CN107944720B - Assembly task planning method for complex product - Google Patents

Assembly task planning method for complex product Download PDF

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CN107944720B
CN107944720B CN201711240523.3A CN201711240523A CN107944720B CN 107944720 B CN107944720 B CN 107944720B CN 201711240523 A CN201711240523 A CN 201711240523A CN 107944720 B CN107944720 B CN 107944720B
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李艳萍
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Abstract

The method for planning the assembly tasks of the complex products comprises four steps of complexity source analysis, classification description and measurement of complexity, establishment of an assembly task planning model and algorithm optimization solution, wherein the complexity source analysis is to analyze the complexity sources of the assembly of the complex products according to the assembly characteristics of complex assemblies and by combining information such as component materials, processes, assembly resources, yield scales and the like; the complexity classification description and measurement are the classification description of assembly complexity from the aspects of product part complexity, assembly process, assembly resources, assembly operation complexity and the like, the assembly process, the assembly resources and the like corresponding to different kinds of parts such as assembly part materials are specific categories or groups, the assembly process and the assembly resource assembly operation are selected and executed to be non-independently related, and the assembly operation under a certain condition needs to establish the measurement of conditional entropy based on the assembly condition according to the corresponding condition.

Description

Assembly task planning method for complex product
Technical Field
The invention relates to the field of product assembly line process planning, in particular to an assembly task planning method for a complex product.
Background
At present, assembly process planning and assembly task allocation of complex product assembly are carried out, manufacturers mostly carry out assembly planning according to sample assembly tests, the workload is huge, the time consumption is long, the process design quality is unstable, the design result is different from person to person, and ideal effects in the aspects of assembly task division, allocation and the like are difficult to achieve. In order to meet the requirements of digital factories and management, researchers apply assembly line balance-oriented assembly task allocation, combine the actual resource constraint condition of assembly production under the condition of meeting the constraint condition of assembly relation of product parts, and perform assembly process planning and assembly task allocation according to assembly node time in an assembly area, so as to ensure the smooth operation of assembly line balance and assembly;
the assembly process planning technology has the advantages that for the assembly process planning of single material varieties in the traditional batch production assembly, the assembly operation is low in complexity, the assembly line is simple in arrangement, and the size of the assembly task amount can be basically measured according to the assembly time or the assembly task allocation can be carried out according to the sample assembly test. For complex assemblies, particularly those that meet the requirements of intelligent manufacturing and personalization, the diversity of the assembly components and the uncertainty of assembly increase, thereby increasing the complexity of assembly operations and the error-prone rate of assembly, increasing the complexity of assembly, which is directly linked to the difficulty of assembly and the assembly time. Therefore, the existing assembly process planning and assembly task allocation technology has obvious limitation in applying the assembly task planning of complex products.
Disclosure of Invention
It is an object of the invention to provide an assembly task planning method that is more efficient for complex product assembly lines with increased personalization and uncertainty.
The technical scheme adopted by the invention for solving the technical problem is as follows:
the assembly task planning method for the complex product comprises four steps of complexity source analysis, classification description and measurement of complexity, assembly task planning model establishment and algorithm optimization solution, and is characterized in that:
(1) the complexity source analysis is to analyze the complexity source of the complex product assembly according to the assembly characteristics of the complex assembly body and combining information such as component materials, processes, assembly resources, yield scale and the like;
(2) the complexity classification description and measurement are the classification description of assembly complexity from the aspects of product part complexity, assembly process, assembly resources, assembly operation complexity and the like, the assembly process, the assembly resources and the like corresponding to different kinds of parts such as assembly part materials and the like are specific categories or groups, the assembly process and the assembly resource assembly operation are selected and executed to be non-independently related, and the assembly operation under a certain condition needs to establish the measurement of conditional entropy based on the assembly condition according to the corresponding condition;
(3) the establishment of the assembly task planning model is based on a complexity analysis assembly task planning model, an assembler is used as a backpack to be distributed, the reciprocal of each complexity of assembly operation is used as the satisfaction degree of whether a task to be distributed is distributed or not, and the assembly task distribution model with the minimum total complexity of an assembly system is established;
(4) the algorithm optimization solution is to obtain the assembly task distribution with the minimum complexity according to algorithm search and realize the solution of the assembly task planning problem by combining the constraint established by the assembly site conditions.
