CN115688605A - Civil aircraft development demand ordering method based on multi-objective optimization algorithm - Google Patents
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Abstract
The invention provides a multi-objective optimization algorithm-based civil aircraft development demand ordering method, which comprises the steps of establishing a civil aircraft development demand realization priority ordering mathematical model, constructing a fitness function, calculating individual fitness and dividing offspring populations, selecting a final decision variable and generating a demand realization priority ordering list after gene selection, intersection and variation, and finally obtaining an ordering result of demand realization priority. According to the method, the implementation priorities of the civil aircraft development requirements of a plurality of interest-relevant parties are sequenced under the constraint of limited cost resources through a quantification method, the expected implementation degrees of the plurality of interest-relevant parties related to civil aircraft design to different requirements are comprehensively considered in the civil aircraft development process under the limited cost resources, and the requirement implementation expectations of the interest-relevant parties are fully considered and met as far as possible on the basis of ensuring the maximum overall expectation implementation of the requirements.
Description
Technical Field
The invention relates to the field of civil aircraft development requirements, in particular to a civil aircraft development requirements sequencing method.
Background
The development of civil aircrafts in a new era is developed towards the trend of complication and high integration, and the variety and the number of the development requirements of the civil aircrafts are greatly increased. In the actual development process of civil aircrafts, the development of the demand faces many problems, and a plurality of problems and challenges exist, which are mainly reflected in the following two aspects:
on one hand, the civil aircraft development relates to a plurality of interest-related parties, and relates to a plurality of departments, a plurality of industries, requirements upstream suppliers and downstream suppliers and the like, each interest-related party hopes that the requirements are met to the maximum extent from the self-perspective, and in the description of a plurality of requirements from different interest-related parties, the phenomena of conflict and even mutual contradiction often occur. On the other hand, due to the limitations of the civil aircraft development period, the development cost, the personnel investment and other conditions, an effective method is urgently needed to assist the demand engineer in optimizing the demand under the limited cost constraint condition under the existing conditions, and a feasible demand subset and demand realization priority ordering are generated.
In the traditional method, a requirement engineer sets the priority of the requirement, so that interest correlators of civil aircraft development and development requirements are not well and directly associated, a sequencing method capable of quantitative calculation is not formed, and an effective effect is hardly played when sequencing for large-scale development requirements. The exploration practice of the existing demand sequencing method is developed in the field of software engineering, but most of the existing demand sequencing method aims at the problem of single-target optimization, the problem of multi-interest related parties in civil aircraft development is difficult to migrate and use to solve the existing problem, and the solution result is insufficient in consideration degree of all parties.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a civil aircraft development demand sequencing method based on a multi-objective optimization algorithm.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
(1) Establishing a civil aircraft development requirement realization priority ordering mathematical model;
the set of stakeholders is S, and satisfies S = { S = { (S) } 1 ,s 2 ,…,s n In which s is 1 ,s 2 ,…,s n Sequentially represent n andstakeholders who are relevant to civil aircraft development needs; if the demand set is R, and R = { R is satisfied 1 ,r 2 ,…,r m In which r is 1 ,r 2 ,…,r m Sequentially representing m requirements participating in realizing priority ordering; let the set of demand realization costs be C = { C = } 1 ,c 2 ,…,c m In which c is i Corresponding representation implementation requirement r i The cost of the need; definition v (r) i ,s j ) For stakeholders s j To the demand r i 0 ≦ v (r) i ,s j ) V (r) is less than or equal to 5 i ,s j ) Is epsilon N, the smaller the value is, the stakeholder s is represented j To the demand r i The smaller the desired degree of realization, and vice versa; defining a demand decision variable X = { X = 1 ,x 2 ,…,x m In which x is i ∈{0,1}，x i 1 represents the priority implementation requirement r i ，x i If =0, it means that the demand r is not realized preferentially i ；
(2) Initializing a population:
maximum evolution algebra is g max If the population scale is N, N individuals in the initial population all comprise a chromosome, and m genes are arranged on one chromosome and correspond to m requirements in the step (1) one by one; any one gene code on the chromosome is an initial randomly generated integer 0 or 1, wherein 0 represents that the requirement corresponding to the gene is not preferentially selected, and 1 represents that the requirement corresponding to the gene is preferentially selected, so that an initial population is generated;
