A remanufacturing decision-making method integrating process planning and scheduling

Abstract

The application discloses a kind of remanufacturing decision-making methods of process planning and scheduling integration, to indicate the machining time with interval number, the objective function of total interval processing energy consumption, total interval idle energy consumption, interval completion time and maximum machine load is constructed, then to minimize energy consumption, minimize maximum completion time and minimize maximum machine load to establish the integrated model of remanufacturing process planning and scheduling, the integrated model of remanufacturing process planning and scheduling is solved, and the optimal remanufacturing process planning and scheduling scheme is obtained, and remanufacturing is carried out according to the optimal remanufacturing process planning and scheduling scheme obtained.The application not only considers the uncertainty of machining time expressed by interval number, but also considers the selection of process planning related to the uncertainty of defective part quality, to more comprehensively coordinate process planning and scheduling in uncertain remanufacturing environment.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of remanufacturing, and particularly relates to a remanufacturing decision-making method integrating process planning and scheduling. BACKGROUND

[0002] In recent years, remanufacturing is increasingly popular due to its good environmental and economic benefits. As an important part of sustainable development, remanufacturing of end-of-life (EOL) products has attracted widespread attention in recent years. In a remanufacturing system, EOL products are restored to a state like a new product through a series of operations such as complete disassembly, reprocessing and reassembly.

[0003] In an actual remanufacturing system, remanufacturing process planning and scheduling problems are two key problems at the operation level. The remanufacturing process planning provides guidance for global scheduling of the workshop according to resource constraints. The workshop scheduling determines the operation sequence of machines within a specified time according to process planning constraints. These two key problems are processed in turn in the traditional remanufacturing system, which hinders the improvement of remanufacturing production efficiency and performance, and may lead to conflicts between remanufacturing process planning and scheduling goals. For example, in the scheduling stage, the predefined process planning may become infeasible.

[0004] Compared with the traditional manufacturing environment, the remanufacturing system has more inherent uncertainties, such as highly uncertain processing time, uncertain defective part quality and uncertain reprocessing operation path. Some scholars have studied the integration of remanufacturing process planning and scheduling (IRPPS) model in the remanufacturing system. The integrated model of remanufacturing process planning and scheduling provides a direction for researchers and practitioners to improve the performance of the remanufacturing system. However, the current research often ignores the uncertainty of defective part quality or the uncertainty of processing time. In addition, the current research does not reasonably consider the integration with resource constraints, which is not conducive to energy-efficient remanufacturing. SUMMARY

[0005] The purpose of the present application is to provide a remanufacturing decision-making method integrating process planning and scheduling, which not only considers the uncertainty of processing time represented by interval numbers, but also considers the selection of process planning related to the uncertainty of defective part quality, so as to more comprehensively coordinate process planning and scheduling in the uncertain remanufacturing environment.

[0006] In order to achieve the above purpose, the technical scheme of the present application is as follows:

[0007] A remanufacturing decision-making method integrating process planning and scheduling, comprising:

[0008] The machining time is expressed by interval number, and objective functions of total interval machining energy consumption, total interval idle energy consumption, interval completion time and maximum machine load are constructed, then an integrated model of remanufacturing process planning and scheduling is established by minimizing energy consumption, minimizing maximum completion time and minimizing maximum machine load;

[0009] Solving the integrated model of remanufacturing process planning and scheduling, an optimal remanufacturing process planning and scheduling scheme is obtained, and remanufacturing is carried out according to the obtained optimal remanufacturing process planning and scheduling scheme.

[0010] Further, the total interval machining energy consumption objective function is as follows:

[0011]

[0012] The total interval idle energy consumption objective function is as follows:

[0013]

[0014]

[0015] The total interval energy consumption is expressed as:

[0016]

[0017] The interval completion time objective function is as follows:

[0018]

[0019]

[0020] The maximum machine load objective function is as follows:

[0021]

[0022] The integrated model of remanufacturing process planning and scheduling is expressed as:

[0023]

[0024] Wherein, represents total interval energy consumption, represents total interval machining energy consumption, represents total interval idle energy consumption, f1 is the total interval energy consumption objective function, f2 is the interval completion time objective function, and f3 is the maximum machine load objective function; represents the unit machining power of M s , M s represents the s th machine, s=1,...,S, and S is the total number of machines; is a 0-1 decision variable, 1 represents O njon machine M s 1 if operation O is executed on machine M s 1 if operation O nj is executed on machine M nj is the jth operation of part P n , j = 1,..., J n , where J n is the number of features of part P n that need reworking; n is the nth part, n = 1,..., N, where N is the total number of parts; is the interval start time of operation O s executed on machine M nj ; is the unit idle power of machine M s ; is a 0-1 decision variable, 1 means machine M s is off between adjacent operations O n'j' and O nj , otherwise 0; P n’ is a part different from P n ; J n’ is the number of features of part P n’ that need reworking; O n’j’ is the j'th operation of part P n’ , j' = 1,..., J n' ; is the interval finish time of the previous operation O s of operation O nj executed on machine M n'j' ; is the interval finish time of operation O s executed on machine M ; is the Jth operation of part P n ; n ; is a 0-1 decision variable, 1 means machine M s is off between adjacent operations O n'j' and O nj , otherwise 0; H s is the time threshold of turning off machine M s ; is the interval processing time of operation O s executed on machine M nj .

[0025] Further, the process planning and scheduling integrated remanufacturing decision method further comprises:

[0026] The total interval energy consumption target function, interval completion time target function and maximum machine load target function are equivalent transformed, interval target values are converted into real values, and the following formula is used:

[0027]

[0028] Wherein, represents the equivalent transformed real value, ω m is the weight of the uncertainty degree of the target function f m , and m represents the mth target function value f m .

