CN101582130A - Method for improving genetic algorithm structural optimization efficiency - Google Patents

Method for improving genetic algorithm structural optimization efficiency Download PDF

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CN101582130A
CN101582130A CNA2009100856533A CN200910085653A CN101582130A CN 101582130 A CN101582130 A CN 101582130A CN A2009100856533 A CNA2009100856533 A CN A2009100856533A CN 200910085653 A CN200910085653 A CN 200910085653A CN 101582130 A CN101582130 A CN 101582130A
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individual
individual identification
identification codes
genetic algorithm
individuality
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CN101582130B (en
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苏瑞意
桂良进
范子杰
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Tsinghua University
Wuxi Research Institute of Applied Technologies of Tsinghua University
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Abstract

The invention relates to a method for improving genetic algorithm structural optimization efficiency, namely a method introducing individual identification codes, comprising the following steps: initializing a species group and an evolutionary history list; calculating the individual identification codes of the current species group; judging whether the individual is an overlapping individual according to the individual identification code; analyzing the structure of the new individual by means of finite element method; updating the evolutionary history list; evaluating the fitness of the overlapping individuals and the new individuals undergoing structural analysis and obtaining corresponding fitness; judging whether the algorithm is finished, if no, obtaining a new species group by carrying out selection, intersection and variation on the species group, and turning to the start step to operate circularly. The invention adopts the individual identification method to solely mark a chromosome with an identification code, thus avoiding the structural analysis of overlapping individuals, decreasing the amount of calculation effectively, improving the calculating efficiency of genetic algorithm structural optimization. The invention can be widely applied to optimization problems in various fields of discrete structures based on genetic algorithm.

