CN111260062A - Rectangular piece optimization layout method based on adaptive genetic algorithm - Google Patents
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Abstract
The invention relates to the technical field of two-dimensional layout of rectangular parts, and discloses a rectangular part optimized layout method based on an adaptive genetic algorithm, which comprises the following steps: A) obtaining the sizes of all rectangular pieces to be normalized; B) performing gene coding on the rectangular piece by adopting a decimal method; C) initializing parameters by adopting heuristic rules; D) according to maximum length of stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*Constructing a fitness function F; E) evaluating each group of solutions in the population; F) setting an algorithm stop condition; G) setting the crossover probability P according to the statistical distribution of population fitness valuescAnd the mutation probability PmObtaining a crossed population; H) according to the mutation probability PmIndividual genetic variation is performed to generate a new generation of population. The invention adopts aThe new population initialization method constructs a fitness function combining multiple factors, the algorithm is fast in convergence, and the rectangular piece optimization effect is good.
Description
Technical Field
The invention relates to the technical field of two-dimensional layout of rectangular parts, in particular to a rectangular part optimized layout method based on an adaptive genetic algorithm.
Background
In the field of current industrial production, two-dimensional layout of rectangular pieces is widely applied, for example, cutting of materials such as stone, glass and leather is performed, how to optimize layout on the materials to utilize the raw materials to the maximum extent needs to find out a permutation and combination of the rectangular pieces to maximize the residual area S, but as the number of the rectangular pieces increases, the permutation and combination increases explosively and cannot find out an optimal solution in a short time.
For example, the invention discloses a 'arrangement optimization method based on genetic algorithm' in Chinese patent literature, which is published under the publication number CN108090650A, and the invention establishes mathematical models of rectangular pieces to be arranged, determines the size scale of the pieces to be arranged, considers the pieces to be arranged and the attributes thereof as a gene, and carries out gene coding; a group of to-be-arranged components form a population, and the genes of the population form a group of chromosomes; real number encoding and interleaving: determining the crossing position, selecting a crossing part, and determining whether to cross according to the crossing probability; performing variation on each position of each group of individuals to judge whether rotation variation and position variation are needed; and after a new population is generated by adopting a selection algorithm in the last generation genetic operation, calculating the fitness of the population, sequencing the individuals in the population according to the fitness, and taking the individuals with high fitness to form a new standard population. The optimization objective function of the method is single in consideration, and in addition, the parameters are also fixed in advance, so that the dependence of the operation result of the algorithm on the parameter setting is large, and the dependence of the optimization effect on the parameter setting is high.
Disclosure of Invention
The invention provides a rectangular piece optimized layout method based on a self-adaptive genetic algorithm, aiming at solving the problem that the dependence on parameter setting is large when the existing algorithm is used for solving the rectangular piece optimized layout. The invention adopts the self-adaptive genetic algorithm to optimize the stock layout problem of the rectangular part, adopts heuristic rules to initialize parameters, and comprehensively considers the maximum length of the stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*These three aspectsA fitness function F is constructed according to the three aspects, and a cross probability P is also set adaptively according to the statistical distribution of the population fitness valuescAnd the mutation probability PmAnd the optimization effect is good.
In order to achieve the purpose, the invention adopts the following technical scheme:
the rectangular piece optimization layout method based on the adaptive genetic algorithm comprises the following steps:
A) collecting rectangular pieces to be arranged, acquiring the size and the mass of each rectangular piece, and normalizing the size;
B) performing gene coding on the rectangular pieces by adopting a decimal method, wherein each rectangular piece represents a gene, each gene forms a chromosome, each chromosome represents a group of solutions, the base factor on each chromosome is the total number of the rectangular pieces, and the population scale is N;
C) initializing parameters by adopting heuristic rules;
D) obtaining maximum length of stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*According to maximum length of stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*Constructing a fitness function F;
E) evaluating each group of solutions in the population, calculating a fitness function value of each group of solutions, and sequencing chromosomes according to the fitness function values;
F) setting an algorithm stopping condition, if the algorithm stopping condition is met, ending the algorithm, and obtaining an optimal layout scheme of the rectangular piece; if the stop condition cannot be met, entering the step G);
G) selecting population, and setting cross probability P according to statistical distribution of population fitness valuecAnd the mutation probability PmAccording to the cross probability PcPerforming cross operation on the selected population, and taking two chromosomes in the population as parentsPerforming cross recombination on partial genes to form a new chromosome and obtain a crossed population;
H) in the crossed population, mutation positions are set, the gene values at the mutation positions are varied, and the mutation probability P is determinedmAnd D), carrying out individual gene variation to generate a new generation of population, and returning to the step D).