(3) Constructing a fitness function:
taking the stakeholders s in the step (1) j Desired implementation function of
And overall expected implementation function f s (X) as a fitness function;
(4) Calculating individual fitness and dividing offspring populations:
calculating the value of the individual fitness function according to the fitness function constructed in the step (3), and setting two archive sets CA and DA for storage, wherein CA is an archive facing convergence, DA is an archive facing diversity, and the capacities of the archive sets CA and DA are set artificially so as to effectively balance convergence and diversity of the population;
population F of each generation n Averagely divided into two archive sets CA n And DA n Population F n-1 And F n First all adding CA n Introducing quality index I in the process of updating archive set CA ε+ As an updating principle, the capacity requirement of the archive set is met by continuously deleting the individuals that are least capable of dominating other individuals; I.C. A ε+ Is to describe a certain body X in the target space of population evolution 1 Dominating another individual X 2 The minimum distance required is indicated by equation (5):
I ε+ (X 1 ,X 2 )＝min ε (f i (X 1 )-f i (X 2 )≥ε) (5)
wherein i is more than or equal to 1 and less than or equal to M, i belongs to N, M is the number of optimization targets, and N represents a natural number; ε is a certain volume X in the target space 1 Dominating another individual X 2 The minimum distance is required and satisfies that epsilon is more than or equal to 0<1；
When the individual X 1 Removed, the loss measure of population fitness is shown in equation (6):
when the subject X * Is removed, then CA n The individual fitness value in (2) is updated as shown in equation (7):
in updating archive set CA n In all process (2), all are from CA n In removing I ε+ Individuals with minimal loss, and updating CA n I of the remaining individuals ε+ A value; finally, CA with a specified number of individuals is obtained n ；
Updating the archive set DA based on pareto optimality, and continuously adding individuals with the lowest similarity to the individuals in the current archive set DA one by one to meet the capacity limit of the archive set DA; on-update archive set DA n In the process of (1), first from the population F n-1 And F n Selecting a boundary individual to be added, wherein the boundary individual is an individual with the maximum or minimum target value; then, an iteration process is carried out, and in each iteration, the individuals with the largest difference from the current DA are added into the archive set DA n Performing the following steps; in measuring inter-individual similarity, based on Lp norm (0)<p<1) The greater the distance between individuals, the lower the similarity between individuals, and the more preferentially the distance is added to DA n (ii) a Setting p to p =1/M according to the number M of optimization objective functions, as shown in equation (8):
in the pair of initial population F 0 In case of division, archive set CA 0 From only the initial population F 0 And the remaining individuals are taken as an archive set DA 0 When the population generation number n is not 0, according to the fitness function value and the similarity measurement between individuals, the population F of each generation is divided into two groups n Equal division into CA n And DA n ；
(5) Gene selection, crossover and variation
Chromosome crossing probability of p c With a cross probability p c Randomly selecting individuals needing to be crossed from the file sets CA and DA, randomly distributing the randomly selected individuals in pairs, randomly determining gene point positions where the crossing occurs, and exchanging genes of the point positions on the paired individuals to obtain a crossed population;
(6) Judging whether a termination condition is met;
aiming at the population subjected to cross and variation in the step (5), if the evolution algebra is less than g max Returning to the step (4), and adding 1 to the evolution algebra; if evolution algebra is equal to g max Then go to stepStep (7);
(7) Selecting a final decision variable and generating a demand realization priority ordering list;
calculating the total expected realization function value of each individual in the last generation of population, and realizing the function value f according to the total expected realization function value s (X) sorting the numerical values from large to small, selecting the first 10 individuals of which the function value sorting is expected to be realized overall as an individual set to be selected, screening and analyzing by adopting a variance method, and calculating the average value of the n interest-related party requirement realization degrees of the individuals in the individual set to be selected, as shown in a formula (9):
calculating the variance of the function value expected to be realized by the interest-related party of the selected individual, as shown in the formula (10):
defining an individual sorting operator S (X), as shown in equation (11):
the larger the sorting operator S (X), the higher the overall desired implementation of the demand and the higher the compromise between the stakeholders under the decision variable X.
