CN111860990A - Multi-product disassembly-oriented multi-target disassembly sequence planning method - Google Patents

Multi-product disassembly-oriented multi-target disassembly sequence planning method Download PDF

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CN111860990A
CN111860990A CN202010660663.1A CN202010660663A CN111860990A CN 111860990 A CN111860990 A CN 111860990A CN 202010660663 A CN202010660663 A CN 202010660663A CN 111860990 A CN111860990 A CN 111860990A
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郭希旺
范振翔
骆文
彭方杰
郭来德
赵健
胡承波
邹英利
宋大鹏
易宝飞
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Abstract

The invention provides a multi-product disassembly-oriented multi-target disassembly sequence planning method, which comprises the following steps: s1, establishing a mathematical model with the aim of maximizing the dismantling profit and minimizing the energy consumption; s2 population initialization; s3 population evolution; s4 external file evolution; s5 further updating the population; if the maximum iteration times g _ max are met, the algorithm is terminated, and a Pareto optimal solution in an external file is output as a disassembly task allocation scheme; otherwise, repeating steps S3-S5 a predetermined number of times. The planning method adopts a double-chain character string to express a solution, adopts population evolution and external archive evolution methods to search a solution space, adopts a random simulation method, and designs a multi-target squirrel search algorithm so as to obtain a feasible solution. The method is beneficial for decision makers to make intelligent decisions, and an effective method is provided for solving the problem of multi-product disassembly sequence planning considering uncertainty and multi-objective optimization.

Description

Multi-product disassembly-oriented multi-target disassembly sequence planning method
Technical Field
The invention belongs to the technical field of information and control, and particularly relates to a multi-product disassembly-oriented multi-target disassembly sequence planning method.
Background
Disassembly is one of the most important steps in the remanufacturing process. It disassembles the end of line product (EOL product) into multiple components and then performs other remanufacturing operations such as rework and reassembly. The focus of the disassembly sequence planning problem (dspp) is to find an optimal disassembly sequence for disassembling waste products and to optimize certain criteria to be considered, such as profit expectations, time-oriented and energy-conscious objectives. In recent years, due to the important role of dspp in improving disassembly efficiency, extensive research has been conducted in academia and industry. However, all existing research has focused on disassembly sequence planning for disassembling one EOL product. In actual production, a plurality of products are generally required to be disassembled within a plan scope, so that a disassembly sequence plan is preferably established for the products together so as to achieve global optimization.
Furthermore, decision makers often show a strong interest in multiple conflicting criteria when resolving dspps (e.g., maximizing the profit on teardown and minimizing the teardown time). In recent years, the goal of energy-oriented has been receiving more and more attention, as we have to pay more attention to environmental protection and economic growth as in the past. In addition, because details of disassembly cannot be obtained in different use processes of the EOL product, uncertainties often occur in the disassembly process. Therefore, in the multi-product disassembly sequence planning model considered by us, the uncertainty of disassembly profit, time and energy consumption and the multi-objective optimization problem need to be considered.
Through analysis of existing studies, we found that there is currently no study for multi-product dspp. In practice, there are often multiple EOL products that must be disassembled within a planned range. To get an overall optimization, we preferably combine them for disassembly sequence planning decisions. Therefore, a solution to multi-product dspp is needed. In addition, multiple optimization objectives, such as profit correlation, time-oriented and energy-aware criteria, are considered from the economic sustainability perspective, and an optimal trade-off decision is selected among them. In addition, because the EOL product is difficult to obtain accurate information due to the variation of the use process, uncertainty is also considered. Therefore, there is a need for a disassembly sequence planning method that can meet the maximum disassembly profit, minimize energy consumption, and meet the requirement of disassembly time.
Disclosure of Invention
The invention aims to overcome the defects of the technology and provides a multi-product disassembly-oriented multi-target disassembly sequence planning method, which is a disassembly sequence planning method under the constraint of SSA optimization algorithms to obtain a plurality of comprehensive better solutions in various aspects.
The technical conception of the invention is as follows: through analysis of existing studies, it was found that there is currently no study for multi-product dspp. SSA has not attracted sufficient attention in industrial applications as a new optimization method, and the present invention utilizes it to solve the dspp problem in remanufacturing. In practice, there are often multiple EOL products that must be disassembled within a planned range. To get an overall optimization, we preferably combine them for disassembly sequence planning decisions. Therefore, a solution to multi-product dspp is needed. In addition, multiple optimization objectives, such as profit correlation, time-oriented and energy-aware criteria, are considered from the economic sustainability perspective, and an optimal trade-off decision is selected among them. In addition, because the EOL product is difficult to obtain accurate information due to the variation of the use process, uncertainty is also considered. Therefore, the present invention proposes a new multi-product dspp that aims to maximize the disassembly profit and minimize the energy consumption while satisfying the disassembly time requirement. According to the characteristics of the method, a method combining multi-target SSA and random simulation is designed.
