CN104598695A - Assembly sequence generating method based on sign ZBDD - Google Patents

Assembly sequence generating method based on sign ZBDD Download PDF

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CN104598695A
CN104598695A CN201510063262.7A CN201510063262A CN104598695A CN 104598695 A CN104598695 A CN 104598695A CN 201510063262 A CN201510063262 A CN 201510063262A CN 104598695 A CN104598695 A CN 104598695A
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zbdd
assembly
assemblies
sub
feasibleoperation
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李凤英
彭瑞
常亮
古天龙
徐周波
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Guilin University of Electronic Technology
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Guilin University of Electronic Technology
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Abstract

The invention discloses an assembly sequence generating method based on a sign ZBDD. The method comprises the following steps that assembly body knowledge, i.e., a connecting matrix and an interference matrix of an assembly body are obtained; according to the connecting matrix of the assembly body, the ZBDD of the connecting matrix is created; according to the interference matrix of the assembly body, the ZBDD of the interference matrix is created; all feasible assemblies are searched out, i.e., a feasible assembly sequence is obtained, and the ZBDD representing the feasible assembly sequence is created; the generated ZBDD for representing the assembly sequence is refined, and the dead state in the assembly process is deleted. The method has the advantages that the completeness of the assembly sequence can be ensured through analyzing all possible assembly operations at higher time and space efficiency, the reliability of the assembly sequence is ensured through judging the local assembly combination feasibility, and finally, the generation on all feasible assembly sequences of assembly bodies is completed.

Description

Based on the assembling sequence generation method of symbols Z BDD
Technical field
The present invention relates to assembly sequence-planning technical field, be specifically related to a kind of assembling sequence generation method based on symbols Z BDD.
Background technology
Assembly sequence-planning (Assembly Sequences Planning, ASP) refer under the prerequisite of given design proposal, should ensure to meet all geometrical constraints, shorten installation time again as far as possible and reduce the complexity of assembling, thus find out rational, feasible Assembly sequences, reduce assembly cost and optimizing product performance with this.ASP problem is NP combinatorial optimization problem in itself, and exhaustive search algorithm complex is exponential.When product is comparatively complicated, number of components is more, very easily there is combinations of states explosion issues.Visible, combinatorial complexity is a key factor of restriction assembly sequence-planning efficiency and automatization level.
Slow down or partial extent avoided a kind of possible strategy of combinatorial complexity problem be symbolization or implicit expression description technique.Ordered Binary Decision Diagrams (Ordered Binary Decision Diagrams, OBDD) and extend type thereof can realize implicit representation and the search of state space or variable combination, are one of the most effective symbol technology up to now.In recent years, OBDD has had some to apply in assembly sequence-planning.Experimental result shows, utilizes OBDD to take less storage space as the expression of Assembly sequences than using AND/OR figure to represent.But when representing Assembly sequences and assembly manipulation with OBDD, be in fact that assembly manipulation is become boolean's fundamental function with assembly sequences representation, then according to the corresponding relation between Boolean function and OBDD, the OBDD setting up Assembly sequences represents.In this expression, be included in the affirmative form of variable of the part in sub-assemblies to represent, be not included in the negative form of variable of the part in sub-assemblies to represent, namely in the assembling process of an assembly, no matter the part that sub-assemblies comprises has how many, represent the variable number of sub-assemblies all as many.
Summary of the invention
The present invention is to solve when representing Assembly sequences with OBDD, no matter a sub-assemblies comprises several part, represent all as many problem of variable number of sub-assemblies, assembly manipulation and Assembly sequences, a kind of assembling sequence generation method based on symbols Z BDD is provided, it can improve the efficiency of assembly sequence-planning, expands the scale of assembly sequence-planning.
For solving the problem, the present invention is achieved by the following technical solutions:
Based on an assembling sequence generation method of symbols Z BDD, comprise step as follows:
Steps A. obtain assembly knowledge, i.e. the connection matrix of assembly and interference matrix;
Step B., according to the connection matrix of assembly, creates the ZBDD of connection matrix;
Step C., according to the interference matrix of assembly, creates the ZBDD of interference matrix;
Step D. searches out all feasible assemblings, gets final product row Assembly sequences, and creates the ZBDD representing feasible Assembly sequences;
Step e. the ZBDD of the feasible Assembly sequences of expression generated is refined, deletes the death situation state in assembling process.
