CN115688605B - Civil aircraft development demand ordering method based on multi-objective optimization algorithm - Google Patents
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Abstract
The invention provides a civil machine development demand ordering method based on a multi-objective optimization algorithm, which comprises the steps of establishing a civil machine development demand implementation priority ordering mathematical model, constructing an adaptability function, calculating individual fitness, dividing offspring populations, selecting a final decision variable and generating a demand implementation priority ordering list after gene selection, crossover and mutation, and finally obtaining an ordering result of the demand implementation priority. According to the method, the implementation priorities of the development demands of the civil aircraft related to a plurality of stakeholders are ordered under the constraint of limited cost resources by a quantification method, the expected implementation degree of the plurality of stakeholders related to the civil aircraft design on different demands can be comprehensively considered in the civil aircraft development process under the limited cost resources, and the demands of all stakeholders are fully considered and met as much as possible to realize the demands on the basis of ensuring the overall expected implementation maximum of the demands.
Description
Technical Field
The invention relates to the field of civil aircraft development demand and development, in particular to a civil aircraft development demand ordering method.
Background
The development of civil aircraft in the new era is towards the trend of complicating and highly integrating, and the variety and the quantity of the development requirements of the civil aircraft are greatly increased. In the actual development process of civil aircraft, the development of requirements faces a plurality of problems, and a plurality of problems and challenges exist, and the problems and challenges mainly appear in the following two aspects:
on one hand, the civil aircraft development relates to a plurality of stakeholders, relates to multiple departments, multiple industries, upstream and downstream suppliers of the requirements and the like, and all stakeholders want to maximally meet the requirements from the self point of view, and in the description of the requirements from different stakeholders, the phenomena of conflict and even mutual contradiction often occur. On the other hand, due to limitations of civil aircraft development period, development cost, personnel investment and other conditions, the demand engineers are urgently required to be assisted to conduct optimization on demands under the limited cost constraint condition by an effective method under the existing conditions, and feasible demand subsets and demand realization priority ordering are generated.
In the traditional method, a demand engineer sets the priority of demands, stakeholders of civil aircraft development and development demands are not directly related well, a quantifiable calculation ordering method is not formed, and the method is difficult to play an effective role in ordering of large-scale development demands. The exploration practice of the existing demand ordering method is developed in the field of software engineering, but most of the demand ordering method aims at single-objective optimization problems, and is difficult to migrate and use for solving the existing problems, and the solving result has insufficient degree of compromise to all parties for civil aircraft development and the like.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a civil aircraft development demand ordering method based on a multi-objective optimization algorithm.
The technical scheme adopted by the invention for solving the technical problems comprises the following steps:
(1) Establishing a mathematical model for realizing priority ordering according to civil aircraft development requirements;
the stakeholder set is S and satisfies s= { S 1 ,s 2 ,…,s n (s is therein 1 ,s 2 ,…,s n Sequentially representing n stakeholders related to the development requirements of the civil aircraft; let the demand set be R and satisfy r= { R 1 ,r 2 ,…,r m -where r 1 ,r 2 ,…,r m Sequentially representing m requirements participating in realizing priority ordering; let the demand realization cost set be c= { C 1 ,c 2 ,…,c m }, wherein c i The corresponding representation of the implementation requirement r i The cost required; definition v (r) i ,s j ) For stakeholder s j For the requirement r i Is 0.ltoreq.v (r) i ,s j ) V (r) is less than or equal to 5 i ,s j ) The smaller the value of E N, the smaller the value of E N represents the stakeholder s j For the requirement r i The smaller the desired degree of realisation, the larger the opposite; define a demand decision variable x={x 1 ,x 2 ,…,x m X, where x i ∈{0,1}，x i When=1, the priority realization requirement r is expressed i ，x i When=0, it means that the demand r is not realized preferentially i ；
(2) Initializing a population:
maximum evolution algebra g max The population scale is N, and N individuals in the initial population all contain a chromosome, and m genes are arranged on one chromosome and are in one-to-one correspondence with the m requirements in the step (1); any gene code on the chromosome is an integer 0 or 1 which is generated randomly initially, wherein 0 indicates that the requirement corresponding to the gene is not selected preferentially, and 1 indicates that the requirement corresponding to the gene is selected preferentially, so that an initial population is generated;
(3) Constructing a fitness function:
taking the stakeholder s in the step (1) j Is a desired implementation function of (2)And overall desired implementation function f s (X) as a fitness function;
(4) Calculating individual fitness and dividing offspring populations:
calculating individual fitness function values according to the fitness function constructed in the step (3), and setting two archiving sets CA and DA for storage, wherein CA is a convergence-oriented archiving, DA is a diversity-oriented archiving, and the capacities of the archiving sets CA and DA are manually set so as to effectively balance the convergence and diversity of the population;
