimal design aiming at the antenna array is a typical multi-target electromagnetic field inverse problem. The invention provides a projection physical planning algorithm-based multi-objective optimization embodiment applied to a point source antenna array.
Step A1: the point source antenna array optimization variables and the objective function are determined, and the spatial arrangement of the optimization variables and the objective function is shown in figure 3. By the distance d between the radiation sourcesiAnd amplitude A of the excitation of the radiation sourceiIn order to optimize variables, a mathematical analysis model of the homogeneous point source antenna array multi-target optimization design problem is established by taking the improvement of the directional gain of the homogeneous point source antenna array and the suppression of the sidelobe noise level of the homogeneous point source antenna array as optimization targets.
Wherein A (n) and d (n) are the amplitude of the excitation of the radiation source and the distance between the radiation sources in the homogeneous point source antenna array. AF is an array factor of a homogeneous point source antenna array; a (n) and d (n) are the excitation amplitude of the radiation source in the homogeneous point source antenna array and the distance between the radiation sources; thetauAnd thetalIs the spatial region boundary of the side lobe level.
Step A2: and searching optimal values corresponding to the directional gain and the sidelobe level suppression single target through a scalar tabu optimization algorithm, and determining a problem anchor point.
Step A3: and determining an optimal line segment L of the optimization problem through the anchor point. And dividing the ideal line segment L into nd uniformly distributed sub-regions according to the number nd of Pareto solutions in the optimal solution set required by a designer.
Step A4: and taking the center point of the nd sub-regions as a vertex to construct nd pseudo preference regions.
Step A5: defining a number N of diversified search iterationsDAnd number of search iterations NIInitialization iterationThe number-indicating variable i is 0; the N initial sampling points are generated using the super-volume sampling.
Step A6: and calculating the objective function value and the pseudo preference area to which the objective function value belongs. And recording the projection coordinates of each sampling point towards the ideal line segment L. And defining the distance between the center point of the nd sub-areas and the projection coordinates as the projection distance of the sampling point. And determining the attribution preference of the sampling points according to the projection distance and the boundary of the nd sub-area.
And calculating an aggregation objective function based on the pseudo preference area, calculating an aggregation objective function value of the sampling point based on the pseudo preference, and constructing an aggregation function value matrix G of the sampling point calculated based on all the pseudo preferences. And classifying and sequencing the data in the matrix G to obtain an optimal solution set in the pseudo-preference, and carrying out contract evolution on the optimal solution set, thereby realizing one-time operation to obtain the whole Pareto solution set.
Wherein, gjkThe aggregation function value calculated by the kth sampling point based on the jth pseudo preference area is calculated according to the following formula:
s.t.fi(x)≤fiM(for Class 1S objectives)
fi(x)≥fim(for Class 2S objectives)
fim≤fi(x)≤fiM(for Class 3S objectives)
fim≤fi(x)≤fiM(for Class 4S objectives)
wherein, gj(x) Is an aggregation function defined based on the jth pseudo-preference area; n isscIs the optimization target number; h isijRank equation based on jth pseudo preference area for ith objective function, fi(x) The objective function of the ith target.
Step A7: judging whether all sampling points are outside the pseudo preference area, if no one point of the current sampling points belongs to the pseudo preference area, namely the sampling points belonging to all the pseudo preference areas are empty, correcting the pseudo preference offset vector, and executing the step A6, and if the current sampling points are not outside the pseudo preference area, executing the step A8;
the pseudo preference offset vector is corrected. Due to the randomness of the initial sampling points and the complexity of the multi-objective optimization algorithm, at the early stage of algorithm evolution, all the current sampling points are probably out of the pseudo-preference range. This results in the algorithm not being able to continue to evolve. To solve this problem, the present invention proposes a method of correcting the pseudo preference offset vector. The pseudo preference offset vector is one of the key factors in deciding the pseudo preference position. And gradually correcting the pseudo preference offset vector, and further changing the pseudo preference position until at least one sampling point is in the current pseudo preference frame. The pseudo preference offset vector is modified as follows.
Wherein the content of the first and second substances,
is a pseudo preference offset vector; t is the current movement times of the pseudo preference offset vector; a isjIs the target space size; k is a scaling factor related to the search direction.
Step A8: calculating an aggregation target function set based on all the pseudo preference areas, dynamically reducing the search range, updating an external file A, recording the optimal solution of each pseudo preference area, comparing the optimal solution with the current optimal solution, and storing the better of the optimal solution into the external file A;
and dynamically narrowing the search range. Since the position of the Pareto solution of the physical planning algorithm is closely related to the pseudo preference position and the size, as shown in fig. 2, the pseudo preference which is often uniformly distributed cannot obtain a uniformly distributed Pareto solution set. Therefore, the present invention provides a method for dynamically narrowing the search range. With the increase of the iteration times, the range of the pseudo preference area is dynamically reduced, so that the search direction is more definite, and the Pareto front edge with uniform distribution is obtained. The angle correction variable α is evolved according to the following formula:
α＝αu+(αl-αu)e-Ni/τ
wherein alpha isu，αlIs the upper and lower limit values corresponding to the angle correction variable alpha; n number of sampling points in the pseudo preference area; i is the current iteration number; τ is the time constant.