The complexity source analysis includes an operation selection complexity CocOperation execution complexity CopThe operation selection complexity comprises six analysis aspects of part selection, process selection, assembly equipment selection, assembly tool selection, assembly fixture selection and assembly sequence selection, and the operation execution complexity comprises positioning and measurement of parts, change and adjustment of fixtures, operation and adjustment of equipment, process adjustment and parameter change and auxiliary tool change and adjustment.
The complexity source analysis is specifically represented as:
Figure GDA0003318574860000031
wherein the content of the first and second substances,
Figure GDA0003318574860000032
is as follows
Figure GDA0003318574860000033
The coefficient of action selected for the class assembly operation,
Figure GDA0003318574860000034
is the kthvThe coefficient of action of class assembly operation execution, if the assembly operation process includes kthuClass assembly operation selection, then order
Figure GDA0003318574860000035
Otherwise
Figure GDA0003318574860000036
If present, the kthvClass assembly operation execution behavior, then
Figure GDA0003318574860000037
Otherwise
Figure GDA0003318574860000038
Is the kthuThe class assembly operation selects the weighting coefficients of the information entropy,
Figure GDA0003318574860000039
is the kthvThe class assembly operation performs weighting factors of the complexity,
Figure GDA00033185748600000310
and
Figure GDA00033185748600000311
respectively represent the kthvClass assembly operation selection complexity and kthuClass assembly operation implementation complexity.
The algorithm optimization solution is concretely as follows:
(1) an objective function:
assuming that there are m assembly workers Mj, assembly operation tasks of n complex product parts, the complexity of assigning the k-th assembly operation of the assembly task i (i ═ 1,2, …, n) to the assembly task j is expressed as the value satisfaction of assigning the k-th assembly operation task of the assembly part i to the assembly worker j
Figure GDA00033185748600000312
Corresponds to the inverse of the complexity measure, i.e.:
Figure GDA00033185748600000313
wherein the constraint condition is as follows:
not exceeding the complexity of the assembly task assigned to a single operating worker Mj
∑Coc+∑CopAnd/n, namely:
Figure GDA0003318574860000041
② comparing the complexity measure of the task quantity of each operator with ∑ Coc+∑CopThe/n approximation, i.e.:
Figure GDA0003318574860000042
(2) coding form and fitness function:
genetically encoding:
and mapping the solution space of the complex product assembly task allocation problem into gene positions by adopting a binary coding mode. Representing the genetic code by a two-level hierarchical matrix of x (m × n) and x (n × k), and representing the action coefficient of the kth assembly operation contained in the assembly of the part i;
the fitness function is expressed as:
Figure GDA0003318574860000043
wherein, Oj(C) Assignment of an objective function, P, of a task to an assembler jj(C) Penalty functions for complexity of assembly worker j exceeding constraints, Di(C) And (3) a penalty function belonging to a plurality of backpacks for the assembly task k, wherein the structure of each function is as follows:
Figure GDA0003318574860000044
Figure GDA0003318574860000051
Figure GDA0003318574860000052
wherein, lambda and gamma are penalty coefficients,
Figure GDA0003318574860000053
a complexity representation assigned to assembly worker j for assembly task i category k assembly operations,
Figure GDA0003318574860000054
a judgment coefficient for judging whether the kth type assembly operation task for assembling the ith part is distributed to the jth assembly worker;
(3) genetic operator:
the genetic operator consists of three operators of selection, intersection and mutation, and the specific implementation strategy is as follows:
selecting: random selection is carried out by adopting a roulette mode in proportion to the adaptive value, and the number of comparison times is effectively reduced by using a half-searching method when roulette is selected, so that the corresponding roulette is ensured to be in O (log)2N), wherein N is the size of the population;
step two, crossing: genetic coding mode gene positions existing in a matrix mode are equivalent to a coding string with the length of m x n x k in the cross operation, a consistent cross operator is adopted, and each position on the coding string is randomly and uniformly crossed according to the same probability;
③ variation: randomly selecting one or more gene positions from individual code strings in a population, and then selecting one or more gene positions according to the variation probability PmAnd (5) carrying out mutation, namely taking the value of the current gene as a non-value.
