CN103383752A - Assembly scheduling method of aircraft - Google Patents

Abstract

An assembly scheduling method of an aircraft is used for scheduling multiple assembly processes. The assembly scheduling method of the aircraft comprises establishing a mathematical model according to the constraint conditions of assembly scheduling through a computer processor; encoding the sequence of the assembly processes according to a genetic algorithm to generate an initial population, wherein the initial population is composed of a plurality of individuals, and every individual contains information with the assembly process sequence different from that of other individuals; selecting the individuals containing information with specific assembly process sequences as parents according to a fitness function; crossing and gene-recombining the parent individuals to obtain new individuals containing the information with the specific assembly process sequences as offsprings; randomly selecting a certain individual for variation to generate a new individual containing the information with the specific assembly process sequence; decoding the individuals with adaptive values reaching a preset value to obtain an optimized assembly sequence; arranging the assembly processes of the aircraft according to the optimized assembly sequence. Therefore, the assembly scheduling problem of the aircraft, which is restrained by multiple resources, can be better solved.

Description

A kind of assembling schedule method of aircraft

Technical field

The invention belongs to the aircraft technology field, particularly, relate to a kind of assembling schedule method of aircraft.

Background technology

The aircraft product component is numerous, Design and manufacturing process is complicated, and product or parts often are comprised of thousands of parts.Due to the stationarity of aircraft product and the mobility of implementation process, its assembling is actually a unbalanced process.According to the arrangement of schedule, the kind of resource, the demand of consumption are usually altered a great deal in the unit interval, and the various resources that department or unit can provide within a certain period of time also have certain limit.In order to guarantee that activity in production can normally carry out and the cost-effective resource of utilizing continuously, just need to be optimized resource distribution, make up.

The aircraft assembling can be regarded the entry sorting optimization problem of resource constraint more than as, and there is certain limitation in traditional optimization method, and such as the increase along with movable number, the calculated amount of finding the solution optimum solution sharply increases.

For the project of this many resource constraints, use genetic algorithm and be optimized and find the solution to obtain best resource distribution and belong to brand-new research direction, be also desirable.Genetic algorithm is the randomization searching algorithm of simulation organic sphere natural selection and natural genetic mechanism, and wherein most important three operators are selection, crossover and mutation.Selection refers to select the operation of winning individuality, superseded worst individual from colony, purpose is an individuality of optimizing to be genetic directly to the next generation or to produce new individuality by cross match be genetic to the next generation again.Intersect to refer to the part-structure of two parent individualities is replaced and recombinate and generate new individual operation, can produce the new assortment of genes, desirable genes is combined in expectation.Variation is that the gene on some gene location of the individuality string in colony is done change.

Summary of the invention

The present invention is decomposed into the aircraft assembly problem under many resource constraints the problem of two single goals, is respectively the shortest and resources balance of installation time minimum.At chromosome coding and decode phase, assemble sequence is encoded to chromosome, and is decoded as feasible assembling sequence according to resource constraint.Crossover and mutation in genetic algorithm is the important step that is optimized and separates, yet, after being genetic to certain algebraically, the same individual that in individuality, adaptive value is high can increase gradually, therefore is necessary the crossover and mutation process in genetic algorithm is carried out certain control to keep population diversity.The present invention improves traditional genetic algorithm, so that the better handy aircraft assembling schedule problem that solves under many resource constraints.

Particularly, the invention discloses a kind of assembling schedule method of aircraft, be used for a plurality of assembling activity are dispatched, described assembling schedule method comprises: computer processor is set up mathematical model according to the constraint condition of assembling schedule; To the assembling activity sequential encoding and produce initial population, described initial population is comprised of a plurality of individualities according to genetic algorithm, and each individuality comprises the information that is different from other individual assembling activity orders; Select to comprise the individuality of specific assembling activity information sequentially as parent according to fitness function; To intersect as the individuality of parent and genetic recombination to obtain comprising the new individuality of specific assembling activity information sequentially as filial generation; Random certain individuality of selecting makes a variation to produce the new individuality that comprises specific assembling activity information sequentially; The individuality that adaptive value is reached predetermined value decodes to obtain optimum assemble sequence; And the assembling activity that arranges aircraft with the assemble sequence of optimum.

