CN107330550A - Space cylindricity assessment method based on double annealing learning aid algorithm - Google Patents
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Abstract
The present invention proposes a kind of space cylindricity assessment method of double annealing learning aid algorithm, pass through space cylinder number of degrees model, set up the object function of problem, the space cylinder measurement data of part is obtained by three coordinate measuring machine, secondly object function is solved using double annealing learning aid algorithm, mainly include information Information Entropy and initialize population, student grouping sorts, the step such as " religion " stage and " " stage, and it is high for above learning aid algorithmic procedure solving precision, the problems such as being easily absorbed in local optimum, use annealing algorithm twice with the poor solution of certain probability selection to update optimal solution in " religion " and " " two stages, strengthen algorithm diversity, so as to fully improve computational accuracy, finally solved, and result of calculation is tried to achieve according to stop criterion.This method can fully use and survey data, and without steps such as the coordinate transforms in surveyed data prediction and computational geometry, more novel in algorithm design method, solution procedure complies fully with the Minimum Area principle in international standard, therefore computational solution precision is higher.
Description
Technical Field
The invention belongs to the field of digital measurement of parts and the field of computer application, and particularly relates to a space cylindricity evaluation method based on a secondary annealing teaching and learning algorithm.
Background
In the precision manufacturing process, the size precision, shape precision and position precision of parts have high requirements. The evaluation method of the geometric error of the part is one of the hot points of research in the field of digital measurement. In order to ensure the detection and evaluation precision of the part and improve the geometric quality of the part, the spatial cylindricity is taken as a key form and position factor in the evaluation factors of the part, and the accuracy of the evaluation result can influence the overall evaluation result of the part to a great extent.
The main algorithm for evaluating the space cylindricity error is a least square method, a calculation geometry method and the like. The method has low precision, cannot meet the minimum regional criterion in relevant standards, cannot be applied to the field of precision measurement, and seriously influences the quality of products. According to the specification of the international standard ISO/1101, the part error calculation adopts a minimum area method as an evaluation method. The method for evaluating the cylindricity error of the minimum area is an irreducible complex optimization problem. At present, a geometric calculation method, an intelligent optimization algorithm and the like are mainly adopted. The intelligent optimization algorithm generally has the characteristics of relatively simple mathematical model, high calculation speed, very accurate result and the like, and can be further optimized; therefore, it is now commonly used in the method for evaluating geometric errors of parts.
Teaching and learning algorithm (TLBO) is a new intelligent optimization algorithm proposed in 2012, which simulates two processes of "teaching" and "learning" of a class: class teachers improve the average performance of a class by sharing knowledge, and students improve their performance by learning to teachers and to other classmates. The TLBO algorithm is widely applied to the fields of engineering design, automatic control, function optimization and the like, and achieves good effect.
The simulated annealing algorithm (SA) is a global stochastic optimization algorithm proposed by a simulated physical annealing process. The initial temperature of the algorithm is high, the temperature parameter is continuously reduced along with the evolution process, and the individual with poor acceptance is determined as a new solution by combining the current temperature parameter and the energy value, so that the algorithm is prevented from falling into local optimum.
Disclosure of Invention
Aiming at the problems of low precision, stability deviation and the like of the existing spatial cylindricity evaluation technology, the invention aims to provide a spatial cylindricity evaluation method based on a secondary annealing teaching and learning algorithm, so that the evaluation precision of spatial cylindricity errors is improved, and the solving efficiency and stability are improved.
The invention adopts the following technical scheme for solving the technical problems: the invention provides a space cylindricity evaluation method of a secondary annealing teaching and learning algorithm, which comprises the steps of establishing a target function of a problem through a space cylindricity mathematical model; the method comprises the steps of acquiring space cylinder measurement data of parts through a three-coordinate measuring machine, solving an objective function by adopting a secondary annealing teaching and learning algorithm, initializing a population by an information entropy value method, grouping and sequencing students, selecting a 'teaching' stage and a 'learning' stage and the like, and aiming at the problems that the teaching and learning algorithm process is low in solving precision and easy to fall into local optimum and the like, updating an optimum solution by adopting an annealing algorithm twice in the 'teaching' and 'learning' stages and selecting a poor solution with a certain probability, so that the calculation precision is fully improved, solving is finally carried out, and a calculation result is obtained according to a termination criterion.