The invention adopts the self-adaptive genetic algorithm to optimize the stock layout problem of the rectangular part, adopts heuristic rules to initialize parameters, and comprehensively considers the maximum length of the stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*In the three aspects, a fitness function F is constructed according to the three aspects, and a cross probability P is also set adaptively according to the statistical distribution of population fitness valuescAnd the mutation probability PmAnd the optimization effect is good.
Further, the normalizing process for the size in the step a) includes the steps of:
the size normalization processing in the step A) comprises the following steps:
A1) setting the number of the rectangular pieces to be n, counting the length and the width of each rectangular piece, and recording the length of each rectangular piece as { h }1,h2,...hi,...,hn}，hiRepresents the length of the ith rectangular piece; let the width of each rectangular piece be { omega1,ω2,...ωi,...,ωn}，ωiRepresents the width of the ith rectangular piece;
A2) normalizing the length of each rectangular piece to obtain the normalized length of each rectangular piece, and recording the normalized length as the length
Indicates the normalized length of the ith rectangle,
hilength of the ith rectangular member, hminRepresents the minimum value of the length of each rectangular piece before normalization, hmaxThe maximum value of the length before normalization of each rectangular piece is represented;
A3) normalizing the width of each rectangular piece to obtain the normalized width of each rectangular piece, and recording the normalized width as
Indicates the normalized width of the ith rectangle,
ωiwidth, ω, of the ith rectangular memberminRepresents the minimum value of the width, ω, of each rectangular piece before normalizationmaxThe maximum value of the width of each rectangular piece before normalization is shown.
The size is normalized, and the convergence rate of parameters in the optimization solving process can be accelerated.
Further, the decimal method adopted in the step B) is used for carrying out gene coding on the rectangular piece, and the method comprises the following steps: and (3) carrying out digital numbering on the rectangular pieces to be subjected to stock layout, wherein the sequence of the digital numbering represents the sequence of stock layout of each rectangular piece, and the negative sign before the digital numbering represents that the rectangular pieces are rotated by 90 degrees.
The coding mode of the genetic algorithm comprises binary coding, decimal coding, real number coding and the like, the invention adopts decimal coding, namely coding is carried out by using subscript indexes of small layout rectangles, if 10 small rectangles are to be laid out, one sample of a population can be [ -9,6,3,10, -5,4,7,1, -2,8], the numerical sequence in the sample represents the layout sequence, and the negative sign represents the 90-degree rotation discharge.
Further, in the step C), a heuristic rule is adopted for parameter initialization, including:
C1) setting the weight of each rectangular piece, the weight of the ith rectangular piece
α is a weight variable, 0 is more than or equal to α is less than or equal to 1;
C2) and sorting the rectangular pieces according to the sequence of the weights from large to small.
In the process of initializing the parameters, the invention does not initialize the population according to the traditional random strategy, but adopts a heuristic rule to sort the samples, preferably α takes 0.9,
this expression indicates that the weight of a rectangular member having a large area is high, and that the layout is prioritized for a rectangular member having a high weight, and that the maximum length of the layout tends to be maximized when the areas of the two rectangular members are the same
As small a strategy as possible. Parameter initialization is carried out by adopting heuristic rules, so that algorithm convergence can be effectively accelerated, and blind search at the initial stage of the algorithm is avoided.
Further, constructing a fitness function in an iterative process in the step D)
λ is the weight of the total stock layout height factor, μ is the weight of the gravity center of the stock layout, and the uniformity of the stock layout
k is the number of unequal lengths of the rectangular parts after stock layout, kminIs the minimum number k of rectangular pieces with unequal lengths after the stock layout in the iterative processmaxThe maximum number of unequal rectangular piece lengths after the stock layout in the iterative process.
