CN106203696A - A kind of hybrid precast sequence generating method based on symbol - Google Patents

Abstract

The invention discloses a kind of hybrid precast sequence generating method based on symbol, including first representing according to the connecting matrix of assembly and the ZBDD of interference matrix establishment connecting matrix and interference matrix；Further according to the interference matrix of assembly, solve precedence relation matrix；Search again for out all feasible assemblings, and create the sub-assemblies generated during file deposits feasible Assembly sequences and assembling, create Dynamic Array and deposit the number of path generating each sub-assemblies；The file afterwards generation being deposited feasible Assembly sequences and sub-assemblies is refined, and deletes the death situation state during assembling.The present invention can be under higher time and space efficiency, the completeness of Assembly sequences is ensured by analyzing all possible assembly manipulation, by judging that subassembly geometric feasibility ensures the reliability of Assembly sequences, ensured the high efficiency of algorithm by the satisfiability judging dominance relation, be finally completed the generation of all feasible Assembly sequences to assembly.

Description

A kind of hybrid precast sequence generating method based on symbol

Technical field

The present invention relates to assembly sequence-planning technical field, be specifically related to a kind of hybrid precast sequence based on symbol and generate Method.

Background technology

Assembly sequence-planning (Assembly Sequence Planning, ASP) is a technology difficulty in assemble planning Point, occupies critically important status in product design and development and production process.For the production of mass product, one outstanding Assembly sequences will greatly shorten the production cycle of product, reduces the producing cost of product, improves the capability and performance of product. ASP is a highly constrained NP combinatorial optimization problem, the geometrical-restriction relation between the selection part to be followed of Assembly sequences, Exhaustive search algorithm complex is exponential.When product is complex, number of components is more, easily occur that combinations of states blast is asked Topic.Visible, combinatorial complexity is restriction assembly sequence-planning efficiency and a key factor of automatization level.

Slowing down or avoiding a kind of possible strategy of combinatorial complexity problem on partial extent is symbolization or implicit expression Description technique.Ordered Binary Decision Diagrams (Ordered Binary Decision Diagram, OBDD) and extension form thereof are permissible Realize state space or the implicit representation of variable combination and search, be one of the most maximally efficient symbol technology.Closely Nian Lai, OBDD and extension form (such as ADD and ZBDD) thereof have had some to apply in terms of assembly sequence-planning.Experiment knot Really show, utilize OBDD or its extension form representing than using AND/OR figure expression to take less storage as Assembly sequences Space.

During limit algorithm generates all Assembly sequences, often generate some sons that cannot carry out again later assembling Assembly, the most infeasible sub-assemblies.If stoping the generation of this kind of sub-assemblies the most in advance, then follow-up will be likely to occur More infeasible sub-assemblies, cause search to occur various death situation state (nonfinal state, but do not have successor states) after terminating.Institute To be also performed to backtracking, delete all death situation states, and when infeasible sub-assemblies number is more, during last handling dead state More complicated, the solution efficiency of assembly sequence-planning problem can be reduced and solve scale.Guide if added in limit algorithm Information generates infeasible sub-assemblies during evading assembly sequences generation, by ensure solve quality on the premise of, effectively Ground improves the efficiency of search, and improves the quality of the feasible Assembly sequences of gained.

Summary of the invention

The present invention provides a kind of hybrid precast sequence generating method based on symbol, and it combines heuristic strategies, it is possible to big The earth improves the efficiency of assembly sequence-planning, expands the scale of assembly sequence-planning.

For solving the problems referred to above, the present invention is achieved by the following technical solutions:

A kind of hybrid precast sequence generating method based on symbol, comprises the following steps that

Step A. obtains assembly knowledge, generates connecting matrix and the interference matrix of assembly；

Step B. represents according to the connecting matrix of assembly, the ZBDD creating connecting matrix；

Step C. represents according to the interference matrix of assembly, the ZBDD creating interference matrix；

Step D., according to the interference matrix of assembly, solves precedence relation matrix；

Step E. represents according to the ZBDD of assembly connecting matrix, the ZBDD of interference matrix represents and dominance relation square Battle array, symbolization ZBDD and layering thought search out all feasible assemblings, get final product row Assembly sequences；Meanwhile, to searching out The sub-assemblies generated during feasible assembling and assembly sequence-planning stores, and preserves each sub-assemblies of generation Number of path；

The death situation state during assembling is searched for and deleted to step F., according to the feasible assembling preserved and sub-assemblies,.

Specifically comprising the following steps that of described step B

Step B1. utilizes variable to encode each part of assembly；

Step B2., according to the connecting matrix of assembly, creates the composite set of assembly connecting relation；

Step B3. according to the mapping relations of the composite set of assembly connecting relation and composite set to ZBDD, and then The ZBDD obtaining assembly connecting relation represents.

Specifically comprising the following steps that of described step C

Step C1. uses 6 i.e. Z={z of binary variable₀,z₁,z₂,z₃,z₄,z₅To+the X of coordinate axes ,+Y ,+Z ,-X ,- Y and these 6 directions of-Z encode；

Step C2., according to the interference matrix of assembly, obtains assembly and interferes the composite set of relation；

Step C3. according to assembly interfere the composite set of relation and composite set to the mapping relations of ZBDD, and then Obtaining assembly interferes the ZBDD of relation to represent.

Specifically comprising the following steps that of described step D

Step D1. application three integer variables, i.e. iterations variable a, b and c, and make iterations variable a=1；

Step D2. makes iterations variable b=1, if now a ≠ b, then goes to step D3, otherwise goes to step D6；

Step D3. makes iterations variable c=b+1, if now a ≠ c, then goes to step D4, otherwise goes to step D5；

If Tx in step D4. interference matrix_b-1x_a-1∧Tx_c-1x_a-1≠ 1, then it represents that part x_a-1Can not be at part x_b-1With Part x_c-1Reassemble after all assembling, and must be prior to part x_b-1With part x_c-1Assemble or assemble between, by iteration The currency of degree variables a, b and c, i.e. (a, b c) are stored in precedence relation matrix；Otherwise, D5 is gone to；Wherein ∧ represent to Amount step-by-step with；

Step D5. makes iterations variable c add up 1, if c≤n, then goes to step D4；Otherwise, step D6 is forwarded to；

Step D6. makes iterations variable b add up 1, if b is ＜ n, then goes to step D3；Otherwise, step D7 is forwarded to；

Step D7. makes iterations variable a add up 1, if a≤n, then goes to step D2；Otherwise, step D terminates, and tries to achieve Complete precedence relation matrix；

Above-mentioned Tx_b-1x_a-1Represent part x_b-1With part x_a-1Motion-vector function in interference matrix, Tx_c-1x_a-1Represent Part x_c-1With part x_a-1Motion-vector function in interference matrix；N is the total number of part.