Has the advantages that: the method can fully use the measured data, does not have the steps of preprocessing the measured data, calculating coordinate transformation in geometry and the like, is novel in algorithm design method, and completely conforms to the minimum area principle in international standards in the solving process, so the calculation result precision is higher. The invention effectively improves the evaluation result of the spatial cylindricity of the part, ensures the detection and evaluation precision of the part and improves the geometric quality of the product.
Drawings
Fig. 1 is a schematic view of spatial cylindricity.
Fig. 2 is a graph of an iteration of the algorithm of the present invention.
Fig. 3 is a flow chart of the algorithm of the present invention.
Detailed Description
In order to more clearly and specifically express the design and advantages of the present invention, the following process will be described in detail with reference to the attached drawings.
A space cylindricity evaluation method based on a secondary annealing teaching and learning algorithm comprises the following specific steps:
step 1, modeling of cylindrical degree mathematical model
Solving by adopting a minimum area calculation method, namely obtaining the information of the measured cylindrical surface by using three coordinates, and obtaining the cylindricity error value meeting the minimum condition by adopting a successive approximation method through multiple operations;
modeling a cylindricity mathematical model by adopting a minimum region calculation method, wherein a cylindricity error refers to the minimum radial distance between two ideal coaxial cylinders of a measured outline, namely the minimum radius difference between the two coaxial cylinders containing the measured point; the key of the cylindricity error calculation is to determine the position and the direction of the axis of the ideal cylindrical surface; a space rectangular coordinate system is established by the rotation center of a measuring head, the Z-axis direction is consistent with the rotation axis of a cylindrical surface, the axis of an ideal cylindrical surface is assumed to be L, the coordinate of the intersection point of the ideal cylindrical surface and a certain end surface of the cylindrical surface in a measuring coordinate system is (a, b, 0), the number of the axis directions is (p, q,1), the position of L is determined by two parameters of a and b, the direction of L is determined by two parameters of p and q, and the expression of the axis of the ideal cylindrical surface is shown as the formula (1):
if any one of the measuring points Pi(xi,yi,zi) (where i is 1,2.. k, k is the number of measurement points), PiDistance r to a certain axis LiCan be represented by formula (2), wherein i, j, k represents a positive direction unit vector;
therefore, the radius difference of the two coaxial cylindrical surfaces containing the measured outline is the difference between the maximum distance and the minimum distance from the measured point to the ideal axis; i.e. the objective function is:
f(a,b,p,q)＝min(max(ri)-min(ri)) (3)
the variables to be optimized are (p, q, a, b) by combining the formulas (1) and (2), the solution of the minimum region of the cylindricity error is converted into the optimization problem of solving the minimum value of the objective function, namely, the values of the axes (p, q, a, b) of the corresponding ideal cylindrical surfaces are searched based on the objective function f, and the objective function value is minimized;
step 2, acquiring spatial cylindrical measurement data of the part through a three-coordinate measuring machine; placing the measured cylinder on a three-coordinate measuring machine, adjusting the axis of the measured cylinder to be parallel to the Z axis, and sampling at five equidistant right sections respectively in order to acquire information as much as possible; on the cylinder to be measured, respectively taking 5 equidistant right sections P from top to bottom1、P2、P3、P4、P5The intersecting lines of the two circles and the surface of the cylinder are 5 circles; all sampling point coordinates are on 5 circlesCoordinate of sampling point is Pi(xi,yi,zi) (where i is 1,2.. k, k is the number of measurement points), and then the distance r from each sampling point to the ideal axis L is calculatediObviously, taking L as the axis, max (r) respectivelyi) And min (r)i) The area between two large and small cylindrical surfaces with radius contains all sampling points, and the difference between the two cylindrical surfaces with radius is min (max (r)i)-min(ri) That is, the f value of the objective function is minimum;
initializing teaching and learning algorithms and simulated annealing algorithms, wherein the algorithms mainly comprise a class scale P, a class group J and a group student number S, XiFor individual students (solutions to problems), problem dimension D (general subject),andrespectively, an upper limit value and a lower limit value (namely a variable value range) of each dimension; intra-group optimal solution XjIteration number K, annealing number N, current annealing number I, and initial annealing temperature TiniTermination temperature Tend；
And 3, initializing a population P by using information entropy, and randomly generating an initial solution by using a basic teaching and learning algorithm, wherein the initial population cannot be uniformly distributed in a search space by the method, the algorithm efficiency is influenced to a certain extent, and the entropy value H of the ith (i ∈ {1, 2.. D } dimension) in the populationiCan be defined as:
