Production Scheduling Method Considering Multi-Chamber Imbalance and Machine Failures

Abstract

The present invention provides a production scheduling method considering multi-cavity imbalance and machine failures, including the following steps: Step S11: Set the multi-cavity imbalance probability and machine failure rate for each machine, and set the corresponding upper and lower limits of the processing threshold; Step S12: Calculate the processing time based on the multi-cavity imbalance probability, machine failure rate, upper limit of the processing threshold, and lower limit of the processing threshold; Step S13: Set a dual-objective function of the maximum completion time of all workpieces and the total production energy consumption of all machines based on the processing time; Step S14: Use an optimization algorithm to solve and obtain a production scheduling plan. When dynamic disturbance events occur, different tasks are reasonably arranged to be processed on different machines, providing theoretical and technical support for enterprise processing.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling planning, and particularly relates to a production scheduling method considering multi-cavity imbalance and machine failures. Background Art

[0002] With the rapid development of the manufacturing industry, the goal of sustainable development has gradually become the focus of attention of countries around the world. Among them, reducing power consumption is the key to achieving sustainable development, which can not only help enterprises reduce operating costs, but also effectively reduce carbon emissions and alleviate global problems such as resource scarcity. At the same time, in the context of manufacturing scheduling, optimizing complex machining workshops is a key challenge. However, in actual machining, changes such as order insertion, cancellation and modification, machine malfunctions, wear, and human factors are inevitable, and these interferences make the static machining scheduling scheme far from the expected effect, seriously affecting machining efficiency. In dynamic events, the machine deterioration effect is inevitable in actual machining. Different from machine malfunctions, the deterioration effect causes the machining performance of the machine to decline, but considering the actual production cost, machining usually continues. For example, in a medical device machining workshop, when a cavity is damaged during the injection extrusion process, plugging operations are often used instead of replacing the entire mold, forming an interference event of multi-cavity imbalance. Multi-cavity imbalance occurs in the injection extrusion stage of plastic part machining.

[0003] However, current enterprise machining is mostly based on machining experience, making it difficult to efficiently plan machining strategies, and thus unable to guarantee the theory of low power consumption for sustainable development. At the same time, existing technologies lack dynamic processing methods for multi-cavity imbalance and ignore the impact of multi-cavity imbalance on the actual machining process. However, multi-cavity imbalance often occurs in machining workshops with injection machining tasks such as building materials, molds, and medical devices. Therefore, how to perform production scheduling planning considering multi-cavity imbalance is a technical problem that urgently needs to be solved. Summary of the Invention

[0004] The present invention proposes a production scheduling method considering multi-cavity imbalance and machine failures to solve the technical problem that the existing scheduling planning method does not consider multi-cavity imbalance and machine failures, resulting in a difficult-to-apply generated scheduling scheme.

[0005] To solve the above technical problems, the present invention provides a production scheduling method considering multi-cavity imbalance and machine failures, including the following steps:

[0006] Step S11: Set the multi-cavity imbalance probability and machine failure rate for each machine, and set the corresponding upper and lower limits of the processing threshold;

[0007] Step S12: Calculate the processing time based on the multi-cavity imbalance probability, machine failure rate, upper limit of the processing threshold, and lower limit of the processing threshold;

[0008] Step S13: Set a bi-objective function for the maximum completion time of all workpieces and the total production energy consumption of all machines based on the processing time;

[0009] Step S14: Use an optimization algorithm to solve and obtain a production scheduling plan.

[0010] Preferably, in step S12, the calculation formula for the processing time is as follows:

[0011] ;

[0012] ;

[0013] ;

[0014] In the formula, T ijk represents the processing time required for operation O ij on machine M k ; WT k represents the cumulative processing time of machine M k ; represents the lower limit of the processing threshold of machine M k ; represents the upper limit of the processing threshold of machine M k ; e k represents the probability of multi-cavity imbalance occurring in machine M k ; N represents the set of workpieces; J i represents the set of operations corresponding to workpiece i ; M represents the set of machines; n represents a random number between 0 and 1; R k represents the time required for machine k to repair a fault; represents the machine failure rate of machine k ; represents the load time of machine M k ; b ijk represents a decision variable. If machine is operating normally, it is 1; otherwise, it is 0.