The concrete steps of described step B are as follows:
Step B1. each part to assembly is numbered, if assembly has n part, then uses n variable X=(x 0, x 1..., x n-1) part and sub-assemblies are encoded.Each variable represents a part, the set expression sub-assemblies of two or more variable composition.According to the connection matrix of assembly, the composite set obtaining assembly connection matrix is expressed as C (X)={ x ix j| x i∈ X, x j∈ X, i ≠ j}, wherein x iand x jrepresent two different parts;
Step B2. is according to the composite set of assembly connection matrix and the composite set mapping relations to ZBDD, and then the ZBDD obtaining assembly connection matrix represents, is designated as ZBDD c.
The concrete steps of described step C are as follows:
The all directions of step C1. to coordinate axis are encoded, and three-dimensional coordinate has+X ,+Y ,+Z ,-X ,-Y and-Z six direction, so use 6 variable Z=(z 0, z 1, z 2, z 3, z 4, z 5) be its coding.According to the interference matrix of assembly, the composite set obtaining assembly interference matrix is expressed as T (XZ)={ x ix jz k| x i∈ X, x j∈ X, z k∈ Z, i ≠ j}, wherein x iand x jrepresent two different parts;
Step C2. is according to the composite set of assembly interference matrix and the composite set mapping relations to ZBDD, and then the zero compression Binary Decision Diagrams obtaining assembly interference matrix represents.
The concrete steps of described step D are as follows:
Step D1. creates one and is designated as representing the ZBDD of feasible Assembly sequences, is initially sky.In addition, the dynamic array having assembly part is designated as FeasibleOperation [], applies for a variable n, make n=FeasibleOperation.Length, for depositing the parts count of assembly;
Step D2. applies for two integer variable i=1, j=0;
It is current location P that step D3. gets FeasibleOperation [i] cur, get FeasibleOperation [j] for reference position P refif, P curthe sub-assemblies of representative does not comprise P refrepresentative sub-assemblies or sub-assemblies in part time, forward step D4 to; Otherwise, forward step D6 to;
Step D4. judges whether part representated by FeasibleOperation [i] or sub-assemblies and the part representated by FeasibleOperation [j] or sub-assemblies meet annexation and to retrain and precedence relationship retrains;
Step D5. dynamically applies for a block space, makes the length of dynamic array FeasibleOperation add 1, then at the assembly that this assembly manipulation of last interpolation of array generates, creates corresponding ZBDD, is designated as ZBDD fS.For each assembly manipulation, be all that two parts and/or sub-assemblies are fitted together.Further, the assembly that one of them part or sub-assemblies can generate according to another part or sub-assemblies and assembly manipulation is derived.Therefore, one is had to the assembly of n part, assembly manipulation can be represented with the composite set of 2n variable (X, Y).Wherein, with a front n variable X=(x 0, x 1..., x n-1) combination represent participate in assembling a part or sub-assemblies, i.e. P currepresentative part or sub-assemblies, with a rear n variable Y=(y 0, y 1..., y n-1) combination represent and perform the sub-assemblies that generates of assembly manipulation.Make ZBDD f=ZBDD f∪ ZBDD fS;
Step D6. makes j=j+1, if j<i, goes to step D3; Otherwise, make i=i+1, if i≤FeasibleOperation.Length-1, then make j=0, go to step D3; Otherwise, perform step e.