in the formula, PjkIs the ith dimension value in the initial individual jDifferent from the value of the ith dimension in the original individual kThe probability of (d);andthe maximum value and the minimum value of the ith dimension in the initial population; the entropy value H of the overall initial population is:
let initialization critical entropy value H0＝0.2，L0Is HiRandomly generating a first student, randomly generating new individuals under the condition that the size of the new individuals does not exceed the initial population P, and calculating the entropy values H of the individuals and the existing individuals; if H is present>H0Receiving the new individual, otherwise refusing;
step 4, grouping and sequencing strategies; all students of the original teaching and learning algorithm learn from a teacher, and when the algorithm is iterated to the later stage, the diversity is reduced; in order to improve algorithm diversity, classifying students of a class into J groups, counting the number S of each group of students, calculating the fitness of each student, then sequencing, putting the first student in the 1 st group, putting the J-th student in the J-th group, putting the J +1 th student in the 1 st group, and so on; group Q of YQThe expression is YQX (q + J (o-1)), o 1,2.. S, q 1,2.. J, while recording the optimal student X in the groupj；
Step 5, teaching; students in each group study according to the difference between the position of the teacher and the average position in the group; assuming a D-dimension optimization objective function f (X), the ith student position is X after groupingiD＝[Xi1，Xi2。。。XiD]Then eachThe teacher position in each team is the best fitness value f (x) of the team of the current generationteacher) Of individual Xteacher. Calculating the average position value X in the current generation group by using the formula (7)meanEach student in the group updates the position of the student according to the formula (8) to form a new population; wherein,for the new position of the ith student in the group,is the position of the student in the group at the previous generation, riIs a random number between 0 and 1, and TF is a teaching factor; the TF value of the original TLBO algorithm is relatively fixed, the TF value is 1 or 2, and the probability is 0.5 respectively; in the initial stage of algorithm iteration, attention should be paid to population diversity, if TF is small, the TF can be obtained according to the step (8), the search range of a solution is expanded, and the algorithm exploration capability is enhanced; in the later stage of algorithm iteration, the fitness values of all solutions are relatively close, if the TF value is large, the final convergence of the solutions is influenced, therefore, (9) is changed into (10), and the original fixed teaching factor TF is changed into the self-adaptive teaching factor TF related to the iteration times of the algorithm; wherein iter is the current iteration number, and K is the total iteration number;
TF＝round(1+rand(0,1)) (9)
step 6, introducing a simulated annealing algorithm to avoid the algorithm from falling into local optimization; as can be seen from the formula (8), the new individuals accepted by the method are better ones in the new solution accepting method, and the new individuals accepted by the method are better onesSome poor solutions are omitted, and the greedy method is adopted to accept the poor solutions, so that the group diversity of the algorithm is lost, and the local optimal solution is easy to fall into; the Metropolis criterion of an annealing algorithm is introduced for judging and selecting a poor solution as an acceptable new solution, the solving direction is guided, and the population diversity is enhanced; if it is notThenWhereinThe fitness value of the new position of the ith student in the group and the fitness value of the previous generation position of the ith student in the group are respectively obtained; otherwise, according to a certain probability PTWill be provided withInstead of the former
Namely: when in useThenWhen in useIf P isT>rand (0,1), thenWherein
Step 7, learning; each student selects the optimal individual in the group as a learning object from the group, compares the difference between the student and other students and then learns; for student XiSelecting the optimal individual X from the populationjIf f (X)i) Is superior to f (X)j) Then, then
Otherwise
Step 8, annealing search is carried out again; if it is notReceiving a new solution; namely, it isWhen in use
If P isT>rand (0,1), then
Step 9, judging a termination condition, judging whether the iteration times meet the maximum iteration times, if so, calculating termination, and if not, returning to the step 5;
and step 10, the fitness function value after iteration is ended is a space cylindricity error of a measuring point, the position coordinate is a solution meeting the objective function (3), namely an equation parameter of a space cylinder, the iteration curve is shown in figure 2, and the algorithm flow is shown in figure 3.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, and any changes and substitutions that can be easily made by those skilled in the art within the technical scope of the present invention will be covered by the scope of the present invention, and therefore, the scope of the present invention should be subject to the claims.