Specifically comprising the following steps that of described step E

Step E1. creates a feasible assembly manipulation file File_FeasibleOperations and deposits feasible assembling Operation；Create n sub-assemblies file successively for depositing the sub-assemblies with i part, i=1,2 ..., n, n are part Total number；The sub-assemblies of all n single parts initially deposited by first sub-assemblies file, and remaining paper is initially empty； Create two-dimentional Dynamic Array Num_Routes and deposit the number of path generating each sub-assemblies；

First assembly file is designated as current layer by step E2., i.e. level variables L=1；

Step E3. reads a sub-assemblies p from current layer, and the composite set setting up sub-assemblies p represents F_p (X)；

If step E4. leaves the sub-assemblies before sub-assemblies p in had the most carried out feasibility judgement with p, then turn To step E11；Otherwise, from leaving one sub-assemblies q of selection the sub-assemblies before sub-assemblies p in；

If the parts count comprised in sub-assemblies q is less than or equal to n-L, then the composite set setting up sub-assemblies q represents F_q(X)；Otherwise, step E11 is forwarded to；

Step E5. judges whether the composite set of 2 sub-assemblies includes common part, i.e. judges F_p(X)∩F_q (X) whether it is empty；If not being empty, then including common part cannot assemble, and goes to step E4, selects next height to assemble Body judges；If sky, the most do not comprise common part, go to step E6；Wherein ∩ represents intersection of sets computing；

Step E6. judges whether sub-assemblies p and sub-assemblies q meets in the precedence relation matrix that step D is generated Dominance relation retrains, and i.e. judges that sub-assemblies p and sub-assemblies q is assembled together according to precedence relation matrix and whether can cause it The part that he is not assembled cannot assemble；If being unsatisfactory for dominance relation constraint, then go to step E4；If meeting dominance relation about Bundle, then go to step E7；

Step E7. judges whether sub-assemblies p and sub-assemblies q meets the connecting relation constraint of connecting matrix and interfere square The interference relation constraint of battle array, i.e. judges whether sub-assemblies p and sub-assemblies q meets assembly feasibility；Can if being unsatisfactory for assembling Row, goes to step E4；If meeting assembly feasibility, then the two can be assembled into new sub-assemblies, goes to step E8；

Step E8. thus generates feasible assembly manipulation NewFeasibleOperation and sub-assemblies NewSubassembly；

Step E9. checks that from i-th sub-assemblies file sub-assemblies NewSubassembly is saved the most；If It is not saved, sub-assemblies NewSubassembly write i-th sub-assemblies file File_i deposits, and moves in two dimension State array Num_Routes internal memory frees into the number of path of this sub-assemblies；If being saved, the most only need to change and originally leaving in The number of path generating this sub-assemblies in two dimension Dynamic Array；Now i=x+y, wherein x represent that sub-assemblies p comprises zero Number of packages and 1≤x ＜ n, y represents number of components and the 1≤y ＜ n that sub-assemblies q comprises；

The feasible assembling that step E10. is created feasible assembly manipulation NewFeasibleOperation write step E1 Operation file File_FeasibleOperations stores, and forwards step E4 to；

If the sub-assemblies that step E11. current layer is deposited is not determined complete, forward step E3 to；Otherwise, then level Variables L adds up 1, if level variables L is less than total number n of part, forwards step E3 to；Otherwise, step E terminates.

In step E9, the computing formula of the number of path generating sub-assemblies is as follows:

$\left\{\begin{array}{cc}{\mathrm{Num}}_{NewSubassembly}={\mathrm{Num}}_p\&times;{\mathrm{Num}}_q+{\mathrm{Num}}_{{\mathrm{NewSubassembly}}^{\&prime;}}& 1\&le;x<n,y=1\\ {\mathrm{Num}}_{NewSubassembly}={\mathrm{Num}}_p\&times;{\mathrm{Num}}_q\&times;\left(\underset{i=x}{\overset{x+y-2}{\&Pi;}}i\right)/(y-1)!+{\mathrm{Num}}_{{\mathrm{NewSubassembly}}^{\&prime;}}& 1\&le;x<n,1<y<n\end{array}\right.$

Wherein, Num_pRepresent the number of path generating sub-assemblies p, Num_qRepresenting the number of path generating sub-assemblies q, x represents Number of components included in sub-assemblies p and 1≤x ＜ n, y represents the number of components included in sub-assemblies q and 1≤y ＜ n, Num_{NewSubassembly}Represent the number of path generating sub-assemblies of current iteration, Num_{NewSubassembly'}Life for last iteration Become the number of path of sub-assemblies；！Represent factorial；

Specifically comprising the following steps that of described step E7

Step E71. calculates F_pAnd F (X)_q(X) cartesian product F_pq(X), i.e. F_pq(X)=F_p(X)×F_q, and create (X) F_pq(X) ZBDD corresponding to, is designated as ZBDD_pq；

Step E72. performs ZBDD_pq∩ZBDD_CIf result is not empty, then 2 representated by sub-assemblies p and sub-assemblies q Individual part or sub-assemblies meet connecting relation constraint, go to step E73；Otherwise, it is unsatisfactory for the constraint of connecting relation, goes to step Rapid E4；

Step E73. creates a ZBDD, is designated as ZBDD_D, for depositing the Lothrus apterus assembling road between parts to be assembled Footpath, initially deposits the six direction z of coordinate axes₀,z₁,z₂,z₃,z₄And z₅；

Step E74. is for ZBDD_pqIn each paths x₀x₁…x_n-1, at ZBDD_TThe path x that middle search is corresponding₀x₁… x_n-1z₀z₁z₂z₃z₄z₅, intercept z₀z₁z₂z₃z₄z₅, create corresponding ZBDD, be designated as ZBDD_DS；And make ZBDD_D=ZBDD_D∩ ZBDD_DS；

If step E75. ZBDD_DBe not empty, then two parts representated by sub-assemblies p and sub-assemblies q or son assembling Body meets interferes relation constraint, step E72 understand sub-assemblies p and sub-assemblies q and also meet connecting relation constraint, and therefore two Person meets assembly feasibility, goes to step E8；Otherwise, it is unsatisfactory for interfering relation constraint, goes to step E4.

Specifically comprising the following steps that of described step F

It is currently quilt that file that is second the sub-assemblies file of the sub-assemblies comprising 2 parts is deposited in the order of step F1. Simplify layer, i.e. simplify level variable SL=2, and make deleted marker variable flag=0；

Step F2. selects a sub-assemblies sa from this layer；

Step F3. is according to the feasible assembly manipulation deposited, it is determined that whether sub-assemblies sa take part in assembling, i.e. judges son dress Whether part sa is infeasible sub-assemblies；If sub-assemblies sa is not all right sub-assemblies, then delete sub-assemblies sub-assemblies Sa and the assembly manipulation of all generation sub-assemblies sa, make flag=1；

If the sub-assemblies that step F4. current layer is deposited does not checks complete, then forward step F2 to；If it is not, then simplification Level variable SL adds up 1, if simplifying level variable SL less than total number n of part, then goes to step F2；Otherwise, if flag= 1, then go to step F1, if flag=0, then step F terminates.