The invention has the advantages that:
1. the invention overcomes the limitation of the existing assembly task planning technology, considers the influence of diversity and uncertainty increased by personalized and intelligent requirements on assembly operation, carries out assembly complexity classification description and measurement, establishes an assembly task distribution optimization model with the minimum complexity of an assembly system based on complexity measure, and obtains the assembly task distribution with the minimum complexity by heuristic search of an intelligent optimization algorithm;
2. the method reflects the problems of difficulty and easiness of complex product assembly tasks and error rate of assembly through the complexity of assembly nodes, more conforms to the actual complex product assembly production, improves the automation level of complex product assembly task planning, improves the efficiency of complex product assembly planning, reduces the error rate, better ensures the assembly quality, reduces the assembly cost and shortens the production period;
3. the method can be used for assembling bodies of various complex products, such as task planning problems of large complex assembly with high diversified and intelligent requirements of multi-material light-weight vehicle bodies, airplanes and the like.
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FIG. 1 is a flow chart of a method for planning assembly tasks of a complex product according to the present invention;
fig. 2 is a schematic diagram of the classification of operation selection complexity and operation execution complexity in the method.
Detailed Description
In order to make the technical means, the original characteristics, the achieved purposes and the effects of the invention easy to understand, the invention is further described with reference to the figures and the specific embodiments.
As shown in fig. 1 and fig. 2, the assembly task planning method for complex products provided by the present invention includes four steps of complexity source analysis, classification description and measurement of complexity, building of an assembly task planning model, and algorithm optimization solution:
(1) the complexity source analysis is to analyze the complexity source of the complex product assembly according to the assembly characteristics of the complex assembly body and combining information such as component materials, processes, assembly resources, yield scale and the like;
(2) the complexity classification description and measurement are the classification description of assembly complexity from the aspects of product part complexity, assembly process, assembly resources, assembly operation complexity and the like, the assembly process, the assembly resources and the like corresponding to different kinds of parts such as assembly part materials and the like are specific categories or groups, the assembly process and the assembly resource assembly operation are selected and executed to be non-independently related, and the assembly operation under a certain condition needs to establish the measurement of conditional entropy based on the assembly condition according to the corresponding condition;
(3) the establishment of the assembly task planning model is based on a complexity analysis assembly task planning model, an assembler is used as a backpack to be distributed, the reciprocal of each complexity of assembly operation is used as the satisfaction degree of whether a task to be distributed is distributed or not, and the assembly task distribution model with the minimum total complexity of an assembly system is established;
(4) the algorithm optimization solution is to obtain the assembly task distribution with the minimum complexity according to algorithm search and realize the solution of the assembly task planning problem by combining the constraint established by the assembly site conditions.