Claims (2)
1. The space cylindricity evaluation method based on the secondary annealing teaching and learning algorithm is characterized in that a target function of a problem is established through a space cylindricity mathematical model; the method comprises the steps of acquiring space cylinder measurement data of parts through a three-coordinate measuring machine, solving an objective function by adopting a secondary annealing teaching and learning algorithm, initializing a population by an information entropy value method, grouping and sequencing students, selecting a 'teaching' stage and a 'learning' stage and the like, and aiming at the problems that the teaching and learning algorithm process is low in solving precision and easy to fall into local optimum and the like, updating an optimum solution by adopting an annealing algorithm twice in the 'teaching' and 'learning' stages and selecting a poor solution with a certain probability, so that the calculation precision is fully improved, solving is finally carried out, and a calculation result is obtained according to a termination criterion.
2. The method for evaluating the spatial cylindricity based on the teaching and learning algorithm of secondary annealing as claimed in claim 1, which comprises the following specific steps:
step 1, modeling of cylindrical degree mathematical model
Solving by adopting a minimum area calculation method, namely obtaining the information of the measured cylindrical surface by using three coordinates, and obtaining the cylindricity error value meeting the minimum condition by adopting a successive approximation method through multiple operations;
modeling a cylindricity mathematical model by adopting a minimum region calculation method, wherein a cylindricity error refers to the minimum radial distance between two ideal coaxial cylinders of a measured outline, namely the minimum radius difference between the two coaxial cylinders containing the measured point; the key of the cylindricity error calculation is to determine the position and the direction of the axis of the ideal cylindrical surface; a space rectangular coordinate system is established by the rotation center of a measuring head, the Z-axis direction is consistent with the rotation axis of a cylindrical surface, the axis of an ideal cylindrical surface is assumed to be L, the coordinate of the intersection point of the ideal cylindrical surface and a certain end surface of the cylindrical surface in a measuring coordinate system is (a, b, 0), the number of the axis directions is (p, q,1), the position of L is determined by two parameters of a and b, the direction of L is determined by two parameters of p and q, and the expression of the axis of the ideal cylindrical surface is shown as the formula (1):
<mrow> <mfrac> <mrow> <mi>x</mi> <mo>-</mo> <mi>a</mi> </mrow> <mi>p</mi> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>y</mi> <mo>-</mo> <mi>b</mi> </mrow> <mi>q</mi> </mfrac> <mo>=</mo> <mi>z</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
if any one measures a pointPi(xi,yi,zi) (where i is 1,2.. k, k is the number of measurement points), PiDistance r to a certain axis LiCan be represented by formula (2), wherein i, j, k represents a positive direction unit vector;
<mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mo>|</mo> <mtable> <mtr> <mtd> <mi>i</mi> </mtd> <mtd> <mi>j</mi> </mtd> <mtd> <mi>k</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>-</mo> <mi>a</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>-</mo> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>z</mi> <mi>i</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>p</mi> </mtd> <mtd> <mi>q</mi> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>|</mo> <mo>|</mo> </mrow> <msqrt> <mrow> <msup> <mi>p</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>q</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>1</mn> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
therefore, the radius difference of the two coaxial cylindrical surfaces containing the measured outline is the difference between the maximum distance and the minimum distance from the measured point to the ideal axis; i.e. the objective function is:
f(a,b,p,q)＝min(max(ri)-min(ri)) (3)
the variables to be optimized are (p, q, a, b) by combining the formulas (1) and (2), the solution of the minimum region of the cylindricity error is converted into the optimization problem of solving the minimum value of the objective function, namely, the values of the axes (p, q, a, b) of the corresponding ideal cylindrical surfaces are searched based on the objective function f, and the objective function value is minimized;
step 2, acquiring spatial cylindrical measurement data of the part through a three-coordinate measuring machine; placing the measured cylinder on a three-coordinate measuring machine, adjusting the axis of the measured cylinder to be parallel to the Z axis, and sampling at five equidistant right sections respectively in order to acquire information as much as possible; on the cylinder to be measured, respectively taking 5 equidistant right sections P from top to bottom1、P2、P3、P4、P5The intersecting lines of the two circles and the surface of the cylinder are 5 circles; all sampling point coordinates are on 5 circles, and the sampling point coordinate is Pi(xi,yi,zi) (where i is 1,2.. k, k is the number of measurement points), and then the distance r from each sampling point to the ideal axis L is calculatediObviously, taking L as the axis, max (r) respectivelyi) And min (r)i) The area between two large and small cylindrical surfaces with radius contains all sampling points, and the difference between the two cylindrical surfaces with radius is min (max (r)i)-min(ri) That is, the f value of the objective function is minimum;