each generation of population F n Average division into two archive sets CA n And DA (DA) n Population F n-1 And F n First adding CA completely n Introducing quality index I in updating archive set CA ε+ As an updating principle, meeting the capacity requirement of the archive set by continuously deleting the individuals which are least capable of controlling other individuals; i ε+ Is a description of a certain body X in a target space of population evolution 1 Dominating another individual X 2 An index of the minimum distance required is shown in formula (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 is E N, M is the number of optimization targets, and N represents a natural number; epsilon is some volume X in the target space 1 Dominating another individual X 2 The minimum distance required is 0.ltoreq.ε<1；
When subject X 1 The loss metric of population overall fitness, removed, is shown in equation (6):
when subject X * Is removed, CA n The individual fitness value of (c) is updated as shown in equation (7):
updating archive set CA n In the process of (1), all from CA n Removing I from ε+ Individuals with minimal loss and update CA n I of the remaining individuals ε+ A value; finally, CA with a specified number of individuals is obtained n ；
Updating the archiving set DA is based on pareto optimality, and the capacity limit of the archiving set DA is met by continuously adding individuals with the lowest similarity with individuals in the current archiving set DA one by one; updating archive set DA n In the process of (1), first from population F n-1 And F n Selecting boundary individuals for adding, wherein the boundary individuals are individuals with the maximum or minimum single target value; then enter an iterative process, taking care in each iteration to add the individual most different from the current DA to the archive set DA n In (a) and (b); in measuring similarity between individuals, the similarity is determined based on Lp norms (0<p<1) The distance between individuals represents the similarity, and the larger the distance between individuals is, the lower the similarity between individuals is, and DA is added preferentially n The method comprises the steps of carrying out a first treatment on the surface of the According to the number M of the optimized objective functionsp is set to p=1/M as shown in equation (8):
in the initial population F 0 Archiving set CA when partitioning 0 From the initial population F only 0 Selecting and taking the rest individuals as an archiving set DA 0 When the population algebra n is not 0, each generation of population F is obtained according to the fitness function value and the similarity measure between individuals n Equally divided into CA n And DA (DA) n ；
(5) Gene selection, crossover and mutation
Chromosome crossover probability p c With cross probability p c Randomly selecting individuals needing to be crossed from the archiving sets CA and DA, randomly carrying out pairwise distribution on the randomly selected individuals, randomly determining gene points where the crossing occurs, and exchanging genes of the points on the pairwise paired individuals to obtain crossed populations;
(6) Judging whether a termination condition is met;
aiming at the population subjected to crossover and mutation 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 the algebra of evolution is equal to g max Step (7) is entered;
(7) Selecting a final decision variable and generating a demand realization priority ordering list;
calculating the overall expected realization function value of each individual in the final generation population, and realizing the function value f according to the overall expected realization function value s Sorting the values of (X) from large to small, selecting the first 10 individuals with overall expected function value sorting as a set of individuals to be selected, performing screening analysis by a variance method, and calculating the average value of the n stakeholder requirements realization degrees of the individuals in the set of individuals to be selected, wherein the average value is shown in a formula (9):
calculating the variance of the expected realization function value of the stakeholder of the selected individual as shown in a formula (10):
an individual ranking operator S (X) is defined as shown in formula (11):
the larger the ranking operator S (X), the higher the overall desired degree of realization of the demand under the decision variable X, and the higher the degree of compromise for each stakeholder.
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 largest sequencing operator value end As a final decision variable. Comparing the one-to-one correspondence between the demand and the gene point location, and determining the variable X end The demand corresponding to the point position with the gene code of 1 is decoded into the demand of preferential realization, and the demand corresponding to the point position with the gene code of 0 is decoded into the demand of non-preferential realization;
calculating the sum of the expected implementation degrees corresponding to each requirement, as shown in a formula (12):
the sum of the expected realization levels for each demand is calculated according to equation (12). Firstly, arranging the demands which are realized preferentially from big to small according to the numerical value of the sum of the expected realization degrees, then arranging the demands which are not realized preferentially from big to small according to the numerical value of the sum of the expected realization degrees, arranging the demands which are realized preferentially before the demands which are not realized preferentially, and finally obtaining the sequencing result of the demands to realize the priority.
The stakeholder s j Is a desired implementation function of (2)As shown in formula (1):
the cost function for achieving demand is shown in equation (2):
defining an overall desired implementation function f s (X) is as shown in formula (3):
wherein alpha is j The weights representing the jth stakeholder may be obtained by hierarchical analysis.