Calculating the sequencing operator value of each individual in the to-be-selected individual set, and selecting the decision variable X corresponding to the individual with the maximum sequencing operator value end As the final decision variable. Comparing the one-to-one correspondence between the demand and the gene point location, and determining the variable X end Decoding the requirement corresponding to the point position with the gene code of 1 into a requirement which is realized preferentially, and decoding the requirement corresponding to the point position with the gene code of 0 into a requirement which is not realized preferentially;
calculating the sum of the expected implementation degrees corresponding to each requirement, as shown in formula (12):
the sum of the desired achievement degrees of each demand is calculated according to equation (12). Firstly, the requirements which are realized preferentially are arranged from large to small according to the numerical value of the sum of the expected realization degrees, then the requirements which are not realized preferentially are arranged from large to small according to the numerical value of the sum of the expected realization degrees, the requirements which are realized preferentially are all arranged before the requirements which are not realized preferentially, and finally, the sequencing result of the priority of realizing the requirements is obtained.
Said stakeholder s j Desired implementation function of
As shown in equation (1):
the cost function to achieve the demand is shown in equation (2):
defining a total expected implementation function f s (X) is shown in formula (3):
wherein alpha is j The weight representing the jth stakeholder may be obtained by an analytic hierarchy process.
In the step (3), the stakeholder s j Desired implementation function of
And overall expected implementation function f s The formula of (X) isBelow) are shown:
in the gene selection, crossing and mutation of the step (5), the probability of chromosomal mutation is p m For the crossed population, the mutation probability p m Randomly selecting individuals from the individuals, carrying out mutation operation on the single individuals, randomly determining the point position where the mutation occurs, changing the gene on the point position into 0 or 1, if the original gene point position is 1, changing the gene into 0, and vice versa, and obtaining a new population; where cross-behavior occurs between CA and DA, while mutation occurs only within CA.
The method has the advantages that through a quantification method, under the constraint of limited cost resources, the realization priorities of civil aircraft development requirements related to a plurality of interest-related parties are sequenced. The method can comprehensively consider the expected realization degrees of a plurality of interest related parties related to civil aircraft design to different requirements under the condition of limited cost resources in the development process of the civil aircraft, fully considers the requirements of all the interest related parties as much as possible and meets the requirement realization expectation of all the interest related parties on the basis of ensuring the maximum overall expectation realization of the requirements, and the generated requirement realization priority ranking result can provide decision assistance for civil aircraft development requirement engineers and provide reference for the subsequent work of the civil aircraft requirement development.
Drawings
FIG. 1 is a flow chart of the Two _ Arch2 algorithm of the present invention
FIG. 2 is a schematic diagram of the crossover and mutation of chromosomes according to the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
(1) Mathematical model for realizing priority sequencing of civil aircraft development requirements
If the existing demand items total 58, the stakeholders s j Is desirably implemented as a function of
As shown in equation (13):
the cost function (constraint) to achieve the demand is shown in equation (14):
overall expected implementation function f s (X) is shown in equation (15):
and setting 6 stakeholders in total, such as suppliers, investors, governments (regulators), enterprises (main manufacturers), customers, operation safeguards and the like, as background objects for example implementation, wherein the number of the stakeholders in the simulation experiment is n =6. When updating diversity-oriented archive set DA, M =6+1=7 is taken when calculating the individual distances using the Lp norm.
Overall expected implementation function f s (X) weight α = (0.038, 0.219,0.128,0.389,0.161, 0.065) in (X), obtained by chromatography;
setting the threshold value of the cost of realizing the requirement to be 70% of the total cost of realizing the requirement
The requirements employed in the examples are shown in Table 1.