Complexity of assembly operation CocPart selection is the primary choice for realizing the assembly of complex products, and information entropy with complexity selectable by corresponding parts is established
Figure GDA0003318574860000071
A metric, as in formula (a); due to the non-independent dependence of the complex product assembly operation choices, as can be seen in FIG. 1, the process choice is a conditional choice under part selection whose complexity can be selected by the conditional entropy of the corresponding part selection
Figure GDA0003318574860000072
A metric, as shown in equation (b); similarly, the selection of equipment and tools is the condition selection under the selection of assembly process, and the condition entropy is selected corresponding to the assembly equipment
Figure GDA0003318574860000073
And assembly tool selection conditional entropy
Figure GDA0003318574860000074
May be represented by formulas (c) and (d), respectively; the selection of the assembling fixture and the assembling sequence is the condition selection under the selection of the corresponding parts, and the complexity of the selection can be respectively expressed as the fixture selection condition entropy
Figure GDA0003318574860000081
And assembly tool selection conditional entropy
Figure GDA0003318574860000082
As shown in formulas (e) and (f);
(a)
Figure GDA0003318574860000083
(b)
Figure GDA0003318574860000084
(c)
Figure GDA0003318574860000085
(d)
Figure GDA0003318574860000086
(e)
Figure GDA0003318574860000087
(f)
Figure GDA0003318574860000088
assembly operation execution complexity CopExecuting objects according to the assembly operation mainly comprises: complexity of operation execution generated during positioning, measuring and adjusting of parts
Figure GDA0003318574860000089
Operation execution complexity in setup, change and adjustment of assembly resources
Figure GDA00033185748600000810
Including in particular device change, debug and tuning complexity
Figure GDA00033185748600000811
Operational complexity of tools and auxiliary tools
Figure GDA00033185748600000812
And complexity of operation execution of mounting, positioning, adjusting and changing of the clamps
Figure GDA00033185748600000813
Describing and measuring the execution complexity of the assembly operation, and realizing the description and measurement by overlapping the execution complexity of various assembly operations; the source of complexity analysis includes operationsSelection complexity CocOperation execution complexity CopThe operation selection complexity comprises six analysis aspects of part selection, process selection, assembly equipment selection, assembly tool selection, assembly fixture selection and assembly sequence selection, and the operation execution complexity comprises positioning and measurement of parts, change and adjustment of fixtures, operation and adjustment of equipment, process adjustment and parameter change and auxiliary tool change and adjustment. Complexity of assembly operation CO, selection of complexity C by assembly operationocComplexity of assembly operation execution CopAnd (4) jointly determining. Assume using kcu(kcu＝kc1,kc2,., KC) for each type of assembly operation choice, kpv(kpv＝kp1,kp2,., KP) performs complexity numbering for each type of assembly operation, taking into account the differences in complexity-affecting weights of each type of operation.
The complexity source analysis is specifically represented as:
Figure GDA00033185748600000814
wherein the content of the first and second substances,
Figure GDA0003318574860000091
the coefficient of action selected for the type kcu fitting operation,
Figure GDA0003318574860000092
is the kthvThe coefficient of action of class assembly operation execution, if the assembly operation process includes kthuClass assembly operation selection, then order
Figure GDA0003318574860000093
Otherwise
Figure GDA0003318574860000094
If present, the kthvClass assembly operation execution behavior, then
Figure GDA0003318574860000095
Otherwise
Figure GDA0003318574860000096
Is the kthuThe class assembly operation selects the weighting coefficients of the information entropy,
Figure GDA0003318574860000097
is the kthvThe class assembly operation performs weighting factors of the complexity,
Figure GDA0003318574860000098
and
Figure GDA0003318574860000099
respectively represent the kthvClass assembly operation selection complexity and kthuClass assembly operation implementation complexity.
Establishing a complex product assembly task planning model based on assembly operation complexity optimization:
since the assembly complexity is directly related to the difficulty of assembly and the error rate thereof, the satisfaction of the assembly complexity as the allocation of the assembly task is a goal that the complexity is smaller and better. The goal of assembly task assignment is to have all personnel complete the assigned task complexity Cj ═ C1,C2,...,CmThe maximum value of (j is the number of assemblers, j is 1,2, …, m) is the smallest, i.e.:
Cj＝min{max{Cj}}＝min{max{C1,C2,...,Cm}}；
suppose there are M assemblers Mj(M1,M2,…,Mm) N parts Pi(P1,P2,…,Pn) The assembly task allocation of (1), wherein the assembly of each part comprises the selection of assembly operations of class K (K ═ 1,2, …, K) and the complexity of the execution tasks of the assembly operations;
the relation between the assembly parts and the assembly personnel is represented by two-stage matrixes of (m multiplied by n) and (n multiplied by k), the complexity matrix of the assembly task of the complex product can be represented by two-stage hierarchical matrixes of C (m multiplied by n) and C (n multiplied by k), and the k type assembly operation task of the assembly parts i is distributed to the operationThe complexity obtained by person j is represented as
Figure GDA00033185748600000910
The smaller the value, the greater the cost of task allocation and the greater the value satisfaction achieved.