Particularly, described constraint condition comprises priority constraint, personnel's constraint and space constraint at least, described priority constraint refers to that all forward direction work are completed and could begin a rear job, described personnel's constraint refers to that the work post of working can not be greater than staff's ability to work, simultaneously, described space constraint refers to that the staff of a work space can not exceed its space constraint.

More specifically, described fitness function I=1,2,3......n, wherein, n represents population scale, f _iRepresent the adaptive value of individual i, P _iRepresent the probability that individual i is selected.

Description of drawings

In order to explain the present invention, its illustrative embodiments will be described with reference to the drawings hereinafter, in accompanying drawing:

Fig. 1 is two parents and the selecteed point of crossing of random selection of the present invention, the order through the genetic fragment of exchange after the point of crossing in protogene and two filial generations obtaining;

Fig. 2 is different genetic comparison between parent 1 and filial generation 1 in Fig. 1;

Fig. 3 is the parent 1 that calculates according to the gene location in Fig. 2 and the diversity factor between filial generation 1;

Fig. 4 is that the parent 1 of Fig. 1 and the first of parent 2 are intersected;

Fig. 5 is that the parent 1 of Fig. 1 and the second of parent 2 intersect;

Fig. 6 obtains filial generation 1 and filial generation 2 after Fig. 4 and Fig. 5 restructuring;

Fig. 7 is a random parent chromosome of selecting, and the gene position of the variation of selection is the position at " 5 " place, by variable 4 positions of gene " 5 ";

Fig. 8 encodes for aircraft concocting method according to the present invention, decoding, minimum manpower and minimum installation time;

Fig. 9 is the process flow diagram according to aircraft concocting method of the present invention.

Similar features in different figure is by similar Reference numeral indication.

Embodiment

In the detailed description of following embodiment, the accompanying drawing that reference consists of the part of this description describes.Accompanying drawing shows specific embodiment in the mode of example, and the present invention is implemented in these embodiments.Shown embodiment is not according to all of the embodiments of the present invention for limit.The embodiment that is appreciated that other can be utilized, and change structural or logicality can be made under the prerequisite that does not depart from the scope of the present invention.For accompanying drawing, the term of directivity, such as D score, " on " etc., with reference to the orientation of described accompanying drawing using.Because the assembly of embodiments of the present invention can be implemented with multiple orientation, these directional terminology are the purposes for explanation, rather than the purpose of restriction.Therefore, following embodiment is not the meaning as restriction, and scope of the present invention is limited by appending claims.

The invention discloses a kind of assembling schedule method of aircraft, it has used genetic algorithm, and this assembling schedule method roughly is divided into following step:

Step 1: problem modeling

The aircraft assembling is comprised of a series of continuous activities, can be represented by J.Activity 1 and n are dummy nodes, represent beginning and the end of project.Aprowl, d _iRepresent the duration, c _iRepresent the position, s _iRepresent required work post, p _iRepresent required number.In addition, m work post arranged, k space, assignable workman's number is H _s, spatial content is b _cMore specifically, described assignable workman's number refers to: the assignable workman's number of assembly line work post, described spatial content refers to: the maximum number of workers that assembly space can hold.

Following table one is listed all required parameters of modeling.

In practice, effectively assembly planning must satisfy a series of constraint, such as priority constraint, personnel's constraint and work space constraint.Priority constraint refers to that all forward direction work are completed and could begin a rear job, can easily show by network node figure.Personnel's constraint refers to that the work post of working can not be greater than the actual manpower of this work post, and in addition, the staff that the work space constraint refers to a work space can not exceed its space constraint.Wherein, personnel's constraint and work space constraint can be called as resource constraint together.

Table 1: parametric description

The mathematical model of problem can be expressed as:

Mina*startTime _n+b*(resource leveling) (1)

endTime _i-startTime _i＝d _i (2)

startTime _i≤endTime _j i∈{1，...，n}，j∈P _i (3)

s∈{1，…，m}，t∈startTime or t∈endTime，i∈{1，...，n} (4)

c∈{1，...，k}，t∈startTime or t∈endTime，i∈{1，...，n} (5)

In this problem, two targets are arranged: the shortest duration and minimum resources balance.Wherein, the implication of " equilibrium " is a kind of number differentiation embodiment by the duration weighting of activity.Particularly, it obtains by following formula:

mean＝(∑p _i*(endTime _i-startTime _i))/MaxEndTime

Balanced=(∑ | p _i-mean|* (endTime _i-startTime _i))/MaxEndTime

p _i: the number that the i item is movable used

Mean: the mean value of the number of users that all are movable

EndTime _i: the concluding time of i item activity

StartTime _i: the start time of i item activity

MaxEndTime: maximum concluding time, i.e. all movable duration.