Description

A kind of method of improving genetic algorithm structural optimization efficiency
Technical field
The present invention relates to a kind of method of structural optimization efficiency, particularly about a kind of method that is used for the improvement genetic algorithm structural optimization efficiency of structure optimization field discrete topology topology, size, shape and optimization of material.
Background technology
Discrtete structural optimization can be divided into topology, size, shape and optimization of material according to the difference of optimizing content.Can't realize the complex optimum of discrete topology with traditional optimized Algorithm, because this is discrete, non-protruding a, multivariate, multi-field optimization problem.Genetic algorithm does not require that objective function and constraint function can lead, be easy to handle dispersed problem, have the global convergence ability, therefore can solve the difficulty of discrete topology complex optimum.But carry out structure optimization with genetic algorithm, the individual fitness evaluation need obtain by structure analysis consuming time, and calculated amount is very big, and it is lower to cause optimizing efficient.
Genetic algorithm mainly is based on Darwinian evolutionism, graceful selection theory and the Mendelian gene theory of thatch Wei, the imitation survival of the fittest in natural selection, the survival of the fittest, the biological heredity of the survival of the fittest and the rule of evolution.Carry out structure optimization with genetic algorithm, at first in physical space, each individuality is carried out structure analysis to obtain its adaptive value, then by coding techniques the structure mapping in the physical space in the gene space, corresponding one by one with chromosome, again chromosome is carried out selection, intersection and mutation operation, better new individual to produce.Because genetic algorithms use " survival of the fittest " strategy, the probability height of the individual survival that adaptive value is high therefore through after the selection operation, exists many height that repeat just when individuality in the mating pond.In addition, because intersection and mutation operation are the operation based on probability, after intersection and mutation operation, having only the part individuality in the population is new individuality, and all the other individualities are the direct copy of parent.Therefore, in all individualities that occur in the genetic algorithm evolutionary process, some is that former generation occurred.When carrying out structure optimization with genetic algorithm, in evolutionary process, structure analysis has occupied most time.Therefore avoid the individuality that repeats is carried out structure analysis, can effectively reduce calculated amount, improve the whole efficiency of genetic algorithm structural optimization.But directly store all chromosomes that occur in the evolutionary process, need huge memory space, to large-scale problem, this will be unacceptable.And, directly store chromosome and also will cause repeating the higher of individuality just when estimating required computation complexity.
Summary of the invention
At the problems referred to above, the purpose of this invention is to provide the method for the improvement genetic algorithm structural optimization efficiency that a kind of computation complexity is low, memory space is few, counting yield is higher.
For achieving the above object, the present invention takes following technical scheme: a kind of method of improving genetic algorithm structural optimization efficiency, promptly introduce the method for individual identification codes, it may further comprise the steps: 1) initialization population and evolutionary history list: adopt random device that population is carried out initialization, set up the empty matrix of a m dimension, as initialized evolutionary history list; 2) individual identification codes of the current population of calculating: calculate each individual identification code in the current population according to the individual identification codes formula, be used for judging whether current population has the repetition individuality; 3) judge according to individual identification codes whether individuality is the repetition individuality: whether the individual identification codes of retrieving current population one by one is identical with certain numerical value in first row in the evolutionary history list, if there is identical value, representing that then this individuality once occurred, is the repetition individuality, forwards step 6) to; If there is not identical value, represent that then this is individual for new individual, forward step 4) to; 4) by Finite Element Method new individuality is carried out structure analysis: new individuality is carried out structure analysis, and individual structural response value must make new advances; 5) upgrade evolutionary history list: on original evolutionary history list basis, increase identification code, the structural response value information of all new individualities by row, what promptly have new individual in this generation, evolutionary history list will how many row of corresponding increase; 6) carry out just when evaluation repeating new individuality individual and that carry out after the structure analysis, draw corresponding just when, the method for evaluation is as follows: fit=f (R 1, R 2..., R m), wherein, fit be individual just when; Ri (i=1,2 ..., m, m are the number of structural response function) and be the structural response value; 7) whether evaluation algorithm stops: if the algorithm iteration number of times reaches the maximum iteration time of permission or finds optimum solution, then algorithm finishes; Otherwise, then forward step 8) to; 8) to population select, intersection and mutation operation, obtain new population after, forward step 2 to), cycling.
The structural response value of described new individuality is obtained by structure analysis, and the described structural response value that repeats individuality is retrieved in evolutionary history list and obtained.
The computing formula of described individual identification codes is: Id = Σ i = 1 N e t i p i p max i - 1 , Wherein, Id is an individual identification codes; Ne is the unit number that based structures comprised; t iAnd p iBe respectively the topology value and the property value of i unit correspondence in the based structures; p MaxBe the maximum attribute value.
Described individual identification codes adopts long to store when the small-scale problem, adopts string format to store when extensive problem.
Chromosome of described individual identification codes sign.
Described repetition is individual to be judged by described individual identification codes, judges that the worst required time complexity is O (TNNe+TN 2), wherein, T is current evolutionary generation, and N is a population scale, and Ne is an element number in the based structures.
The present invention is owing to take above technical scheme, it has the following advantages: 1, the present invention is owing to adopted individual discrimination method, come chromosome of unique identification with an identification code, therefore avoided carrying out structure analysis to repeating individuality, effectively reduce calculated amount, improved the counting yield of genetic algorithm structural optimization.2, therefore whether the present invention only need numerical value of storage individual identification codes, rather than store whole chromosome owing to adopted by calculating each chromosomal identification code and discern individuality and repeat, and realized that memory space is few, reduced the space of required memory.3, the present invention is owing to adopted by the retrieval individual identification codes to judge whether individuality repeats, and the worst time complexity that makes evaluation algorithm is than the required little order of magnitude of time complexity of direct storage chromosome, so counting yield is higher.The present invention can be widely used in the optimization problem based on each field of the discrete topology of genetic algorithm.
Description of drawings
Fig. 1 is the genetic algorithm process flow diagram that the present invention adopts individual discrimination method
Fig. 2 is the based structures synoptic diagram of plane of the present invention six node truss