The invention does not take into account the stock run length when calculating the individual adaptation function values, i.e. the objective function values to be optimized
Two additional factors are also considered: stock layout center of gravity position ρ*And the regularity of stock layout k*. Using the upper left corner or the upper right corner of the sample plate as the origin of coordinatesAfter rectangular piece layout is carried out on the sample plate, the layout gravity center position rho is obtained according to the mass and the mass center coordinate of each rectangular piece*Center of gravity of stock layout ρ*The lower the better. Regularity of stock layout k*Smaller, indicating a more orderly stock layout, is more advantageous for feed operations in actual industrial production. The optimization goal of the algorithm is to maximize F. Preferably, λ is 0.6 and μ is 0.3.
Further, setting the cross probability P according to the statistical distribution of the population fitness value in the step G)cAnd the mutation probability PmThe statistical distribution comprises the variance D of the function value of the population fitness and the mean value of the function value of the population fitness
Computing
Obtaining the cross probability, calculating
The variation probability is obtained, and delta represents the offset.
In the selection, crossing and mutation operations, the selection is to select which individuals to cross and mutate, and the crossing and the mutation are the core of the genetic algorithm, wherein the crossing probability PcThe size of (A) represents the global search capability of the population and the mutation probability PmThe size of the P represents the local searching capacity, the traditional genetic algorithm adopts a constant value, but the algorithm is easy to be trapped into local optimization, so the P is required to be enabled in the early stage of the algorithmcGreater, PmSmaller, later, the opposite. The invention is based on the distribution situation of the population fitness value to the cross probability PcAnd the mutation probability PmAn adaptive strategy is adopted, and preferably, the offset delta is 0.01. At cross probability PcAnd the mutation probability PmIn the calculation formula (2), since the variance of the population fitness value is large (the variance represents the data divergence degree) at the early stage of the algorithm, and the fitness mean value is small, the cross probability P is obtained along with the convergence of the algorithmcGradually decreasing, mutation probability PmThe opposite is true.
Further, the step G) of selecting the population comprises the following steps:
G1) calculating a fitness function value of each chromosome;
G2) obtaining the probability that the g-th chromosome is inherited to the next generation
FgThe fitness function value of the g-th chromosome,
for the population global fitness function value, the probability of each chromosome being inherited to the next generation is obtained in turn { ξ1，ξ2，...，ξN}；
G3) Calculating the cumulative probability of each chromosome, the cumulative probability of the g-th chromosome being
Obtaining N cumulative probability intervals;
G4) generating N random numbers, wherein the range of the random numbers is [0,1], and obtaining the cumulative probability interval to which each random number belongs;
G5) and obtaining chromosomes inherited to the next generation according to the accumulation probability interval to which each random number belongs, and obtaining the population after selection.
The population is selected based on the idea of roulette algorithm, and the cumulative probability interval can be a closed interval or a half-open interval.
Further, adopting double-point crossing in step G) according to the crossing probability PcThe selected chromosomes are subjected to crossover operations.
Setting a variation position in the step H), comprising the following steps: and randomly generating three position coordinates, exchanging the gene values corresponding to the first two position coordinates, and performing numerical value negation on the gene value corresponding to the third position coordinate.
In the crossing operation, the invention adopts double-point crossing, namely two position coordinates are randomly generated, and the part between the position coordinates of two individuals to be crossed is exchanged; in the variation operation, the strategy adopted by the invention is to randomly generate three position coordinates, the numbers of the first two coordinates are exchanged, and the inversion of the number of the third coordinate represents that the rectangular piece is rotated by 90 degrees and then discharged.
And F), setting the maximum iteration times, and setting the algorithm stopping condition as whether the maximum iteration times are reached.
Therefore, the invention has the following beneficial effects: the invention adopts the self-adaptive genetic algorithm to optimize the stock layout problem of the rectangular part, adopts heuristic rules to initialize parameters, and comprehensively considers the maximum length of the stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*In the three aspects, a fitness function F is constructed according to the three aspects, and a cross probability P is also set adaptively according to the statistical distribution of population fitness valuescAnd the mutation probability PmNot only is the algorithm fast converging, but also a better result is obtained than the common genetic algorithm.