In the expression formula of aforesaid mathematical model (1): a and b are for time and resources balance are converted to the coefficient of the variable that can calculate under same unit.Whole expression formula can be illustrated in the integrated value minimum of duration and resources balance two aspects.Coefficient a can be made as 0, like this, just become the problem of least resource equilibrium, in like manner, also coefficient b can be made as 0, like this, just become the problem of the shortest duration.

What above-mentioned expression formula (2) represented is: the start time that the concluding time of movable i deducts movable i equals its duration.

Above-mentioned expression formula (3) expression be: the start time of movable i early than or equal concluding time of movable i.

In above-mentioned expression formula (4), active _{I, t}Two states is arranged, be respectively ongoing state, that is, its value is " 1 ", and non-ongoing state, that is, its value is " 0 "; Work as s _iWhen determining, p _iThe number of the specific work post s that expression activity i is required; Therefore, expression formula (4) expression is: workman's number of each work post that is assigned with in arbitrary time period in the assembly platoon program process all can not surpass the maximum number that each work post can be distributed.Need to prove, undertaken by same work post because may have several assembly processes in arbitrary time period, can not surpass so need under these circumstances to satisfy the required work post number of these assembly processes the maximum number that this type of work post can be distributed.

In like manner, above-mentioned expression formula (5) expression is: workman's number of the assembly space that is assigned with in the random time section in the assembly platoon program process can not surpass the maximum galleryful of this assembly space.In like manner, undertaken by same assembly space because may have several assembly processes in arbitrary time period, can not surpass so need under these circumstances to satisfy these assembly process requisite spaces the maximum galleryful that this space-like can be distributed.

Therefore, according to foregoing description, at this, be two independent project planning problems with PROBLEM DECOMPOSITION, be described below:

When target is minimum length in time, mathematical model can for:

Min(startTime _n)(b＝0)

endTime _i-startTime _i＝d _i

startTime _i≤endTime _j i∈{1，...，n}，j∈P _i

s∈{1，...，m}，i∈{1，...，n}

c∈{1，...，k}，i∈{1，...，n}

When target is minimum resources balance, mathematical model can for:

Min resource leveling(a＝0)

endTime _i-startTime _i＝d _i

startTime _i≤endTime _j i∈{1，...，n}，j∈P _i

s∈{1，...，m}，i∈{1，...，n}

c∈{1，...，k}，i∈{1，...，4}

Step 2: coding

By assemble sequence is encoded, produce initial population.A chromosome is exactly a character string with priority relationship, represents assemble sequence, and it is comprised of all activities of assembly project, and each gene in chromosome represents an activity.

The deciding means of gene order is:

1) Resources allocation and obtain each movable start time, the start time of dummy activity is set to 0;

2) according to the assembling series arrangement activity with priority relationship;

3) under the prerequisite of not violating constraint, give the feasible earliest start time of each activity schedule;

Illustrate coding method by following example, problem description is as shown in the table:

Table 2: problem description

In table 2, the A0 coding refers to the serial number of assembling activity, preposition A0 refers to the serial number of the assembling activity that is preferable over this assembling activity, for example, A0 be encoded to 2 preposition A0 be 1 entry represent be: serial number is that 2 assembling activity must just can be carried out after serial number is 1 assembling activity; A0 be encoded to 5 preposition A0 be the entry of 2_3 represent be: serial number is that 5 assembling activity must just can be carried out after serial number is two assembling activity of 2 and 3, but sequentially makes stipulations in the front and back that are not two assembling activity of 2 and 3 to serial number; What A0 was encoded to that 8 entry represents is: serial number is that 8 assembling activity must just can be carried out after serial number is two assembling activity of 6 and 7, required specific work post is (at this, suppose that work post only has a kind of, so just work post is not classified) workman's number be 4 people, the workman of the specific work post that assembly line can provide is 4 people, workman's number that the space of the aircraft particular segment (as fuselage, head or tail) of assembling can hold is 8 people, and the duration of assembling is 20 days.

