CN109214576B - Balance optimization method for low-carbon efficient disassembly line - Google Patents

Balance optimization method for low-carbon efficient disassembly line Download PDF

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CN109214576B
CN109214576B CN201811060442.XA CN201811060442A CN109214576B CN 109214576 B CN109214576 B CN 109214576B CN 201811060442 A CN201811060442 A CN 201811060442A CN 109214576 B CN109214576 B CN 109214576B
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张雷
金志峰
赵希坤
宋豪达
郑雨
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Abstract

The invention provides a low-carbon efficient disassembly line balance optimization method, which comprises the following steps: establishing a disassembly line optimization model taking the shortest disassembly time and the lowest carbon emission as optimization targets; carrying out real number coding on serial numbers of parts of the disassembled product; converting the multi-target problem into a single-target problem by using a weight method, and establishing a target function; randomly generating an initial population from the encoded disassembly sequence, selecting two random character strings from the initial population, and performing a crossover operation to form a new individual; and (5) carrying out mutation operation.

Description

Balance optimization method for low-carbon efficient disassembly line
Technical Field
The invention belongs to the technical field of flexible production line design and control, relates to a low-carbon efficient disassembly line balance optimization method, and particularly relates to a multi-objective optimization method for the low-carbon efficient disassembly line balance problem.
Background
Along with the process of world industrialization, the living standard and the living quality of people are greatly improved, and meanwhile, hundreds of millions of tons of living and industrial wastes are generated. By the end of 2015, the annual recovery total amount of ten categories of renewable resources such as waste steel and iron, waste electrical and electronic products, scrapped automobiles and the like in China is about 2.46 hundred million tons. Relatively strict laws and regulations are continuously provided in various countries, and the recovery and the remanufacturing of waste products are more and more concerned. The remanufacturing engineering takes the full life cycle theory of electromechanical products as guidance, takes the performance leap-type promotion of old parts as a target, takes the high quality, high efficiency, energy saving, material saving and environmental protection as the criteria, and takes the advanced technology and industrialized production as means to repair and reform the old parts. An important feature of remanufacturing is that the quality and performance of the remanufactured product meets or exceeds that of the virgin product.
Disassembly is the first step in the product recovery process, which is the process of systematically separating valuable parts, components, and materials from the discarded disassembled items, and is a necessary link to achieve the lifecycle integrity and containment of the disassembled items. Disassembly has attracted academic and industrial attention due to its important role in product recovery. The disassembly line is the best choice for realizing large-scale disassembly, so that the effective design and the balance of the disassembly line are critical to improving the disassembly efficiency. Therefore, the research on the Problem of Disassembling Line Balancing (DLBP) has important theoretical and practical significance. Considerable effort has been devoted to the study of the DLPB problem, but the major considerations in building multi-objective optimization models have focused on minimizing the number of workstations, balancing idle times of the workstations, early removal of hazardous parts, and removal of high demand parts as early as possible, as well as algorithms.
Disclosure of Invention
In view of the defects of the prior art, the invention aims to provide a low-carbon and high-efficiency disassembly line balance optimization method aiming at the carbon emission characteristic in the disassembly process, construct a low-carbon and high-efficiency multi-objective optimization model, and then optimally solve the disassembly line balance problem by using a genetic algorithm.
The technical scheme adopted by the invention is as follows:
the embodiment of the invention provides a low-carbon efficient disassembly line balance optimization method, which comprises the following steps:
s101, establishing a disassembly line optimization model taking the shortest disassembly time and the lowest carbon emission as optimization targets;
s102, carrying out real number coding on serial numbers of parts of the disassembled product;
s103, converting the multi-target problem in the step S101 into a single-target problem by using a weight method, and establishing a target function;
s104, randomly generating an initial population from the coded disassembly sequence, selecting two random character strings from the initial population, and performing cross operation to form a new individual;
and S105, performing mutation operation.