[0015] Preferably, in step S13, the expression for the maximum complete processing time is:

[0016] ;

[0017] The expression for the total power consumption of processing for all machines is:

[0018] ;

[0019] In the formula, represents the processing power of machine M k ; represents the standby power of machine M k ; T ijk represents the time required for processing operation O ij on machine M k ; T i represents the total processing time of workpiece i ; E ij represents the completion time of processing operation O ij on machine M k ; E k represents the end time of processing of machine M k ; a ijk represents a decision variable, which is 1 if operation O ij is selected to be processed on machine M k , and 0 otherwise.

[0020] Preferably, when solving step S14, the following one or more constraint conditions are set:

[0021] 1) Each operation of each workpiece can only be processed by one feasible processing machine:

[0022] ;

[0023] In the formula, N represents the set of workpieces; J i represents the set of operations corresponding to workpiece i ; M represents the set of machines; a ijk represents a decision variable, which is 1 if operation Oij If it is selected to be processed on the machine M k it is 1, otherwise it is 0;

[0024] 2) There is a sequence constraint between different workpieces on the same processing machine:

[0025] ;

[0026] In the formula, S ij represents the start time of the operation O ij ; T ijk represents the operation O ij on the machine M k required processing time;

[0027] 3) The completion time of the workpiece must be not less than the sum of the start time of the workpiece and the processing time of the workpiece:

[0028] ;

[0029] In the formula, C i represents J i completion time; S i represents the start time of the workpiece i ; R k represents the time required for the machine k to repair the fault;

[0030] 4) Each workpiece must be processed according to its specific process route, and there is a sequence between each process of the same workpiece:

[0031] ;

[0032] In the formula, E ij represents the completion time of the process operation O ij on the machine M k ;

[0033] 5) Once the workpiece starts processing, it cannot be interrupted:

[0034] .

[0035] Preferably, in step S14, a multi-objective genetic programming method is used for solving, including the following steps:

[0036] Step S21: Initialize the population according to the workpiece processing information and the encoding and decoding strategies;

[0037] Step S22: Perform grafting, mutation, and elite selection operations;

[0038] Step S23: When the running time of the algorithm reaches the maximum number of running times, the algorithm terminates and a planning scheme is obtained.

[0039] Preferably, the encoding strategy in Step S21 includes: setting the workpiece arrangement sequence and the machine arrangement sequence; encoding the workpiece arrangement sequence and the machine arrangement sequence using a binary tree; the elements in the binary tree are all terminal symbol set rules; the terminal symbol set uses "+", "-", "x", and " / " as the function symbol set for connection;

[0040] The terminal symbol set rules of the workpiece arrangement sequence include:

[0041] 1) NAPT: The average processing time of the next process;

[0042] 2) NOR: The remaining number of processes;

[0043] 3) NAO: The average number of available machines for the next process of the workpiece;

[0044] 4) NCO: The number of operations completed for the current workpiece;

[0045] 5) EAT: The earliest available processing time of the workpiece;

[0046] 6) TS: The processing time of the workpiece that has been processed;

[0047] 7) PTC: The processing time of the current process workpiece;

[0048] 8) EER: The energy efficiency ratio, that is, the ratio of the energy required to complete the task to the processing time;

[0049] 9) WT Workpiece waiting time;

[0050] 10) ECN Average energy consumption of the next process;

[0051] The terminal symbol set rules of the machine arrangement sequence include:

[0052] 1) MLU: The machine with the lowest utilization rate;

[0053] 2) MSPT: The earliest available time of the machine;

[0054] 3) SWT: The shortest processing time of the machine for the next component.

[0055] Preferably, the decoding strategy in step S21 includes: input workpiece terminal symbol set rules, machine terminal symbol set rules, function symbol sets, population size, and binary tree depth; perform individual decoding, and select workpieces and machines one by one for allocation; record the processing time of each machine, the processed status of the workpiece, and the current maximum completion time during allocation. Wait until all workpiece processes are arranged, and determine the completion time of each workpiece. E ij , the maximum completion time of production is , and the current individual decoding is completed; determine the operation time window and the maximum completion time of all tasks arranged by all binary tree rules in the population, and the decoding is completed.