Step 3: select

Determine the individual choice probability according to chromosomal adaptive value, each individual selecteed probability is directly proportional to the size of its adaptive value.If population scale is n, the adaptive value of individual i is f _i, the selected probability P of individual i _iFor

$P_i=\frac{\mathrm{fi}}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{fi}},$ i＝1，2，3......n

Step 4: intersect

(1) select the point of crossing

Carry out the selection of point of crossing by calculating parent with the diversity factor (OD) of intersecting in certain point of crossing between the filial generation of gained.The diversity factor of filial generation and parent is larger, and the selecteed probability in this point of crossing is larger; Otherwise if the diversity factor of filial generation and parent is less, the selecteed probability in point of crossing is just less.

As Figure 1-3, Fig. 1 schematically shows two parents of random selection and two filial generations that selecteed point of crossing obtains by the exchange point of crossing order of genetic fragment in protogene afterwards.Different genetic comparison between the offspring 1 who obtains after Fig. 2 schematically shows parent 1 and it intersects.Fig. 3 schematically shows the parent 1 that calculates according to the gene location in Fig. 2 and the diversity factor between filial generation 1, and its computing method are the absolute value sum that the order at each gene place in parent deducts its order in filial generation.

Calculate the filial generation of all effective point of crossing generations and the diversity factor of its parent, the point of crossing that is elected to be crossover algorithm of diversity factor maximum.

(2) referring to Fig. 4, calculating according to diversity factor, selecting the point of crossing is the 4th position, with the gene of the 1-4 position of parent 1 front four genes as filial generation 1, in parent 2 from last gene position obtain forward 5 with the equal not identical gene of described front four genes, these 5 genes are respectively the 4th, 5 and the locational gene of 7-9.

(3) referring to Fig. 5, with the gene of the 1-4 position of parent 2 front four genes as filial generation 2, in parent 1 from last gene position obtain forward 5 with the equal not identical gene of described front four genes, these 5 genes are respectively the 2nd, 5 and the locational gene of 7-9.

(4) reconstitution steps, referring to Fig. 6, obtain filial generation 1 after the 4th, 5 and the locational genetic recombination of 7-9 of the locational gene of 1-4 of parent 1 and parent 2, obtain filial generation 2 after the 2nd, 5 and the locational genetic recombination of 7-9 of the locational gene parent 1 of 1-4 of parent 2.

Step 5: variation

At first, calculate each gene position variable interval, the interval that can make a variation is larger, and the probability that is selected as change point is larger.

As shown in Figure 7, be wherein a random parent chromosome of selecting in (a) in Fig. 7, intending this moment selecting the gene position of variation is the position at " 5 " place.The preposition node of supposing " 5 " is " 1 ", and its rearmounted node is " 8 ".(b) from Fig. 7 can find out that gene position " 5 " variable position has 4, is respectively gene position " 3 ", " 2 ", " 7 ", the position at " 4 " place, therefore, the made a variation interval of gene position " 5 " is 4.Behind the made a variation interval of having calculated all variable gene position, then select change point with the roulette method in mutation process each time and make a variation.

Step 6: adaptive value is calculated

Calculate individual adaptive value, reaching satisfied result or adaptive value no longer increases, or when iterations reaches default algebraically, stops iteration, obtains optimum solution, otherwise repeating step three, step 4 and step 5.

Step 7: decoding

Chromosome is decoded as a feasible plan, and in this chromosome sequence, an activity has lower right of priority than its all forward direction activity, and all backward activities have higher right of priority than it.

Fig. 8 has represented to use genetic algorithm from being encoded to the process of decoding, and wherein, (a) in Fig. 8 represents the network planning figure of project, (b) representative (a) the desired feasible assemble sequence in Fig. 8.(c) in Fig. 8 and (d) be the project scheduling figure that is decoded and obtain by feasible assemble sequence.(c) in Fig. 8 schematically shows the planning chart when maximum number is 4, and because the workman can only be according to an assembled in sequence, this planning chart appears to linear.(d) in Fig. 8 schematically shows the planning chart when maximum number is 12, in this case, because the workman is enough, in the time of decoding, just only needs to consider the priority constraint of assemble sequence.(c) although in Fig. 8 and (d) be two extreme examples, can obtain identical rule: for planning chart, maximum number is a very important factor, if maximum number is enough large, the duration of project can be shorter, and correspondingly, resources balance is little.

The present invention is applied to the crossover and mutation process in genetic algorithm in the assembling schedule of aircraft, thereby solves the aircraft assembling schedule problem under many resource constraints, has optimized the assembling schedule flow process of aircraft.