Optionally, in step S101, the disassembly line optimization model is established by:
(1) the minimum idle time of the minimum workstation and each disassembling station is integrated to obtain an objective function based on the idle time of the minimum workstation and the disassembling station, wherein the objective function is as follows:
Figure GDA0003100446770000021
wherein m represents the number of the working tables, CT is the maximum working time of the working station, STiIs the working time allocated to the workbench i;
(2) the risk index is used as a performance index for evaluating the risk degree of the part, and an objective function based on the risk index is obtained, wherein the objective function is as follows:
Figure GDA0003100446770000022
wherein the content of the first and second substances,
Figure GDA0003100446770000023
representing a hazard index of the component; n represents the number of product parts, and k represents the positions of the parts in the product disassembly sequence; h iskAre 0, 1 and 2, where h is a high hazard for the component partkHas a value of 2; when the parts are generally hazardous, hkHas a value of 1; when the part is not at risk, hkIs 0;
(3) constructing an objective function based on the product disassembly time, wherein the objective function is as follows:
Figure GDA0003100446770000031
wherein T is the time taken to complete the entire disassembly process; n represents the number of parts of the product; BT (BT)iA base disassembly time for the ith part in the disassembly sequence; t is ti,i+1The indexing time of the workbench required from the ith disassembled part to the (i + 1) th part; t is tTIndicating the time of each change of the removal tool, if the removal tools from the ith part to the (i + 1) th part are the same, then p i,i+10, otherwise, pi,i+1＝1；
(4) Constructing an objective function based on the carbon emission, wherein the objective function is as follows:
Figure GDA0003100446770000032
wherein, GEiRepresents the material carbon emission of the ith worktable system, and m represents the number of the worktable.
Optionally, step S103 specifically includes:
normalizing the target function constructed in the step S101 to obtain a normalized target function, wherein the normalization method is as follows:
Figure GDA0003100446770000033
Figure GDA0003100446770000034
Figure GDA0003100446770000035
wherein
Figure GDA0003100446770000036
Representing a normalization parameter;
obtaining a final objective function based on the normalized objective function, wherein the final objective function is defined as follows:
Figure GDA0003100446770000037
wherein ω is1,ω2,ω3Calculated by analytic hierarchy process.
Optionally, step S104 specifically includes:
the first step is as follows: taking a uniformly distributed random number k as a cross point in the interval [1,9], and setting k to be 4;
the second step is that: copying the genes before the intersection point into the children in the order in the parent string;
the third step: the gene behind the child's intersection is scanned from another parent, and if not, the next gene is scanned and stored in the child in order.
Optionally, the step S105 specifically includes:
step 1: calculating the gene factors needing mutation according to the mutation probability and the gene number;
step 2: taking a random integer M as the position of gene mutation in the interval [1, n-1 ];
and 3, step 3: swapping the positions of the M and M +1 genes;
and 4, step 4: judging whether the new disassembly sequence meets the priority constraint and the connection matrix;
and 5, step 5: if the new disassembly sequence satisfies the precedence constraints and the connection matrix, the new chromosome is placed in the population.
Alternatively, in step 1, the number of genes to be mutated is determined by the following formula:
Figure GDA0003100446770000041
Figure GDA0003100446770000042
wherein f ismaxRepresenting the maximum fitness value, f, in the populationavgRepresenting the average fitness of each generation of population, f' representing the greater fitness of the two crossed individuals, f representing the fitness of the individual to be mutated, PC1＝0.9,PC2＝0.6,Pm1＝0.1,Pm2＝0.001。
Optionally, the preferential constraint and connection matrix are determined according to a product part entity assembly drawing.
The low-carbon efficient disassembly line balance optimization method provided by the embodiment of the invention establishes a multi-objective optimization model of the disassembly line balance problem with the shortest disassembly time and the lowest carbon emission as optimization targets on the basis of minimizing the number of workstations and balancing the idle time of each workstation. And (3) performing multi-objective optimization on the disassembly sequence in the disassembly line layout by applying a genetic algorithm, so that the disassembly efficiency is improved and the carbon emission is reduced.