The concrete steps of described step D4 are as follows:
Step D41. sets up the composite set F of part representated by FeasibleOperation [i] or sub-assemblies i(X) the composite set F of part representated by FeasibleOperation [j] or sub-assemblies, is set up j(X);
Step D42. calculates F iand F (X) j(X) cartesian product, is designated as F ij(X), i.e. F ij(X)=F i(X) × F j, and create F (X) ij(X) ZBDD corresponding to, is designated as ZBDD ij;
Step D43. performs ZBDD ij∩ ZBDD cif result is not empty, then the part representated by FeasibleOperation [i] or sub-assemblies and the part representated by FeasibleOperation [j] or sub-assemblies meet annexation constraint, forward step D44 to; Otherwise, do not meet annexation constraint, forward step D6 to;
Step D44. is for ZBDD ij∩ ZBDD cin a certain paths x 0x 1x n-1, at ZBDD tthe path x that middle search is corresponding 0x 1x n-1z 0z 1z 2z 3z 4z 5, intercept z 0z 1z 2z 3z 4z 5, create corresponding ZBDD, be designated as ZBDD dS.Create ZBDD d, and make ZBDD d=ZBDD dS;
Step D45. is for ZBDD ij∩ ZBDD cin remaining each paths x 0x 1x n-1, at ZBDD tthe path x that middle search is corresponding 0x 1x n-1z 0z 1z 2z 3z 4z 5, intercept z 0z 1z 2z 3z 4z 5, create corresponding ZBDD, be designated as ZBDD dS.Then ZBDD is performed d=ZBDD d∩ ZBDD dS;
If step D46. is ZBDD dbe not empty, then the part representated by FeasibleOperation [i] or sub-assemblies and the part representated by FeasibleOperation [j] or sub-assemblies meet precedence relationship constraint, forward step D5 to; Otherwise, do not meet precedence relationship constraint, forward step D6 to.
The concrete steps of described step e are as follows:
Step e 1. applies for an integer variable pos=FeasibleOperation.Length-2;
Step e 2. judges the ZBDD representing feasible Assembly sequences fin whether there is a paths: the sub-assemblies of front n position representated by FeasibleOperation [pos] in this path.If there is no, then ZBDD is deleted fin after the path of the sub-assemblies of n position representated by FeasibleOperation [pos];
Step e 3. makes pos=pos-1, if pos>=n, wherein n is the parts count of assembly, then continue to perform step e 2; Otherwise, return ZBDD f, algorithm terminates.
In order to reduce in assembly sequence-planning the variable number representing sub-assemblies, assembly manipulation and Assembly sequences, and then improve the efficiency of assembly sequence-planning, expand the scale of assembly sequence-planning, the feature of the present invention to sub-assemblies, assembly manipulation and Assembly sequences is analyzed, be expressed as composite set, make the part not in sub-assemblies, its variable does not appear in the set representing this sub-assemblies, to reduce coding variable number used; In addition, the present invention also utilizes ZBDD to represent and processes the feature of composite set high efficiency, reduces the demand to space in assembly sequences generation process, solves combinatorial problem better, have higher counting yield.
Compared with prior art, the present invention generates feasible Assembly sequences under being used for the prerequisite of known assembly knowledge, it can under higher Time and place efficiency, the completeness of Assembly sequences is ensured by analyzing all possible assembly manipulation, by judging that partial assembled geometric feasibility ensures the reliability of Assembly sequences, finally complete the generation of all feasible Assembly sequences to assembly.
Accompanying drawing explanation
The process flow diagram of a kind of assembling sequence generation method based on symbols Z BDD of Fig. 1.
Fig. 2 is the illustraton of model of one embodiment of the present of invention.
Fig. 3 is connection matrix embodiment illustrated in fig. 2.
Fig. 4 is interference matrix embodiment illustrated in fig. 2.
Fig. 5 is the ZBDD expression figure of connection matrix embodiment illustrated in fig. 2.
Fig. 6 is the ZBDD expression figure of interference matrix embodiment illustrated in fig. 2.
Fig. 7 is the ZBDD expression figure of feasible Assembly sequences embodiment illustrated in fig. 2.
Fig. 8 is the ZBDD expression figure of the feasible Assembly sequences after deletion death situation state embodiment illustrated in fig. 2.
Embodiment
A kind of assembling sequence generation method based on symbols Z BDD.Comprise five steps, as shown in Figure 1, specifically comprise five large steps, that is:
Step 1. obtains assembly knowledge, and definition stores the dynamic array of assembly part and sub-assemblies, initially deposits the part of assembly, provides connection matrix and the interference matrix of assembly.Fig. 2 is the illustraton of model of an assembly.
Step 2., according to the connection matrix of assembly, creates the ZBDD of connection matrix.Fig. 3 is the connection matrix of Fig. 2 assembly.
Step S21. each part to assembly is numbered, because the assembly in embodiment has 4 parts, then uses 4 variable X=(x 0, x 1, x 2, x 3) part and sub-assemblies are encoded.Each variable represents a part, the set expression sub-assemblies of two or more variable composition.According to the connection matrix of embodiment, the composite set obtaining assembly connection matrix represents C (x0, x 1, x 2, x 3)={ x 0x 1, x 0x 2, x 0x 3, x 1x 3, x 2x 1;
Step S22. is according to the composite set of assembly connection matrix, and then the ZBDD obtaining assembly connection matrix represents, as shown in Figure 5, is designated as ZBDD c.