Embodiment:

Given problem is as shown in table 3 below, and in table, information comprises preposition node, duration and the number of workers etc. of assemble sequence, activity

Table 3: problem description

In table 3, similar with table 2, the A0 numbering represents the entry number of assembling activity and the entry name that the A0 title represents assembling activity, preposition node is that the expression of null does not have the high assembling activity of right of priority than the assembling activity of this entry number representative, the entry number of the assembling activity that the digitized representation right of priority in preposition node is high.In addition, represent the needed time of assembling activity standard work force; Number represents the number that this assembling activity is required; Section's name section represents the title of the load segment of aircraft, and as representing plane nose with numeral 1,2 represent airframe, and 3 represent the aircraft tail; When the station title represents if a plurality of station is arranged, distinguish with the station title, if only have a station, can omit; The work post code represents the code of required work post, and as mechanical work post or electric work post, in upper table, 1 can represent mechanical work post; Work post can refer to operational number in this work post workshop with number; Section's section code is consistent with the section name section, has several sections just to have several section codes to represent; Section's section space refers to the maximum numbers that can hold in specific section section, for example, can hold 12 people at most in section's section code is 1 aircraft assembly interval, can hold 9 people at most in section's section code is 2 aircraft assembly interval.

In the present invention, the setting parameter of genetic algorithm is as shown in table 4.

Table 4: the setting parameter of genetic algorithm

Initial population

20

Crossover probability

0.6

The variation probability

0.45

In upper table 4, initial population, crossover probability and variation probability are the basic parameters in genetic algorithm, wherein, initial population refers to population scale, crossover probability refers to that being selected to right solution with this probability from initial population in the intersection process intersects to produce new solution, and the variation probability refers to that choosing single solution with this probability from initial population in mutation process carries out mutation operation to produce new solution.

When optimization aim is the duration, as calculated, obtain equilibrium, duration and the method resource utilization of corresponding constraint condition, as shown in table 5.

Table 5: target bit duration result

Succinct in order to narrate, only describe as an example of the sequence number 1 of table 5 example, its expression: in the assembly platoon program process, when peak-peak was defined as 10, the duration was 85, and equilibrium is 6.738547.Wherein, after aforesaid peak-peak refers to all assembly processes has been sorted, people's numerical value of upper work post number maximum of all time periods.

When optimization aim is resources balance, as calculated, obtain equilibrium, duration and the resource utilization of corresponding constraint condition, as shown in table 6.

Table 6: target is the resources balance result

Succinct in order to narrate, only describe as an example of the sequence number 1 of table 6 example, it is illustrated in the assembly platoon program process, and when peak-peak was defined as 10, the duration was 95, and equilibrium is 2.494626.Compared to take the duration as target the time (as shown in table 5 sequence number 1), the duration increases, and equilibrium reduces accordingly.

Above-mentioned two tables have been described the constraint of maximum number for the impact of duration and resources balance, can determine deflection for target according to actual conditions, thereby determine the maximum constrained number.Such as, when tending to assemble the duration the most in short-term, can select the maximum constrained number is 20, when tending to resources balance, can select maximum number to be constrained to 10, at this moment equilibrium can reach 2.494626.

The those skilled in the art of those the art can be by research instructions, disclosed content and accompanying drawing and appending claims, understanding and enforcement other changes to the embodiment of disclosure.In the claims, word " comprises " element and the step of not getting rid of other, and wording " one " is not got rid of plural number.In the practical application of invention, the function of a plurality of technical characterictics of quoting during a part possibility enforcement of rights requires.Any Reference numeral in claim should not be construed as the restriction to scope.

The present invention is limited to the illustrative embodiments that presents never in any form in instructions and accompanying drawing.Within all combinations of the embodiment that illustrates and describe (part) are interpreted as clearly and incorporate this instructions into and be interpreted as clearly and fall within the scope of the present invention.And in the scope of the present invention of summarizing as claims, a lot of distortion are possible.In addition, any reference marker in claims should be configured to limit the scope of the invention.