[0056] Preferably, the grafting operation in step S22 includes: compare the quality of the lower binary tree results after grafting by pruning the binary tree and replacing the branches; according to the greedy rule, use the better new binary tree as the winning tree; if the quality of the binary tree is not improved, keep the original binary tree unchanged.

[0057] Preferably, the mutation operation in step S22 includes: select a binary tree, and mutate it into other rules in the set by pruning the terminal symbol rules or function symbols in the branches; according to the greedy rule, if the mutated binary tree is excellent, use it as the winning tree, and if the quality of the binary tree is not improved, keep the original binary tree unchanged; among them, the mutated category is subject to the high-quality mutation probability of the terminal symbols in the high-quality binary tree species.

[0058] Preferably, the elite selection operation in step S22 includes: evaluate the multi-objective machining binary tree scheduling result through the hypervolume index, and set the reference point as , then the HV value is the hypervolume between the binary tree scheduling result x and the reference point , and its expression is:

[0059] ;

[0060] Calculate the selection probability of the binary tree P ( x i ) is:

[0061] ;

[0062] In the formula, represents the maximum completion time; represents the total production energy consumption of all machines; N represents the part set;

[0063] Then perform non-dominated sorting for elite selection, use the ones with higher sorting levels as the new binary tree group, and count the occurrence frequency of terminal symbols in the new binary tree group as the mutation probability. The non-dominated sorting includes:

[0064] 1) Calculate the crowding degree of the new population;

[0065] 2) Determine the mutation probability of the terminator according to the combination scheduling rule with a higher dominance level;

[0066] 3) Select the population individuals with a higher dominance level according to the set population number to form a new population.

[0067] The beneficial effects of the present invention at least include: The present invention aims at the mathematical models of multi-cavity imbalance and machine abnormal processing in the actual processing of injection molding enterprises such as medical appliances, plates and various plastic products. For the processing tasks in the two cases of machine failure and multi-cavity imbalance, on the premise of meeting the processing procedure sequence, select the processable machines for processing. When dynamic disturbance events occur, reasonably arrange different tasks to be processed on different machines, providing theoretical and technical support for enterprise processing. Brief Description of the Drawings

[0068] Figure 1 It is a schematic flowchart of the method in an embodiment of the present invention;

[0069] Figure 2 It is a schematic diagram of multi-cavity imbalance occurring in an enterprise in an embodiment of the present invention;

[0070] Figure 3 It is a schematic diagram of production scheduling machine failure and multi-cavity imbalance in an embodiment of the present invention;

[0071] Figure 4 It is a scatter plot of processing duration and energy dissipation considering all cases in performance evaluation in 5 independent tests in an embodiment of the present invention;

[0072] Figure 5 It is a Pareto surface and Gantt chart in an embodiment of the present invention. Detailed Embodiments

[0073] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0074] Embodiment 1

[0075] As Figure 1 shown, the embodiment of the present invention provides a production scheduling method considering multi-cavity imbalance and machine failure.

[0076] Before presenting the embodiment, the production tasks considering multi-cavity imbalance and machine failure are elaborated as follows in this embodiment.

[0077] Multi-cavity imbalance mostly occurs in the case of damaged die cavities. Since workers will seal the damaged cavities, muzzle imbalance will occur during the processing. In the production of medical devices, this deterioration effect is particularly obvious, as Figure 2 shown. Multi-cavity imbalance also often occurs in the production of general plastics, whole vehicles and dies. Multi-cavity imbalance does not mean that the machine has failed. More importantly, in order to ensure profits during the processing, multi-cavity imbalance is allowed to exist while not affecting the integrity of the processing. At the same time, it cannot be ignored that machine failure is still one of the most common disturbance events in actual production. During the failure stage, if a workpiece fails during the processing stage, the processing can still be shifted or rescheduled according to the processing status and recovery time. As Figure 3 shown in the processing tasks of machine failure and multi-cavity imbalance, under the premise of meeting the processing sequence of the process, select the available processing machines for processing. The difficulty of this problem lies in how to reasonably arrange different tasks on different machines for processing and optimize the evaluation index when dynamic disturbance events occur.

[0078] The differences between multi-cavity imbalance and machine failure are as follows: ① When multi-cavity imbalance occurs, the machine can still continue to process; ② As the processing progresses, the cavities will be randomly blocked, and the degree of blockage will directly affect the processing time.