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Fig. 1 is a schematic flow chart of a low-carbon efficient disassembly line balance optimization method according to an embodiment of the present invention;
FIG. 2 is a flow chart of a genetic algorithm used in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a crossover operation performed in an embodiment of the present invention;
FIGS. 4 and 5 are schematic diagrams of a connection relationship matrix and a priority relationship matrix, respectively, of an automobile engine model in an embodiment of the invention;
fig. 6 to 8 are schematic diagrams of an algorithm convergence map of a disassembly route with high-efficiency low carbon as a target, an algorithm convergence map with high-efficiency disassembly as a target, an algorithm convergence map with low carbon as a target, and an optimal chromosome manifestation pattern with high-efficiency low carbon as a target, respectively.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
The low-carbon efficient disassembly line balance optimization method provided by the invention aims at reducing carbon emission and disassembly time, and belongs to the multi-objective optimization problem. Because the objective functions of the multi-objective optimization problem are mutually restricted, the optimal solution of the objective function is difficult to find. In the embodiment of the invention, when the problem is optimized, a weight method is used for converting a multi-objective problem into a single-objective problem, and then a genetic algorithm is used for optimizing and solving the problem of the balance of the disassembly line. As shown in fig. 1, the optimization method includes the following steps:
s101, establishing a disassembly line optimization model taking the shortest disassembly time and the lowest carbon emission as optimization targets;
s102, carrying out real number coding on serial numbers of parts of the disassembled product;
s103, converting the multi-target problem in the step S101 into a single-target problem by using a weight method, and establishing a target function;
s104, randomly generating an initial population from the coded disassembly sequence, and selecting two random character strings U from the initial population1And U2Performing crossover operations to form new individuals;
and S105, performing mutation operation.
The above steps are steps of obtaining a high-efficiency low-carbon disassembly sequence by using a genetic algorithm in the embodiment of the present invention, and a flowchart of the genetic algorithm used in the embodiment of the present invention is shown in fig. 2.
Wherein, in the step S101, the disassembly line optimization model is established by:
(1) the minimum workstation number and the shortest idle time of every dismantlement station can make the dismantlement efficiency of individual dismantlement line strengthen, integrate the shortest idle time of minimum workstation and every dismantlement station, obtain the objective function based on the idle time of minimum workstation and dismantlement station, and this objective function is:
Figure GDA0003100446770000051
wherein m represents the number of the working tables, CT is the maximum working time of the working station, STiIs the working time allocated to the workbench i;
(2) the risk index is used as a performance index for evaluating the risk degree of the part, and an objective function based on the risk index is obtained, wherein the objective function is as follows:
Figure GDA0003100446770000061
wherein the content of the first and second substances,
Figure GDA0003100446770000062
representing a hazard index of the component; n represents the number of product parts, and k represents the positions of the parts in the product disassembly sequence; h iskHas values of 0, 1 and 2, where, when zeroWhen the component harmfulness is high, hkHas a value of 2; when the parts are generally hazardous, hkHas a value of 1; when the part is not at risk, hkThe value of (d) is 0. The degree of damage of the component is strongly related to its position, the more dangerous parts are at the front of the disassembly sequence during the product disassembly process, so that the more dangerous parts are at the front of the disassembly sequence
Figure GDA0003100446770000063
As small as possible.
(3) The product disassembly time is an important index for measuring the disassembly sequence, and the smaller the disassembly time is, the higher the disassembly efficiency is. The product removal time mainly includes the basic removal time, the orientation change time, and the removal tool change time. In the embodiment of the invention, an objective function is constructed based on the product disassembly time, and the objective function is as follows:
Figure GDA0003100446770000064
wherein T is the time taken to complete the entire disassembly process; n represents the number of parts of the product; BT (BT)iA base disassembly time for the ith part in the disassembly sequence; t is ti,i+1The indexing time of the workbench required from the ith disassembled part to the (i + 1) th part; t is tTIndicating the time of each change of the removal tool, if the removal tools from the ith part to the (i + 1) th part are the same, then p i,i+10, otherwise, pi,i+1＝1；
(4) And constructing a low-carbon objective function based on the carbon emission. The low-carbon objective function is mainly embodied by optimizing on the basis of a reasonable disassembly sequence in the whole disassembly process so as to achieve the minimum carbon emission. The low-carbon objective function constructed by the embodiment of the invention is as follows:
Figure GDA0003100446770000065
wherein, GEiRepresents the carbon emission of the material of the ith worktable system, and m represents the workThe number of the making tables.
Further, in step S102, the encoding and decoding processes may be omitted by using the real number encoding of the part number encoding, and the encoding manner of the chromosome in the embodiment of the present invention uses the real number encoding, which may be 32 parts for simplicity.
Further, step S103 specifically includes:
normalizing the target function constructed in the step S101 to obtain a normalized target function, wherein the normalization method is as follows:
Figure GDA0003100446770000071
Figure GDA0003100446770000072
Figure GDA0003100446770000073
wherein
Figure GDA0003100446770000074
Representing a normalization parameter;
obtaining a final objective function based on the normalized objective function, wherein the final objective function is defined as follows:
Figure GDA0003100446770000075
wherein ω is1,ω2,ω3Calculated by analytic hierarchy process.