[0029] Further, the integrated model of the remanufacturing process planning and scheduling is solved by using an improved second-generation non-dominated sorting genetic algorithm, and the improved second-generation non-dominated sorting genetic algorithm comprises the following steps:

[0030] Step F1, initialization, a multi-dimensional coding method is used to randomly generate a new population P G (N);

[0031] Step F2, a genetic operation is performed to generate a child population Q G1 (N);

[0032] Step F3, P G (N) and Q G1 (N) are combined, a fast non-dominated sorting and crowding distance method is used to generate a next child population Q G2 (N);

[0033] Step F4, a local search strategy is performed on Q G2 (N) to generate a new population P G+1 (N) for the next iteration;

[0034] Step F5, the iteration number G is equal to G+1;

[0035] Step F6, it is judged whether G reaches a maximum iteration number, if yes, an approximate Pareto optimal solution set in P G (N) is output, and if not, the step F2 is returned for the next iteration.

[0036] Further, the multi-dimensional coding method comprises two layers, i.e., a feature layer and a reprocessing layer, the feature layer represents part index, feature and failure mode information, the reprocessing layer represents candidate operation index and candidate machine index, the feature layer is a first dimension, the candidate operation index of the reprocessing layer is a second dimension, and the candidate machine index is a third dimension.

[0037] Further, the genetic operation is performed to generate a child population, and the genetic operation comprises performing a crossover operator and a mutation operator, and wherein:

[0038] ​The crossover operator employs an extended priority operation to cross over POX, which performs the following operations:

[0039] Randomly divide all parts into two non-empty sets, part set 1 and part set 2;

[0040] For the two chromosomes involved in the crossover operation, the gene whose part number belongs to part 1 is copied to the two offspring chromosomes respectively, and their order is preserved;

[0041] For the two chromosomes involved in the crossover operation, the gene whose part number belongs to part 2 is crossover copied into the two offspring chromosomes respectively, and their order is preserved;

[0042] Alternatively, the crossover operator employs an extended job-based sequential crossover JOX, which performs the following operations:

[0043] Randomly divide all parts into two non-empty sets, part set 1 and part set 2;

[0044] For the two chromosomes involved in the cross-mutation operation, the gene with the part number belonging to part set 1 in the first chromosome is copied to the offspring corresponding to the first chromosome, and the gene with the part number belonging to part set 2 in the second chromosome is copied to the offspring corresponding to the second chromosome, keeping the same position.

[0045] For the two chromosomes involved in the crossover operation, the gene whose part number belongs to part set 1 in the first chromosome is copied to the corresponding offspring of the second chromosome, and the gene whose part number belongs to part set 2 in the second chromosome is copied to the corresponding offspring of the first chromosome, while preserving their order.

[0046] The mutation operator includes using a two-point exchange operator for the mutation feature layer and a single-point mutation operator for the mutation reprocessing layer. The two-point exchange operator randomly selects two positions and exchanges the corresponding genes, while the single-point mutation operator randomly selects a gene and replaces it with a different gene from the candidate set.

[0047] Furthermore, the adaptive crossover rate calculation formula for the crossover operator is as follows:

[0048]

[0049] Among them, P c P represents the adaptive crossover rate. c_initial The initial crossover rate is given by `iter_max` and `iter_current`, which represent the maximum number of iterations and the current number of iterations, respectively.

[0050] Furthermore, the adaptive mutation rate P of the mutation operatorm The calculation formula is as follows:

[0051]

[0052] where P m_initial represents the initial mutation rate, iter_max and iter_current represent the maximum iteration number and the current iteration number respectively.

[0053] Further, the local search strategy comprises:

[0054] performing the first local search operator, or the second local search operator, or the third local search operator according to a probability;

[0055] The first local search operator performs the following operations:

[0056] randomly selecting a chromosome p from the Pareto front, comparing the feature order of each part between the chromosome i to be locally searched and the chromosome p, copying the genes in the chromosome i into a new chromosome in the same order as the corresponding genes in the chromosome p for the parts with the same feature order, copying the genes in the chromosome i into the new chromosome in a preset order for the parts with different feature order, and copying the genes in the chromosome p into the new chromosome in the same order as the corresponding genes in the chromosome i for the parts with different feature order;

[0057] The second local search operator performs the following operations:

[0058] randomly selecting a chromosome in the population, generating a string vector H with the same length as the selected chromosome, the string vector H consisting of random 0 or 1;

[0059] copying the genes in the corresponding positions of H that are 1 into the new chromosome in the same order as the corresponding genes in the reprocessing layer;

[0060] selecting another candidate operation and candidate machine to replace the genes in the corresponding positions of H that are 0 into the new chromosome, the selected candidate operation and candidate machine corresponding to the candidate operation and candidate machine with the shortest processing time in the candidate set respectively;

[0061] The third local search operator performs the following operations:

[0062] randomly selecting two different genes and inserting the former in front of the latter to make them adjacent.

[0063] Further, the third local search operator is followed by a fourth local search operator to repair infeasible solutions, and the fourth local search operator performs the following operations:

[0064] Check whether the feature sequence of each part meets the feature constraint, if not, randomly recombine the feature gene according to the feature constraint of the part and replace the original position;

[0065] Check whether the operation can complete the processing of the corresponding feature, and whether the machine can complete the corresponding operation, if not, randomly select a feasible operation or machine gene in the corresponding candidate set to meet the processing requirements of the corresponding feature.

[0066] The application provides a remanufacturing decision-making method for process planning and scheduling integration, proposes a new IRPPS model in an uncertain environment, and uses an ENSGA-II algorithm for solving. The IRPPS model uses interval numbers to represent the uncertainty of processing time, and integrates a process planning selection method related to the uncertain quality of defective parts, so as to obtain a more practical and effective process planning and scheduling scheme. The application not only considers the uncertainty of processing time represented by interval numbers, but also considers the selection of process planning related to the uncertainty of the quality of defective parts, so as to more comprehensively coordinate process planning and scheduling in the uncertain remanufacturing environment. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 A flowchart of the remanufacturing decision-making method for process planning and scheduling integration of the application;

[0068] Figure 2 A scheduling example of a Gantt chart with interval processing time;

[0069] Figure 3 A flowchart of the ENSGA-II algorithm of the embodiment of the application;

[0070] Figure 4 A schematic diagram of multi-dimensional coding of the embodiment of the application;

[0071] Figure 5 A schematic diagram of a crossover operator of the application;

[0072] Figure 6 A schematic diagram of another crossover operator of the application;

[0073] Figure 7 A schematic diagram of a local search operator of the embodiment of the application;

[0074] Figure 8 A schematic diagram of another local search operator of the embodiment of the application. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical scheme and advantages of the application clearer, the application is further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application, and are not used to limit the application.