Assuming that the assembly component i needs to complete the assembly operation tasks of the K (K ═ 1,2, …, K) class (including the assembly operation selection and the assembly operation execution), the assembly task complexity of the assembly component i can be expressed as
Figure GDA0003318574860000101
(k＝1,2,…,K)。Cj(j ═ 1,2, …, m) for the complexity of the assembly task assigned to operator j,
Figure GDA0003318574860000102
maximum complexity that each operator can afford for an appointment;
Figure GDA0003318574860000103
the complexity of the implementation for assigning the kth (K ═ 1,2, …, K) assembly task to the jth (j ═ 1,2, …, m) operator for the ith (i ═ 1,2, …, n) part. Then, according to the actual assembly process design and the field requirements, the decomposition of the assembly task of each part of the vehicle door is determined. And then, according to the work area constraints of the assembly personnel and the assembly equipment, firstly, performing primary task grouping on the assembly tasks, and then, performing assembly task allocation of a public area. In the actual situation of an assembly field, an assembly task can be distributed to one assembly worker to independently assemble parts, and can also be distributed to two assembly workers to jointly realize assembly operation according to needs.
Establishing an objective function of a multi-material vehicle door assembly task allocation problem:
Figure GDA0003318574860000104
Figure GDA0003318574860000105
(II)F∈r(Mj),j＝1,2,…,m；
(III)R(g)∈φy,i＝1,2,…,n；k＝1,2,…,K；
(IV)S(g)∈φx,i＝1,2,…,n；k＝1,2,…,K；
(V)P(g)∈φp,i＝1,2,…,n；k＝1,2,…,K；
(VI)C(Mj)＝∑Coc+∑Cop,j＝1,2,…,m；
Figure GDA0003318574860000111
wherein F is a heuristic intelligent optimization algorithm, F is an assembly task allocation problem,
Figure GDA0003318574860000112
(i ═ 1,2, …, n; K ═ 1,2, …, K) is the complexity of the class K assembly operation for part i to be assigned;
Figure GDA0003318574860000113
the task grouping is realized by a technician according to the assembly field conditions of the complex products. MjTo the assembler (j ═ 1,2, …, m), φzFor the position of the assembly tasks in the assembly group (positional compactness), phipGrouping assembly tasks according to the type of assembly process:
Figure GDA0003318574860000114
Figure GDA0003318574860000115
C(Mj)＝∑Coc+∑Copcomplexity of assembly operations for each assembler; r (g) allocating tasks according to the position of the part group, namely the inner frame or the outer frame; s (g) is based on the position of the component group being horizontalOr vertically to distribute tasks; p (g) is a task grouping according to the type of the assembly process;
Figure GDA0003318574860000116
is a decision variable, if
Figure GDA0003318574860000117
A type k assembly operation representing an assembly task i is assigned to the operator j,
Figure GDA0003318574860000118
indicating no allocation;
the constraint condition (I) is expressed in that all the assembly part connecting points are grouped according to the factors of the positions (horizontal or vertical), the arrangement compactness, the area direction, the assembly process and the like of the connecting point group, so that the number of targets is reduced; the constraint (II) represents the process range of the operator or the equipment which needs to be considered in task allocation; when the constraint condition (III) indicates that tasks are distributed, the tasks at the same position side of the vehicle door assembly are distributed to the same person as much as possible; when the constraint condition (IV) indicates that tasks at the same type position (horizontal or vertical) for assembling the vehicle door are distributed to the same person as much as possible when the tasks are distributed; the constraint condition (V) indicates that the assembly tasks with the same assembly process type or the same used equipment are distributed to the same person as much as possible; constraint (VI) is the distribution assembly complexity calculation method; the constraint (VII) is the value range of the decision variable.