Embodiment
Below in conjunction with drawings and Examples the present invention is described in detail.
The present invention utilizes Finite Element Method that discrete topology is carried out structure analysis, because in Finite Element Method, the attribute of beam element can be expressed its shape of cross section and size, and the material information of this element, so the attribute that the present invention adopts beam element can be realized the complex optimum of shape of cross section, size and material as design variable.The topological optimization of structure need adopt the topological optimization variable in the discrtete structural optimization.For fear of carrying out structure analysis, need all that occur in the evolutionary process not repeated that individuality is discerned, record, and need judge whether the individuality in the current population occurred repeating individuality.Therefore the present invention introduces a kind of individual discrimination method, comes chromosome of unique identification with an identification code, has avoided carrying out structure analysis to repeating individuality.The computing method of individual identification codes are as follows:
Id = Σ i = 1 N e t i p i p max i - 1 - - - ( 1 )
Wherein, Id is an individual identification codes; Ne is the unit number that based structures comprised; t iAnd p iBe respectively the topology value and the property value of i unit correspondence in the based structures; p MaxBe the maximum attribute value.Individual identification codes can adopt long to store when the small-scale problem, when problem scale is bigger, can adopt string format storage identification code to store, and prevents that internal memory from overflowing.After chromosome sign finished, with each for information stores such as the identification code of the new individuality in the population and structural responses in evolutionary history list, so that retrieve.As shown in table 1, be the evolutionary history list data structure.Wherein Ri (i=1,2 ..., m, m are the number of structural response function) and be the structural response functional value.
Table 1
Id R 1 R 2 … R m
As shown in Figure 1, the present invention introduces the method for individual identification codes, and to avoid carrying out structure analysis to repeating individuality, its step is as follows:
1) initialization population and evolutionary history list: adopt random device that population is carried out initialization; Set up the empty matrix of a m dimension, as initialized evolutionary history list.
2) individual identification codes of the current population of calculating: calculate each individual identification code in the current population according to individual identification codes formula (1), be used for judging whether current population has the repetition individuality.
3) judge according to individual identification codes whether individuality is the repetition individuality: whether the individual identification codes of retrieving current population one by one is identical with certain numerical value in first row in the evolutionary history list, if there is identical value, representing that then this individuality once occurred, is the repetition individuality, forwards step 6) to; If there is not identical value, represent that then this is individual for new individual, forward step 4) to.
4) by Finite Element Method new individuality is carried out structure analysis: new individuality is carried out structure analysis, and individual structural response value must make new advances.
5) upgrade evolutionary history list: on original evolutionary history list (as shown in table 1) basis, press identification code, structural response value information that row increases all new individualities, what new individualities are promptly arranged in this generation, evolutionary history list will how many row of corresponding increase.
6) carry out just when evaluation repeating new individuality individual and that carry out after the structure analysis, draw corresponding just when, the method for evaluation is as follows:
fit＝f(R 1，R 2，…，R m) (2)
Wherein, fit be individual just when; Ri (i=1,2 ..., m, m are the number of structural response function) and be the structural response value.New individual structural response value is by above-mentioned steps 4) structure analysis obtains, repeats individual structural response value and obtain by retrieving in evolutionary history list (as shown in table 1).
7) whether evaluation algorithm stops: if the algorithm iteration number of times reaches the maximum iteration time of permission or finds optimum solution, then algorithm finishes; Otherwise, then forward step 8) to.
8) to population select, intersection and mutation operation, obtain new population, forward step 2 to), cycling.
By above steps as can be known,, therefore avoided carrying out structure analysis, effectively reduced calculated amount, improved the counting yield of genetic algorithm structural optimization repeating individuality because the present invention introduces individual recognition methods in genetic algorithm structural optimization.And discern individuality and whether repeat by calculating each chromosomal identification code, only need numerical value of storage individual identification codes, rather than store whole chromosome, so the required memory space has reduced a lot.Simultaneously, owing to judge that by the retrieval individual identification codes the individual the worst time complexity that whether repeats is O (TNNe+TN 2), the time complexity O (TN that this is more required than direct storage chromosome 2Ne) (wherein, T is current evolutionary generation, and N is a population scale, and Ne is an element number in the based structures to want a little order of magnitude.), therefore memory space of the present invention is less, computing velocity is higher.Be described further below by the effect of specific embodiment the inventive method.
As shown in Figure 2, in the based structures of plane six node truss, rod member length a is 9.14m, and loading force P is 444.5kN.The Young modulus of bar material is 68.9GPa, and density is 2.768 * 103kg/cm3, and Poisson ratio is 0.3.The field of definition of rod member cross-sectional area is a set that contains 32 discrete values: { 1.05,1.16,1.54,1.69,1.86,1.99,2.02,2.18,2.34,2.48,2.50,2.70,2.90,3.10,3.21,3.30,3.70,4.66,5.14,7.42,8.71,8.97,9.16,10.00,10.32,12.13,12.84,14.19,14.77,17.10,19.35,21.61} * 10 -3m 2, the rod member attribute number of difference corresponding from 1 to 32.To minimize architecture quality is objective function, requires all rod member stress mustn't surpass 172MPa, and the maximum displacement of node 2 and node 5 mustn't surpass 5.08cm, utilizes method of the present invention to ask the optimum topology and the size of structure.
In the foregoing description, introduce the genetic algorithm of individual discrimination method of the present invention and find the solution, the population scale of employing is 40, maximum iteration time is 400, carried out 10 computings respectively, new individuality that occurs in the statistics evolutionary process and the quantity that repeats individuality, statistics is as shown in table 2.
Table 2
Calculation times New number of individuals Repeat number of individuals Total individual number Repeat individual ratio
1 5983 3577 9560 37.42％
2 9749 6251 16000 39.07％
3 9732 6268 16000 3918％
4 2408 1432 3840 37.29％
5 4101 2419 6520 37.10％
6 1281 759 2040 37.21％
7 2824 1616 4440 36.40％
8 9748 6252 16000 39.08％
9 3381 2019 5400 37.39％
10 9528 6472 16000 40.45％
On average 5873.5 3706.5 9580 38.06％
By above-mentioned statistics as can be known, repeat individual ratio in 10 computings, promptly adopt individual discrimination method on average can reduce by 38.06% number of structural analysis afterwards on average up to 38.06%.In the present embodiment, if do not introduce individual discrimination method, the shared time of then structure analysis link is 92.60%.Therefore, after introducing individual discrimination method, on average can improve 35.42% counting yield.
The foregoing description is an application of the present invention, is not to be used to limit practical range of the present invention.All based on the changes and improvements on the technical solution of the present invention, should not get rid of outside protection scope of the present invention.