Claims (6)

1. the assembling schedule method of an aircraft, be used for a plurality of assembling activity are dispatched, and described assembling schedule method comprises:

Computer processor is set up mathematical model according to the constraint condition of assembling schedule;

To the assembling activity sequential encoding and produce initial population, described initial population is comprised of a plurality of individualities according to genetic algorithm, and each individuality comprises the information that is different from other individual assembling activity orders;

Select to comprise the individuality of specific assembling activity information sequentially as parent according to fitness function;

To intersect as the individuality of parent and genetic recombination to obtain comprising the new individuality of specific assembling activity information sequentially as filial generation;

Random certain individuality of selecting makes a variation to produce the new individuality that comprises specific assembling activity information sequentially;

The individuality that adaptive value is reached predetermined value decodes to obtain optimum assemble sequence; And

Arrange the assembling activity of aircraft with the assemble sequence of optimum.

2. assembling schedule method according to claim 1, wherein, described constraint condition comprises priority constraint, personnel's constraint and space constraint at least, described priority constraint refers to that all forward direction work are completed and could begin a rear job, described personnel's constraint refers to that the work post of working can not be greater than staff's ability to work, simultaneously, described space constraint refers to that the staff of a work space can not exceed its space constraint.

3. assembling schedule method according to claim 1, wherein, described mathematical model is set up by following condition:

Min a*startTime _n+b*(resource leveling) (1)

endTime _i-startTime _i＝d _i(2)

startTime _i≤endTime _j i∈{1，...，n}，j∈P _i (3)

s∈{1，...，m}，t∈startTime or t∈endTime，i∈(1，...，n} (4)

c∈{1，...，k}，t∈startTime ort∈endTime，i∈{1，...，n} (5)；

Wherein:

N: deputy activity quantity;

J={0,1,2 ..., n}: represent the activity of assembly project;

P _i={ p _i1... }, n=1 ... n-1: all forward direction active sets of deputy activity i;

G _i={ g _i1... }, n=1 ..., n-1: the backward active set of all of deputy activity i;

d _i: the duration of deputy activity i;

StartTime _i: the start time of deputy activity i;

EndTime _i: the concluding time of deputy activity i;

s _i: the work post that deputy activity i is required;

c _i: the locus of deputy activity i;

Active _{I, t}: the state that represents movable i of t time;

M: represent personnel's kind;

H _s, s=1 ..., m: the ability that represents workman s;

K: represent amount of space;

b _c, c=1 ..., k: the capacity that represents space c;

Wherein:

The a of expression formula (1) and b are for time and resources balance being converted to the coefficient of the variable that can calculate under same unit, expression formula (1) expression be: the integrated value aspect duration and resources balance two is minimum;

What expression formula (2) represented is: the start time that the concluding time of movable i deducts movable i equals its duration.

Expression formula (3) expression be: the start time of movable i early than or equal concluding time of movable i.

What expression formula (4) represented is: workman's number of each work post that is assigned with in arbitrary time period in the assembly platoon program process all can not surpass the maximum number that each work post can be distributed.

What expression formula (5) represented is: workman's number of the assembly space that is assigned with in the random time section in the assembly platoon program process can not surpass the maximum galleryful of this assembly space.

4. assembling schedule method according to claim 3, wherein, the mathematical model with assembling activity order of minimum length in time is:

Min(startTime _n)(b=0) (1)

endTime _i-startTime _i=d _i (2)

startTime _i≤endTime _j i∈{1，...，n}，j∈P _i (3)

s∈{1，...，m}，i∈{1，...，n} (4)

$\underset{c_i\∈c}{\mathrm{\Σ}}{p}_i*{\mathrm{active}}_{i,t}\≤b_s$

c∈{1，…，k}，j∈{1，…，n}

c∈{1，…，k}，t∈startTime or t∈endTime，i∈{1，...，n} (5)；

Wherein:

What expression formula (1) represented is: when b=0, the value of duration aspect is minimum.

5. assembling schedule method according to claim 3, wherein, the mathematical model with assembling activity order of minimum resources balance is:

Min b*resource leveling(a=0) (1)

cndTime _i-startTime _i=d _i (2)

startTime _i≤endTime _j i∈{1，...，n}，j∈P _i (3)

s∈{1，...，m}，i∈{1，...，n} (4)

c∈{1，...，k}，i∈{1，...，n} (5)；

Wherein:

Expression formula (1) expression be: when a=0, the value of resources balance aspect is minimum.

6. assembling schedule method according to claim 1, wherein, described fitness function

I=1,2,3......n, wherein, n represents population scale, f _iRepresent the adaptive value of individual i, P _iRepresent the probability that individual i is selected.

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