Table 1 sample list of requirements
(2) Initializing a population
Taking the size of a population N =200 and the maximum algebra g max And =500, the population contains 200 individuals in total, each individual contains one chromosome, and 58 genes are distributed on one chromosome. Each gene in the chromosome is initially a randomly generated integer 0 or 1, thereby forming an initial population;
(3) Constructing a fitness function
Taking the stakeholders s in the step (1) j Desired implementation function of
And overall expected implementation function f s (X) as a fitness function, as shown in equation (16):
(4) Calculating individual fitness and dividing offspring groups
When DA is updated, p is set to p =1/M =1/7 as shown in equation (17).
Wherein, the first and the second end of the pipe are connected with each other,
representing decision variable X i The value of the l gene site.
(5) Gene selection, crossover and variation
Let the chromosome crossover probability p c =0.8, cross probability p for selected population c =0.8 randomly selects individuals to be crossed from the selected population, randomly distributes the individuals in pairs, randomly determines the gene point positions where the crossing occurs, and exchanges the genes of the point positions on the paired individuals to obtain the crossed population; let the probability of chromosomal variation be p m =0.01, with a mutation probability p for the crossed population m =0.01 randomly selects individuals from the group, performs mutation operation on individual individuals, randomly determines a mutation site, changes a gene at the site to 0 or 1 (if the original gene site is 1, it is 0, and vice versa), and obtains a new population. Where cross-behavior occurs between CA and DA, while mutation occurs only within CA.
(6) Judging whether the termination condition is satisfied
Set up g max =500, and if the evolution algebra is less than 500, returning to the step (4) and keeping the evolution algebra +1 for the new population subjected to crossing and mutation in the step (5); if the evolution algebra is equal to 500, go to step (7).
Through calculation, the decision variable X is obtained end Then, variance s 2 (X end )＝5.3769×10 -4 Sorting operator S (X) end ) =1180.7292. The expected achievement degrees of the demands of the interest-interested parties are respectively 0.8125, 0.8051, 0.8017, 0.8182, 0.7525 and 0.7742, and the overall demand achievement degree is 0.7996. Decision variable X resulting from final calculation end Is a single line of vectors of 1 × 58, and the codes at the corresponding positions of the vectors are shown in table 2.
TABLE 2 computationally generated decision variables X end And the corresponding sum v of the desired degree of realization sum (r i )
In table 2, the number of the position item corresponds to the ID in table 1, and when the number is 1, it indicates that the requirement is realized preferentially, and when the number is 0, it indicates that the requirement is not realized preferentially; v. of sum (r i ) The numerical value of a term represents the sum of the desired achievement levels for that requirement.
Firstly, the requirements which are realized preferentially are arranged from large to small according to the numerical value of the sum of the expected realization degrees, then the requirements which are not realized preferentially are arranged from large to small according to the numerical value of the sum of the expected realization degrees, and the sequencing result of the priority level of the requirements is obtained, wherein the sequencing result is shown in a table 3.
TABLE 3 implementation of prioritization results
As can be seen from the sorting results in table 3, the invention can effectively incorporate the achievement expectation of the demand of the interest-related parties into the civil engineering development process, can comprehensively consider the appeal of different interest-related parties, and simultaneously sorts the civil engineering demand achievement priority under the constraints of cost, resources and the like through the multi-objective optimization method, thereby avoiding the influence of excessive subjective factors caused by manually determining the demand priority, clearly showing the achievement priority of a large number of demand items under the constraints for demand engineers, giving consideration to a plurality of interest-related parties, providing reference for the work of the demand engineers in the demand analysis stage of the civil engineering development, and ensuring that the civil engineering process based on demand drive can be better implemented and developed.
The invention can effectively bring the achievement expectation of interest relatives to the demand into the civil aircraft development process, can comprehensively consider the appeal of different interest relatives, and simultaneously sequences the priority of the civil aircraft development demand under the constraints of cost, resources and the like through a multi-objective optimization method, avoids the influence of excessive subjective factors caused by manually determining the demand priority, clearly shows the achievement priority of a large number of demand items under the constraints for demand engineers, can give consideration to a plurality of interest relatives, provides reference for the demand engineers to work in the demand analysis stage of the civil aircraft development, and ensures that the current demand-driven civil aircraft development process can be better implemented and developed.