Claims (10)

1, a kind of method of improving genetic algorithm structural optimization efficiency is promptly introduced the method for individual identification codes, and it may further comprise the steps:
1) initialization population and evolutionary history list: adopt random device that population is carried out initialization, set up the empty matrix of a m dimension, as initialized evolutionary history list;
2) individual identification codes of the current population of calculating: calculate each individual identification code in the current population according to the individual identification codes formula, be used for judging whether current population has the repetition individuality;
3) judge according to individual identification codes whether individuality is the repetition individuality: whether the individual identification codes of retrieving current population one by one is identical with certain numerical value in first row in the evolutionary history list, if there is identical value, representing that then this individuality once occurred, is the repetition individuality, forwards step 6) to; If there is not identical value, represent that then this is individual for new individual, forward step 4) to;
4) by Finite Element Method new individuality is carried out structure analysis: new individuality is carried out structure analysis, and individual structural response value must make new advances;
5) upgrade evolutionary history list: on original evolutionary history list basis, increase identification code, the structural response value information of all new individualities by row, what promptly have new individual in this generation, evolutionary history list will how many row of corresponding increase;
6) carry out just when evaluation repeating new individuality individual and that carry out after the structure analysis, draw corresponding just when, the method for evaluation is as follows:
fit＝f(R 1，R 2，...，R m)
Wherein, fit be individual just when; Ri (i=1,2 ..., m, m are the number of structural response function) be the structural response value;
7) whether evaluation algorithm stops: if the algorithm iteration number of times reaches the maximum iteration time of permission or finds optimum solution, then algorithm finishes; Otherwise, then forward step 8) to;
8) to population select, intersection and mutation operation, obtain new population after, forward step 2 to), cycling.
2, a kind of method of improving genetic algorithm structural optimization efficiency as claimed in claim 1, it is characterized in that: the structural response value of described new individuality is obtained by structure analysis, and the described structural response value that repeats individuality is retrieved in evolutionary history list and is obtained.
3, a kind of method of improving genetic algorithm structural optimization efficiency as claimed in claim 1, it is characterized in that: the computing formula of described individual identification codes is:
Id = Σ i = 1 N e t i p i p max i - 1 ,
Wherein, Id is an individual identification codes; Ne is the unit number that based structures comprised; t iAnd p iBe respectively the topology value and the property value of i unit correspondence in the based structures; p MaxBe the maximum attribute value.
4, a kind of method of improving genetic algorithm structural optimization efficiency as claimed in claim 2, it is characterized in that: the computing formula of described individual identification codes is:
Id = Σ i = 1 N e t i p i p max i - 1 ,
Wherein, Id is an individual identification codes; Ne is the unit number that based structures comprised; t iAnd p iBe respectively the topology value and the property value of i unit correspondence in the based structures; p MaxBe the maximum attribute value.
5, as claim 1 or 2 or 3 or 4 described a kind of methods of improving genetic algorithm structural optimization efficiency, it is characterized in that: described individual identification codes adopts long to store when the small-scale problem, adopts string format to store when extensive problem.
6, as claim 1 or 2 or 3 or 4 described a kind of methods of improving genetic algorithm structural optimization efficiency, it is characterized in that: chromosome of described individual identification codes sign.
7, a kind of method of improving genetic algorithm structural optimization efficiency as claimed in claim 5 is characterized in that: chromosome of described individual identification codes sign.
8, as claim 1 or 2 or 3 or 4 or 7 described a kind of methods of improving genetic algorithm structural optimization efficiency, it is characterized in that: described repetition is individual to be judged by described individual identification codes, judges that the worst required time complexity is O (TNNe+TN 2), wherein, T is current evolutionary generation, and N is a population scale, and Ne is an element number in the based structures.
9, a kind of method of improving genetic algorithm structural optimization efficiency as claimed in claim 5 is characterized in that: described repetition is individual to be judged by described individual identification codes, judges that the worst required time complexity is O (TNNe+TN 2), wherein, T is current evolutionary generation, and N is a population scale, and Ne is an element number in the based structures.
10, a kind of method of improving genetic algorithm structural optimization efficiency as claimed in claim 6 is characterized in that: described repetition is individual to be judged by described individual identification codes, judges that the worst required time complexity is O (TNNe+TN 2), wherein, T is current evolutionary generation, and N is a population scale, and Ne is an element number in the based structures.
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