[0076] In one embodiment, as shown in Figure 1 a process planning and scheduling integrated remanufacturing decision-making method is provided, comprising:

[0077] Step S1, representing the processing time as an interval number, constructing the objective functions of total interval processing energy consumption, total interval idle energy consumption, interval completion time and maximum machine load, and then establishing an integrated model of remanufacturing process planning and scheduling by minimizing energy consumption, minimizing maximum completion time and minimizing maximum machine load.

[0078] In many previous studies, mathematical analysis theories based on uncertainty (such as rough set theory, fuzzy theory, grey system theory, etc.) have been used to describe the uncertainty of remanufacturing systems. However, it is difficult to determine the membership degree and probability distribution function before establishing the uncertainty model. The combination of interval number theory and uncertainty modeling can overcome these difficulties.

[0079] The present application represents the processing time as an interval number to construct a reasonable uncertainty model. The basic operation rules of interval number are shown in formulas (1)-(3).

[0080] For example, let A = [A L ,A R ] (or A = {A C ,A W}) and B = [B L ,B R ] (or B = {B C ,B W}) be two interval numbers.

[0081]

[0082]

[0083]

[0084] where A L and A R denote the lower bound and upper bound of interval number A, respectively, and λ is a scalar. If A L = A R , then A is a real number. A C and A W denote the midpoint and radius of interval number A, respectively, where A C = (A L + A R ) / 2 and A W = (A R - A L ) / 2.

[0085] The order relation between two interval numbers A and B is minimized as shown in equation (4):

[0086]

[0087] where ≤ min denotes the order relation between two interval numbers, and are interval number addition and subtraction operators, respectively.

[0088] The integrated remanufacturing process planning and scheduling (IRPPS) model under uncertainty can be described as follows: for a set of identical parts (e.g., crankshafts) in a batch of EOL products, each part has one or more features that need to be reprocessed. Each feature has one or more failure modes of different degrees or types. For example, the failure modes of the "surface" feature include "slight wear", "severe wear", "slight crack", and "severe crack", which need to be reprocessed by different operations. Therefore, features with different failure modes will affect the selection of defect part process planning.

[0089] Table 1 gives an example: the IRPPS model is described by several sets, including a set of machines M = {M1, M2,..., M4}, a set of operations O = {O1, O2,..., O 10 , a set of parts P = {P1, P2, P3}, and a set of features F = {F1, F2,..., F5}. For example: three features (i.e., F1, F3, and F4) in P1, two features (i.e., F1 and F2) in P2, and one feature (i.e., F5) in P3 need to be reprocessed. F1 has four possible failure modes: FM 11 , FM 12 , FM 13 , FM 14}. If feature F1 fails due to failure mode FM 12 , it can be restored by operation O2 or O4. Operation O2 can be performed on machine M1 or M4 with interval processing time [5, 9] or [8, 13], respectively. Operation O4 can be performed on machine M2 or M3 with interval processing time [4, 9] or [9, 12], respectively. The other features F2, F3, F4, and F5 are the same. According to the corresponding feature constraints, the reprocessing feature F1 needs to be prioritized over all other features.

[0090]

[0091] An example of flexible process planning for Table 1

[0092] Suppose that features F1, F3, and F4 of part P1 fail due to failure modes FM 11 , FM 32 , and FM41 And failure; the characteristics F1 and F2 of part P2 are due to failure mode FM respectively. 12 and FM 21 And failure; characteristic F5 of part P3 due to failure mode FM 51 And fail. The candidate process planning sets for parts P1, P2, and P3 are {O1–O7–O8, O1–O8–O7, O1–O7–O9, O1–O9–O7}, {O2–O 10 ,O4–O 10} and {O4,O6}.

[0093] After reasonable machine allocation, the process planning for each part yields an approximately optimal scheduling scheme for each part. For example, a feasible process planning for parts P1, P2, and P3 is O1(M1)–O7(M3)–O8(M2), O2(M4)–O7(M3)–O8(M2), respectively. 10 (M1) and O4(M2). Based on this process planning, a near-optimal scheduling scheme was obtained, such as... Figure 2 The Gantt chart is shown below. The start time is marked below the time axis, and the end time is marked above the time axis. The scheduling schemes for different parts are represented by solid lines of different thicknesses and distances from the time axis. For part P1, operation O1 is performed on machine M1 with a start time [0,0] and an end time [1,4]; operation O7 is performed on machine M3 with a start time [1,4] and an end time [5,17]; operation O8 is performed on machine M2 with a start time [5,17] and an end time [13,29]; the same applies to other parts P2 and P3.

[0094] The IRPPS model proposed in this application studies and balances three conflicting objectives: minimizing energy consumption, minimizing maximum completion time, and minimizing maximum machine load. To solve the IRPPS model, the following notation and assumptions are used to describe it:

[0095] P n The nth part, n = 1, ..., N, where N is the total number of parts;

[0096] F i The i-th feature, i = 1,...,I, where I is the total number of features of the part;

[0097] FM ik F i The k-th failure mode, k = 1,...,K i K i It is F i The total number of failure modes;

[0098] O nj P nthe jth operation of part P, j = 1,..., J n where J n is the number of features in part P n that require reworking, and is also equal to the number of operations on P n ;

[0099] O l the lth operation, l = 1,..., L, where L is the total number of operations;

[0100] M s the sth machine, s = 1,..., S, where S is the total number of machines;

[0101] P n’ denotes a part different from P n ; J n’ is the number of features in part P n’ that require reworking;

[0102] O n’j’ P n’ the j'th operation of part P, j' = 1,..., J n' ;

[0103] denotes the interval completion time of the previous operation O s of O nj performed on M n'j' ;

[0104] denotes the interval completion time of operation s performed on M n ; denotes the J n th operation of P m ;

[0105] denotes the interval number form of the mth objective function value f s , m = 1 for the total interval energy consumption objective function value; m = 2 for the interval completion time objective function value; m = 2 for the maximum machine load objective function value;

[0106] total interval energy consumption;

[0107] total interval processing energy consumption;

[0108] total interval idle energy consumption;

[0109] interval processing time of O nj performed on machine M s ;

[0110] In machine M s Execute O nj The start time of the interval;

[0111] In machine M s Execute O nj The interval completion time;

[0112] M s The unit processing power;

[0113] M s Unit idle power;

[0114] H s Close M s Time threshold;

[0115] 0-1 decision variables, where 1 represents part P n Feature F i Due to failure mode FM ik If it fails, then it is 0; otherwise, it is 0.