In order to realize the purpose of the invention, the invention is realized by the following technical scheme:
to build a mathematical model of the problem under study, the symbols involved in the present invention are defined as follows:
g EOL product index, g representing the number of disassembled products; g e {1, 2, …, G }
i part index, NgRepresenting the number of parts in the product; i e {1, 2, …, Ng} j，k，m {0，1，2，…，JgOperation index of (1) }, where JgRepresenting operands in product g, 0 is a virtual operation;
Figure BDA0002578434990000031
disassembly time when operation j is performed in product g;
Figure BDA0002578434990000032
performing the set time of operation k if performed after operation j in product g;
Figure BDA0002578434990000033
energy consumption per unit time to perform operation j in product g;
Figure BDA0002578434990000034
energy consumption per unit time in setting operation k if performed after operation j in product g;
Figure BDA0002578434990000035
a cost per unit time to perform operation j in product g;
Figure BDA0002578434990000036
setting a cost per unit time for process k if performed after operation j in product g;
rgithe recycling value of the component i in the product g;
t total disassembly time given;
α gives the secret level of the tear-down time at the total tear-down time;
Sgan inheritance matrix of a given AND/OR graph of a product g;
Dga disassembly correlation matrix for a given AND/OR graph of product g;
sgjkSgRow and column k;
dgijDgrow and column k;
it is noted that,
Figure BDA0002578434990000041
and
Figure BDA0002578434990000042
is a random number;
decision variables:
xgja disassembly indication; if operation j, x in product g is performedgj1 is ═ 1; otherwise xgj＝0
ygjkAn adjacent indication; if operation k is performed after operation j in product g, y gjk1 is ═ 1; otherwise ygjk＝0；
The following specifically describes the multi-product disassembly-oriented multi-target disassembly sequence planning method of the present invention, which comprises the following steps:
s1, establishing a mathematical model with the goals of maximizing disassembly profit and minimizing energy consumption;
s2 population initialization
Generating an initial population, comparing objective function values of the initial population through Pareto to obtain a Pareto better solution, storing the Pareto better solution in an external file, and evolving the external file;
s3 population evolution
Calculating by adopting an SSA optimization algorithm to obtain a new population;
s4 evolution of external files
Adopting a Pareto comparison step S3 to calculate an objective function value of a mixed population consisting of the new population and the external file, and further updating the external file;
s5 further updating of the population
Adopting a Pareto comparison step S3 to calculate the objective function value of the new population, and further updating the population;
s6 stop criteria: if the maximum iteration times g _ max are met, the algorithm is terminated, and a Pareto optimal solution in an external file is output as a disassembly task allocation scheme; otherwise, repeating the steps S3-S5 according to the preset times;
Further, the step S1 is implemented as follows:
s101: establishing a matrix for each product to be disassembled, specifically, setting i as a component index, j and k as disassembling operation indexes, and defining three matrices based on product structures and/or graphs:
priority matrix P ═ Pjk]It is used to describe the priority and conflict relationship of two teardown operations, defined as follows:
Figure BDA0002578434990000051
the inheritance matrix S ═ Sjk]It is used to represent the relationship between two adjacent disassembly operations, which is described as:
Figure BDA0002578434990000052
the disassembly association matrix D ═ Dij]It is used to describe the relationship between the components and the disassembly operation, defined as follows:
Figure BDA0002578434990000053
s102: establishing a mathematical model with the goals of maximizing the dismantling profit and minimizing the energy consumption:
Figure BDA0002578434990000054
Figure BDA0002578434990000055
Figure BDA0002578434990000061
Figure BDA0002578434990000062
Figure BDA0002578434990000063
sgjk-ygjk≥0，j，k＝1，2，…，J，g＝1，2，…，G. (6)
Figure BDA0002578434990000064
Figure BDA0002578434990000065
Figure BDA0002578434990000066
xgj，ygjk∈{0，1}，j，k＝1，2，…，J，g＝1，2，…，G. (10)
wherein formula (1) and formula (2) represent the goals of maximizing the removal profit and minimizing the energy consumption, respectively, and since the mounting and dismounting times are random, they are represented as their expected values, ξ is a random variable, and E (ξ) represents its expected value; formula (3) ensures that at least one disassembly operation is performed when the off-line product is disassembled; equation (4) indicates that each disassembly operation in the end-of-line product can be performed at most once; equation (5) represents the opportunity constraint for total disassembly time, which is the probability that the total disassembly time is less than or equal to a given total disassembly time; equation (6) demonstrates that a feasible disassembly sequence for an off-line product must satisfy priority and conflict constraints; equation (7) indicates the disassembly relationship between the operations and sub-components in the end-of-line product; equation (8) demonstrates a balanced relationship between in-degree and out-degree of operation; equation (9) requires that the sub-components in the end-of-line product must be disassembled in at most one operation; equation (10) gives the range of decision variables.