Further, step S104 specifically includes:
the first step is as follows: taking a uniformly distributed random number k as a cross point in the interval [1,9], and setting k to be 4;
the second step is that: genes before the cross point are assigned to parent U1Copying the order in the string to child O1Performing the following steps;
the third step: in children O1The gene behind the cross point is to be from another parent U2Scanning, scanning the next gene if the gene is in the parent, and storing the gene in the child O in sequence if the gene is not in the parent1As shown in fig. 3.
Further, the step S105 specifically includes:
step 1: calculating the gene factors needing mutation according to the mutation probability and the gene number;
step 2: taking a random integer M as the position of gene mutation in the interval [1, n-1 ];
and 3, step 3: swapping the positions of the M and M +1 genes;
and 4, step 4: judging whether the new disassembly sequence meets the priority constraint and the connection matrix;
and 5, step 5: and if the new disassembly sequence meets the preferential constraint and the connection matrix, putting the new chromosome into the population, thereby obtaining the high-efficiency low-carbon disassembly sequence.
Wherein, in the step 1, the number of genes to be mutated is determined by the following formula:
Figure GDA0003100446770000081
Figure GDA0003100446770000082
wherein f ismaxRepresenting the maximum fitness value, f, in the populationavgRepresenting the average fitness of each generation of population, f' representing the greater fitness of the two crossed individuals, f representing the fitness of the individual to be mutated, PC1＝0.9,PC2＝0.6,Pm1＝0.1,Pm2＝0.001。
In step 4, the preferential constraint and connection matrix is determined according to the product part entity assembly drawing.
[ examples ] A method for producing a compound
The disassembly sequence of an engine of a certain model is used for analysis, if the disassembly model is completely expressed according to parts of a product, a model diagram is extremely easy to be excessively complicated, and great difficulty is brought to the planning of the disassembly sequence, so that the disassembly sequence of the engine of the automobile simplifies certain parts in an assembly body of the engine of the automobile: the belts, toothed belts, bearings, keys and pins are removed from the model drawing, introduced into the sub-assembly and the set of fasteners are taken as one part, so that the number of parts participating in disassembly is reduced, and the planning efficiency is improved.
G is used as the connection relation matrix among the functional elements of the productcIndicating, for example, the priority relationship matrix between product functions by GpShowing that the product needs the tilter to convert the direction in the process of disassembly, and the oil base and the tilter are fixed, thereby obtaining the G of the automobile engine modelc、GpAs shown in figures 4 and 5, respectively. In the present invention, elements of the connection relation matrix Gc
Figure GDA0003100446770000083
Which represents the connection relationship between the functions i and j, and when there is a connection relationship between the functions i and j,
Figure GDA0003100446770000084
when there is no connection between the functions i and j,
Figure GDA0003100446770000085
as shown in fig. 4; priority relation matrix GpOf (2) element(s)
Figure GDA0003100446770000086
Representing the constraint relation of the function j to i; if it is
Figure GDA0003100446770000087
Indicating that the jth function is to be disassembled before the ith function; if it is
Figure GDA0003100446770000088
Indicating that the ith function is not constrained by the jth function, as shown in fig. 5.
Separating individual parts from an automobile engine, the following two conditions must be met:
firstly, the method is not preferentially restricted by other parts;
② only having contact constraint relation with a certain part in the assembly body.
The final objective function is defined as follows:
Figure GDA0003100446770000089
wherein ω is1,ω2,ω3Calculated by an analytic hierarchy process to obtain the product,
Figure GDA0003100446770000091
Figure GDA0003100446770000092
Figure GDA0003100446770000093
Figure GDA0003100446770000094
representing the normalization parameters.
The constraint relation and the disassembly process requirements among automobile engine parts are comprehensively considered, the given beat CT is 120s, the power of a tilter of an engine disassembly line is 12KW, the time spent in overturning for 180 degrees is 4s, and the time spent in overturning for 90 degrees is 2 s. The time that the workman changed extracting tool is the definite value 4s, and electric spanner power is 4 KW.
When the genetic algorithm is calculated, the algorithm parameters are set as follows: the population size is set to 50, the maximum iteration number of the algorithm is MAXGEN which is 150, and the channel GGAP which is 0.9.
The MATLAB software was used to optimize for low carbon and high efficiency, and the results are shown in Table 1 below in comparison with the results obtained from the individual optimization of high efficiency and low carbon.