[0116] 0-1 decision variables, where 1 represents part P n Feature F i By operation O l Reprocess; otherwise, return 0.

[0117] 0-1 decision variables, where 1 indicates choosing O l As O nj To process P n Otherwise, it is 0;

[0118] 0-1 decision variables, where 1 represents 0 nj In machine M s Execute if specified, otherwise return 0;

[0119] 0-1 decision variables, where 1 represents 0 n'j' and O nj It is in M s The adjacent operations performed above, and O n'j' In O nj Previously, it was 0; otherwise, it was 0.

[0120] 0-1 decision variables, where 1 represents machine M s In adjacent operation O n'j' and Onj turn off (O n'j' turn off (O nj turn off (O

[0121] 0-1 decision variable, 1 indicates O nj is the first operation performed on machine M s , otherwise 0.

[0122] In the description of the IRPPS model, for the sake of simplicity, it is assumed that all parts and features are independent of each other, all parts have no priority, all parts and machines are available at the beginning, all interruptions are ignored, all transportation times are ignored, each machine can only process one part at a time, cannot process multiple features of the same part at the same time, the setup time of the machine is ignored, and the energy consumption of auxiliary equipment is ignored. Of course, the above factors can also be considered, and these factors can be added to the corresponding objective function.

[0123] In this embodiment, the processing time is represented by interval numbers, and the objective functions of total interval processing energy consumption, total interval idle energy consumption, interval completion time and maximum machine load are constructed as follows:

[0124] 1. The objective function of total interval energy consumption includes total interval processing energy consumption and total interval idle energy consumption.

[0125] In the IRPPS model, the total energy consumption is composed of two parts: total interval processing energy consumption and total interval idle energy consumption. In addition, the on / off strategy is also used in this model to reduce energy consumption. In order to reduce the complexity of the model, the on / off strategy is simplified in this application. If the idle time of the machine exceeds a given time threshold, the machine needs to be turned off. For example, H s = 7 indicates that if the idle time of the machine exceeds 7 hours, the machine M s needs to be turned off.

[0126] The total interval processing energy consumption is calculated using formula (5):

[0127]

[0128] The variable used to determine the total interval idle energy consumption uses formula (6), and the idle energy consumption is calculated using formula (7)

[0129]

[0130]

[0131] wherein formula (6) is used to check whether the machine M s needs to be turned off between two adjacent operations on it.

[0132] The objective function of total interval energy consumption is calculated using equation (8):

[0133]

[0134] 2. The objective function of interval completion time.

[0135] Equations (9) and (10) are used to determine the interval completion time, as follows:

[0136]

[0137]

[0138] wherein equations (9) and (10) represent the interval start time and interval completion time of operation O s on machine M nj , respectively, represents the interval completion time of operation O n(j-1) on machine M s′ , M s′ represents the s'th machine, s' = 1, 2,... S, wherein S is the total number of machines, represents the interval completion time of the previous operation O n'j' performed on machine M nj and preceding operation O s of operation O s .

[0139] The objective function of interval completion time is calculated by equation (11):

[0140]

[0141] wherein is the interval completion time of operation O on machine M s .

[0142] 3. The objective function of maximum machine load.

[0143] In the IRPPS model, the maximum machine load is calculated using equation (12):

[0144]

[0145] After the above objective functions are constructed, the integrated model of remanufacturing process planning and scheduling can be established to minimize energy consumption, minimize maximum completion time, and minimize maximum machine load. The integrated model of remanufacturing process planning and scheduling of the present application is a multi-objective optimization model, as shown in equation (13):

[0146]

[0147] The above-mentioned object is subject to the following constraints:

[0148]

[0149]

[0150]

[0151]

[0152] Formula (14) ensures that each defect feature in the part fails due to one failure mode, formula (15) indicates that each defect feature can only be reprocessed by one operation, formula (16) indicates that each operation can only be performed on one machine, and formula (17) indicates that there is only one operation O l is selected as the operation O nj to process the part P n .

[0153] In a specific embodiment, the present application also performs equivalent transformation on the above-mentioned objective function, converting the interval target value into a real value:

[0154] The mean and variance of the interval number can be calculated using formulas (18) and (19), and then the interval target value is converted into a real value using formula (20):

[0155]

[0156]

[0157]

[0158] wherein represents the real value after equivalent transformation, and ω m (the value is between 0 and 1) is the weight of the uncertainty degree (i.e. variance) of the objective function m. ω m can be adjusted according to the requirements of the actual remanufacturing environment. m is the index of the above-mentioned objective function, which is 1, 2 and 3 respectively.

[0159] Step S2, solving the integrated model of remanufacturing process planning and scheduling to obtain an optimal remanufacturing process planning and scheduling scheme, and performing remanufacturing according to the obtained optimal remanufacturing process planning and scheduling scheme.

[0160] The integrated model of remanufacturing process planning and scheduling of the present application is a multi-objective optimization problem, which can be solved by using the second generation non-dominated sorting genetic algorithm (NSGA-II algorithm), which has become a widely recognized multi-objective optimization method in the past twenty years. Or using SPEA2, MOPSO and other algorithms to solve.