initializing teaching and learning algorithms and simulated annealing algorithms, wherein the algorithms mainly comprise a class scale P, a class group J and a group student number S, XiFor individual students (solutions to problems), problem dimension D (general subject),andupper and lower limits per dimension (i.e., variables), respectivelyValue range); intra-group optimal solution XjIteration number K, annealing number N, current annealing number I, and initial annealing temperature TiniTermination temperature Tend；
Step 3, initializing a population P by using the information entropy; the basic teaching and learning algorithm randomly generates an initial solution, which cannot ensure that the initial population is uniformly distributed in a search space, influences the efficiency of the algorithm to a certain extent,
entropy H of i (i ∈ {1, 2.. D } dimension) in the populationiCan be defined as:
<mrow> <msub> <mi>H</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mi>P</mi> </mrow> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mi>P</mi> </mrow> </munderover> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msub> <mi>log</mi> <mn>2</mn> </msub> <msub> <mi>P</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>P</mi> <mrow> <mi>j</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mo>|</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>j</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mo>|</mo> </mrow> <mrow> <msubsup> <mi>x</mi> <mi>i</mi> <mi>max</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>min</mi> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
in the formula, PjkIs the ith dimension value in the initial individual jDifferent from the value of the ith dimension in the original individual kThe probability of (d);andthe maximum value and the minimum value of the ith dimension in the initial population; the entropy value H of the overall initial population is:
<mrow> <mi>H</mi> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>L</mi> <mn>0</mn> </msub> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>L</mi> <mn>0</mn> </msub> </munderover> <msub> <mi>H</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
let initialization critical entropy value H0＝0.2，L0Is HiRandomly generating a first student, randomly generating new individuals under the condition that the size of the new individuals does not exceed the initial population P, and calculating the entropy values H of the individuals and the existing individuals; if H is present>H0Receiving the new individual, otherwise refusing;
step 4, grouping and sequencing strategies; all students of the original teaching and learning algorithm learn from a teacher, and when the algorithm is iterated to the later stage, the diversity is reduced; in order to improve algorithm diversity, classifying students of a class into J groups, counting the number S of each group of students, calculating the fitness of each student, then sequencing, putting the first student in the 1 st group, putting the J-th student in the J-th group, putting the J +1 th student in the 1 st group, and so on; group Q of YQThe expression is YQX (q + J (o-1)), o 1,2.. S, q 1,2.. J, while recording the optimal student X in the groupj；
Step 5, teaching; students in each group study according to the difference between the position of the teacher and the average position in the group; assuming a D-dimension optimization objective function f (X), the ith student position is X after groupingiD＝[Xi1，Xi2。。。XiD]Then, the teacher's position within each team is the best fitness value f (x) for the current generation of that teamteacher) Of individual Xteacher(ii) a Calculating the average position value X in the current generation group by using the formula (7)meanEach student in the group updates the position of the student according to the formula (8) to form a new population; wherein,for the new position of the ith student in the group,is the position of the student in the group at the previous generation, riIs a random number between 0 and 1, and TF is a teaching factor; the TF value of the original TLBO algorithm is relatively fixed, the TF value is 1 or 2, and the probability is 0.5 respectively; at the initial stage of algorithm iteration, attention should be paid to population diversity,if the TF is smaller, the TF can be obtained according to the step (8), the search range of the solution is expanded, and the algorithm exploration capability is enhanced; in the later stage of algorithm iteration, the fitness values of all solutions are relatively close, if the TF value is large, the final convergence of the solutions is influenced, therefore, (9) is changed into (10), and the original fixed teaching factor TF is changed into the self-adaptive teaching factor TF related to the iteration times of the algorithm; wherein iter is the current iteration number, and K is the total iteration number;