Further, the method for generating the initial population in step S2 includes:
s201: designing a double-linked string to represent a solution, i.e.
π＝((π'1,π”1),(π'2,π”2),…,(π'g,π”g))；
Each component (pi'g,π”g) Indicating the decision of the product, G-1, 2, …, G,
π'g＝(og1,og2,…,ogj) Is a disassembly operation sequence string, which represents the order of all disassembly operations;
ogjis the operation index of the jth location;
π”g＝(xg1,xg2,…,xgj) Is the tear down operability string, if xgjEqual to 1, then in π "gThe j-th position of (1) performs the operation; otherwise, not executing;
s202: if a solution violates the priority and inheritance constraints, it may not be feasible, and if the solution is not feasible, each element will be repaired using the following method.
If the executed operations conflict with each other, adjusting each component (pi ') based on the priority matrix of the product'g,π”g) In pi'gIn the order of operations ofWhich satisfy the precedence relationship. By adjusting pi'gSo that it satisfies inheritance constraint and avoids conflict relationship, i.e. pi'gIf the corresponding elements in the list are 1, adjusting the corresponding elements to 0 to enable the corresponding elements to meet inheritance constraint and avoid conflict relationship; if the operations performed are sequential and they are at π "gIf the corresponding elements in (1) are 1, they keep the same value and the resulting solution is generated as an initial population.
Further, the step S2 of evolving the external file specifically includes:
using a multi-directional local search (MDLS) operation, the outer archive is iteratively refined by searching a neighborhood of non-dominant solutions:
setting MAAnd MBTwo parameters, which are respectively used to determine the number of solutions evolved by the multi-directional local search (MDLS) and the number of obtained neighborhood solutions, and three neighborhood structures are used to generate the neighborhood solutions, specifically:
s203: selecting a solution from an external archive, randomly selecting two positions in a disassembly operation sequence string of the obtained solution, and then inserting the disassembly operation of the first position into the other position;
s204: selecting a solution from an external file, randomly selecting two positions in a disassembly operation sequence string of the obtained solution, and then exchanging disassembly operations for the two positions;
s205: selecting a solution from an external archive, randomly selecting a position p in a disassembly operation sequence string of the obtained solutionoThen the value thereon
Figure BDA00025784349900000810
Is changed into
Figure BDA00025784349900000811
S206: the external archive is updated with all newly generated solutions.
Further, the SSA optimization algorithm in step S3 includes the following steps:
s301: initializing algorithm parameters including maximum iteration times g _ max, population size n and predator existence probability p;
S302: three clusters are constructed by adopting a binary selection method and respectively represent the hickory trees
Figure BDA0002578434990000081
Oak tree
Figure BDA0002578434990000082
And common tree
Figure BDA0002578434990000083
The squirrel above;
s303: respectively in the hickory
Figure BDA0002578434990000084
Oak tree
Figure BDA0002578434990000085
And common tree
Figure BDA0002578434990000086
The best solution is generally stored in
Figure BDA0002578434990000087
In the method, the better solutions are stored in
Figure BDA0002578434990000088
In (1), the rest are stored in
Figure BDA0002578434990000089
Performing the following steps;
s304: sliding to generate a new position:
(1) considering the existence probability p of predators, the squirrels on the oak tree move to the randomly selected hickory tree;
(2) squirrels on ordinary trees will move towards randomly selected oak trees to meet their daily energy requirements, while taking into account the probability of existence p of predators;
(3) if the squirrels on the regular trees have met their energy requirements, taking into account the probability of presence of predators p, they will move towards the randomly chosen pecan tree;
s305: checking seasonal monitoring conditions to prevent the algorithm from falling into a local optimal solution; checking whether the current population loses diversity using a seasonal monitoring program, in fact, population diversity enhances search capability by expanding the search area in the solution space; to improve search capability and maintain a highly diverse population, the probability of performing a solution that is generated after the evolution of an external archive is p mThe mutation operation of (3).
Compared with the prior art, the invention has the beneficial effects that:
because the prior art does not aim at the research of the multi-product dspp, the invention provides a novel random multi-target multi-product dspp, aiming at maximizing the disassembly profit and minimizing the energy consumption on the premise of meeting the requirement of the disassembly time. The invention establishes an opportunity constraint planning model, carries out mathematical description on the model, and in addition, the invention designs a multi-target squirrel search algorithm by combining the characteristics of a random simulation method, adopts double-chain character strings to represent solutions, and adopts population evolution and external archive evolution methods to search solution space. In addition, the invention adopts a population evolution and external archiving evolution method for searching candidate solutions from a solution space, and designs a random simulation method for evaluating the performance of the obtained solutions. Therefore, the planning method can help a decision maker to make an intelligent decision, and an effective method is provided for solving the multi-product disassembly sequence planning problem considering uncertainty and multi-objective optimization.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a box line graph of the planning method of the present invention and IGD experimental results of three algorithms, NSGA-II and MOEA/D;
FIG. 3 is a box plot of the results of the planning method of the present invention and three HV (hyper-volume) algorithms NSGA-II and MOEA/D.