Claims (4)
1. A civil aircraft development demand sequencing method based on a multi-objective optimization algorithm is characterized by comprising the following steps:
(1) Establishing a civil aircraft development requirement realization priority ordering mathematical model;
the set of stakeholders is S, and satisfies S = { S = { (S) } 1 ,s 2 ,…,s n In which s 1 ,s 2 ,…,s n Sequentially representing n interest correlators related to civil aircraft development requirements; if the requirement set is R, and R = { R is satisfied 1 ,r 2 ,…,r m In which r is 1 ,r 2 ,…,r m Sequentially representing m requirements participating in realizing priority ordering; let C = { C) set of demand implementation costs 1 ,c 2 ,…,c m In which c is i Corresponding representation implementation requirement r i The cost required; definition v (r) i ,s j ) For stakeholders s j To the demand r i 0 ≦ v (r) i ,s j ) V (r) is less than or equal to 5 i ,s j ) Is epsilon N, the smaller the value is, the stakeholder s is represented j To the demand r i The smaller the desired degree of realization, and vice versa; defining a demand decision variable X = { X = 1 ,x 2 ,…,x m In which x i ∈{0,1}，x i The time of =1 represents the priority implementation requirement r i ，x i If =0, it means that the demand r is not realized preferentially i ；
(2) Initializing a population:
maximum evolution algebra is g max If the population scale is N, N individuals in the initial population all comprise a chromosome, and m genes are arranged on one chromosome and correspond to m requirements in the step (1) one by one; any one gene code on the chromosome is an initial randomly generated integer 0 or 1, wherein 0 represents that the requirement corresponding to the gene is not preferentially selected, and 1 represents that the requirement corresponding to the gene is preferentially selected, so that an initial population is generated;
(3) Constructing a fitness function:
taking the stakeholders s in the step (1) j Desired implementation function of
And overall expected implementation function f s (X) as a fitness function;
(4) Calculating individual fitness and dividing offspring populations:
calculating the value of the individual fitness function according to the fitness function constructed in the step (3), and setting two archive sets CA and DA for storage, wherein CA is an archive facing convergence, DA is an archive facing diversity, and the capacities of the archive sets CA and DA are set artificially so as to effectively balance convergence and diversity of the population;
population F of each generation n Average division into two archive sets CA n And DA n Population F n-1 And F n First all adding CA n Introducing quality index I in the process of updating archive set CA ε+ As an updating principle, the capacity requirement of the archive set is met by continuously deleting the individuals that are least capable of dominating other individuals; i is ε+ Is to describe a certain body X in the target space of population evolution 1 Dominating another individual X 2 The minimum distance required is indicated by equation (5):
I ε+ (X 1 ,X 2 )＝min ε (f i (X 1 )-f i (X 2 )≥ε) (5)
wherein i is more than or equal to 1 and less than or equal to M, i belongs to N, M is the number of optimization targets, and N represents a natural number; ε is a certain volume X in the target space 1 Dominating another individual X 2 The minimum distance required and satisfies 0 ≦ epsilon<1；
When the individual X 1 Removed, the loss measure of population fitness is shown in equation (6):
when the individual X * Is removed, then CA n The individual fitness value in (2) is updated as shown in equation (7):
in updating archive set CA n In all process (2), all are from CA n In which removal of I ε+ Individuals with minimal loss, and updating CA n I of the remaining individuals ε+ A value; finally obtaining CA with specified number of individuals n ；
Updating the archive set DA based on pareto optimality, and continuously adding individuals with the lowest similarity to the individuals in the current archive set DA one by one to meet the capacity limit of the archive set DA; on-update archive set DA n In the process of (2), first from the population F n-1 And F n Selecting boundary individuals to join, wherein the boundary individuals are individuals with the maximum or minimum single target value; then, an iteration process is carried out, and in each iteration, the individuals with the largest difference from the current DA are added into the archive set DA n Performing the following steps; when measuring the similarity between individuals, the distance based on Lp norm embodies the similarity between individuals, 0<p<1, the greater the distance between individuals, the lower the similarity between individuals, and the more will be preferentially added to DA n (ii) a Setting p to p =1/M according to the number M of optimization objective functions, as shown in equation (8):