Compared with prior art, the present invention is for generating feasible Assembly sequences, its energy on the premise of known assembly knowledge Enough under higher time and space efficiency, the completeness of Assembly sequences is ensured by analyzing all possible assembly manipulation, logical Cross the reliability judging that subassembly geometric feasibility ensures Assembly sequences, ensure to calculate by the satisfiability judging dominance relation The high efficiency of method, is finally completed the generation of all feasible Assembly sequences to assembly.With OBDD representing as Assembly sequences, No matter a sub-assemblies comprises several part, represents the variable number of sub-assemblies, assembly manipulation and Assembly sequences the most as many Problem be resolved, solve the generation problem avoiding more infeasible sub-assemblies the most in advance simultaneously.

Accompanying drawing explanation

The flow chart of a kind of hybrid precast sequence generating method based on symbol of Fig. 1.

Fig. 2 is the illustraton of model of one embodiment of the present of invention.

Fig. 3 is the connecting matrix of embodiment illustrated in fig. 2.

Fig. 4 is the interference matrix of embodiment illustrated in fig. 2.

Fig. 5 is the ZBDD expression figure of the connecting matrix of embodiment illustrated in fig. 2.

Fig. 6 is the ZBDD expression figure of the interference matrix of embodiment illustrated in fig. 2.

Fig. 7 is the precedence relation matrix of embodiment illustrated in fig. 2.

Fig. 8 is the file File_1 of embodiment illustrated in fig. 2, i.e. has the sub-assemblies of 1 part.

Fig. 9 is the file File_2 of embodiment illustrated in fig. 2, i.e. has the sub-assemblies of 2 parts.

Figure 10 is the file File_3 of embodiment illustrated in fig. 2, i.e. has the sub-assemblies of 3 parts.

Figure 11 is the file File_4 of embodiment illustrated in fig. 2, i.e. has the sub-assemblies of 4 parts.

Figure 12 is the file File_5 of embodiment illustrated in fig. 2, i.e. has the sub-assemblies of 5 parts.

Figure 13 is the file File_6 of embodiment illustrated in fig. 2, i.e. complete assembly.

Figure 14 is all feasible assembly manipulation of embodiment illustrated in fig. 2.

Detailed description of the invention

The invention discloses a kind of hybrid precast sequence generating method based on symbol, have including step: obtain assembly The connecting matrix of knowledge, i.e. assembly and interference matrix；According to the connecting matrix of assembly, create the ZBDD table of connecting matrix Show；According to the interference matrix of assembly, the ZBDD creating interference matrix represents；According to the interference matrix of assembly, solve preferential Relational matrix；Search out all feasible assemblings, can row Assembly sequences, and create file and deposit feasible Assembly sequences and assembling During generate sub-assemblies, create Dynamic Array deposit the number of path generating each sub-assemblies；Depositing generation can The file of row Assembly sequences and sub-assemblies is refined, and deletes the death situation state during assembling.The present invention can be higher Under time and space efficiency, ensure the completeness of Assembly sequences by analyzing all possible assembly manipulation, by judging local Assembling geometric feasibility ensures the reliability of Assembly sequences, ensures the efficient of algorithm by the satisfiability judging dominance relation Property, it is finally completed the generation of all feasible Assembly sequences to assembly.

Below by a concrete example, the present invention is further elaborated:

A kind of hybrid precast sequence generating method based on symbol, as it is shown in figure 1, specifically include following steps, it may be assumed that

Step 1. obtains assembly knowledge, generates connecting matrix and the interference matrix of assembly.Fig. 2 is an assembly Illustraton of model.

Step 2. represents according to the connecting matrix of assembly, the ZBDD creating connecting matrix.Fig. 3 is the connection of Fig. 2 assembly Connect matrix.

Each part and the sub-assemblies of assembly are encoded by step S21., because the assembly in embodiment has 6 Individual part, then with 6 variable X={ x₀,x₁,x₂,x₃,x₄,x₅Part and sub-assemblies are encoded.Each variable represents one Individual part, the set expression sub-assemblies of two or more variablees composition.

Step S22. represents C (x according to the connecting matrix of embodiment, the composite set obtaining assembly connecting relation₀,x₁, x₂,x₃,x₄,x₅)={ x₀x₁,x₁x₂,x₁x₃,x₃x₄,x₃x₅,x₄x₅}；

Step S23., according to the composite set C (X) of assembly connecting relation, obtains the ZBDD table of assembly connecting relation Show, as it is shown in figure 5, be designated as ZBDD_C。

Step 3., according to the interference matrix of assembly, creates and interferes the ZBDD of square to represent.Fig. 4 is the interference of Fig. 2 assembly Matrix.

The all directions of coordinate axes are encoded by step S31., and three-dimensional coordinate has+X ,+Y ,+Z ,-X ,-Y and-Z six Direction, so using 6 binary variable Z={z₀,z₁,z₂,z₃,z₄,z₅It it is its coding.

Step S32., according to the interference matrix of embodiment, obtains assembly and interferes the composite set of relation to be expressed as T (x₀, x₁,x₂,x₃,x₄,x₅,z₀,z₁,z₂,z₃,z₄,z₅)={ x₀x₁z₀,x₀x₂z₀,x₀x₂z₁,x₀x₂z₂,x₀x₂z₄,x₀x₂z₅,x₀x₃z₀, x₀x₄z₀,x₀x₅z₀,x₁x₂z₀,x₁x₃z₃,x₁x₄z₀,x₁x₄z₃,x₁x₅z₀,x₁x₅z₃,x₂x₃z₁,x₂x₃z₂,x₂x₃z₃,x₂x₃z₄, x₂x₃z₅,x₂x₄z₁,x₂x₄z₂,x₂x₄z₃,x₂x₄z₄,x₂x₄z₅,x₂x₅z₁,x₂x₅z₂,x₂x₅z₃,x₂x₅z₄,x₂x₅z₅,x₃x₄z₀, x₃x₅z₀,x₄x₅z₀,x₄x₅z₃}。

Step S33. interferes the composite set T (XZ) of relation according to assembly, obtains assembly and interferes the ZBDD table of relation Show, as shown in Figure 6, be designated as ZBDD_T。

Step 4., according to the interference matrix of assembly, solves precedence relation matrix.

Step S41. application three integer variables, i.e. iterations variable a, b and c, and make a=1.

Step S42. makes b=1, if now a ≠ b, then goes to step S43, otherwise goes to step S46.