[0079] When the number of processing machines is fixed, the operation times of the processes of different workpieces on different machines are different. The optimization goal is to minimize the processing time and the total processing energy consumption. The processing time is the maximum complete processing time of all machines. The complete processing time of each machine includes the processing operation time and the standby time. The standby time is mainly the waiting time caused by precedence constraints. The machine will generate corresponding energy consumption during different processing time periods, that is, the machine production energy consumption includes the processing operation energy consumption and the standby energy consumption.

[0080] The method of this embodiment includes the following steps:

[0081] Step S11: Set the multi-cavity imbalance probability and machine failure rate for each machine, and set the corresponding upper and lower limits of the processing threshold.

[0082] Specifically, first, according to the processing equipment situation, determine the interference factors that occur during the processing, the machines with multi-cavity imbalance and failure during the processing, and according to the processing information of the production order, determine the processes of each workpiece, the number of available processing machines, and the available processing machine information corresponding to each process.

[0083] For the convenience of description, the symbols and decision variables used in the embodiments of the present invention are as follows:

[0084] i : workpiece number,j : Total number of processes for the workpiece , k : Machine number, workpiece set is N , machine set is M ;

[0085] J i : The workpiece i corresponding process;

[0086] M k : The k rd machine;

[0087] P k : The machining power of machine M k ;

[0088] P´ k : The standby power of machine M k ;

[0089] O ij : The i th process of the workpiece j ;

[0090] E k : The machining end time of machine M k ;

[0091] e k : The probability of multi - cavity imbalance occurring in machine M k ;

[0092] WT k : The cumulative machining time of machine M k ;

[0093] : The lower machining threshold of machine M k ;

[0094] : The upper machining threshold of machine M k ;

[0095] C i : J i completion time;

[0096] T ijk : Process O ij The time required for processing on the machine M k

[0097] E ij : Process O ij The time required for processing on the machine M k The completion time of processing;

[0098] S ij : Process O ij The start time of processing;

[0099] n : A random number between 0 and 1;

[0100] R k : The machine k The time required to repair the fault;

[0101] T i : The workpiece i The total processing time;

[0102] S i : The workpiece i The start time

[0103] a ijk : Decision variable, if process O ij Is selected to be processed on the machine M k Then it is 1, otherwise it is 0;

[0104] b ijk : Decision variable, if the machine Is in normal processing then it is 1, otherwise it is 0;

[0105] Step S12: Calculate the processing time based on the multi - cavity imbalance probability, machine failure rate, upper processing threshold, and lower processing threshold.

[0106] Specifically, the processing time Is calculated through the following expression.

[0107] ;

[0108] ​ ;

[0109] ;

[0110] In the formula, T ijk represents the processing time required for process O ij on machine M k ; WT k represents the cumulative processing time of machine M k ; represents the lower limit of the processing threshold of machine M k ; represents the upper limit of the processing threshold of machine M k ; e k represents the probability of multi - cavity imbalance occurring in machine M k ; N represents the workpiece set; J i represents the process set corresponding to workpiece i ; M represents the machine set; n represents a random number between 0 and 1; R k represents the time required for machine k to repair a fault; represents the machine failure rate of machine k ; represents the load time of machine M k ; b ijk represents a decision variable. If machine is processing normally, it is 1, otherwise it is 0.

[0111] Step S13: Based on the processing time, set a two - objective function for the maximum completion time of all workpieces and the total production energy consumption of all machines.

[0112] Specifically, minimize the completion time and processing energy consumption, and its expression is:

[0113] ;

[0114] Sub - objective 1: The maximum completion time of all workpieces, expressed as:

[0115] .

[0116] Sub - objective 2: The total production energy consumption of all machines, expressed as:

[0117] 。

[0118] Step S14: Use an optimization algorithm to solve and obtain a production scheduling plan.

[0119] The optimization algorithms used in this embodiment include, but are not limited to, genetic algorithms, particle swarm optimization, non - dominated sorting genetic algorithms, differential evolution algorithms, and simulated annealing algorithms.

[0120] In this embodiment, in order to be more in line with the actual processing situation, the following constraints are also set.