The algorithm optimization solution is concretely as follows:
(1) an objective function:
assuming that there are m assembly workers Mj, assembly operation tasks of n complex product parts, the complexity of assigning the k-th assembly operation of the assembly task i (i ═ 1,2, …, n) to the assembly task j is expressed as the value satisfaction of assigning the k-th assembly operation task of the assembly part i to the assembly worker j
Figure GDA0003318574860000121
Corresponds to the inverse of the complexity measure, i.e.:
Figure GDA0003318574860000122
wherein the constraint condition is as follows:
(ii) the complexity of the assembly task given to a single operator Mj does not exceed
∑Coc+∑CopAnd/n, namely:
Figure GDA0003318574860000123
② comparing the complexity measure of the task quantity of each operator with ∑ Coc+∑CopThe/n approximation, i.e.:
Figure GDA0003318574860000124
(2) coding form and fitness function:
genetically encoding:
and mapping the solution space of the complex product assembly task allocation problem into gene positions by adopting a binary coding mode. Representing the genetic code by a two-level hierarchical matrix of x (m × n) and x (n × k), and representing the action coefficient of the kth assembly operation contained in the assembly of the part i;
③ the fitness function is expressed as:
Figure GDA0003318574860000131
wherein, Oj(C) Assignment of an objective function, P, of a task to an assembler jj(C) Penalty functions for complexity of assembly worker j exceeding constraints, Di(C) And (3) a penalty function belonging to a plurality of backpacks for the assembly task k, wherein the structure of each function is as follows:
Figure GDA0003318574860000132
Figure GDA0003318574860000133
Figure GDA0003318574860000134
wherein, lambda and gamma are penalty coefficients,
Figure GDA0003318574860000135
a complexity representation assigned to assembly worker j for assembly task i category k assembly operations,
Figure GDA0003318574860000136
a judgment coefficient for judging whether the kth type assembly operation task for assembling the ith part is distributed to the jth assembly worker;
(3) genetic operator:
the genetic operator consists of three operators of selection, intersection and mutation, and the specific implementation strategy is as follows:
selecting: random selection is carried out by adopting a roulette mode in proportion to the adaptive value, and the number of comparison times is effectively reduced by using a half-searching method when roulette is selected, so that the corresponding roulette is ensured to be in O (log)2N), wherein N is the size of the population;
step two, crossing: genetic coding mode gene positions existing in a matrix mode are equivalent to a coding string with the length of m x n x k in the cross operation, a consistent cross operator is adopted, and each position on the coding string is randomly and uniformly crossed according to the same probability;
③ variation: randomly selecting one or more gene positions from individual code strings in a population, and then selecting one or more gene positions according to the variation probability PmAnd (5) carrying out mutation, namely taking the value of the current gene as a non-value.
The above embodiments are merely illustrative of the technical concept and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the content of the present invention and implement the present invention, and not to limit the scope of the present invention, and all equivalent changes or modifications made according to the spirit of the present invention should be covered by the scope of the present invention.

Claims (2)

1. The assembly task planning method for the complex product comprises four steps of complexity source analysis, classification description and measurement of complexity, assembly task planning model establishment and algorithm optimization solution, and is characterized in that:
(1) the complexity source analysis is to analyze the complexity source of the complex product assembly according to the assembly characteristics of the complex assembly body and by combining the material, the process, the assembly resource and the yield scale information of the parts;
(2) the complexity classification description and measurement is the classification description of assembly complexity from the aspects of product part complexity, assembly process, assembly resources and assembly operation complexity, the assembly process and the assembly resources corresponding to different varieties of parts of assembly part materials are all specific categories or groups, the assembly operation selection and execution of the assembly process and the assembly resources are non-independently related, and the assembly operation under a certain condition needs to establish the measurement of condition entropy based on the assembly condition according to the corresponding condition;
(3) the establishment of the assembly task planning model is based on a complexity analysis assembly task planning model, an assembler is used as a backpack to be distributed, the reciprocal of each complexity of assembly operation is used as the satisfaction degree of whether a task to be distributed is distributed or not, and the assembly task distribution model with the minimum total complexity of an assembly system is established;
(4) the algorithm optimization solution is to obtain the assembly task distribution with the minimum complexity according to algorithm search and realize the solution of the assembly task planning problem by combining the constraint established by the assembly site conditions;
the complexity source analysis includes an operation selection complexity CocOperation execution complexity CopThe operation selection complexity comprises six analysis aspects of part selection, process selection, assembly equipment selection, assembly tool selection, assembly fixture selection and assembly sequence selection, and the operation execution complexity comprises positioning and measurement of parts, fixture changeAdjusting, operating and adjusting equipment, adjusting process and changing parameters, and changing and adjusting auxiliary tools;
the complexity source analysis is specifically represented as:
Figure FDA0003318574850000021
wherein the content of the first and second substances,
Figure FDA0003318574850000022
is the kthuThe coefficient of action selected for the class assembly operation,
Figure FDA0003318574850000023
is the kthvThe coefficient of action of class assembly operation execution, if the assembly operation process includes kthuClass assembly operation selection, then order
Figure FDA0003318574850000024
Otherwise
Figure FDA0003318574850000025
If present, the kthvClass assembly operation execution behavior, then
Figure FDA0003318574850000026
Otherwise
Figure FDA0003318574850000027
Figure FDA0003318574850000028
Is the kthuThe class assembly operation selects the weighting coefficients of the information entropy,
Figure FDA0003318574850000029
is the kthvThe class assembly operation performs weighting factors of the complexity,
Figure FDA00033185748500000210
and
Figure FDA00033185748500000211
respectively represent the kthvClass assembly operation selection complexity and kthuClass assembly operation implementation complexity.