[0161] By solving the integrated model of remanufacturing process planning and scheduling, the optimal remanufacturing process planning and scheduling scheme can be obtained and applied to actual remanufacturing tasks for remanufacturing.

[0162] In a specific embodiment, the improved second generation non-dominated sorting genetic algorithm (ENSGA-II algorithm) is used for solving.

[0163] As shown in Figure 3 , wherein N represents the initial population size. P G and O G represent the parent and child population of the Gth generation, respectively. The ENSGA-II algorithm of the embodiment includes:

[0164] Step F1, initialization, randomly generates a new population P G (N) using a multi-dimensional encoding method;

[0165] Step F2, execute genetic operation to generate child population Q G1 (N);

[0166] Step F3, combine P G (N) and Q G1 (N), and use fast non-dominated sorting and crowding distance method to generate the next child population Q G2 (N);

[0167] Step F4, execute local search strategy on Q G2 (N) to generate a new population P G+1 (N) for the next iteration;

[0168] Step F5, the iteration number G is equal to G+1;

[0169] Step F6, judge whether G reaches the maximum iteration number, if yes, output the approximate Pareto optimal solution set in P G (N), otherwise return to step F2 for the next iteration.

[0170] In the above ENSGA-II algorithm, the multi-dimensional encoding method includes two layers: feature layer and reprocessing layer, the feature layer represents part index, feature and failure mode information, and the reprocessing layer represents candidate operation index and candidate machine index.

[0171] In the embodiment, a chromosome needs to represent both part information and processing flexibility, as shown in Figure 4 , the feature layer is the first dimension, the candidate operation index of the reprocessing layer is the second dimension, and the candidate machine index is the third dimension.

[0172] Each value in the first dimension indicates that a certain defect feature of a certain part fails due to a certain failure mode, and the length of the first dimension indicates the total number of all defect features of all parts that need reprocessing. For example, the last gene [4, 5, 1] in the first dimension indicates that the defect feature 5 of part 4 fails due to failure mode 1 (FM 51 ).

[0173] Each value in the second dimension indicates that the rth candidate operation is selected to reprocess the corresponding defect feature. For example, the last gene 2 in the second dimension indicates that the 2nd candidate operation (i.e., O6) is selected to reprocess the corresponding defect feature [4, 5, 1].

[0174] Each value in the third dimension indicates that the corresponding operation is performed on the qth candidate machine. For example, the last gene 1 in the third dimension indicates that the operation O6 is performed on the 1st candidate machine (i.e., M3).

[0175] In one specific embodiment, performing the genetic operation generates the offspring population, including performing the crossover operator and the mutation operator.

[0176] This embodiment combines the priority operation crossover POX and the job-based order crossover JOX with the multi-dimensional encoding representation method proposed in this application to obtain an extended POX and an extended JOX, and then randomly selects one of them as the current crossover operator to generate offspring.

[0177] wherein the extended priority operation crossover POX performs the following operations:

[0178] Randomly divide all parts into two non-empty sets, part set 1 and part set 2;

[0179] For the two chromosomes participating in the crossover operation, copy the genes of part numbers belonging to part 1 into the two offspring chromosomes respectively, and keep their order;

[0180] For the two chromosomes participating in the crossover operation, copy the genes of part numbers belonging to part 2 into the two offspring chromosomes respectively, and keep their order.

[0181] Figure 5 An example of an extended priority operation crossover POX is shown, which first divides the parts into part set 1 and part set 2, part set 1 includes parts 1 and 3, and part set 2 includes parts 2 and 4.

[0182] For two chromosomes Pa1 and Pa2 participating in the crossover operation, the genes of part numbers belonging to part set 1 are the gray parts, which are respectively copied into the corresponding offspring Q1 and Q2. The genes of part numbers belonging to part set 2 are the white parts, which are copied into the corresponding offspring Q1 and Q2 through crossover, and the white part of Pa1 is copied into Q2, and the white part of Pa2 is copied into Q1.

[0183] The extended job-based order crossover JOX of the embodiment performs the following operations:

[0184] Randomly divide all parts into two non-empty sets, part set 1 and part set 2;

[0185] For two chromosomes participating in the crossover operation, copy the genes of part numbers belonging to part set 1 in the first chromosome into the offspring corresponding to the first chromosome, copy the genes of part numbers belonging to part set 2 in the second chromosome into the offspring corresponding to the second chromosome, and keep the same position.

[0186] For two chromosomes participating in the crossover operation, copy the genes of part numbers belonging to part set 1 in the first chromosome into the offspring corresponding to the second chromosome, copy the genes of part numbers belonging to part set 2 in the second chromosome into the offspring corresponding to the first chromosome, and keep the order.

[0187] Figure 6 An example of an extended job-based order crossover JOX is shown, in which the parts are first divided into part set 1 and part set 2, part set 1 includes parts 1 and 3, and part set 2 includes parts 2 and 4.

[0188] For two chromosomes Pa1 and Pa2 participating in the crossover operation, copy the genes of part numbers belonging to part set 1 in Pa1 (gray part) into the corresponding offspring Q1, and copy the genes of part numbers belonging to part set 2 in Pa2 (gray part) into the corresponding offspring Q2; copy the genes of part numbers belonging to part set 1 in Pa1 (gray part) into the offspring Q2 (become white part), and copy the genes of part numbers belonging to part set 2 in Pa2 (gray part) into the offspring Q1 (become white part).

[0189] The embodiment proposes an adaptive crossover rate P c As shown in equation (21), where P c_initial is the initial crossover rate, iter_max and iter_current represent the maximum number of iterations and the current number of iterations, respectively:

[0190]

[0191] The mutation operator of the embodiment includes using a two-point crossover operator to mutate the feature layer and using a single-point mutation operator to mutate the reprocessing layer.

[0192] The two-point crossover operator randomly selects two positions and exchanges the corresponding genes, and the single-point mutation operator randomly selects a gene and replaces the gene with a different gene in the candidate set. If there is only one gene in the candidate set, no operation is performed.