[0121] 1) Each process of each workpiece can only be processed by one feasible processing machine:

[0122] ;

[0123] In the formula, N represents the set of workpieces; J i represents the workpiece i corresponding process set; M represents the set of machines; a ijk represents the decision variable. If process O ij is selected to be processed on machine M k it is 1, otherwise it is 0;

[0124] 2) There is a precedence constraint between different workpieces on the same processing machine:

[0125] ;

[0126] In the formula, S ij represents the start time of process O ij ; T ijk represents the time required for process O ij to be processed on machine M k ;

[0127] 3) The completion time of a workpiece must be not less than the sum of the start time of the workpiece and the processing time of the workpiece:

[0128] ;

[0129] In the formula, C i representsJ i Completion time; S i Indicates the workpiece i Start time;

[0130] 4) Each workpiece must be processed according to its specific process route, and there is a sequence between the processes of the same workpiece:

[0131] ;

[0132] Wherein, E ij Indicates the process operation O ij On the machine M k Processing completion time;

[0133] 5) Once a workpiece starts processing, it cannot be interrupted:

[0134] 。

[0135] Embodiment 2

[0136] On the basis of Embodiment 1, this embodiment provides an optimization algorithm. By designing an adaptive terminator mutation mechanism for the genetic programming algorithm, an improved multi-objective genetic programming algorithm is obtained, which replaces the traditional optimization algorithm in step S14 of Embodiment 1, and its solution method is as follows.

[0137] Step S21: Initialize the algorithm parameters;

[0138] Step S22: Complete the population initialization according to the workpiece processing information and the encoding and decoding strategies;

[0139] Step S23: Execute the grafting stage, mutation stage, and elite selection stage respectively;

[0140] Step S24: When the running time of the algorithm reaches the maximum number of running times, the algorithm terminates and outputs the optimization result.

[0141] Specifically, in the coding strategy, the production and processing arrangement includes the workpiece arrangement sequence and the machine arrangement sequence. The workpiece and machine arrangement sequences are encoded using a binary tree. The elements in the binary tree are all terminal symbol set rules. The terminal symbol set uses "+", "-", "x", and " / " as the function symbol set for connection. In the terminal symbol set rules for workpiece arrangement: ① NAPT: The average processing time of the next process; ② NOR: The number of remaining processes; ③ NAO: The average available machines for the next process of the workpiece; ④ NCO: The number of operations completed for the current workpiece; ⑤ EAT: The earliest available processing time of the workpiece; ⑥ TS: The processing time of the workpiece that has been processed; ⑦ PTC: The processing time of the workpiece for the current process; ⑧ EER: The energy efficiency ratio (the ratio of the energy required to complete the task to the processing time); ⑨ WT: The waiting time of the workpiece; ⑩ ECN: The average energy consumption of the next process. The terminal set rules for machine arrangement: ① MLU: The machine with the lowest utilization rate; ② MSPT: The earliest available time of the machine; ③ SWT: The shortest processing time of the machine for the next workpiece.

[0142] The specific coding process is as follows: ① Input the terminal symbol set rules for workpieces, the terminal symbol set rules for machines, the function symbol set, the population size, and the depth of the binary tree; ② According to the determined depth of the binary tree, use the terminal set to fill in the complete production complete binary tree rules, where some nodes are not filled as incomplete binary tree rules;

[0143] When decoding, it is necessary to determine the time window for workpiece processing. When arranging workpieces and corresponding machines according to the generation rules, the process sequence of the workpieces needs to be considered. When adding the time window, it is necessary to make the time between tasks as idle-free as possible, so as to ensure the shortest complete processing time and the minimum required energy consumption. The specific decoding process is as follows:

[0144] Step S221: Input the terminal symbol set rules for workpieces, the terminal symbol set rules for machines, the function symbol set, the population size P, and the depth of the binary tree D;

[0145] Step S222: Perform individual decoding, and select workpieces and machines one by one for allocation;

[0146] Step S223: Record the processing time of each machine, the processed situation of the workpiece, the current maximum completion time during allocation. After all the waiting workpiece processes are arranged, determine the completion time of each workpiece E ij , the maximum completion time of production is , and the current individual decoding is completed.

[0147] Step S224: Determine the operation time window and the maximum completion time of all tasks arranged by all binary tree rules in the population, and the decoding is completed.