Step A9: when the iteration number i is less than or equal to NDThen, the algorithm is in a diversified searching stage, and next iterative sampling points are generated by using the optimal solution; when the number of iterations (N)D+NI)≥i>NDThen, the algorithm is in an enhanced search stage, and a next iteration sampling point is generated by using the current optimal solution;
step A10: judging whether the iteration times reach the maximum value, and when the iteration times i reach the maximum value>(ND+NI) Outputting the result of the external file A, entering the step A11, and when the iteration times i is less than or equal to (N)D+NI) When yes, return to step A6;
step A11: the flow ends.
In order to verify the effectiveness of the algorithm, a point source antenna array optimization example is used for testing. Selecting main parameters: nd is 20, ND＝30,NITable 1 shows the optimization results of the original physical planning algorithm and the improved physical planning algorithm in the point source antenna array optimization problem, 120 and τ being 100. Fig. 4 shows Pareto fronts obtained by solving this problem using a projection range physics planning algorithm.
TABLE 1
The optimization problem of the point source antenna array takes the results of the uniformly distributed spatial structure and the equal-amplitude excitation source as comparison reference values. As can be seen from Table 1, Pareto solutions obtained by the original physical algorithm and the improved physical algorithm are all superior to the reference solution; the boundary solution obtained by improving the physical programming algorithm has higher precision, which shows that the improved algorithm has stronger searching capability; the iteration times of the improved algorithm are reduced by nearly 50% compared with the original algorithm, which shows that the convergence rate of the improved algorithm is greatly improved.
The above; but are merely preferred embodiments of the invention; the scope of the invention is not limited thereto; any person skilled in the art is within the technical scope of the present disclosure; the technical scheme and the improved concept of the invention are equally replaced or changed; are intended to be covered by the scope of the present invention.
Claims (4)
1. The physical planning algorithm based on projection ranging is characterized in that: the specific steps are as follows,
step 1: determining an objective function;
step 2: searching an optimal value corresponding to the single target through a scalar tabu optimization algorithm, and determining a problem anchor point;
and step 3: determining an ideal line segment L or an ideal space omega of an optimization problem through an anchor point, and dividing the ideal line segment L or the ideal space omega into nd uniformly-distributed sub-areas according to the number nd of Pareto solutions in an optimal solution set, which is required to be obtained by a designer;
and 4, step 4: taking the center point of the nd sub-regions as a vertex, and constructing nd pseudo preference regions;
and 5: defining a number N of diversified search iterationsDAnd number of search iterations NIInitializing an iteration time indication variable i to be 0, and generating N initial sampling points by using super-volume sampling;
step 6: calculating an objective function value and a pseudo preference area to which the objective function value belongs, projecting a sampling point to an ideal line segment L or an ideal space omega, determining a projection point position corresponding to the sampling point and a sub-area to which the sampling point belongs, and calculating the distance between the projection point and the sampling point to serve as a subsequent evolution basis;
and 7: judging whether all sampling points are outside the pseudo preference area, if no one point of the current sampling points belongs to the pseudo preference area, namely the sampling points belonging to all the pseudo preference areas are empty, correcting the pseudo preference offset vector, executing the step 6, and if the current sampling points are not outside the pseudo preference area, executing the step 8;
and 8: calculating an aggregation target function set based on all the pseudo preference areas, dynamically reducing the search range, updating an external file A, recording the optimal solution of each pseudo preference area, comparing the optimal solution with the current optimal solution, and storing the better of the optimal solution into the external file A;
and step 9: when the iteration number i is less than or equal to NDThen, the algorithm is in a diversified searching stage, and next iterative sampling points are generated by using the optimal solution; when the number of iterations (N)D+NI)≥i>NDThen, the algorithm is in an enhanced search stage, and a next iteration sampling point is generated by using the current optimal solution;
step 10: judging whether the iteration times reach the maximum value, and when the iteration times i reach the maximum value>(ND+NI) Outputting the result of the external file A, entering step 11, and when the iteration times i is less than or equal to (N)D+NI) If yes, returning to the step 6;
step 11: the flow ends.
2. The projected range-based physical planning algorithm of claim 1, wherein: step 6, specifically calculating a classification method of the pseudo preference to which the sampling point belongs; projecting all sampling points to an ideal line segment L or an ideal space omega, and recording projection coordinates of each sampling point; defining the distance between the center point of the nd sub-areas and the projection coordinates as the projection distance of the sampling point; and determining the attribution preference of the sampling points according to the projection distance and the boundary of the nd sub-area.
3. The projected range-based physical planning algorithm of claim 1, wherein: the step 8 specifically includes a method for dynamically narrowing the search range:
α＝αu+(αl-αu)e-Ni/τ
wherein alpha isu，αlIs the upper and lower limit values corresponding to the angle correction variable alpha; n number of sampling points in the pseudo preference area; i is the current iteration number; τ is the time constant.
4. The projected range-based physical planning algorithm of claim 1, wherein: the step 7 specifically includes a method of correcting the pseudo preference offset vector:
wherein the content of the first and second substances,
is a pseudo preference offset vector; t is the current movement times of the pseudo preference offset vector; a isjIs the target space size; k is a scaling factor related to the search direction.
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