Step 3., according to the interference matrix of assembly, creates the ZBDD interfering square.Fig. 4 is the interference matrix of Fig. 2 assembly.
The all directions of step S31. to coordinate axis are numbered, and three-dimensional coordinate has+X ,+Y ,+Z ,-X ,-Y and-Z six direction, so use 6 variable Z=(z 0, z 1, z 2, z 3, z 4, z 5) be its coding.According to the interference matrix of embodiment, the composite set obtaining assembly interference matrix is expressed as T (x0, x 1, x 2, x 3, z 0, z 1, z 2, z 3, z 4, z 5)={ x 0x 1z 0, x 0x 1z 2, x 0x 1z 5, x 0x 2z 0, x 0x 2z 1, x 0x 2z 2, x 0x 2z 3, x 0x 2z 5, x 0x 3z 1, x 1x 2z 0, x 1x 2z 1, x 1x 2z 2, x 1x 2z 3, x 1x 2z 5, x 1x 3z 1, x 2x 3z 1}
Step S32. is according to the composite set of assembly interference matrix, and then the ZBDD obtaining assembly interference matrix represents, as shown in Figure 6, is designated as ZBDD t.
Step 4. searches out all feasible assembly manipulations, and creates the ZBDD representing feasible Assembly sequences.That is: combination of two is carried out to all parts in dynamic array and sub-assemblies, whenever two parts and/or sub-assemblies combine meet connection constraints relation and priority constraint relationship time, just the new sub-assemblies that two parts and/or sub-assemblies combine is stored in dynamic array, this assembly manipulation is added in the ZBDD representing feasible Assembly sequences simultaneously, judged until each part deposited in array or sub-assemblies carry out combination feasibility with other part or sub-assemblies.
Step S41. creates one for representing the ZBDD of feasible Assembly sequences, is designated as ZBDD f, be initially sky, in addition, the dynamic array having assembly part be designated as FeasibleOperation []={ a, b, c, d}, apply for a variable n, make n=FeasibleOperation.Length=4, for depositing the parts count of assembly;
Step S42. applies for two integer variable i=1, j=0;
It is current location P that step S43. gets FeasibleOperation [i] cur, therefore, now P cur=b.Get FeasibleOperation [j] for reference position P ref, therefore, now P ref=a.Because part b does not comprise part a, so perform step S44;
Step S44. judges whether the part a representated by part b and FeasibleOperation [0] representated by FeasibleOperation [1] meets annexation constraint and precedence relationship constraint.
With reference to the ZBDD of the interference matrix of embodiment in ZBDD and Fig. 6 of the connection matrix of embodiment in Fig. 5, described step S44, comprises step:
Step S441. sets up the composite set F of part representated by FeasibleOperation [i] or sub-assemblies i(X), now F 1(X)={ x 1, set up the composite set F of part representated by FeasibleOperation [j] or sub-assemblies j(X), now F 0(X)={ x 0;
Step S442. carries out following computing: F ij(X)=F i(X) × F j(X), now F 10(X)=F 1(X) × F 0(X)={ x 0x 1, and create F 10(X) ZBDD corresponding to, is designated as ZBDD 10;
Step S443. performs ZBDD ij∩ ZBDD cif result is not empty, then the part representated by FeasibleOperation [i] or sub-assemblies and the part representated by FeasibleOperation [j] or sub-assemblies meet annexation constraint, forward step S444 to; Otherwise, do not meet annexation constraint, forward step S46 to.Because ZBDD 10∩ ZBDD cthere is a paths { x 0x 1, be not empty.So the part a representated by part b and FeasibleOperation [0] representated by FeasibleOperation [1] meets annexation constraint, forwards step S444 to.