Detailed Description
The invention is further illustrated by the following specific examples. It is important to note here that the present embodiment is for illustrative purposes only and that the scope of the present invention is not limited to the illustrative scope.
To build a mathematical model of the problem under study, the symbols involved in the present invention are defined as follows:
g EOL product index, g representing the number of disassembled products; g e {1, 2, …, G }
i part index, NgRepresenting the number of parts in the product; i e {1, 2, …, Ng} j，k，m {0，1，2，…，JgOperation index of (1) }, where JgRepresenting operands in product g, 0 is a virtual operation;
Figure BDA0002578434990000101
disassembly time when operation j is performed in product g;
Figure BDA0002578434990000102
performing the set time of operation k if performed after operation j in product g;
Figure BDA0002578434990000103
energy consumption per unit time to perform operation j in product g;
Figure BDA0002578434990000104
energy consumption per unit time in setting operation k if performed after operation j in product g;
Figure BDA0002578434990000105
a cost per unit time to perform operation j in product g;
Figure BDA0002578434990000106
Setting a cost per unit time for process k if performed after operation j in product g;
rgithe recycling value of the component i in the product g;
t total disassembly time given;
α gives the secret level of the tear-down time at the total tear-down time;
Sgan inheritance matrix of a given AND/OR graph of a product g;
Dga disassembly correlation matrix for a given AND/OR graph of product g;
sgjkSgrow and column k;
dgijDgrow and column k;
it is noted that,
Figure BDA0002578434990000111
and
Figure BDA0002578434990000112
is a random number;
2) decision variables
xgjA disassembly indication; if operation j, x in product g is performedgi1 is ═ 1; otherwise xgi＝0；
ygjkAn adjacent indication; if operation k is performed after operation j in product g, y gjk1 is ═ 1; otherwise ygjk＝0；
The following specifically describes the multi-product disassembly-oriented multi-target disassembly sequence planning method of the present invention, which comprises the following steps:
s1, establishing a mathematical model with the aim of maximizing the disassembly profit and minimizing the energy consumption, and specifically realizing the following steps:
s101: the invention considers the goals of decomposing a plurality of waste products, simultaneously maximizing the disassembly profit and minimizing the energy consumption, and simultaneously satisfying the disassembly time limit, when a group of EOL products need to be disassembled, each product is decomposed into some parts by using the disassembly operation.
Establishing a matrix for each product to be disassembled, specifically, setting i as a component index, j and k as disassembling operation indexes, and defining three matrices based on product structures and/or graphs:
priority matrix P ═ Pjk]It is used to describe the priority and conflict relationship of two teardown operations, defined as follows:
Figure BDA0002578434990000113
the inheritance matrix S ═ Sjk]It is used to represent the relationship between two adjacent disassembly operations, which is described as:
Figure BDA0002578434990000121
the disassembly association matrix D ═ Dij]It is used to describe the relationship between the components and the disassembly operation, defined as follows:
Figure BDA0002578434990000122
since a plurality of products and/or graphs are needed to represent the decomposed products/structures respectively for decomposing the plurality of products, three matrixes of each decomposed product are respectively established according to the above-mentioned matrix defining manner;
s102: establishing a mathematical model with the goals of maximizing the dismantling profit and minimizing the energy consumption:
Figure BDA0002578434990000123
Figure BDA0002578434990000124
Figure BDA0002578434990000125
Figure BDA0002578434990000126
Figure BDA0002578434990000127
sgjk-ygjk≥0，j，k＝1，2，…，J，g＝1，2，…，G. (6)
Figure BDA0002578434990000128
Figure BDA0002578434990000129
Figure BDA0002578434990000131
xgj，ygjk∈{0，1}，j，k＝1，2，…，J，g＝1，2，…，，G. (10)
wherein formula (1) and formula (2) represent the goals of maximizing the removal profit and minimizing the energy consumption, respectively, and since the mounting and dismounting times are random, they are represented as their expected values, ξ is a random variable, and E (ξ) represents its expected value; formula (3) ensures that at least one disassembly operation is performed when the off-line product is disassembled; equation (4) indicates that each disassembly operation in the end-of-line product can be performed at most once; equation (5) represents the opportunity constraint for total disassembly time, which is the probability that the total disassembly time is less than or equal to a given total disassembly time; equation (6) demonstrates that a feasible disassembly sequence for an off-line product must satisfy priority and conflict constraints; equation (7) indicates the disassembly relationship between the operations and sub-components in the end-of-line product; equation (8) demonstrates a balanced relationship between in-degree and out-degree of operation; equation (9) requires that the sub-components in the end-of-line product must be disassembled in at most one operation; equation (10) gives the range of decision variables.