In the step (3), stakeholder s j Is a desired implementation function of (2)And overall desired implementation function f s The formula of (X) is as follows):
in the gene selection, crossover and mutation in the step (5), the chromosome mutation probability is p m For the crossed population, the mutation probability p is calculated m Randomly selecting individuals from the genes, performing mutation operation on the individual individuals, randomly determining the position of the mutation occurrence point, changing the gene on the position to 0 or 1, and changing the gene to 0 if the original gene position is 1, and vice versa, so as to obtain a new population; wherein cross-behavior occurs between CA and DA, whereas variation occurs only inside CA.
The method has the beneficial effects that the implementation priorities of the development demands of the civil aircraft related to a plurality of stakeholders are ordered under the constraint of limited cost resources by a quantification method. According to the invention, under the condition of limited cost resources, the expected implementation degree of a plurality of stakeholders related to civil aircraft design on different demands is comprehensively considered in the civil aircraft development process, the demands of all stakeholders are fully considered and met as far as possible to realize the demands on the basis of ensuring the overall expected implementation of the demands to be maximum, and the generated demand implementation priority ordering result can provide decision assistance for civil aircraft development demand engineers and provide references for subsequent work of civil aircraft demand development.
Drawings
FIG. 1 is a flow chart of the two_Arch2 algorithm of the present invention
FIG. 2 is a schematic representation of chromosome crossover and mutation according to the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
(1) Establishing a mathematical model for realizing priority ordering of civil engineering development requirements
The existing demand items total 58, then interested party s j Is as followsAs shown in equation (13):
the cost function (constraint) to achieve demand is shown in equation (14):
overall desired implementation function f s (X) is as shown in formula (15):
setting up a total of 6 stakeholders, such as suppliers, investors, governments (supervisors), enterprises (main manufacturers), clients and operation guarantees, as background objects for example implementation, the number of stakeholders in the simulation experiment is n=6. When updating the diversity-oriented archive set DA, m=6+1=7 is taken when calculating the individual distances using the Lp norm.
Overall desired implementation function f s Weight α= (0.038,0.219,0.128,0.389,0.161,0.065) in (X), obtained by analytic hierarchy process;
setting the demand realization cost threshold value to be 70% of the total demand realization cost, and then
The requirements for the examples are shown in Table 1.
Table 1 demand sample table
(2) Initializing a population
Taking the population scale N=200, and the maximum algebra g max =500, then in the populationA total of 200 individuals were included, each of which contained one chromosome with 58 genes 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 fitness functions
Taking the stakeholder s in the step (1) j Is a desired implementation function of (2)And overall desired implementation function f s (X) as a fitness function, as shown in equation (16):
(4) Calculating individual fitness and dividing offspring population
At the time of DA update, p is set to p=1/m=1/7 as shown in formula (17).
Wherein,,representing decision variable X i Is the value of the first gene locus.
(5) Gene selection, crossover and mutation
Setting chromosome crossover probability p c =0.8, cross probability p for selected populations c The method comprises the steps of (1) randomly selecting individuals needing crossing from a selected population, randomly distributing the individuals in pairs, randomly determining gene points where the crossing occurs, and exchanging genes at the gene points on the paired individuals to obtain a crossed population; let the chromosome variation probability be p m =0.01, with variation probability p for crossing population m =0.01 randomly selecting individuals, performing mutation operation on individual individuals, randomly determining the mutation occurrence point, and changing the gene at the point into0 or 1 (0 if the origin is 1 and vice versa) to obtain a new population. Wherein cross-behavior occurs between CA and DA, whereas variation occurs only inside CA.
(6) Judging whether or not the termination condition is satisfied
Setting g max =500, returning to step (4) and the algebra of evolution +1 if the algebra of evolution is less than 500 for the new population crossed and mutated in step (5); if the algebra of evolution is equal to 500, go to step (7).
Through calculation, the decision variable X is obtained end Lower variance s 2 (X end )＝5.3769×10 -4 Sorting operator S (X end ) = 1180.7292. The demand desired achievement level for each stakeholder is 0.8125, 0.8051, 0.8017, 0.8182, 0.7525, 0.7742, respectively, and the overall demand achievement level is 0.7996. Final calculation of the generated decision variable X end The codes at the corresponding positions of the vectors are shown in table 2 for a single row of 1×58 vectors.
Table 2 calculation of the resulting decision variable X end Sum v of corresponding expected realization degrees 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, the requirement is preferably fulfilled, and when the number is 0, the requirement is not preferably fulfilled; v sum (r i ) The numerical value of the term represents the sum of the desired degrees of realization corresponding to the demand.