[0193] The embodiment proposes an adaptive mutation rate P m as shown in equation (22), where P m_initial represents the initial mutation rate.

[0194]

[0195] In a specific embodiment, in order to improve the performance of the algorithm, the local search strategy of the application uses the local search strategies of four local search operators LS1, LS2, LS3 and LS4 to extend the basic NSGA-II algorithm. The local search operators LS1 or LS2 or LS3 are executed according to a probability, and LS4 is executed after LS3 is executed, for repairing infeasible solutions that may be generated by LS3.

[0196] The first local search operator (LS1) aims to find a better process plan for each part. The second local search operator (LS2) aims to find a new process plan and generate a better scheduling scheme than the current one. The third local search operator (LS3) aims to jump out of a local optimal solution. The fourth local search operator (LS4) aims to repair infeasible solutions generated by LS3.

[0197] The four local search operators are described in detail as follows:

[0198] Local search operator LS1: The process plan of each part depends on the order of the defective features in the feature layer. The local search operator LS1 performs the following operations:

[0199] A chromosome p is randomly selected from the Pareto front. For a chromosome i to be locally searched, the feature orders of each part between the chromosomes are compared. For parts with the same feature order, the corresponding genes in chromosome i are copied into a new chromosome and the order is preserved. For parts with different feature orders, a preset part of the genes in chromosome i is copied into the new chromosome and the order is preserved. For parts with different feature orders, the remaining part of the genes in chromosome p is copied into the new chromosome and the order is preserved.

[0200] As Figure 7As shown, compare the feature sequence of each part between chromosomes i and p. The feature sequence of part P1 (i.e. feature F1 followed by feature F3) and part P2 (i.e. feature F1 followed by feature F2) are the same between chromosomes i and p, copy the corresponding genes into the new chromosome i' (i.e. four white genes) and keep the sequence. The feature sequence of part P3 and P4 are different between chromosomes i and p, copy about half of the part with different feature sequence (i.e. part P4 followed by feature F3 and feature F5) into the new chromosome i' (i.e. two gray genes) and keep the sequence. Copy the remaining part (i.e. part P3 followed by feature F4 and feature F2) from chromosome p into the new chromosome i' (i.e. two diagonal genes) and keep the sequence.

[0201] Local search operator LS2: LS2 acts on the rework layer, aiming to find a new process plan and generate a new scheduling scheme. The following operations are performed:

[0202] Randomly select a chromosome in the population, generate a string vector H with the same length as the selected chromosome, the string vector H consists of random 0 or 1;

[0203] In the rework layer, keep the genes in the corresponding positions of H that are 1 to the new chromosome and keep the sequence;

[0204] In the rework layer, select another candidate operation and candidate machine to replace the genes in the corresponding positions of H that are 0 to the new chromosome, the selected candidate operation and candidate machine correspond to the candidate operation with the shortest required processing time and the candidate machine in the candidate set, respectively.

[0205] Figure 8 An example of a local search operator LS2 is shown, the white part of the gene in chromosome i is directly retained in the new chromosome i', and the gray part of the gene is reselected from the candidate operation and candidate machine to replace the genes in the corresponding positions of H that are 0 in the new chromosome i'.

[0206] Local search operator LS3: LS3 is an insertion operator. For a chromosome in the current population, randomly select two different genes, insert the former in front of the latter to make them adjacent, and generate a new chromosome.

[0207] Local search operator LS4: Executing local search operator LS3 may produce infeasible solutions, such as the feature layer may not meet the feature constraints, or the selected operation or machine may not be able to complete the corresponding part or operation. Therefore, local search operator LS4 aims to repair infeasible solutions, with the following specific steps:

[0208] Check if the feature sequence of each part meets the feature constraint, if not, randomly recombine the feature genes according to the feature constraint of the part and replace the original position;

[0209] Check if the operation can complete the processing of the corresponding feature, and if the machine can complete the corresponding operation. If not, randomly select a feasible operation or machine gene in the corresponding candidate set to meet the processing requirements of the corresponding feature.

[0210] Specifically, the fourth local search operator is used to repair the feature layer. When repairing, according to the feature constraint, that is, the constraint of the order of feature processing, it is checked whether the feature order of each part meets the feature constraint. If not, randomly recombine the feature gene according to the feature constraint of the part and replace the original position. It is also used to repair the reprocessing layer. According to the repaired feature, it is checked whether the operation can complete the processing of the corresponding feature, and whether the machine can complete the corresponding operation. If not, randomly select a feasible operation or machine gene in the corresponding candidate set to meet the corresponding requirements.

[0211] The effect of the integrated model of the remanufacturing process planning and scheduling of the present application is further described below through experimental data. The performance of the ENSGA-II algorithm is evaluated through simulation experiments, and then it is compared with other three multi-objective comparison algorithms, namely NSGA-II, MOPSO and SPEA2. All experiments are implemented using Python language programming and run on a computer with an operating system of 64-bit Windows 10, a processor of Intel(R) Core 3.10 GHz, and a memory of 16 GB RAM.

[0212] To simulate the real remanufacturing environment, the experimental data and simulation parameters are defined as follows: In each instance, the number of parts is randomly generated in the range of 4-30, and the number of machines is randomly generated in the range of 6-12. The reference data of the parts are shown in Table 2, including the range of feature number and the total number of operations. For each feature, the number of failure modes that may exist is in the range of 1-4, the number of candidate operations for each failure mode is in the range of 1-3, and the number of candidate machines for each operation is in the range of 1-3. Other simulation parameters are randomly generated in the range shown in Table 3. The name of each instance in the database consists of three numbers, such as the total number of parts, the ID of the reference data set, and the total number of machines. For example, the instance "Exp(4 / 1 / 6)" represents that the total number of parts is 4, the reference data set is #1, and the total number of machines is 6.

[0213] To reduce errors in the experiment, all experiments are independently run 10 times and the average value is taken as the experimental result.