Step S46. makes iterations variable b add up 1, if b≤n-1, is wherein parts count, then goes to step S43； Otherwise, step S47 is forwarded to；Now b=2 and b≤5, go to step S43.

Step S43. makes c=b+1, if now a ≠ c, then goes to step S44, otherwise goes to step S45；Now calculate C=3 and a ≠ c can be obtained, then go to step S44.

Step S44. is in interference matrix, and the motion-vector function representation between two part p1 and p2 is T_p1p2=(T₀, T₁,T₂,T₃,T₄,T₅), referred to as transfer function or T-function.It is defined as: T_p1p2=T_i→ { 0,1}, i=0,1,2,3,4,5.Its In, T_p1p2I-th component T_i=1 (i=0,1,2,3,4,5) represents the freedom of movement that part p2 exists on the i of direction for p1 Degree, i.e. part p2 has a Lothrus apterus assembly path to part p1 on the i of direction；T_i=0 (i=0,1,2,3,4,5), represents The one-movement-freedom-degree on the i of direction, i.e. part p2 is there is not and there is interference, nothing with part p1 on the i of direction in part p2 for p1 Method implements assembling.Wherein, 0,1,2,3,4,5 six direction corresponding respectively to three-dimensional coordinate system :+X ,+Y ,+Z ,-X ,-Y ,- Z.According to above-mentioned information, if Tx in interference matrix_b-1x_a-1∧Tx_c-1x_a-1≠ 1, then part x_a-1Can not be at part x_b-1With x_c-1Reassemble after all assembling, and must be prior to part x_b-1And x_c-1Assemble or assemble between.Therefore, if Tx_{b- 1}x_a-1∧Tx_c-1x_a-1≠ 1, then by (a, b c) are stored in precedence relation matrix；Now a=1, b=2, c=3, and Tx₁x₀With Tx₂x₀It is unsatisfactory for condition Tx_b-1x_a-1∧Tx_c-1x_a-1≠ 1, so (1,2,3) is not preserved in precedence relation matrix In PrecedenceMatrix.

Step S45. makes iterations variable c add up 1, if c≤n, wherein n is parts count, then go to step S44； Otherwise, step S46 is forwarded to；Now c=4, c≤6, so forwarding step S44 to.

Circulation performs step S44～step S45, until c ＞ 6, then can search for out on the premise of a=1, b=2 is preferential Relation constraint.

Step S46. makes iterations variable b add up 1, if b≤n-1, is wherein parts count, then goes to step S43； Otherwise, step S47 is forwarded to；Now b=3 and b≤5, go to step S43.

Circulation performs step S43～step S46, until b ＞ 5, then can search for out the dominance relation on the premise of a=1 Constraint.

Step S47. makes iterations variable a add up 1, if a≤n, then goes to step S42；Otherwise, step S4 terminates, Try to achieve complete precedence relation matrix.Now a=2 and a≤6, go to step S42.

Circulation performs step S42～step S47, until a ＞ 6, then can search for out the constraint of all of dominance relation, i.e. tries to achieve Complete precedence relation matrix PrecedenceMatrix, as shown in Figure 7.

Step 5. searches out all feasible assemblings, can row Assembly sequences, and create file and deposit feasible assembly manipulation With the sub-assemblies generated during assembling, create Dynamic Array and deposit the number of path generating each sub-assemblies.That is: to all Deposit the sub-assemblies in the file of sub-assemblies and carry out combination of two, meet matrix whenever two sub-assemblies are combined When dominance relation constraint in PrecedenceMatrix, connecting relation retrain and interfere relation constraint, just arrive corresponding file The new sub-assemblies that two sub-assemblies of middle inspection combine has existed, if it is not, then new sub-assemblies is added It is added in file, and applies for a block space, deposit the number of path generating this sub-assemblies；Otherwise, without, only need to change original The number of path generating this sub-assemblies deposited.Meanwhile, this assembly manipulation is added in the file depositing feasible assembly manipulation, Until each sub-assemblies and other sub-assemblies carried out combination feasibility and judged.

First, creating that the file of an entitled File_FeasibleOperations is used for depositing can luggage for step S51. Join operation.Create 6 files, the most named File_1, File_2, File_3, File_4, File_5 and File_6.File_ I is used for depositing the sub-assemblies with i part, wherein i=1 ..., 6.File File_1 initially deposits 6 zero of assembly Part, file File_2, File_3, File_4, File_5 and File_6 are initially empty.Create two-dimentional Dynamic Array Num_ Routes, for depositing the number of path generating each sub-assemblies.Wherein, what Num_Routes [i-1] [j-1] deposited is to generate The number of path of jth sub-assemblies in file File_i.Deposit in Num_Routes [5] [0] is i.e. the institute generating assembly There is feasible Assembly sequences number.It addition, the generation path of regulation single part is 1, i.e. Num_Routes deposits 6 in [1] successively 1；

Step S52. will deposit the file File_1 of the single part of assembly, be designated as current layer L=1, that is to say first Process the single part in file File_1, allow current layer point to file File_1；

Step S53. reads a sub-assemblies c from this layer, is designated as p.The composite set setting up p represents { x₀, it is designated as F_p (X)；

If step S54. leaves the sub-assemblies before p in had the most carried out feasibility judgement with p, then forward step to S511.Because the sub-assemblies c representated by p is stored in the sub-assemblies of first, before p, therefore there is no sub-assemblies, Then step S511 is forwarded to；

If the sub-assemblies that step S511. current layer is deposited is not determined complete, forward step S53 to.Because ground floor File File_1 in house 6 single part sub-assemblies, so not being determined complete, forward step S53 to；

Step S53. reads a sub-assemblies from this layer, now reads second sub-assemblies b, is designated as p, sets up it Composite set represents { x₁, it is designated as F_p(X)；

Step S54. from leaving the sub-assemblies before the sub-assemblies b representated by p one sub-assemblies of selection in, this Time read first sub-assemblies c depositing before p, be designated as q.Further, the parts count comprised in q is less than or equal to n-L, also I.e. being less than equal to 5, therefore, the composite set setting up q represents { x₀, it is designated as F_q(X)；

Step S55. judges whether the composite set of 2 sub-assemblies includes common part, i.e. judges F_p(X)∩F_q (X) whether it is empty；If not being empty, then including common part cannot assemble, and goes to step S54, selects next height to assemble Body judges；If sky, the most do not comprise common part, go to step S56 and judge whether the two meets dominance relation about Bundle.Because F_p(X)∩F_q(X) it is empty, so, p and q does not comprise common part, goes to step S56.

Step S56. judges whether sub-assemblies p and sub-assemblies q meets in the precedence relation matrix that step S4 is generated Dominance relation constraint, i.e. judge that sub-assemblies p and sub-assemblies q is assembled together according to precedence relation matrix and whether can cause Other parts not being assembled cannot assemble；If being unsatisfactory for dominance relation constraint, then go to step S54；If meeting dominance relation Constraint, then go to step S57 and the two carried out assembly feasibility judgement.