Firstly, arranging the demands which are realized preferentially from big to small according to the numerical value of the sum of the expected realization degrees, and then arranging the demands which are not realized preferentially from big to small according to the numerical value of the sum of the expected realization degrees to obtain a sequencing result of the demand realization priorities, wherein the sequencing result is shown in a table 3.
TABLE 3 Requirements implement prioritization results
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As can be seen from the sorting results in Table 3, the method can effectively bring the realization expectations of stakeholders on demands into the civil aircraft development process, can comprehensively consider the demands of different stakeholders, sorts the civil aircraft development demand realization priorities 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 priorities, clearly shows the realization priorities of a large number of demand items under the constraints for demand engineers, can simultaneously consider a plurality of stakeholders, provides references for the work of the demand engineers in the demand analysis stage of civil aircraft development, and ensures that the civil aircraft development flow based on demand driving can be better implemented and developed.
The method and the system can effectively bring the realization expectations of stakeholders on the demands into the civil aircraft development process, comprehensively consider the demands of different stakeholders, sort the civil aircraft development demand realization priorities under the constraints of cost, resources and the like through the multi-objective optimization method, avoid the influence of excessive subjective factors caused by manually determining the demand priorities, clearly show the realization priorities of a large number of demand entries under the constraints for demand engineers, simultaneously consider a plurality of stakeholders, provide reference for the demand engineers to work in a demand analysis stage of civil aircraft development, and ensure that the civil aircraft development flow based on demand driving at present can be better implemented and developed.
Claims (4)
1. A civil aircraft development demand ordering method based on a multi-objective optimization algorithm is characterized by comprising the following steps:
(1) Establishing a mathematical model for realizing priority ordering according to civil aircraft development requirements;
the stakeholder set is S and satisfies s= { S 1 ,s 2 ,…,s n (s is therein 1 ,s 2 ,…,s n Sequentially representing n stakeholders related to the development requirements of the civil aircraft; let the demand set be R and satisfy r= { R 1 ,r 2 ,…,r m -where r 1 ,r 2 ,…,r m Sequentially representing m requirements participating in realizing priority ordering; let the demand realization cost set be c= { C 1 ,c 2 ,…,c m }, wherein c i The corresponding representation of the implementation requirement r i The cost required; definition v (r) i ,s j ) For stakeholder s j For the requirement r i Is 0.ltoreq.v (r) i ,s j ) V (r) is less than or equal to 5 i ,s j ) The smaller the value of E N, the smaller the value of E N represents the stakeholder s j For the requirement r i The smaller the desired degree of realisation, the larger the opposite; define the demand decision variable x= { X 1 ,x 2 ,…,x m X, where x i ∈{0,1}，x i When=1, the priority realization requirement r is expressed i ，x i When=0, it means that the demand r is not realized preferentially i ；
(2) Initializing a population:
maximum evolution algebra g max The population scale is N, and N individuals in the initial population all contain a chromosome, and m genes are arranged on one chromosome and are in one-to-one correspondence with the m requirements in the step (1); any gene code on the chromosome is an integer 0 or 1 which is generated randomly initially, wherein 0 indicates that the requirement corresponding to the gene is not selected preferentially, and 1 indicates that the requirement corresponding to the gene is selected preferentially, so that an initial population is generated;
(3) Constructing a fitness function:
taking the stakeholder s in the step (1) j Is a desired implementation function of (2)And overall desired implementation function f s (X) asA fitness function;
(4) Calculating individual fitness and dividing offspring populations:
calculating individual fitness function values according to the fitness function constructed in the step (3), and setting two archiving sets CA and DA for storage, wherein CA is a convergence-oriented archiving, DA is a diversity-oriented archiving, and the capacities of the archiving sets CA and DA are manually set so as to effectively balance the convergence and diversity of the population;
each generation of population F n Average division into two archive sets CA n And DA (DA) n Population F n-1 And F n First adding CA completely n Introducing quality index I in updating archive set CA ε+ As an updating principle, meeting the capacity requirement of the archive set by continuously deleting the individuals which are least capable of controlling other individuals; i ε+ Is a description of a certain body X in a target space of population evolution 1 Dominating another individual X 2 An index of the minimum distance required is shown in formula (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 is E N, M is the number of optimization targets, and N represents a natural number; epsilon is some volume X in the target space 1 Dominating another individual X 2 The minimum distance required is 0.ltoreq.ε<1；
When subject X 1 The loss metric of population overall fitness, removed, is shown in equation (6):
when subject X * Is removed, CA n The individual fitness value of (c) is updated as shown in equation (7):
updating archive set CA n In the process of (1), all from CA n Removing I from ε+ Individuals with minimal loss and update CA n I of the remaining individuals ε+ A value; finally, CA with a specified number of individuals is obtained n ；