2. The assembly task planning method for complex products according to claim 1, wherein:
the algorithm optimization solution is concretely as follows:
(1) an objective function:
assuming that there are m assembly workers Mj, assembly operation tasks of n complex product parts, the complexity of the k-th assembly operation assigned to the assembly task j of the assembly task i (i ═ 1,2, …, n) is represented as
Figure FDA00033185748500000212
The value satisfaction of the assignment of the class k assembly operation task of the assembly parts i to the task of the assembly operation worker j is
Figure FDA00033185748500000213
Corresponds to the inverse of the complexity measure, i.e.:
Figure FDA00033185748500000214
wherein the constraint condition is as follows:
(ii) the complexity of the assembly task assigned to a single operator Mj does not exceed ∑ Coc+∑CopAnd/n, namely:
Figure FDA0003318574850000031
② comparing the complexity measure of the task quantity of each operator with ∑ Coc+∑CopThe/n approximation, i.e.:
Figure FDA0003318574850000032
(2) coding form and fitness function:
genetically encoding:
mapping the solution space of the complex product assembly task allocation problem into gene positions by adopting a binary coding mode; the genetic code is represented by a two-level hierarchical matrix of x (m x n) and x (n x k),
Figure FDA0003318574850000033
representing the coefficient of action of the kth assembly operation included in the assembly of the part i;
the fitness function is expressed as:
Figure FDA0003318574850000034
wherein, Oj(C) Assignment of an objective function, P, of a task to an assembler jj(C) Penalty functions for complexity of assembly worker j exceeding constraints, Di(C) And (3) a penalty function belonging to a plurality of backpacks for the assembly task k, wherein the structure of each function is as follows:
Figure FDA0003318574850000035
Figure FDA0003318574850000041
Figure FDA0003318574850000042
wherein, lambda and gamma are penalty coefficients,
Figure FDA0003318574850000043
a complexity representation assigned to assembly worker j for assembly task i category k assembly operations,
Figure FDA0003318574850000044
a judgment coefficient for judging whether the kth type assembly operation task for assembling the ith part is distributed to the jth assembly worker;
(3) genetic operator:
the genetic operator consists of three operators of selection, intersection and mutation, and the specific implementation strategy is as follows:
selecting: random selection is carried out by adopting a roulette mode in proportion to the adaptive value, and the number of comparison times is effectively reduced by using a half-searching method when roulette is selected, so that the corresponding roulette is ensured to be in O (log)2N), wherein N is the size of the population;
step two, crossing: genetic coding mode gene positions existing in a matrix mode are equivalent to a coding string with the length of m x n x k in the cross operation, a consistent cross operator is adopted, and each position on the coding string is randomly and uniformly crossed according to the same probability;
③ variation: randomly selecting one or more gene positions from individual code strings in a population, and then selecting one or more gene positions according to the variation probability PmAnd (5) carrying out mutation, namely taking the value of the current gene as a non-value.
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