Because the coding of sub-assemblies c and b representated by q and p is x respectively₀And x₁, according to this assembly shown in Fig. 7 Precedence relation matrix PrecedenceMatrix understands, and there is dominance relation constraint (4,1,2), that is to say expression part x₀With zero Part x₁Part x can be caused after being assembled together₃Cannot assemble.Therefore, p and q is unsatisfactory for precedence relation matrix Dominance relation constraint in PrecedenceMatrix.Go to step S54.

If step S54. leaves the sub-assemblies before p in had the most carried out feasibility judgement with p, then forward step to S511.Because the sub-assemblies b representated by p is stored in the sub-assemblies of second, and, leave first before b in Sub-assemblies c was carried out judgement, and the sub-assemblies not therefore being determined before p then forwards step S511 to；

If the sub-assemblies that step S511. current layer is deposited is not determined complete, forward step S53 to.Because ground floor File File_1 in house 6 single part sub-assemblies, the most only determined the first two, thus this layer deposit son assembling Body is not determined complete, forwards step S53 to；

Step S53. reads a sub-assemblies from this layer, now reads the 3rd sub-assemblies u, is designated as p, sets up it Composite set represents { x₂, it is designated as F_p(X)；

Step S54. from leaving the sub-assemblies before the sub-assemblies u representated by p one sub-assemblies of selection in, this Time read first sub-assemblies c depositing before p, be designated as q.Further, the parts count comprised in q is less than or equal to n-L, also I.e. being less than equal to 5, therefore, the composite set setting up q represents { x₀, it is designated as F_q(X)；

Step S55. judges whether the composite set of 2 sub-assemblies includes common part, i.e. judges F_p(X)∩F_q (X) whether it is empty；If sky, the most do not comprise common part, go to step S56.Because F_p(X)∩F_q(X) it is empty, so, P and q does not comprise common part.Go to step S56.

Step S56. judges whether sub-assemblies p and sub-assemblies q meets in the precedence relation matrix that step S4 is generated Dominance relation constraint, i.e. judge that sub-assemblies p and sub-assemblies q is assembled together according to precedence relation matrix and whether can cause Other parts not being assembled cannot assemble；If being unsatisfactory for dominance relation constraint, then go to step S54；If meeting dominance relation Constraint, then go to step S57 and the two carried out assembly feasibility judgement.

Because the coding of sub-assemblies c and u representated by q and p is x respectively₀And x₂, according to this assembly shown in Fig. 7 Precedence relation matrix PrecedenceMatrix understand, exist dominance relation constraint (2,1,3), (4,1,3), (5,1,3) and (6, 1,3), that is to say expression part x₀With part x₂Part x can be caused after being assembled together₁、x₃、x₄And x₅Cannot assemble.Therefore, The dominance relation constraint that p and q is unsatisfactory in precedence relation matrix PrecedenceMatrix.Go to step S54.

Step S54. from leaving the sub-assemblies before the sub-assemblies u representated by p one sub-assemblies of selection in, this Time read leave second sub-assemblies b before p in, be designated as q.Further, the parts count comprised in q is less than or equal to n-L, also I.e. being less than equal to 5, therefore, the composite set setting up q represents { x₁, it is designated as F_q(X)；

Step S55. judges whether the composite set of 2 sub-assemblies includes common part, i.e. judges F_p(X)∩F_q (X) whether it is empty；If sky, the most do not comprise common part, go to step S56.Because F_p(X)∩F_q(X) it is empty, so, P and q does not comprise common part.Go to step S56.

Step S56. judges whether sub-assemblies p and sub-assemblies q meets in the precedence relation matrix that step S4 is generated Dominance relation constraint, i.e. judge that sub-assemblies p and sub-assemblies q is assembled together according to precedence relation matrix and whether can cause Other parts not being assembled cannot assemble；If being unsatisfactory for dominance relation constraint, then go to step S54；If meeting dominance relation Constraint, then go to step S57 and the two carried out assembly feasibility judgement.

Because the coding of sub-assemblies b and u representated by q and p is x respectively₁And x₂, according to this assembly shown in Fig. 7 Precedence relation matrix PrecedenceMatrix understands, part x₀With part x₂It is assembled together and is not result in that other parts cannot Assembling.Therefore, the dominance relation constraint during p and q meets precedence relation matrix PrecedenceMatrix.Perform downwards step S57 carries out assembly feasibility judgement to the two；

Step S57. judges whether sub-assemblies p and sub-assemblies q meets the connecting relation constraint of connecting matrix and interfere The interference relation constraint of matrix, i.e. judges whether sub-assemblies p and sub-assemblies q meets assembly feasibility；If being unsatisfactory for, go to Step S54；If meeting assembly feasibility, then the two can be assembled into new sub-assemblies, goes to step S58；

Step S571. calculates F_pAnd F (X)_q(X) cartesian product F_pq(X), i.e. F_pq(X)=F_p(X)×F_q(X)= {x₁x₂, and create F_pq(X) ZBDD corresponding to, is designated as ZBDD_pq；

Step S572. performs ZBDD_pq∩ZBDD_CIf result is not empty, then representated by sub-assemblies p and sub-assemblies q 2 parts or sub-assemblies meet connecting relation constraint, go to step S573；Otherwise, it is unsatisfactory for the constraint of connecting relation, goes to Step S54；Because now ZBDD_pq∩ZBDD_C={ x₁x₂, so, p and q meets connecting relation constraint, goes to step S573.

Step S573. creates a ZBDD, is designated as ZBDD_D, for depositing the Lothrus apterus assembling between parts to be assembled Path, initially deposits the six direction z of coordinate axes₀,z₁,z₂,z₃,z₄And z₅；

Step S574. is for ZBDD_pqIn each paths x₀x₁…x_n-1, at ZBDD_TThe path that middle search is corresponding x₀x₁…x_n-1z₀z₁z₂z₃z₄z₅, intercept z₀z₁z₂z₃z₄z₅, create corresponding ZBDD, be designated as ZBDD_DS；And make ZBDD_D=ZBDD_D∩ ZBDD_DS；Then, to ZBDD_pqIn path x₁x₂Operate.At ZBDD_TIn respective path x that searches out₁x₂z₀.Therefore, cut Take and can obtain { z₀}.Therefore have, ZBDD_DS={ z₀}.Perform ZBDD_D=ZBDD_D∩ZBDD_DS, ZBDD can be obtained_D={ z₀}。

If step S575. ZBDD_DBe not empty, then two parts representated by sub-assemblies p and sub-assemblies q or son assembling Body meets interferes relation constraint, goes to step S58；Otherwise, it is unsatisfactory for interfering relation constraint, goes to step S54.By step S574 In result of calculation to understand be empty, so p and q meets interference relation constraint.Sub-assemblies p and son dress is understood by step S572 Part q also meets connecting relation constraint, and therefore the two meets assembly feasibility, goes to step S58.