S2 population initialization
Generating an initial population, comparing objective function values of the initial population through Pareto to obtain a Pareto better solution, storing the Pareto better solution in an external file, and evolving the external file;
the method for generating the initial population comprises the following steps:
s201: designing a double-linked string to represent a solution, i.e.
π＝((π'1,π”1),(π'2,π”2),…,(π'g,π”g))；
Each component (pi'g,π”g) Indicating the decision of the product, G-1, 2, …, G,
π'g＝(og1,og2,…,ogj) Is a disassembly operation sequence string, which represents the order of all disassembly operations;
ogjis the operation index of the jth location;
π”g＝(xg1,xg2,…,xgj) Is the tear down operability string, if xgjEqual to 1, then in π "gThe j-th position of (1) performs the operation; otherwise, not executing;
s202: if a solution violates the priority and inheritance constraints, it may not be feasible, and if the solution is not feasible, each element will be repaired using the following method.
If the executed operations conflict with each other, adjusting each component (pi ') based on the priority matrix of the product'g,π”g) In pi'gSo that they satisfy the priority relationship. By adjusting pi'gSo that it satisfies inheritance constraint and avoids conflict relationship, i.e. pi'gIf the corresponding elements in the list are 1, adjusting the corresponding elements to 0 to enable the corresponding elements to meet inheritance constraint and avoid conflict relationship; if the operations performed are sequential and they are at π " gIf the corresponding elements in (1) are 1, they keep the same value and the resulting solution is generated as an initial population.
The specific evolution of the external file is as follows:
using a multi-directional local search (MDLS) operation, the outer archive is iteratively refined by searching a neighborhood of non-dominant solutions:
setting MAAnd MBTwo parameters, respectively for determining the arrival of a multidirectional local search (MDLS)The number of solutions to be refined and the number of neighborhood solutions to be obtained, three neighborhood structures are used to generate the neighborhood solutions, specifically:
s203: selecting a solution from an external archive, randomly selecting two positions in a disassembly operation sequence string of the obtained solution, and then inserting the disassembly operation of the first position into the other position;
s204: selecting a solution from an external file, randomly selecting two positions in a disassembly operation sequence string of the obtained solution, and then exchanging disassembly operations for the two positions;
s205: selecting a solution from an external archive, randomly selecting a position p in a disassembly operation sequence string of the obtained solutionoThen the value thereon
Figure BDA00025784349900001511
Is changed into
Figure BDA00025784349900001510
S206: the external archive is updated with all newly generated solutions.
S3 population evolution
Calculating to obtain a new population by adopting an SSA optimization algorithm, and comprising the following steps:
S301: initializing algorithm parameters including maximum iteration times g _ max, population size n and predator existence probability p;
s302: three clusters are constructed by adopting a binary selection method and respectively represent the hickory trees
Figure BDA0002578434990000151
Oak tree
Figure BDA0002578434990000152
And common tree
Figure BDA0002578434990000153
The squirrel above;
s303: respectively in the hickory
Figure BDA0002578434990000154
Oak tree
Figure BDA0002578434990000155
And common tree
Figure BDA0002578434990000156
The best solution is generally stored in
Figure BDA0002578434990000157
In the method, the better solutions are stored in
Figure BDA0002578434990000158
In (1), the rest are stored in
Figure BDA0002578434990000159
Performing the following steps;
s304: sliding to generate a new position:
(1) considering the existence probability p of predators, the squirrels on the oak tree move to the randomly selected hickory tree;
(2) squirrels on ordinary trees will move towards randomly selected oak trees to meet their daily energy requirements, while taking into account the probability of existence p of predators;
(3) if the squirrels on the regular trees have met their energy requirements, taking into account the probability of presence of predators p, they will move towards the randomly chosen pecan tree;
s305: checking seasonal monitoring conditions to prevent the algorithm from falling into a local optimal solution; checking whether the current population loses diversity using a seasonal monitoring program, in fact, population diversity enhances search capability by expanding the search area in the solution space; to improve search capability and maintain a highly diverse population, the probability of performing a solution that is generated after the evolution of an external archive is p mThe mutation operation of (3).