[0148] In the grafting stage, by pruning the binary tree and replacing branches, the quality of the resulting lower binary tree after grafting is compared. According to the greedy rule, the better new binary tree is taken as the winning tree. If the quality of the binary tree is not improved, the original binary tree remains unchanged.

[0149] The specific steps of the grafting stage are as follows: ① Input the binary tree individuals ; ② Randomly select a binary tree different from in the population, randomly select different branches, perform grafting, and obtain a new binary tree , and and ; ③ If , then replace the binary tree with the non-dominated solution ; if , then replace the binary tree with the non-dominated solution ; otherwise, if no non-dominated solution is found, keep the binary tree unchanged; ④ Output the binary tree population .

[0150] In the mutation stage, a binary tree is selected. By pruning the terminal symbol rules or function symbols in the branches, it mutates into other rules in the set. According to the greedy rule, if the mutated binary tree is excellent, it is taken as the winning tree. If the quality of the binary tree is not improved, the original binary tree remains unchanged. Among them, the mutated category undergoes high-quality mutation according to the terminal symbol mutation probability of the high-quality binary tree species.

[0151] The specific steps of the mutation stage are as follows: ① Input the binary tree individuals ; ② Randomly select a terminal symbol or function symbol on the branch and perform mutation to obtain a new binary tree ; ③ If , then replace the binary tree with the non-dominated solution , otherwise, if no non-dominated solution is found, keep the binary tree unchanged; ④ Output the binary tree population .

[0152] In the elite selection stage, the multi-objective production binary tree scheduling results are evaluated by the hypervolume indicator. Let the reference point be , then the HV value is the hypervolume between the binary tree scheduling result x and the reference point , and its expression is

[0153] ;

[0154] The selection probability P ( x i ) of the binary tree can be calculated as

[0155] ;

[0156] Elite selection is carried out by non - dominated sorting, and those with a higher sorting level are used as the new binary tree population, and the occurrence frequency of terminal symbols in the new binary tree population is counted as the mutation probability. The non - dominated sorting includes

[0157] 1) Calculate the crowding degree of the new population;

[0158] 2) Determine the mutation probability of the terminal symbol according to the combination scheduling rule with a higher domination level;

[0159] 3) Select the population individuals with a higher domination level according to the set population number to form a new population.

[0160] Example 3

[0161] Taking the production workshop of a medical infusion device manufacturing enterprise as an example, the performance analysis of the planning method in Example 1 and the optimization algorithm in Example 2 is carried out. A production problem of multi - cavity imbalance and machine failure is constructed to analyze the application performance of the method of the present invention in an actual engineering case. The types of workpieces to be produced are 10 kinds, and the quantity of each kind is 100,000 pieces. The number of processes for each workpiece is 3 and there are strict precedence constraints. The processing equipment and its related energy consumption information are shown in Table 1, and the detailed information of the processing tasks is shown in Table 2. Table 1 gives the types of available machines and gives the operating energy consumption and standby energy consumption. Table 2 gives the processes of 10 workpiece types and the available machines for each process, and gives the processing time on each machine.

[0162] Table 1

[0163]

[0164] Table 2

[0165]

[0166] The scheduling rules (NAPT, NOR, NAO, NCO, EAT, TS, PTC, EER, WT, ECN) of 10 terminal symbol sets, genetic programming (GP) and the designed multi - objective genetic programming algorithm (MOGPA) are compared. The population number of all algorithms is set to 200, and the algorithm termination condition is to run 500 times. The crossover and mutation probabilities of MOGPA are set to 0.8 and 0.2 respectively. The optimal terminal symbol set scheduling rules, GP and MOGPA are compared under 5 standard data sets as Figure 4 shown.

[0167] From Figure 4It can be seen that compared with the scheduling rules of the optimal 10 terminal symbol sets, MOGPA has achieved relatively excellent results, with a maximum optimization rate of 30% in terms of the total project duration and total energy consumption. Under the standard of the benchmark rule, the deviation box plot in the lower right corner is compared with it. Compared with the ordinary scheduling rules, the vast majority of cases achieve optimality under the same goal, further proving the superiority of MOGPA in processing production under multi-cavity imbalance and machine failures.

[0168] Solve under the above example. In the whole example, each machine will have a failure, and at the same time, the maximum number of failures is set to 5. Multi-cavity imbalance will occur in injection molding and extrusion machines. Combining the actual production situation, the maximum cavity imbalance on the two types of machines is 50%. The solution results are as Figure 5 shown.