Step S58. thus generates feasible assembly manipulation NewFeasibleOperation and sub-assemblies NewSubassembly；Composite set according to the sub-assemblies representated by p and q represents can obtain NewFeasibleOperation ={ x₂y₁y₂, NewSubassembly={bu}.

Step S59. checks that from i-th sub-assemblies file sub-assemblies NewSubassembly is saved the most； If not being saved, sub-assemblies NewSubassembly write i-th sub-assemblies file File_i deposits, and in two dimension Dynamic Array Num_Routes internal memory frees into the number of path of this sub-assemblies；If being saved, the most only need to change and originally depositing The number of path generating this sub-assemblies in two dimension Dynamic Array；Now i=x+y, wherein x represents what sub-assemblies p comprised Number of components and 1≤x ＜ n, y represents number of components and the 1≤y ＜ n that sub-assemblies q comprises.

Because NewSubassembly comprises two parts, so checking from corresponding file File_2 NewSubassembly is saved the most.First sub-assemblies being to solve for due to this, so, this sub-assemblies not by Preserve, the file File_2 in sub-assemblies NewSubassembly write hard disk deposits.Owing to having 6 parts, because of This is with 6 binary variable X={x₀,x₁,x₂,x₃,x₄,x₅Represent, it is x respectively according to the coding of b and u₁And x₂Sub-dress can be obtained { the storage form of bu} is part " 011000 ".

It addition, the two-dimensional array Num_Routes internal memory in internal memory frees into the number of path of this sub-assemblies Num_{NewSubassembly}.Owing to NewSubassembly is to generate for the first time, so Num_{NewSubassembly}It is initially 0.Further, because of For x=1, y=1, so Num_p=1, Num_q=1.Formula according to number of path calculated as below understands Num_{NewSubassembly}=1 × 1+0=1.Therefore, the Num tried to achieve_{NewSubassembly}Value 1 leave in the Num_Routes [1] [0] of two-dimensional array.

$\left\{\begin{array}{cc}{\mathrm{Num}}_{NewSubassembly}={\mathrm{Num}}_p\&times;{\mathrm{Num}}_q+{\mathrm{Num}}_{{\mathrm{NewSubassembly}}^{\&prime;}}& 1\&le;x<n,y=1\\ {\mathrm{Num}}_{NewSubassembly}={\mathrm{Num}}_p\&times;{\mathrm{Num}}_q\&times;\left(\underset{i=x}{\overset{x+y-2}{\&Pi;}}i\right)/(y-1)!+{\mathrm{Num}}_{{\mathrm{NewSubassembly}}^{\&prime;}}& 1\&le;x<n,1<y<n\end{array}\right.$

Step S510. feasible assembly manipulation NewFeasibleOperation write step S51 created can luggage Join in operation file File_FeasibleOperations and store, and forward step S54 to；

For this assembly, owing to having 6 parts, 12 binary variables (X, Y) are therefore used to represent assembling behaviour Make.Wherein X={x₀,x₁,x₂,x₃,x₄,x₅It is used for representing p, Y={y₀,y₁,y₂,y₃,y₄,y₅Be used for representing NewSubassembly.Therefore, feasible assembly manipulation { x₂y₁y₂Be stored in file File_FeasibleOperations Coding form is " 001000011000 ".Forward step S54 to.

If step S54. leaves the sub-assemblies before p in had the most carried out feasibility judgement with p, then forward step to S511.Because the sub-assemblies u representated by p is stored in the sub-assemblies of the 3rd, and, leave two sons before u in Assembly c and b is determined the most, the sub-assemblies not therefore being determined before p, then forwards step S511 to；

If the sub-assemblies that step S511. current layer is deposited is not determined complete, forward step S53 to；Otherwise, then layer Secondary variables L adds up 1, if L is less than total number n of part, forwards step S53 to；Otherwise, step S5 terminates.

Circulation performs step S53～step S511, until each sub-assemblies in each layer fills with the sub of other Part carried out assembly feasibility and judged, step S5 terminates.

Generation is deposited the file of feasible assembly manipulation and sub-assemblies and is refined by step S6., deletes assembling process In death situation state.Including step:

The order of step S61. deposits the file of the sub-assemblies comprising 2 parts for be currently simplified layer, is designated as present simplified Layer SL=2, first processes the sub-assemblies in file File_2, allows present simplified layer point to file File_2, and order is deleted Except indexed variable flag=0；

Step S62. reads out first sub-assemblies " 011000 " from this layer, and i.e. { bu} is designated as sa；

Step S63. is according to the feasible assembly manipulation deposited, it is determined that whether sub-assemblies sa take part in assembling, i.e. judges son Whether assembly sa is infeasible sub-assemblies；If sub-assemblies sa is not all right sub-assemblies, then delete the assembling of sub-assemblies Body sa and the assembly manipulation of all generation sub-assemblies sa, make flag=1.Therefore, to file File_ FeasibleOperations searches for and whether there is the assembly manipulation that sub-assemblies sa participates in.

Read first assembly manipulation " 001000011000 " in file File_FeasibleOperations, i.e. {x₂y₁y₂}.This assembly manipulation represents that part " 010000 " and part " 001000 " are assembled together generation sub-assemblies " 011000 ", therefore, this assembly manipulation cannot prove that can " 011000 " assemble with other sub-assemblies, i.e. cannot illustrate Whether " 011000 " is death situation state.

Then the assembly manipulation left in below it is successively read, during until reading assembly manipulation " 000111011111 ", Find that sub-assemblies " 011000 " can assemble with sub-assemblies " 000111 ", generate sub-assemblies " 011111 ".Thus Understanding, " 011000 " is not death situation state, it is not necessary to deleting, flag's is still 0.Perform step S64, read next sub-assemblies Judge.

If the sub-assemblies that step S64. current layer is deposited does not checks complete, then forward step S62 to；If it is not, then letter Change level variable SL and add up 1, if SL is less than total number n of part, then go to step S62；Otherwise, if flag=1, then step is gone to Rapid S61, if flag=0, then step S6 terminates.Because now the sub-assemblies of the second layer does not checks complete, therefore go to step Rapid S62 reads next sub-assemblies, goes to next layer without allowing SL add 1 and judges.

Circulation performs step S61～step S64, until all of sub-assemblies in file File_2～file File_5 (that is to say the intermediateness of assembling) all checks complete, it is ensured that do not have death situation state, then step S6 terminates, and whole algorithm is also Leave it at that.Now can try to achieve all feasible Assembly sequences of assembly.