Step S444. is for ZBDD ij∩ ZBDD cin a certain paths x 0x 1x n-1, at ZBDD tthe path x that middle search is corresponding 0x 1x n-1z 0z 1z 2z 3z 4z 5, intercept z 0z 1z 2z 3z 4z 5, create corresponding ZBDD, be designated as ZBDD dS.Create ZBDD d, and make ZBDD d=ZBDD dS.For ZBDD 10∩ ZBDD ca paths { x 0x 1, so search out respective path { x 0x 1z 0, x 0x 1z 2, x 0x 1z 5.Intercepting can obtain { z 0, z 2, z 5.And create corresponding ZBDD, be designated as ZBDD dS.Create ZBDD d, and make ZBDD d=ZBDD dS.
Step S445. is for ZBDD ij∩ ZBDD cin remaining each paths x 0x 1x n-1, at ZBDD tthe path x that middle search is corresponding 0x 1x n-1z 0z 1z 2z 3z 4z 5, intercept z 0z 1z 2z 3z 4z 5, create corresponding ZBDD, be designated as ZBDD dS.Then ZBDD is performed d=ZBDD d∩ ZBDD dS.Because ZBDD 10∩ ZBDD conly there is a paths, so this step does not perform.
If step S446. is ZBDD dbe not empty, then the part representated by FeasibleOperation [i] or sub-assemblies and the part representated by FeasibleOperation [j] or sub-assemblies meet precedence relationship constraint, forward step S45 to; Otherwise, do not meet precedence relationship constraint, forward step S46 to.Because ZBDD dcomprise { z 0, z 2, z 5, be not empty, so the part a representated by part b and FeasibleOperation [0] representated by FeasibleOperation [1] meets priority constraint relationship, forward step S45 to.
Step S45. dynamically applies for a block space, makes the length of dynamic array FeasibleOperation add 1, then at the assembly that this assembly manipulation of last interpolation of array generates, then and FeasibleOperation []={ a, b, c, d, ab}, creates corresponding ZBDD, is designated as ZBDD fS.Because the assembly in embodiment is the assembly with 4 parts, with 8 binary variable (x 0, x 1, x 2, x 3, y 0, y 1, y 2, y 3) represent assembly manipulation, wherein, front 4 variable (x 0, x 1, x 2, x 3) combination represent participate in assembling a part or sub-assemblies, if the part i of assembly assembles, then x i-1appear in composite set; Otherwise, x i-1do not occur.Rear 4 variable (y 0, y 1, y 2, y 3) combination represent and perform the sub-assemblies that generates of assembly manipulation, if the part i of assembly assembles, y i-1appear in composite set; Otherwise, y i-1do not occur.Front 4 unifications are taken as P currepresentative part or sub-assemblies.Therefore, ZBDD fSinside comprise path { x 1y 0y 1.Then ZBDD is made f=ZBDD f∪ ZBDD fS, so, now ZBDD finside only comprise path { x 1y 0y 1.
Step S46. performs j=j+1=1, so j ≮ i, so do not continue to perform step S43, S44 and S45.But make i=i+1=2, because FeasibleOperation.Length=5, so i≤FeasibleOperation.Length-1, therefore make j=0, perform step S43, S44 and S45;
Circulation performs above-mentioned steps S43, S44, S45 and S46, until i=FeasibleOperation.Length, j=FeasibleOperation.Length-1, then performs step S5.For the present embodiment, final FeasibleOperation.Length=14, so when i=14, j=13, circulation terminates.Circulation terminates the ZBDD obtained fas shown in Figure 7.
The ZBDD that step 5. pair step 4 generates refines, and deletes the death situation state in assembling process.
Step S51. applies for an integer variable pos=FeasibleOperation.Length-2=12;
Step S52. judges the ZBDD representing feasible Assembly sequences fin whether there is a paths: the sub-assemblies of X variable representated by FeasibleOperation [pos] in this path.If there is no, then ZBDD is deleted fthe path of the sub-assemblies of middle Y variable representated by FeasibleOperation [pos].Because ZBDD fin there is not the path of the sub-assemblies bcd of X variable representated by FeasibleOperation [12], therefore, delete ZBDD fpath { the x of the sub-assemblies bcd of middle Y variable representated by FeasibleOperation [12] 2x 3y 1y 2y 3.
Step S53. makes pos=pos-1, if pos>=4, then continues to perform step S52; Otherwise, return ZBDD f, algorithm terminates.
Circulation performs step S52 and S53, until pos=3, algorithm terminates, and deletes the ZBDD after death situation state fas shown in Figure 8.