<mrow> <msub> <mi>X</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mo>&lsqb;</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>s</mi> </munderover> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>s</mi> </munderover> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>s</mi> </munderover> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>D</mi> </mrow> </msub> <mo>&rsqb;</mo> </mrow> <mi>S</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msubsup> <mi>x</mi> <mi>i</mi> <mrow> <mi>n</mi> <mi>e</mi> <mi>w</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mrow> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msubsup> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&times;</mo> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>t</mi> <mi>e</mi> <mi>a</mi> <mi>c</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>-</mo> <mi>T</mi> <mi>F</mi> <mo>&times;</mo> <msub> <mi>X</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
TF＝round(1+rand(0,1)) (9)
<mrow> <mi>T</mi> <mi>F</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>r</mi> <mi>o</mi> <mi>u</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mrow> <mn>0.4</mn> <mo>+</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mo>&le;</mo> <mn>0.5</mn> <mi>K</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>r</mi> <mi>o</mi> <mi>u</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mrow> <mo>(</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>i</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> <mo>></mo> <mn>0.5</mn> <mi>K</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
step 6, introducing a simulated annealing algorithm to avoid the algorithm from falling into local optimization; from the formula (8), it can be seen that in the method for receiving new solutions, the received new individuals are all better individuals, some poor solutions are ignored, and the greedy method is adopted for receiving substantially, so that the group diversity of the algorithm is lost, and the algorithm is easy to fall into the local optimal solution; met incorporating annealing algorithm thereinJudging and selecting a poor solution as an acceptable new solution by a ropolis criterion, guiding the solving direction and enhancing the population diversity; if it is notThenWhereinThe fitness value of the new position of the ith student in the group and the fitness value of the previous generation position of the ith student in the group are respectively obtained; otherwise, according to a certain probability PTWill be provided withInstead of the former
PT＝e－Δf(x)/T i
<mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>T</mi> <mrow> <mi>e</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>T</mi> <mrow> <mi>e</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> <mo>)</mo> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mi>I</mi> <mo>)</mo> </mrow> <mi>N</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
Namely: when in useThenWhen in useIf P isT>rand (0,1), thenWherein
Step 7, learning; each student selects the optimal individual in the group as a learning object from the group, compares the difference between the student and other students and then learns; for student XiSelecting the optimal individual X from the populationjIf f (X)i) Is superior to f (X)j) Then, then
<mrow> <msubsup> <mi>X</mi> <mi>i</mi> <mrow> <mi>n</mi> <mi>e</mi> <mi>w</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mrow> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msubsup> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
Otherwise
<mrow> <msubsup> <mi>X</mi> <mi>i</mi> <mrow> <mi>n</mi> <mi>e</mi> <mi>w</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>X</mi> <mi>i</mi> <mrow> <mi>o</mi> <mi>l</mi> <mi>d</mi> </mrow> </msubsup> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
Step 8, annealing search is carried out again; if it is notReceiving a new solution; namely, it isWhen in useIf P isT>rand (0,1), then
Step 9, judging a termination condition, judging whether the iteration times meet the maximum iteration times, if so, calculating termination, and if not, returning to the step 5;
and step 10, the fitness function value after iteration is ended is a space cylindricity error of the measuring point, and the position coordinate is a solution meeting the objective function (3), namely an equation parameter of the space cylinder.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108319764A (en) * | 2018-01-15 | 2018-07-24 | 湖北汽车工业学院 | Evaluation method for spatial straightness errors method based on longicorn palpus searching algorithm |
| CN109099877A (en) * | 2018-06-29 | 2018-12-28 | 湖北汽车工业学院 | Space Cylindricity error evaluation based on longicorn palpus searching algorithm |
| CN110047088A (en) * | 2019-04-01 | 2019-07-23 | 南京邮电大学 | A kind of HT-29 image partition method based on improvement learning aid optimization algorithm |
| CN110147888A (en) * | 2018-10-25 | 2019-08-20 | 腾讯科技（深圳）有限公司 | The method, apparatus and equipment of multi-objective optimization question are solved based on learning aid algorithm |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108319764A (en) * | 2018-01-15 | 2018-07-24 | 湖北汽车工业学院 | Evaluation method for spatial straightness errors method based on longicorn palpus searching algorithm |
| CN109099877A (en) * | 2018-06-29 | 2018-12-28 | 湖北汽车工业学院 | Space Cylindricity error evaluation based on longicorn palpus searching algorithm |
| CN110147888A (en) * | 2018-10-25 | 2019-08-20 | 腾讯科技（深圳）有限公司 | The method, apparatus and equipment of multi-objective optimization question are solved based on learning aid algorithm |
| CN110147888B (en) * | 2018-10-25 | 2023-06-20 | 腾讯科技（深圳）有限公司 | Method, device and equipment for solving multi-objective optimization problem based on teaching and learning algorithm |
| CN110047088A (en) * | 2019-04-01 | 2019-07-23 | 南京邮电大学 | A kind of HT-29 image partition method based on improvement learning aid optimization algorithm |
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