File File_1, File_2, File_3, File_4, File_5 and the File_6 tried to achieve after program end of run Successively as shown in Fig. 8, Fig. 9, Figure 10, Figure 11, Figure 12 and Figure 13, all of sub-assemblies deposited by 6 files.File File_FeasibleOperations deposits all of feasible Assembly sequences, as shown in figure 14.

The method of the present invention provides connecting matrix and the interference matrix of assembly；Connecting matrix according to assembly creates connection The ZBDD connecing matrix represents；Interference matrix according to assembly creates the ZBDD of interference matrix and represents；Interference according to assembly Matrix, solves precedence relation matrix；Sub-assemblies in all files depositing sub-assemblies is carried out combination of two, whenever two Individual sub-assemblies is combined dominance relation constraint, the connecting relation constraint met in matrix PrecedenceMatrix and does When relating to relation constraint, just in corresponding file, check that the new sub-assemblies that two sub-assemblies combine has been deposited , if it is not, then new sub-assemblies is added in file, and apply for a block space, deposit the path generating this sub-assemblies Number；Otherwise, without, only need to change the number of path generating this sub-assemblies originally deposited.Meanwhile, this assembly manipulation is added In the file depositing feasible assembly manipulation, until each sub-assemblies and other sub-assemblies carried out combine feasible Property judge；Delete the death situation state during assembling.The present invention can be all by analyzing under higher time and space efficiency Possible assembly manipulation ensures the completeness of Assembly sequences, can by judge subassembly geometric feasibility guarantee Assembly sequences By property, being ensured the high efficiency of algorithm by the satisfiability judging dominance relation, being finally completed can luggage to all of assembly Join the generation of sequence.

In order to reduce, assembly sequence-planning represents sub-assemblies, assembly manipulation and the variable number of Assembly sequences and pre- First avoid the generation of more infeasible sub-assemblies, and then the efficiency of raising assembly sequence-planning, expand assembly sequence-planning Scale, the feature of sub-assemblies, assembly manipulation and Assembly sequences is analyzed, is expressed as composite set, makes by the present invention The not part in sub-assemblies, its variable is not present in representing that in the set of this sub-assemblies, coding is used to be become to reduce Amount number；Secondly, utilize ZBDD to represent and process the feature of composite set high efficiency, reducing during assembly sequences generation sky Between demand, preferably solve combinatorial problem, there is higher computational efficiency；Finally, the present invention herein in connection with heuristic strategies, In the case of not affecting the generation of feasible assembly manipulation, avoid the generation of more infeasible sub-assemblies in advance, thus simplify The process of rear deletion death situation state.Therefore, the present invention has higher time and space efficiency.

By combining the accompanying drawing description to the specific embodiment of the invention, other aspects of the present invention and feature are to this area It is apparent from for technical staff.

Being described and illustrated the specific embodiment of the present invention above, these embodiments should be considered to be only exemplary , it being not used to limit the invention, the present invention should be according to appended claim interpretation.

Claims (8)

1. a hybrid precast sequence generating method based on symbol, is characterized in that, comprise the following steps that

Step A. obtains assembly knowledge, generates connecting matrix and the interference matrix of assembly；

Step B. represents according to the connecting matrix of assembly, the ZBDD creating connecting matrix；

Step C. represents according to the interference matrix of assembly, the ZBDD creating interference matrix；

Step D., according to the interference matrix of assembly, solves precedence relation matrix；

Step E. represents according to the ZBDD of assembly connecting matrix, the ZBDD of interference matrix represents and precedence relation matrix, adopts All feasible assemblings are searched out with symbols Z BDD and layering thought, can row Assembly sequences；Meanwhile, can luggage to search out The sub-assemblies being equipped with and generate during assembly sequence-planning stores, and preserves the path generating each sub-assemblies Number；

The death situation state during assembling is searched for and deleted to step F., according to the feasible assembling preserved and sub-assemblies,.

A kind of hybrid precast sequence generating method based on symbol, is characterized in that, described step B Specifically comprise the following steps that

Step B1. utilizes variable to encode each part of assembly；

Step B2., according to the connecting matrix of assembly, creates the composite set of assembly connecting relation；

Step B3. is according to the mapping relations of the composite set of assembly connecting relation and composite set to ZBDD, and then obtains The ZBDD of assembly connecting relation represents.

A kind of hybrid precast sequence generating method based on symbol, is characterized in that, described step C Specifically comprise the following steps that

Step C1. uses 6 i.e. Z={z of binary variable₀,z₁,z₂,z₃,z₄,z₅To+the X of coordinate axes ,+Y ,+Z ,-X ,-Y and- These 6 directions of Z encode；

Step C2., according to the interference matrix of assembly, obtains assembly and interferes the composite set of relation；

Step C3. interferes the composite set of relation and composite set to the mapping relations of ZBDD according to assembly, and then obtains Assembly interferes the ZBDD of relation to represent.

A kind of hybrid precast sequence generating method based on symbol, is characterized in that, described step D Specifically comprise the following steps that

Step D1. application three integer variables, i.e. iterations variable a, b and c, and make iterations variable a=1；

Step D2. makes iterations variable b=1, if now a ≠ b, then goes to step D3, otherwise goes to step D6；

Step D3. makes iterations variable c=b+1, if now a ≠ c, then goes to step D4, otherwise goes to step D5；

If Tx in step D4. interference matrix_b-1x_a-1∧Tx_c-1x_a-1≠ 1, then it represents that part x_a-1Can not be at part x_b-1And part x_c-1Reassemble after all assembling, and must be prior to part x_b-1With part x_c-1Assemble or assemble between, by iterations The currency of variable a, b and c, i.e. (a, b c) are stored in precedence relation matrix；Otherwise, D5 is gone to；

Step D5. makes iterations variable c add up 1, if c≤n, then goes to step D4；Otherwise, step D6 is forwarded to；

Step D6. makes iterations variable b add up 1, if b is ＜ n, then goes to step D3；Otherwise, step D7 is forwarded to；

Step D7. makes iterations variable a add up 1, if a≤n, then goes to step D2；Otherwise, step D terminates, and tries to achieve complete Precedence relation matrix；

Above-mentioned Tx_b-1x_a-1Represent part x_b-1With part x_a-1Motion-vector function in interference matrix, Tx_c-1x_a-1Represent part x_c-1With part x_a-1Motion-vector function in interference matrix；N is the total number of part.