Updating the archiving set DA is based on pareto optimality, and the capacity limit of the archiving set DA is met by continuously adding individuals with the lowest similarity with individuals in the current archiving set DA one by one; updating archive set DA n In the process of (1), first from population F n-1 And F n Selecting boundary individuals for adding, wherein the boundary individuals are individuals with the maximum or minimum single target value; then enter an iterative process, taking care in each iteration to add the individual most different from the current DA to the archive set DA n In (a) and (b); in measuring similarity between individuals, the distance based on Lp norm represents similarity between individuals, 0<p<1, the larger the inter-individual distance, the lower the inter-individual similarity, the more the DA is added preferentially n The method comprises the steps of carrying out a first treatment on the surface of the Setting p to p=1/M according to the number M of optimization objective functions, as shown in formula (8):
in the initial population F 0 Archiving set CA when partitioning 0 From the initial population F only 0 Selecting and taking the rest individuals as an archiving set DA 0 When the population algebra n is not 0, each generation of population F is obtained according to the fitness function value and the similarity measure between individuals n Equally divided into CA n And DA (DA) n ；
(5) Gene selection, crossover and mutation
Chromosome crossover probability p c With cross probability p c Randomly selecting individuals needing to be crossed from the archiving sets CA and DA, randomly carrying out pairwise distribution on the randomly selected individuals, randomly determining gene points where the crossing occurs, and exchanging genes of the points on the pairwise paired individuals to obtain crossed populations;
(6) Judging whether a termination condition is met;
aiming at the population subjected to crossover and mutation 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 the algebra of evolution is equal to g max Step (7) is entered;
(7) Selecting a final decision variable and generating a demand realization priority ordering list;
calculating the overall expected realization function value of each individual in the final generation population, and realizing the function value f according to the overall expected realization function value s Sorting the values of (X) from large to small, selecting the first 10 individuals with overall expected function value sorting as a set of individuals to be selected, performing screening analysis by a variance method, and calculating the average value of the n stakeholder requirements realization degrees of the individuals in the set of individuals to be selected, wherein the average value is shown in a formula (9):
calculating the variance of the expected realization function value of the stakeholder of the selected individual as shown in a formula (10):
an individual ranking operator S (X) is defined as shown in formula (11):
when the sequencing operator S (X) is larger, the overall expected realization degree of the demand is higher under the decision variable X, and the degree of consideration of all stakeholders is higher;
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 largest sequencing operator value end As a final decision variable; for a pair ofAccording to the one-to-one correspondence between the demand and the gene point, the decision variable X end The demand corresponding to the point position with the gene code of 1 is decoded into the demand of preferential realization, and the demand corresponding to the point position with the gene code of 0 is decoded into the demand of non-preferential realization;
calculating the sum of the expected implementation degrees corresponding to each requirement, as shown in a formula (12):
calculating the expected implementation degree sum of each demand according to a formula (12), firstly arranging the demands which are realized preferentially according to the value of the expected implementation degree sum from large to small, then arranging the demands which are not realized preferentially according to the value of the expected implementation degree sum from large to small, arranging the demands which are realized preferentially all before the demands which are not realized preferentially, and finally obtaining the sequencing result of the demand implementation priority.
2. The civil aircraft development demand ordering method based on the multi-objective optimization algorithm according to claim 1, wherein the method comprises the following steps:
the stakeholder s j Is a desired implementation function of (2)As shown in formula (1):
the cost function for achieving demand is shown in equation (2):
defining an overall desired implementation function f s (X) is as shown in formula (3):
wherein alpha is j The weights representing the jth stakeholder may be obtained by hierarchical analysis.
3. The civil aircraft development demand ordering method based on the multi-objective optimization algorithm according to claim 1, wherein the method comprises the following steps:
in the step (3), stakeholder s j Is a desired implementation function of (2)And overall desired implementation function f s The formula of (X) is as follows):
4. the civil aircraft development demand ordering method based on the multi-objective optimization algorithm according to claim 1, wherein the method comprises the following steps:
in the gene selection, crossover and mutation in the step (5), the chromosome mutation probability is p m For the crossed population, the mutation probability p is calculated m Randomly selecting individuals from the genes, performing mutation operation on the individual individuals, randomly determining the position of the mutation occurrence point, changing the gene on the position to 0 or 1, and changing the gene to 0 if the original gene position is 1, and vice versa, so as to obtain a new population; wherein cross-behavior occurs between CA and DA, whereas variation occurs only inside CA.
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