[0214]

[0215] Table 2

[0216]

[0217] Table 3

[0218] Three performance indicators, set coverage (SC), spacing indicator (SI) and hypervolume (HV), are used to evaluate the performance of the three multi-objective algorithms in the experiments. The maximum number of iterations for all algorithms is set to 300. Since the HV indicator can comprehensively evaluate the performance of an algorithm, the HV indicator is used to analyze the sensitivity of the parameters in the proposed ENSGA-II algorithm, including the selection probability of the local search operator and the population size.

[0219] The first experiment tests the performance of the ENSGA-II algorithm under different selection probability combinations of the local search operators (LS1, LS2 and LS3) on the instance Exp(15 / 1 / 8), and the initial population size of all algorithms is set to 40. Table 4 shows the 13 selection probability combinations of the local search operators used in this experiment.

[0220]

[0221] Table 4

[0222] The experimental results show that the HV value of C06 is higher than that of the other combinations. Therefore, in the following experiments, the selection probability combinations of the local search operators are set to 0.1, 0.6 and 0.3, respectively.

[0223] The second experiment tests the performance of the ENSGA-II algorithm under different initial population sizes on different size datasets. The experiment shows that when the initial population size exceeds 40, the HV value changes slowly. Since a large population size increases the computational cost of the simulation experiment, in the following experiments, the initial population size is set to 40. This population size also ensures a fair comparison between the algorithms.

[0224] In order to allow a fair comparison between the ENSGA-II algorithm and the other algorithms, the number of times that the local search operation is performed in the ENSGA-II algorithm and the NSGA-II algorithm, and the number of neighborhoods in the MOPSO algorithm are all set to 10. According to the results of the trial experiments, the other parameters of the multi-objective algorithms are shown in Table 5:

[0225]

[0226] Table 5

[0227] In the following experiments, the performance of the ENSGA-II algorithm and the other comparative algorithms (including NSGA-II, SPEA2 and MOPSO) is comprehensively evaluated by comparing the performance indicators. Tables 6, 7 and 8 show the experimental comparison results of the SC, SI and HV indicators of the algorithms, respectively.

[0228] The comparison results of SC index obtained by four algorithms are shown in Table 6.

[0229]

[0230] Table 6

[0231] The comparison results of SI index obtained by four algorithms are shown in Table 7.

[0232]

[0233]

[0234] Table 7

[0235] The comparison results of HV index of four algorithms are shown in Table 8.

[0236]

[0237] Table 8

[0238] The comparison results of ENSGA-II algorithm and other algorithms based on SC index are shown in Table 5. It can be found that ENSGA-II algorithm is obviously superior to other comparative algorithms in all experiments. The second column and the third column show that in most experiments at least one solution obtained by ENSGA-II algorithm dominates all solutions obtained by NSGA-II algorithm, and the solutions obtained by NSGA-II algorithm cannot dominate any solution obtained by ENSGA-II algorithm. The fourth column and the fifth column show that at least one solution obtained by ENSGA-II algorithm dominates all solutions obtained by SPEA2 algorithm, and the solutions obtained by SPEA2 algorithm cannot dominate any solution obtained by ENSGA-II algorithm. The sixth column and the seventh column show that in most experiments at least one solution obtained by ENSGA-II algorithm dominates part of solutions obtained by MOPSO algorithm, and the solutions obtained by MOPSO algorithm cannot dominate any solution obtained by ENSGA-II algorithm.

[0239] The comparison results of ENSGA-II algorithm and other algorithms based on SI index are shown in Table 6. In most experiments, the solution set obtained by ENSGA-II algorithm has better distribution and extensiveness than the solution set obtained by other algorithms.

[0240] The comparison results of ENSGA-II algorithm and other algorithms based on HV index are shown in Table 7. Wherein the reference point R=(r1, r2, r3) is set as (1, 1, 1) T T ​In most experiments, the HV values generated by ENSGA-II algorithm are significantly higher than those of the comparative algorithms. The experimental results show that the solution set obtained by ENSGA-II algorithm has better convergence and distribution than those obtained by other algorithms.

[0241] The experimental results show that most of the solutions generated by the comparative algorithms are dominated by the solutions generated by ENSGA-II algorithm. In different scale instances, the solution set obtained by ENSGA-II algorithm is superior to that of the comparative algorithms in terms of convergence and distribution. In addition, as the scale of the test instance increases, ENSGA-II algorithm is more likely to achieve the approximate Pareto optimal solution set than other comparative algorithms.

[0242] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the patent scope of the present application. It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the patent protection scope of the present application should be subject to the appended claims.

Claims

1. A method for remanufacturing decision making with integrated process planning and scheduling, characterized in that, The remanufacturing decision-making method integrated with process planning and scheduling comprises the following steps: The interval number is used to represent the machining time, and the objective functions of total interval machining energy consumption, total interval idle energy consumption, interval completion time and maximum machine load are constructed, and then the integrated model of remanufacturing process planning and scheduling is established by minimizing energy consumption, minimizing maximum completion time and minimizing maximum machine load; The integrated model of remanufacturing process planning and scheduling is solved to obtain an optimal remanufacturing process planning and scheduling scheme, and remanufacturing is performed according to the obtained optimal remanufacturing process planning and scheduling scheme; The total interval machining energy consumption objective function is as follows: ； The total interval idle energy consumption objective function is as follows: ； ； The total interval energy consumption is expressed as: ； The interval completion time objective function is as follows: ； ； The maximum machine load objective function is as follows: ； The integrated model of remanufacturing process planning and scheduling is expressed as: ； in, Indicates the total energy consumption of the interval. This indicates the total energy consumption for processing within the interval. This indicates the total idle energy consumption of the interval. Let the total interval energy consumption objective function be... Let the objective function be the interval completion time. The objective function is the maximum machine load. M represents s unit processing power, M s This represents the s-th machine. S is the total number of machines; For 0-1 decision variables, 1 represents 0. nj In machine M s Execute if specified, otherwise return 0; Indicates in machine M s Execute O nj The interval completion time, O nj P represents n The j-th operation, J n It is part P n The number of features that need further processing, P n This represents the nth part. , where N is the total number of parts; Indicates in machine M s Execute O nj The start time of the interval; M represents s unit idle power, The variable M represents a 0-1 decision variable, and 1 represents the machine. s In adjacent operations and O nj Close between; otherwise, return 0; P n’ Indicates that it is different from P n One of the parts, J n’ It is part P n’ The number of features that need further processing; O n’j’ P represents n’ The j'th operation, ; Indicates in M s O executed on nj Previous operation The interval completion time; Indicates in M s Operations performed on The interval completion time, P represents n The Jth n One operation; denotes a 0-1 decision variable, 1 means that machine M s is closed between adjacent operations and O nj , otherwise 0. denotes the time threshold for closing M s . denotes the interval processing time for performing O s on machine M nj .