Drawings
Fig. 1 is a flow chart of a first embodiment of the present invention.
Fig. 2 is a schematic diagram of a layout of a rectangular member according to the first embodiment of the present invention.
FIG. 3 is a schematic diagram of a rectangular part after layout by using an adaptive genetic algorithm according to a first embodiment of the present invention.
FIG. 4 is a schematic diagram of a rectangular piece after being subjected to layout by using a conventional genetic algorithm according to the first embodiment of the present invention.
FIG. 5 is a comparison graph of a rectangular piece after the rectangular piece has been sampled according to the first embodiment of the present invention.
1. The method of the invention, 2, traditional genetic algorithm.
Detailed Description
The invention is further described with reference to the following detailed description and accompanying drawings.
Example one, as shown in fig. 1 and 2, W in fig. 2 represents the total length of the sample plate, H represents the total width of the sample, and H representsmaxShowing the maximum length of the rectangular piece after stock layout,s represents the remaining area.
The rectangular piece optimization layout method based on the adaptive genetic algorithm comprises the following steps:
A) the method comprises the following steps of collecting 23 rectangular pieces to be subjected to stock layout, obtaining the size and the quality of each rectangular piece, and carrying out normalization processing on the size, wherein the method comprises the following steps:
A1) setting the number of the rectangular pieces to be n, counting the length and the width of each rectangular piece, and recording the length of each rectangular piece as { h }1,h2,...hi,...,hn}，hiRepresents the length of the ith rectangular piece; let the width of each rectangular piece be { omega1,ω2,...ωi,...,ωn}，ωiRepresents the width of the ith rectangular piece;
A2) normalizing the length of each rectangular piece to obtain the normalized length of each rectangular piece, and recording the normalized length as the length
Indicates the normalized length of the ith rectangle,
hilength of the ith rectangular member, hminRepresents the minimum value of the length of each rectangular piece before normalization, hmaxThe maximum value of the length before normalization of each rectangular piece is represented;
A3) normalizing the width of each rectangular piece to obtain the normalized width of each rectangular piece, and recording the normalized width as
Indicates the normalized width of the ith rectangle,
ωiwidth, ω, of the ith rectangular memberminRepresents the minimum value of the width, ω, of each rectangular piece before normalizationmaxThe maximum value of the width of each rectangular piece before normalization is shown.
B) Performing gene coding on the rectangular piece by adopting a decimal method, wherein the method comprises the following steps: and (3) carrying out digital numbering on the rectangular pieces to be subjected to stock layout, wherein the sequence of the digital numbering represents the sequence of stock layout of each rectangular piece, and the negative sign before the digital numbering represents that the rectangular pieces are rotated by 90 degrees. Each rectangular element represents a gene, each gene constitutes a chromosome, each chromosome represents a set of solutions, the gene factor on each chromosome is the total number of the rectangular elements, and the population size is N.
C) Adopting heuristic rules to initialize parameters, comprising the following steps:
C1) setting the weight of each rectangular piece, the weight of the ith rectangular piece
α is a weight variable, 0 is more than or equal to α is less than or equal to 1;
C2) and sorting the rectangular pieces according to the sequence of the weights from large to small.
D) Obtaining maximum length of stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*According to maximum length of stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*Constructing fitness function in iterative process
λ is the weight of the total stock layout height factor, μ is the weight of the gravity center of the stock layout, and the uniformity of the stock layout
k is the number of unequal lengths of the rectangular parts after stock layout, kminIs the minimum number k of rectangular pieces with unequal lengths after the stock layout in the iterative processmaxThe maximum number of unequal rectangular piece lengths after the stock layout in the iterative process.
E) Evaluating each group of solutions in the population, calculating a fitness function value of each group of solutions, and sequencing chromosomes according to the fitness function values;
F) setting the maximum iteration times, setting the algorithm stopping condition as whether the maximum iteration times are reached, and if the stopping condition is met, ending the algorithm to obtain the optimal layout scheme of the rectangular piece; if the stop condition cannot be satisfied, the process proceeds to step G).