S4 evolution of external files
Adopting a Pareto comparison step S3 to calculate an objective function value of a mixed population consisting of the new population and the external file, and further updating the external file;
s5 further updating of the population
Adopting a Pareto comparison step S3 to calculate the objective function value of the new population, and further updating the population;
s6 stop criteria: if the maximum iteration times g _ max are met, the algorithm is terminated, and a Pareto optimal solution in an external file is output as a disassembly task allocation scheme; otherwise, repeating steps S3-S5 a predetermined number of times.
To test the performance of the multi-product-disassembly-oriented multi-objective disassembly sequence planning Method (MSSA) of the present invention in dealing with the problem we considered, the present example selects two popular multi-objective optimization algorithms (MOOA), namely NSGA-ii and MOEA/D, as comparison methods. NSGA-II is one of the classical multi-objective optimization algorithms (MOOA) based on Pareto rule; MOEA/D is a widely recognized MOOA which uses a decomposition method. The two methods are also applied to solving various optimization problems and have excellent searching performance. In recent years, these two methods have also been applied to solving decision problems. Their experimental results show their powerful efficacy in addressing such problems. Thus, the present invention selects NSGA-II and MOEA/D as peer-to-peer methods, which also employ priority-preserving crossover and reference-based mutation operations to generate new solutions.
The practical case is as follows: the Radio (RS) contains 29 parts that need to be disassembled using 30 disassembling operations, the basic data of which are shown in tables S1-S4. Note that the disassembly and set times of the disassembly operation follow a normal distribution. Their removal and installation times in tables S1-S4 are taken as their mean values, and their variance values are the product of the mean values and a coefficient equal to 0.0001. Using the radio machine (RS) example test, the confidence level is equal to 0.95.
Table S1 recycle value r of RS Componentsgi
Figure BDA0002578434990000171
Table S2. conventional operating costs of RS
Figure BDA0002578434990000172
Energy consumption
Figure BDA0002578434990000173
And average run time
Figure BDA0002578434990000174
Figure BDA0002578434990000175
Conventional installation costs of Table S3.RS
Figure 1
Mean time
Figure 2
Energy consumption and inter-operational failure rate
Figure 3
Figure BDA0002578434990000179
Figure BDA0002578434990000181
The parameters for NSGA-II and MOEA/D were set as follows: the population size of NSGA-II is 100, and the mutation probability is 0.1. The population size of MOEA/D is 100, the mutation probability is 0.1, and the neighborhood size is 20. To verify the effect of parameters in MSSA, we used the design of Taguchi experiments (DOE) to test the sensitivity of four parameters, i.e., Q (initial population), pm(probability of mutation operation), MAAnd MB(MAAnd MBTwo parameters are used to determine the number of solutions evolved by MDLS and the number of neighborhood solutions obtained, respectively). They each have four levels, Q ∈ {20, 40, 60, 80}, p m∈{0.05，0.10，0.15，0.20},MAE {0.1, 0.4, 0.7, 1.0} and MBE.g. {0.5, 1.0, 1.5, 2.0 }. Thus, the use of orthogonal arrays as shown in Table 1 gives 16 different combinations, each employing the present inventionThe wireless motor (RS) is solved 20 times by the MinMSSA algorithm, the IGD value of each time is used as a Response Value (RV), and the experimental result is analyzed by the average RV of 20 times. The ARV (average RV) values for each combination are given in table 1 and the effective rank of the four parameters is given in table 2. From this we can see that Q plays an important role, MAAnd MBArranged in second and third positions, p, respectivelymAnd is ranked in the fourth position.
TABLE 1 orthogonal arrays and RV values
Figure BDA0002578434990000191
TABLE 2 significance ranking of four parameters
Figure BDA0002578434990000192
Figure BDA0002578434990000201
In addition, in this embodiment, the radio machine (RS) is respectively tested by using the multi-product-disassembly-oriented multi-target disassembly sequence planning method of the present invention and two comparison methods, namely NSGA-II and MOEA/D, and in order to analyze the performance of the MSSA and its peer machines, three metrics are used to compare their results, namely, C metric (solution coverage), IGD metric (Inverted generation Distance) (average of the Distance from each reference point to the nearest solution, the smaller the IGD value, the better the comprehensive performance of the algorithm), and hyper-volumetric metric (hyperbolume, HV: the volume of the region in the target space surrounded by the non-dominated solution set obtained by the algorithm and the reference point).
Table 3 gives the experimental results of the mean and variance values by C-measure. From these experimental results, it can be seen that most of the solutions obtained by MSSA dominate those obtained by NSGA-II and MOEA/D, since C (MSSA, NSGA-II) and C (MSSA, MOEA/D) are larger than C (NSGA-II, MSSA) and C (MOEA/D, MSSA), respectively. In five cases, all solutions obtained by MSSA may dominate the solution obtained by NSGA-II. Meanwhile, in 6 cases where C (MSSA, MOEA/D) is equal to 1, MSSA shows better superiority than MOEA/D. The mean values for C (MSSA, NSGA-II), C (NSGA-II, MSSA), C (MSSA, MOEA/D) and C (MOEA/D, MSSA) were 0.9878, 0.6034, 0.9751 and 0.6104, respectively. These results demonstrate that MSSA is superior to NSGA-II and MOEA/D in terms of treatment-related problems.