Method definition of the present invention stores the dynamic array of assembly part and sub-assemblies, provides connection matrix and the interference matrix of assembly; The ZBDD creating connection matrix according to the connection matrix of assembly represents; The ZBDD creating interference matrix according to the interference matrix of assembly represents; Combination of two is carried out to all parts in dynamic array and sub-assemblies, whenever two parts and/or sub-assemblies combine meet connection constraints relation and priority constraint relationship time, just the new sub-assemblies that two parts and/or sub-assemblies combine is stored in dynamic array, this assembly manipulation adds in the ZBDD representing feasible assembly manipulation simultaneously, judges until each part deposited in array or sub-assemblies carry out combination feasibility with other part or sub-assemblies; Delete the death situation state in assembling process.The present invention can under higher Time and place efficiency, the completeness of Assembly sequences is ensured by analyzing all possible assembly manipulation, by judging that partial assembled geometric feasibility ensures the reliability of Assembly sequences, finally complete the generation of all feasible Assembly sequences to assembly.
In conjunction with the drawings to the description of the specific embodiment of the invention, other aspects of the present invention and feature are apparent to those skilled in the art.
Be described specific embodiments of the invention above and illustrate, these embodiments should be considered to just exemplary, and are not used in and limit the invention, and the present invention should make an explanation according to appended claim.

Claims (6)

1. based on the assembling sequence generation method of symbols Z BDD, it is characterized in that, comprise step as follows:
Steps A. obtain assembly knowledge, store the dynamic array of assembly part, and the connection matrix of assembly and interference matrix;
Step B., according to the connection matrix of assembly, creates the ZBDD of connection matrix;
Step C., according to the interference matrix of assembly, creates the ZBDD of interference matrix;
Step D. carries out combination of two to all parts of dynamic array and sub-assemblies, when two parts and/or sub-assemblies combine meet connection constraints relation and priority constraint relationship time, then the new sub-assemblies that these two parts and/or sub-assemblies combine is stored in dynamic array, and forms the ZBDD building feasible Assembly sequences according to this dynamic number;
Step e. the ZBDD of the feasible Assembly sequences of expression generated is refined, namely judge whether to exist in the ZBDD of feasible Assembly sequences do not participate in assemble sub-assemblies, if have, the assembly manipulation generating this sub-assemblies is deleted from ZBDD, namely delete the death situation state in assembling process.
2. according to claim 1 based on the assembling sequence generation method of symbols Z BDD, it is characterized in that, the concrete steps of described step B are as follows:
Step B1. each part to assembly is numbered, if assembly has n part, then uses n variable X=(x 0, x 1..., x n-1) part and sub-assemblies are encoded; Each variable represents a part, the set expression sub-assemblies of two or more variable composition; According to the connection matrix of assembly, the composite set obtaining assembly connection matrix is expressed as C (X)={ x ix j| x i∈ X, x j∈ X, i ≠ j}, wherein x iand x jrepresent two different parts;
Step B2. is according to the composite set of assembly connection matrix and the composite set mapping relations to ZBDD, and then the ZBDD obtaining assembly connection matrix represents.
3. according to claim 1 based on the assembling sequence generation method of symbols Z BDD, it is characterized in that, the concrete steps of described step C are as follows:
The all directions of step C1. to coordinate axis are numbered, and use 6 variable Z=(z 0, z 1, z 2, z 3, z 4, z 5) be+the X ,+Y of three-dimensional coordinate ,+Z ,-X, these 6 direction encodings of-Y and-Z; According to the interference matrix of assembly, the composite set obtaining assembly interference matrix is expressed as T (XZ)={ x ix jz k| x i∈ X, x j∈ X, z k∈ Z, i ≠ j}, wherein x iand x jrepresent 2 different parts;
Step C2. is according to the composite set of assembly interference matrix and the composite set mapping relations to ZBDD, and then the zero compression Binary Decision Diagrams obtaining assembly interference matrix represents.