G) Selecting a population, comprising the steps of:
G1) calculating a fitness function value of each chromosome;
G2) obtaining the probability that the g-th chromosome is inherited to the next generation
FgThe fitness function value of the g-th chromosome,
for the population global fitness function value, the probability of each chromosome being inherited to the next generation is obtained in turn { ξ1，ξ2，...，ξN}；
G3) Calculating the cumulative probability of each chromosome, the cumulative probability of the g-th chromosome being
Obtaining N cumulative probability intervals;
G4) generating N random numbers, wherein the range of the random numbers is [0,1], and obtaining the cumulative probability interval to which each random number belongs;
G5) and obtaining chromosomes inherited to the next generation according to the accumulation probability interval to which each random number belongs, and obtaining the population after selection.
Setting the crossover probability P according to the statistical distribution of population fitness valuescAnd the mutation probability PmThe statistical distribution comprises the variance D of the function value of the population fitness and the mean value of the function value of the population fitness
Computing
Obtaining the cross probability, calculating
The variation probability is obtained, and delta represents the offset.
By taking two-point cross according to cross probability PcAnd carrying out cross operation on the selected population, taking two chromosomes in the population as parents, and carrying out cross recombination on partial genes of the chromosomes to form new chromosomes so as to obtain the crossed population.
H) In the population after crossing, the setting of variation positions comprises the following steps: and randomly generating three position coordinates, exchanging the gene values corresponding to the first two position coordinates, and performing numerical value negation on the gene value corresponding to the third position coordinate. The gene value at the mutation position is changed according to the mutation probability PmAnd D), carrying out individual gene variation to generate a new generation of population, and returning to the step D).
As shown in fig. 3 and 4, fig. 3 and 4 are schematic diagrams of layout of rectangular pieces by using an adaptive genetic algorithm and a conventional genetic algorithm, respectively. In the rectangular part layout by adopting the adaptive genetic algorithm, 6 rows are provided, the number of the rectangular parts with unequal lengths from left to right is respectively 2, 3 and 3, in the rectangular part layout by adopting the common genetic algorithm, the number of the rectangular parts with unequal lengths from left to right is respectively 3, 5,4, 3, 2 and 3, and the rectangular part layout by adopting the adaptive genetic algorithm is more orderly, and the obtained residual area is larger. The comparison of the parameters using the adaptive genetic algorithm and the general genetic algorithm is shown in table 1. As shown in FIG. 5, curve 1 is the variation curve of the fitness function value with the increase of the number of iterations in the method of the present invention, and curve 2 is the variation curve of the fitness function value with the increase of the number of iterations in the conventional genetic algorithm, and it can be seen through comparison that the population fitness function values obtained by the adaptive genetic algorithm are all the sameValue of
And the algorithm is larger, the convergence is faster, and the optimization effect is better.
TABLE 1 parameter comparison of adaptive genetic algorithm and general genetic algorithm
TABLE 1
The invention adopts the self-adaptive genetic algorithm to optimize the stock layout problem of the rectangular part, adopts heuristic rules to initialize parameters, and comprehensively considers the maximum length of the stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*In the three aspects, a fitness function F is constructed according to the three aspects, and a cross probability P is also set adaptively according to the statistical distribution of population fitness valuescAnd the mutation probability PmNot only is the algorithm fast converging, but also a better result is obtained than the common genetic algorithm.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (10)
1. The rectangular piece optimal layout method based on the adaptive genetic algorithm is characterized by comprising the following steps of:
A) collecting rectangular pieces to be arranged, acquiring the size and the mass of each rectangular piece, and normalizing the size;
B) performing gene coding on the rectangular pieces by adopting a decimal method, wherein each rectangular piece represents a gene, each gene forms a chromosome, each chromosome represents a group of solutions, the base factor on each chromosome is the total number of the rectangular pieces, and the population scale is N;
C) initializing parameters by adopting heuristic rules;
D) obtaining maximum length of stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*According to maximum length of stock layout
Stock layout center of gravity position ρ*And the regularity of stock layout k*Constructing a fitness function F;
E) evaluating each group of solutions in the population, calculating a fitness function value of each group of solutions, and sequencing chromosomes according to the fitness function values;
F) setting an algorithm stopping condition, if the algorithm stopping condition is met, ending the algorithm, and obtaining an optimal layout scheme of the rectangular piece; if the stop condition cannot be met, entering the step G);
G) selecting population, and setting cross probability P according to statistical distribution of population fitness valuecAnd the mutation probability PmAccording to the cross probability PcPerforming cross operation on the selected population, taking two chromosomes in the population as parents, and performing cross recombination on partial genes of the chromosomes to form new chromosomes and obtain the crossed population;
H) in the crossed population, mutation positions are set, the gene values at the mutation positions are varied, and the mutation probability P is determinedmAnd D), carrying out individual gene variation to generate a new generation of population, and returning to the step D).