TABLE 3C-metric comparison of the three algorithms
Figure BDA0002578434990000211
Table 4 shows the experimental results of the three algorithms as measured by IGD. From these results, it can be seen that the IGD value of MSSA is smaller than NSGA-II and MOEA/D in all cases, so that MSSA performs better than NSGA-II and MOEA/D in terms of solving the related problems. The average values of the three algorithms on the RS examples are 0.2150, 0.5737 and 0.5569, respectively. These results indicate that MSSA can find a well-converged, well-diversified non-dominated solution set of the problem.
In order to further reveal the performances of the MSSA and the peer system thereof, the experimental results are analyzed by adopting an ultra-volume method. Table 5 shows their hyper-volume values. The results show that the MSSA gave a higher hypervolume value than the NSGA-II and MOEA/D in all cases. The average values of the three algorithms on the RS examples are 0.7066, 0.3548 and 0.3737, respectively. These results show that the MSSA method results in a solution set that is more closely approximated and more evenly distributed than the NSGA-II and MOEA/D methods, and thus is more suitable for solving the problem we consider.
To illustrate the experimental results more clearly and intuitively, we plot the block diagram of the results of 10 experiments for the three algorithms based on IGD-and hyper-volumetric measurements, as shown in fig. 2 and 3. From observation and analysis of the above results, it was concluded that MSSA has better performance than NSGA-II and MOEA/D in dealing with the related problems.
Table 4 comparison of three algorithms by IGD metric
Figure BDA0002578434990000221
TABLE 5 comparison of the three algorithms for the measurement of the hyper-volume method
Figure BDA0002578434990000222
It should be understood that the detailed description of the present invention is only for illustrating the present invention and is not limited by the technical solutions described in the embodiments of the present invention, and those skilled in the art should understand that the present invention can be modified or substituted equally to achieve the same technical effects; as long as the use requirements are met, the method is within the protection scope of the invention.

Claims (5)

1. The multi-product disassembly-oriented multi-target disassembly sequence planning method comprises the following steps:
s1, establishing a mathematical model with the goals of maximizing disassembly profit and minimizing energy consumption;
s2 population initialization
Generating an initial population, comparing objective function values of the initial population through Pareto to obtain a Pareto better solution, storing the Pareto better solution in an external file, and evolving the external file;
s3 population evolution
Calculating by adopting an SSA optimization algorithm to obtain a new population;
s4 evolution of external files
Adopting a Pareto comparison step S3 to calculate an objective function value of a mixed population consisting of the new population and the external file, and further updating the external file;
s5 further updating of the population
Adopting a Pareto comparison step S3 to calculate the objective function value of the new population, and further updating the population;
s6 stop criteria: if the maximum iteration times g _ max are met, the algorithm is terminated, and a Pareto optimal solution in an external file is output as a disassembly task allocation scheme; otherwise, repeating steps S3-S5 a predetermined number of times.
2. The multi-product-disassembly-oriented multi-target disassembly sequence planning method of claim 1, wherein the step S1 is implemented by the following steps:
s101: establishing a matrix for each product to be disassembled, specifically, setting i as a component index, j and k as disassembling operation indexes, and defining three matrices based on product structures and/or graphs:
Priority matrix P ═ Pjk]It is used to describe the priority and conflict relationship of two teardown operations, defined as follows:
Figure FDA0002578434980000021
the inheritance matrix S ═ Sjk]It is used to represent the relationship between two adjacent disassembly operations, which is described as:
Figure FDA0002578434980000022
the disassembly association matrix D ═ Dij]It is used to describe the relationship between the components and the disassembly operation, defined as follows:
Figure FDA0002578434980000023
s102: establishing a mathematical model with the goals of maximizing the dismantling profit and minimizing the energy consumption:
Figure FDA0002578434980000024
Figure FDA0002578434980000025
Figure FDA0002578434980000026
Figure FDA0002578434980000027
Figure FDA0002578434980000028
sgjk-ygjk≥0，j，k＝1，2，…，J，g＝1，2，…，G. (6)
Figure FDA0002578434980000029
Figure FDA0002578434980000031
Figure FDA0002578434980000032
xgj，ygjk∈{0，1}，j，k＝1，2，…，J，g＝1，2，…，G. (10)
wherein formula (1) and formula (2) represent the goals of maximizing the disassembly profit and minimizing the energy consumption, respectively, ξ is a random variable, and E (ξ) represents its desired value; formula (3) ensures that at least one disassembly operation is performed when the off-line product is disassembled; equation (4) indicates that each disassembly operation in the end-of-line product can be performed at most once; equation (5) represents the opportunity constraint for total disassembly time, which is the probability that the total disassembly time is less than or equal to a given total disassembly time; equation (6) demonstrates that a feasible disassembly sequence for an off-line product must satisfy priority and conflict constraints; equation (7) indicates the disassembly relationship between the operations and sub-components in the end-of-line product; equation (8) demonstrates a balanced relationship between in-degree and out-degree of operation; equation (9) requires that the sub-components in the end-of-line product must be disassembled in at most one operation; equation (10) gives the range of decision variables.