Table 1: optimizing results
Figure GDA0003100446770000095
An algorithm convergence chart of a disassembly route with high-efficiency low carbon as a target, an algorithm convergence chart with high-efficiency disassembly as a target, an algorithm convergence chart with low carbon as a target and an optimal chromosome manifestation mode with high-efficiency low carbon as a target are respectively shown in fig. 6 to 8.
The high efficiency low carbon disassembly sequence according to the above is converted into a disassembly line layout scheme as shown in table 2.
Table 2: disassembly line layout task allocation scheme
Figure GDA0003100446770000096
Figure GDA0003100446770000101
The above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (6)

1. A low-carbon efficient disassembly line balance optimization method is characterized by comprising the following steps:
s101, establishing a disassembly line optimization model taking the shortest disassembly time and the lowest carbon emission as optimization targets;
s102, carrying out real number coding on serial numbers of parts of the disassembled product;
s103, converting the multi-target problem in the step S101 into a single-target problem by using a weight method, and establishing a target function;
s104, randomly generating an initial population from the coded disassembly sequence, selecting two random character strings from the initial population, and performing cross operation to form a new individual;
s105, performing mutation operation;
in step S101, the disassembly line optimization model is established by:
(1) the minimum idle time of the minimum workstation and each disassembling station is integrated to obtain an objective function based on the idle time of the minimum workstation and the disassembling station, wherein the objective function is as follows:
Figure FDA0003100446760000011
wherein m represents the number of the working tables, CT is the maximum working time of the working station, STiIs the working time allocated to the workbench i;
(2) constructing an objective function based on the product disassembly time, wherein the objective function is as follows:
Figure FDA0003100446760000012
wherein T is the time taken to complete the entire disassembly process; n represents the number of parts of the product; BT (BT)iA base disassembly time for the ith part in the disassembly sequence; t is ti,i+1The indexing time of the workbench required from the ith disassembled part to the (i + 1) th part; t is tTIndicating the time of each change of the removal tool, if the removal tools from the ith part to the (i + 1) th part are the same, then pi,i+10, otherwise, pi,i+1＝1；
(3) Constructing an objective function based on the carbon emission, wherein the objective function is as follows:
Figure FDA0003100446760000013
wherein, GEiRepresents the material carbon emission of the ith worktable system, and m represents the number of the worktable.
2. The method according to claim 1, wherein step S103 specifically comprises:
normalizing the target function constructed in the step S101 to obtain a normalized target function, wherein the normalization method is as follows:
Figure FDA0003100446760000021
Figure FDA0003100446760000022
Figure FDA0003100446760000023
wherein
Figure FDA0003100446760000024
T*Representing a normalization parameter;
obtaining a final objective function based on the normalized objective function, wherein the final objective function is defined as follows:
Figure FDA0003100446760000025
wherein ω is1,ω2,ω3Calculated by analytic hierarchy process.
3. The method according to claim 1, wherein step S104 specifically includes:
the first step is as follows: taking a uniformly distributed random number k as a cross point in the interval [1,9], and setting k to be 4;
the second step is that: copying the genes before the intersection point into the children in the order in the parent string;
the third step: the genes behind the child's intersection are scanned from another parent, so that if a gene is in a parent, the next gene is scanned, and if not, the genes are stored in order in the child.
4. The method according to claim 1, wherein the step S105 specifically comprises:
step 1: calculating the gene factors needing mutation according to the mutation probability and the gene number;
step 2: taking a random integer M as the position of gene mutation in the interval [1, n-1 ];
and 3, step 3: swapping the positions of the M and M +1 genes;
and 4, step 4: judging whether the new disassembly sequence meets constraint conditions or not;
and 5, step 5: if the new disassembly sequence satisfies the constraint, the new chromosome is placed in the population.
5. The method according to claim 4, wherein in step 1, the number of genes to be mutated is determined by the following formula:
Figure FDA0003100446760000031
Figure FDA0003100446760000032
wherein f ismaxRepresenting the largest of the representative populationFitness value favgRepresenting the average fitness of each generation of population, f' representing the greater fitness of the two crossed individuals, f representing the fitness of the individual to be mutated, PC1＝0.9,PC2＝0.6,Pm1＝0.1,Pm2＝0.001。
6. The method of claim 4, wherein the constraints are determined from a product part physical assembly drawing.
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