2. The adaptive genetic algorithm-based rectangular piece optimized layout method according to claim 1, wherein the normalization processing of the sizes in the step A) comprises the steps of:
A1) setting the number of the rectangular pieces to be n, counting the length and the width of each rectangular piece, and recording the length of each rectangular piece as { h }1,h2,...hi,...,hn}，hiRepresents the length of the ith rectangular piece; let the width of each rectangular piece be { omega1,ω2,...ωi,...,ωn}，ωiRepresents the width of the ith rectangular piece;
A2) normalizing the length of each rectangular piece to obtain the normalized length of each rectangular piece, and recording the normalized length as the length
Indicates the normalized length of the ith rectangle,
hilength of the ith rectangular member, hminRepresents the minimum value of the length of each rectangular piece before normalization, hmaxThe maximum value of the length before normalization of each rectangular piece is represented;
A3) normalizing the width of each rectangular piece to obtain the normalized width of each rectangular piece, and recording the normalized width as
Indicates the normalized width of the ith rectangle,
ωiwidth, ω, of the ith rectangular memberminRepresents the minimum value of the width, ω, of each rectangular piece before normalizationmaxThe maximum value of the width of each rectangular piece before normalization is shown.
3. The method for optimized layout of rectangular parts based on adaptive genetic algorithm as claimed in claim 1 or 2, wherein the decimal method is used to encode genes for the rectangular parts in step B), comprising: the decimal method is adopted in the step B) to carry out gene coding on the rectangular piece, and the method comprises the following steps: and (3) carrying out digital numbering on the rectangular pieces to be subjected to stock layout, wherein the sequence of the digital numbering represents the sequence of stock layout of each rectangular piece, and the negative sign before the digital numbering represents that the rectangular pieces are rotated by 90 degrees.
4. The rectangular piece optimal layout method based on the adaptive genetic algorithm as claimed in claim 3, wherein in the step C), heuristic rules are adopted for parameter initialization, and the method comprises the following steps:
C1) setting the weight of each rectangular piece, the weight of the ith rectangular piece
α is a weight variable, 0 is more than or equal to α is less than or equal to 1;
C2) and sorting the rectangular pieces according to the sequence of the weights from large to small.
5. The method for optimized layout of rectangular parts based on adaptive genetic algorithm as claimed in claim 1 or 4, wherein the fitness function in the iterative process is constructed in step D)
λ is the weight of the total stock layout height factor, μ is the weight of the gravity center of the stock layout, and the uniformity of the stock layout
k is the number of unequal lengths of the rectangular parts after stock layout, kminIs the minimum number k of rectangular pieces with unequal lengths after the stock layout in the iterative processmaxThe maximum number of unequal rectangular piece lengths after the stock layout in the iterative process.
6. The adaptive genetic algorithm-based rectangular piece optimal layout method according to claim 5, wherein the cross probability P is set according to the statistical distribution of population fitness values in the step G)cAnd the mutation probability PmThe statistical distribution includes populationVariance D of fitness function values and mean of population fitness function valuesFCalculating
Obtaining the cross probability, calculating
The variation probability is obtained, and delta represents the offset.