A kind of hybrid precast sequence generating method based on symbol, is characterized in that, described step E Specifically comprise the following steps that

Step E1. creates a feasible assembly manipulation file File_FeasibleOperations and deposits feasible assembly manipulation； Create n sub-assemblies file successively for depositing the sub-assemblies with i part, i=1,2 ..., n, wherein n is part Total number；The sub-assemblies of all n single parts initially deposited by first sub-assemblies file, and remaining paper is initially empty； Create two-dimentional Dynamic Array Num_Routes and deposit the number of path generating each sub-assemblies；

First assembly file is designated as current layer by step E2., i.e. level variables L=1；

Step E3. reads a sub-assemblies p from current layer, and the composite set setting up sub-assemblies p represents F_p(X)；

If step E4. leaves the sub-assemblies before sub-assemblies p in had the most carried out feasibility judgement with p, then forward step to Rapid E11；Otherwise, from leaving one sub-assemblies q of selection the sub-assemblies before sub-assemblies p in；

If the parts count comprised in sub-assemblies q is less than or equal to n-L, then the composite set setting up sub-assemblies q represents F_q(X)； Otherwise, step E11 is forwarded to；

Step E5. judges whether the composite set of 2 sub-assemblies includes common part, i.e. judges F_p(X)∩F_q(X) it is No is empty；If not being empty, then including common part cannot assemble, and goes to step E4, selects next sub-assemblies to enter Row judges；If sky, the most do not comprise common part, go to step E6；

It is preferential that step E6. judges whether sub-assemblies p and sub-assemblies q meets in the precedence relation matrix that step D is generated According to precedence relation matrix, relation constraint, i.e. judges that sub-assemblies p and sub-assemblies q is assembled together and whether can cause other not The part being assembled cannot assemble；If being unsatisfactory for dominance relation constraint, then go to step E4；If meeting dominance relation constraint, then Go to step E7；

Step E7. judges whether sub-assemblies p and sub-assemblies q meets connecting relation constraint and the interference matrix of connecting matrix Interfere relation constraint, i.e. judge whether sub-assemblies p and sub-assemblies q meets assembly feasibility；If being unsatisfactory for assembly feasibility, Go to step E4；If meeting assembly feasibility, then the two can be assembled into new sub-assemblies, goes to step E8；

Step E8. thus generates feasible assembly manipulation NewFeasibleOperation and sub-assemblies NewSubassembly；

Step E9. checks that from i-th sub-assemblies file sub-assemblies NewSubassembly is saved the most；If not by Preserve, sub-assemblies NewSubassembly write i-th sub-assemblies file File_i deposits, and in two dimension dynamic number Group Num_Routes internal memory frees into the number of path of this sub-assemblies；If being saved, the most only need to change and originally leaving two dimension in The number of path generating this sub-assemblies in Dynamic Array；Now i=x+y, wherein x represents the number of components that sub-assemblies p comprises And 1≤x ＜ n, y represent number of components and the 1≤y ＜ n that sub-assemblies q comprises；

The feasible assembly manipulation that step E10. is created feasible assembly manipulation NewFeasibleOperation write step E1 File File_FeasibleOperations stores, and forwards step E4 to；

If the sub-assemblies that step E11. current layer is deposited is not determined complete, forward step E3 to；Otherwise, then level variable L adds up 1, if level variables L is less than total number n of part, forwards step E3 to；Otherwise, step E terminates.

A kind of hybrid precast sequence generating method based on symbol, is characterized in that, in step E9, The computing formula of the number of path generating sub-assemblies is as follows:

$\left\{\begin{array}{cc}{\mathrm{Num}}_{NewSubassembly}={\mathrm{Num}}_p\&times;{\mathrm{Num}}_q+{\mathrm{Num}}_{{\mathrm{NewSubassembly}}^{\&prime;}}& 1\&le;x<n,y=1\\ {\mathrm{Num}}_{NewSubassembly}={\mathrm{Num}}_p\&times;{\mathrm{Num}}_q\&times;\left(\underset{i=x}{\overset{x+y-2}{\&Pi;}}i\right)/(y-1)!+{\mathrm{Num}}_{{\mathrm{NewSubassembly}}^{\&prime;}}& 1\&le;x<n,1<y<n\end{array}\right.$

Wherein, Num_pRepresent the number of path generating sub-assemblies p, Num_qRepresenting the number of path generating sub-assemblies q, x represents son dress Number of components included in part p and 1≤x ＜ n, y represents the number of components included in sub-assemblies q and 1≤y ＜ n, Num_{NewSubassembly}Represent the number of path generating sub-assemblies of current iteration, Num_{NewSubassembly′}Life for last iteration Become the number of path of sub-assemblies.

A kind of hybrid precast sequence generating method based on symbol, is characterized in that, described step E7 Specifically comprise the following steps that

Step E71. calculates F_pAnd F (X)_q(X) cartesian product F_pq(X), i.e. F_pq(X)=F_p(X)×F_q, and create F (X)_pq(X) Corresponding ZBDD, is designated as ZBDD_pq；

Step E72. performs ZBDD_pq∩ZBDD_CIf result is not empty, then 2 zero representated by sub-assemblies p and sub-assemblies q Part or sub-assemblies meet connecting relation constraint, go to step E73；Otherwise, it is unsatisfactory for the constraint of connecting relation, goes to step E4；

Step E73. creates a ZBDD, is designated as ZBDD_D, for depositing the Lothrus apterus assembly path between parts to be assembled, just Begin to deposit the six direction z of coordinate axes₀,z₁,z₂,z₃,z₄And z₅；

Step E74. is for ZBDD_pqIn each paths x₀x₁…x_n-1, at ZBDD_TThe path x that middle search is corresponding₀x₁…x_{n- 1}z₀z₁z₂z₃z₄z₅, intercept z₀z₁z₂z₃z₄z₅, create corresponding ZBDD, be designated as ZBDD_DS；And make ZBDD_D=ZBDD_D∩ZBDD_DS；

If step E75. ZBDD_DBe not empty, then two parts or sub-assemblies representated by sub-assemblies p and sub-assemblies q meet Interfering relation constraint, step E72 understand sub-assemblies p and sub-assemblies q and also meet connecting relation constraint, therefore the two meets Assembly feasibility goes to step E8；Otherwise, it is unsatisfactory for interfering relation constraint, goes to step E4.

A kind of hybrid precast sequence generating method based on symbol, is characterized in that, described step F Specifically comprise the following steps that

The order of step F1. deposits file that is second the sub-assemblies file of the sub-assemblies comprising 2 parts for be currently simplified Layer, i.e. simplifies level variable SL=2, and makes deleted marker variable flag=0；

Step F2. selects a sub-assemblies sa from this layer；

Step F3. is according to the feasible assembly manipulation deposited, it is determined that whether sub-assemblies sa take part in assembling, i.e. judges sub-assemblies Whether sa is infeasible sub-assemblies；If sub-assemblies sa is not all right sub-assemblies, then delete sub-assemblies sub-assemblies sa with And the assembly manipulation of all generation sub-assemblies sa, make flag=1；

If the sub-assemblies that step F4. current layer is deposited does not checks complete, then forward step F2 to；If it is not, then simplifying level Variable SL adds up 1, if simplifying level variable SL less than total number n of part, then goes to step F2；Otherwise, if flag=1, then Going to step F1, if flag=0, then step F terminates.