2. The method of claim 1, wherein, The remanufacturing decision-making method integrated with process planning and scheduling further comprises the following steps: The total interval energy consumption objective function, the interval completion time objective function and the maximum machine load objective function are equivalently transformed to convert the interval objective values into real values, and the following formula is used: ； wherein, denotes the real value after equivalent transformation, is the target function is the weight of the uncertainty degree of the target function denotes the interval number form of the mth target function value .

3. The method of claim 1, wherein, The integrated model of remanufacturing process planning and scheduling is solved by using an improved second-generation non-dominated sorting genetic algorithm, which comprises the following steps: Step F1, initialization, randomly generate new population using multi-dimensional encoding method ; Step F2, performing genetic operations to produce a population of offspring ; Step F3, combining, using fast non-dominated sorting and crowded distance method to produce next sub-population and ;​ Step F4, performing a local search strategy on the population produces a new population for the next iteration ; Step F5, the iteration number G is equal to G+1; Step F6, determine if G reaches the maximum iteration number, if yes, output the approximate Pareto optimal solution set in F, otherwise return to Step F2 for the next iteration.

4. The method of claim 3, wherein, The multi-dimensional coding method comprises two layers, i.e., a feature layer and a reprocessing layer, the feature layer represents part index, feature and failure mode information, the reprocessing layer represents candidate operation index and candidate machine index, the feature layer is the first dimension, the candidate operation index of the reprocessing layer is the second dimension, and the candidate machine index is the third dimension.

5. The method of claim 3, wherein, The genetic operation is performed to generate a child population, which comprises performing a crossover operator and a mutation operator, wherein: The crossover operator uses an extended priority operation crossover POX, which performs the following operations: All parts are randomly divided into two non-empty sets, i.e., part set 1 and part set 2; For the two chromosomes participating in the crossover operation, the genes of part numbers belonging to part 1 are respectively copied into two child chromosomes, and the sequence is preserved; For the two chromosomes participating in the crossover operation, the genes of part numbers belonging to part 2 are respectively crossed and copied into two child chromosomes, and the sequence is preserved; Alternatively, the crossover operator uses an extended job-based order crossover JOX, which performs the following operations: All parts are randomly divided into two non-empty sets, i.e., part set 1 and part set 2; For the two chromosomes participating in the mutation operation, the genes of part numbers belonging to part set 1 in the first chromosome are copied into the child corresponding to the first chromosome, and the genes of part numbers belonging to part set 2 in the second chromosome are copied into the child corresponding to the second chromosome, and the positions are preserved; For the two chromosomes participating in the crossover operation, the genes of part numbers belonging to part set 1 in the first chromosome are copied into the child corresponding to the second chromosome, and the genes of part numbers belonging to part set 2 in the second chromosome are copied into the child corresponding to the first chromosome, and the sequence is preserved. The mutation operator includes a two-point crossover operator for mutating the feature layer and a single-point mutation operator for mutating the reprocessing layer, wherein the two-point crossover operator randomly selects two positions and exchanges the corresponding genes, and the single-point mutation operator randomly selects a gene and replaces it with a different gene in the candidate set.

6. The method of claim 5, wherein, The adaptive crossover rate of the crossover operator is calculated according to the following formula: ； where P c denotes the adaptive crossover rate, is the initial crossover rate, and denotes the maximum number of iterations and the current iteration number, respectively.

7. The method of claim 5, wherein, The adaptive mutation rate P of the mutation operator m The calculation formula is as follows: ； wherein denotes the initial mutation rate, and denotes the maximum number of iterations and the current iteration number, respectively.

8. The method of claim 3, wherein, The local search strategy includes: The first local search operator, the second local search operator or the third local search operator is executed according to a probability. The first local search operator performs the following operations: A chromosome p is randomly selected from the Pareto front, and for a chromosome i to be locally searched, the feature sequences of each part are compared between the chromosomes, for the parts with the same feature sequence, the corresponding genes in the chromosome i are copied into a new chromosome while keeping the sequence, for the parts with different feature sequences, a preset part of the genes in the chromosome i is copied into the new chromosome while keeping the sequence, and for the parts with different feature sequences, the remaining part of the genes in the chromosome p is copied into the new chromosome while keeping the sequence. The second local search operator performs the following operations: A chromosome is randomly selected from the population, and a string vector H with the same length as the selected chromosome is generated, wherein the string vector H is composed of random 0 or 1. In the reprocessing layer, the genes in the corresponding positions of H that are 1 are retained into the new chromosome while keeping the sequence. In the reprocessing layer, another candidate operation and candidate machine are selected to replace the genes in the corresponding positions of H that are 0 into the new chromosome, and the selected candidate operation and candidate machine correspond to the candidate operation with the shortest processing time and the candidate machine in the candidate set, respectively. The third local search operator performs the following operations: Two different genes are randomly selected, and the former is inserted in front of the latter so that they are adjacent.

9. The method of claim 8, wherein, After the third local search operator, a fourth local search operator is further executed to repair infeasible solutions, and the fourth local search operator performs the following operations: It is checked whether the feature sequence of each part meets the feature constraint, and if not, the feature genes are randomly recombined and replaced according to the feature constraint of the part. It is checked whether the operation can complete the processing of the corresponding feature and whether the machine can complete the corresponding operation, and if not, a feasible operation or machine gene is randomly selected from the corresponding candidate set to meet the processing requirement of the corresponding feature.

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