7. The adaptive genetic algorithm-based optimal layout method for rectangular parts according to claim 1 or 6, wherein the population is selected in the step G), and the method comprises the following steps:
G1) calculating a fitness function value of each chromosome;
G2) obtaining the probability that the g-th chromosome is inherited to the next generation
FgThe fitness function value of the g-th chromosome,
for the population global fitness function value, the probability of each chromosome being inherited to the next generation is obtained in turn { ξ1，ξ2，...，ξN}；
G3) Calculating the cumulative probability of each chromosome, the cumulative probability of the g-th chromosome being
Obtaining N cumulative probability intervals;
G4) generating N random numbers, wherein the range of the random numbers is [0,1], and obtaining the cumulative probability interval to which each random number belongs;
G5) and obtaining chromosomes inherited to the next generation according to the accumulation probability interval to which each random number belongs, and obtaining the population after selection.
8. The method of claim 7The rectangular part optimal layout method based on the adaptive genetic algorithm is characterized in that double-point crossing is adopted in the step G) according to the crossing probability PcAnd performing cross operation on the selected population.
9. The adaptive genetic algorithm-based rectangular part optimal layout method according to claim 1 or 8, wherein the setting of the variation positions in step H) comprises: and randomly generating three position coordinates, exchanging the gene values corresponding to the first two position coordinates, and performing numerical value negation on the gene value corresponding to the third position coordinate.
10. The adaptive genetic algorithm-based optimal layout method for rectangular parts according to claim 9, wherein in step F), the maximum number of iterations is set, and the algorithm stop condition is set as whether the maximum number of iterations is reached.
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| CN113033419A (en) * | 2021-03-24 | 2021-06-25 | 河南中烟工业有限责任公司 | Method and system for identifying equipment fault based on evolutionary neural network |
| CN113642264A (en) * | 2021-10-19 | 2021-11-12 | 深圳须弥云图空间科技有限公司 | Layout method and device based on genetic algorithm |
| CN114118916A (en) * | 2021-11-24 | 2022-03-01 | 无锡唯因特数据技术有限公司 | Silicon ingot combination method, device and storage medium |
| CN114528701A (en) * | 2022-01-26 | 2022-05-24 | 广东工业大学 | Variable-size two-dimensional irregular layout method and system for multi-specification plates |
| CN117077524A (en) * | 2023-08-18 | 2023-11-17 | 广州市市政工程机械施工有限公司 | Concrete laminated slab mold intelligent arrangement method based on hybrid algorithm |
| CN118485010A (en) * | 2024-07-16 | 2024-08-13 | 湘潭大学 | Graphic layout method based on nested multi-group classification genetic algorithm |
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| CN113033419A (en) * | 2021-03-24 | 2021-06-25 | 河南中烟工业有限责任公司 | Method and system for identifying equipment fault based on evolutionary neural network |
| CN113642264A (en) * | 2021-10-19 | 2021-11-12 | 深圳须弥云图空间科技有限公司 | Layout method and device based on genetic algorithm |
| WO2023066266A3 (en) * | 2021-10-19 | 2023-09-21 | 深圳须弥云图空间科技有限公司 | Genetic algorithm-based sample layout method and apparatus |
| US12131106B2 (en) | 2021-10-19 | 2024-10-29 | Shenzhen Xumi Yuntu Space Technology Co., Ltd. | Layout method and apparatus based on genetic algorithm |
| CN114118916A (en) * | 2021-11-24 | 2022-03-01 | 无锡唯因特数据技术有限公司 | Silicon ingot combination method, device and storage medium |
| CN114528701A (en) * | 2022-01-26 | 2022-05-24 | 广东工业大学 | Variable-size two-dimensional irregular layout method and system for multi-specification plates |
| CN117077524A (en) * | 2023-08-18 | 2023-11-17 | 广州市市政工程机械施工有限公司 | Concrete laminated slab mold intelligent arrangement method based on hybrid algorithm |
| CN118485010A (en) * | 2024-07-16 | 2024-08-13 | 湘潭大学 | Graphic layout method based on nested multi-group classification genetic algorithm |
| CN118485010B (en) * | 2024-07-16 | 2024-09-06 | 湘潭大学 | Graphic layout method based on nested multi-group classification genetic algorithm |
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