4. according to claim 1 based on the assembling sequence generation method of symbols Z BDD, it is characterized in that, the concrete steps of described step D are as follows:
Step D1. creates one for representing the ZBDD of feasible Assembly sequences, is designated as ZBDD f, be initially sky, in addition, the dynamic array having assembly part be designated as FeasibleOperation [], apply for a variable n, make n=FeasibleOperation.Length, for depositing the parts count of assembly;
Step D2. applies for two integer variable i=1, j=0;
It is current location P that step D3. gets FeasibleOperation [i] cur, get FeasibleOperation [j] for reference position P refif, P curthe sub-assemblies of representative does not comprise P refrepresentative sub-assemblies or sub-assemblies in part time, forward step D4 to; Otherwise, forward step D6 to;
Step D4. judges whether part representated by FeasibleOperation [i] or sub-assemblies and the part representated by FeasibleOperation [j] or sub-assemblies meet annexation and to retrain and precedence relationship retrains;
Step D5. dynamically applies for a block space, makes the length of dynamic array FeasibleOperation add 1, then at the assembly that this assembly manipulation of last interpolation of array generates, creates corresponding zero compression Binary Decision Diagrams, is designated as ZBDD fS; One is had to the assembly of n part, represent assembly manipulation with the composite set of 2n variable (X, Y), wherein with a front n variable X=(x 0, x 1..., x n-1) combination represent participate in assembling a part or sub-assemblies, i.e. P currepresentative part or sub-assemblies, with a rear n variable Y=(y 0, y 1..., y n-1) combination represent and perform the sub-assemblies that generates of assembly manipulation, make ZBDD f=ZBDD f∪ ZBDD fS;
Step D6. performs j=j+1, if j<i, performs step D3, D4 and D5; Otherwise, make i=i+1, if i≤FeasibleOperation.Length-1, then make j=0, perform step D3, D4 and D5; Otherwise, perform step e.
5. according to claim 4 based on the assembling sequence generation method of symbols Z BDD, it is characterized in that, the concrete steps of described step D4 are as follows:
Step D41. sets up the composite set F of part representated by FeasibleOperation [i] or sub-assemblies i(X) the composite set F of part representated by FeasibleOperation [j] or sub-assemblies, is set up j(X);
Step D42. calculates F iand F (X) j(X) cartesian product, is designated as F ij(X), i.e. F ij(X)=F i(X) × F j, and create F (X) ij(X) the zero compression Binary Decision Diagrams corresponding to, is designated as ZBDD ij;
Step D43. performs ZBDD ij∩ ZBDD cif result is not empty, then the part representated by FeasibleOperation [i] or sub-assemblies and the part representated by FeasibleOperation [j] or sub-assemblies meet annexation constraint, forward step D44 to; Otherwise, do not meet annexation constraint, forward step D6 to;
Step D44. is for ZBDD ij∩ ZBDD cin a certain paths x 0x 1x n-1, at ZBDD tthe path x that middle search is corresponding 0x 1x n-1z 0z 1z 2z 3z 4z 5, intercept z 0z 1z 2z 3z 4z 5, create corresponding ZBDD, be designated as ZBDD dS; Create ZBDD d, and make ZBDD d=ZBDD dS;
Step D45. is for ZBDD ij∩ ZBDD cin remaining each paths x 0x 1x n-1, at ZBDD tthe path x that middle search is corresponding 0x 1x n-1z 0z 1z 2z 3z 4z 5, intercept z 0z 1z 2z 3z 4z 5, create corresponding zero compression Binary Decision Diagrams, be designated as ZBDD dS; Then ZBDD is performed d=ZBDD d∩ ZBDD dS;
If step D46. is ZBDD dbe not empty, then the part representated by FeasibleOperation [i] or sub-assemblies and the part representated by FeasibleOperation [j] or sub-assemblies meet precedence relationship constraint, forward step D5 to; Otherwise, do not meet precedence relationship constraint, forward step D6 to.
6. according to claim 1 based on the assembling sequence generation method of symbols Z BDD, it is characterized in that, the concrete steps of described step e are as follows:
Step e 1. applies for an integer variable pos=FeasibleOperation.Length-2;
Step e 2. judges to represent in the ZBDD of feasible Assembly sequences whether there is a paths: the sub-assemblies of front n position representated by FeasibleOperation [pos] in this path, if there is no, then the path of the sub-assemblies of n position representated by FeasibleOperation [pos] after in zero compression Binary Decision Diagrams is deleted;
Step e 3. makes pos=pos-1, if pos>=n, wherein n is the parts count of assembly, then continue to perform step e 2; Otherwise, return ZBDD f, algorithm terminates.
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