in the case of the initial population F 0 In case of division, archive set CA 0 From only the initial population F 0 And the remaining individuals are taken as an archive set DA 0 When the population generation number n is not 0, according to the fitness function value and the similarity measurement between individuals, the population F of each generation is divided into two groups n Equal division into CA n And DA n ；
(5) Gene selection, crossover and variation
Probability of chromosome crossing p c With a cross probability p c Randomly selecting individuals needing to be crossed from the file sets CA and DA, randomly distributing the randomly selected individuals in pairs, randomly determining gene point positions where the crossing occurs, and exchanging genes of the point positions on the paired individuals to obtain a crossed population;
(6) Judging whether a termination condition is met;
aiming at the population subjected to crossing and variation in the step (5), if the evolution algebra is less than g max Returning to the step (4), and adding 1 to the evolution algebra; if evolution algebra is equal to g max Entering the step (7);
(7) Selecting a final decision variable and generating a demand realization priority ordering list;
calculating the total expected realization function value of each individual in the last generation of population, and realizing the function value f according to the total expected realization function value s (X) sorting the numerical values from large to small, selecting the first 10 individuals of which the function value sorting is expected to be realized overall as an individual set to be selected, screening and analyzing by adopting a variance method, and calculating the average value of the n interest-related party requirement realization degrees of the individuals in the individual set to be selected, as shown in a formula (9):
calculating the variance of the function value expected to be realized by the interest-related party of the selected individual, as shown in the formula (10):
defining an individual sorting operator S (X), as shown in equation (11):
the larger the sorting operator S (X) is, the higher the overall expected implementation degree of the demand is and the higher the consideration degree of each interest-related party is;
calculating the sequencing operator value of each individual in the to-be-selected individual set, and selecting the decision variable X corresponding to the individual with the maximum sequencing operator value end As final decision variables; comparing the one-to-one correspondence between the demand and the gene point location, and determining the variable X end Decoding the requirement corresponding to the point position with the gene code of 1 into a requirement which is realized preferentially, and decoding the requirement corresponding to the point position with the gene code of 0 into a requirement which is not realized preferentially;
calculating the sum of the expected implementation degrees corresponding to each requirement, as shown in formula (12):
calculating the sum of the expected implementation degrees of each demand according to a formula (12), firstly arranging the demands which are realized preferentially from large to small according to the numerical value of the sum of the expected implementation degrees, then arranging the demands which are not realized preferentially from large to small according to the numerical value of the sum of the expected implementation degrees, arranging all the demands which are realized preferentially before the demands which are not realized preferentially, and finally obtaining the ordering result of the priority for realizing the demands.
2. The civil aircraft development demand sequencing method based on the multi-objective optimization algorithm as claimed in claim 1, wherein:
the stakeholder s j Desired implementation function of
As shown in equation (1):
the cost function to achieve the demand is shown in equation (2):
defining a total expected implementation function f s (X) is shown in formula (3):
wherein alpha is j The weight representing the jth stakeholder may be obtained by an analytic hierarchy process.
3. The civil aircraft development demand sequencing method based on the multi-objective optimization algorithm as claimed in claim 1, wherein:
in the step (3), the stakeholder s j Desired implementation function of
And overall expected implementation function f s The formula of (X) is as follows):
4. the civil aircraft development demand sequencing method based on the multi-objective optimization algorithm as claimed in claim 1, wherein:
in the gene selection, crossover and mutation of step (5), chromosomeThe probability of variation is p m For the crossed population, the mutation probability p m Randomly selecting individuals from the individuals, carrying out mutation operation on the single individuals, randomly determining the point position where the mutation occurs, changing the gene on the point position into 0 or 1, if the original gene point position is 1, changing the gene into 0, and vice versa, and obtaining a new population; where cross-behavior occurs between CA and DA, while mutation occurs only within CA.
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