3. The multi-product disassembly-oriented multi-target disassembly sequence planning method of claim 1, wherein the method for generating the initial population in the step S2 is as follows:
s201: designing a double-link string to represent a solution, i.e., (pi ═ pi'1,π”1),(π'2,π”2),…,(π'g,π”g))；
Each component (pi'g,π”g) Indicating the decision of the product, G-1, 2, …, G,
π'g＝(og1,og2,…,ogj) Is a disassembly operation sequence string, which represents the order of all disassembly operations;
ogjis the operation index of the jth location;
π”g＝(xg1,xg2,…,xgj) Is the tear down operability string, if xgjEqual to 1, then in π "gThe j-th position of (1) performs the operation; otherwise, not executing;
s202: if a solution violates the priority and inheritance constraints, the solution is not feasible and each element will be repaired using the following method:
if the executed operations conflict with each other, adjusting each component (pi ') based on the priority matrix of the product'g,π”g) In pi'gThe operation sequence in (1) so as to satisfy the priority relationship; by adjusting pi'gSo that it satisfies inheritance constraint and avoids conflict relationship, i.e. pi'gIf the corresponding elements in the list are 1, adjusting the corresponding elements to 0 to enable the corresponding elements to meet inheritance constraint and avoid conflict relationship; if the operations performed are sequential and they are at π " gIf the corresponding elements in (1) are 1, they keep the same value and the resulting solution is generated as an initial population.
4. The multi-product disassembly-oriented multi-target disassembly sequence planning method of claim 1, wherein the step S2 of evolving the external file specifically comprises:
the external archive is iteratively improved by searching a neighborhood of non-dominant solutions using a multi-directional local search operation:
setting MAAnd MBThe two parameters are respectively used for determining the number of evolved solutions and the number of obtained neighborhood solutions for the multi-directional local search, and three neighborhood structures are used for generating the neighborhood solutions, specifically:
s203: selecting a solution from an external archive, randomly selecting two positions in a disassembly operation sequence string of the obtained solution, and then inserting the disassembly operation of the first position into the other position;
s204: selecting a solution from an external file, randomly selecting two positions in a disassembly operation sequence string of the obtained solution, and then exchanging disassembly operations for the two positions;
s205: selecting a solution from an external archive, randomly selecting a position p in a disassembly operation sequence string of the obtained solutionoThen the value thereon
Figure FDA0002578434980000041
Is changed into
Figure FDA0002578434980000042
S206: the external archive is updated with all newly generated solutions.
5. The multi-product-disassembly-oriented multi-objective disassembly sequence planning method of claim 1, wherein the SSA optimization algorithm in the step S3 comprises the following steps:
s301: initializing algorithm parameters including maximum iteration times g _ max, population size n and predator existence probability p;
s302: three clusters are constructed by adopting a binary selection method and respectively represent the hickory trees
Figure FDA0002578434980000051
Oak tree
Figure FDA0002578434980000053
And common tree
Figure FDA0002578434980000052
The squirrel above;
s303: respectively in the hickory
Figure FDA0002578434980000054
Oak tree
Figure FDA0002578434980000055
And common tree
Figure FDA0002578434980000056
The upper squirrel, in general, is best stored in
Figure FDA0002578434980000057
In the method, the better solutions are stored in
Figure FDA0002578434980000058
In (1), the rest are stored in
Figure FDA0002578434980000059
Performing the following steps;
s304: sliding to generate a new position:
(1) considering the existence probability p of predators, the squirrels on the oak tree move to the randomly selected hickory tree;
(2) squirrels on ordinary trees will move towards randomly selected oak trees to meet their daily energy requirements, while taking into account the probability of existence p of predators;
(3) if the squirrels on the regular trees have met their energy requirements, taking into account the probability of presence of predators p, they will move towards the randomly chosen pecan tree;
s305: checking seasonal monitoring conditions to prevent the algorithm from falling into a local optimal solution; checking whether the current population loses diversity using a seasonal monitoring program, in fact, population diversity enhances search capability by expanding the search area in the solution space; to improve the search ability and maintain a highly diverse population, The probability of the solution generated after the evolution of the external archive is pmThe mutation operation of (3).
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