[0169] Figure 5 In (a), the Pareto surface of the solution case is shown. Taking the solution result with the maximum completion time of 65 and the total energy consumption of 25.3409, the processing Gantt chart is drawn as Figure 5 shown in (b) below. Among them, the red box line represents machine failure, and the dotted line following the processing represents multi-cavity imbalance. Figure 5 In (c) below, the scheduling Gantt chart with the goal of minimizing the maximum completion time is shown. The optimal completion time is 55, Figure 5 and in (d) below, the Gantt chart with the goal of minimizing the total energy consumption is shown. The minimum energy consumption is 24.985. Among them, both (c) and (d) are the optimal solutions obtained under the condition of no disturbance factors. Combining (a) and (b), it can be found that the algorithm proposed in this embodiment has obtained the optimal solution in considering the maximum completion time and energy consumption in the actual case.

[0170] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. Only the preferred embodiments of the present invention are expressed. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the present invention. As long as the combination of these technical features does not conflict, it should be considered as the scope recorded in this specification.

[0171] It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims

1. A production scheduling method considering multi - cavity imbalance and machine failures, characterized in that: It includes the following steps: Step S11: Set the multi-cavity imbalance probability and machine failure rate for each machine, and set the corresponding upper and lower limits of the processing threshold; Step S12: Calculate the processing time based on the multi-cavity imbalance probability, machine failure rate, upper limit of the processing threshold, and lower limit of the processing threshold; Step S13: Set a bi-objective function for the maximum completion time of all workpieces and the total production energy consumption of all machines based on the processing time; Step S14: Use an optimization algorithm to solve and obtain a production scheduling plan; In step S12, calculate the processing time The expression for ； ； ； In the formula, represents the processing time of the process without considering the probability of multi-cavity imbalance, machine failure rate, upper processing threshold, and lower processing threshold O ij on the machine M k required for processing; T ijk represents the process O ij on the machine M k required for processing; WT k represents the cumulative processing time of the machine M k ; represents the lower processing threshold of the machine M k ; represents the upper processing threshold of the machine M k ; e k represents the probability of multi-cavity imbalance occurring in the machine M k ; N represents the workpiece set; J i represents the workpiece i corresponding process set; M represents the machine set; n represents a random number between 0 and 1; R k represents the time required for the machine k to repair the fault; represents the machine failure rate of the machine k ; represents the load time of the machine M k ; b ijk represents the decision variable. If the machine is normally processed, it is 1; otherwise, it is 0. In Step S13, the expression for the maximum completion time is: ； The expression for the total production energy consumption of all machines is: ； Wherein, represents the processing power of the machine M k ; represents the standby power of the machine M k ; T ijk represents the processing time required for the process O ij on the machine M k ; T i represents the total processing time of the workpiece i ; E ij represents the completion time of the process O ij on the machine M k ; E k represents the end time of the processing of the machine M k ; represents a decision variable, if the process O ij is selected to be processed on the machine M k it is 1, otherwise it is 0.

2. The production scheduling method considering multi - cavity imbalance and machine failure according to claim 1, characterized in that: When performing the solution in Step S14, set one or more of the following constraint conditions: 1) Each process of each workpiece can only be processed by one feasible processing machine: ； Wherein, N represents the workpiece set; J i represents the workpiece i corresponding process set; M represents the machine set; represents a decision variable. If the process O ij is selected to be processed on the machine M k it is 1, otherwise it is 0; 2) There is a precedence constraint between different workpieces on the same processing machine: ； In the formula, S ij represents the start time of the process O ij ; T ijk represents the time required for the process O ij on the machine M k ; 3) The completion time of a workpiece must be not less than the sum of the start time of the workpiece and the processing time of the workpiece: ； In the formula, C i represents J i the completion time; S i represents the start time of the workpiece; 4) Each workpiece must be processed according to its specific process route, and there is a precedence between each process of the same workpiece: ； In the formula, E ij represents the process operation O ij on the machine M k the processing completion time; 5) Once a workpiece starts processing, it cannot be interrupted: 。 3. The production scheduling method considering multi-chamber imbalance and machine failure according to claim 1, characterized in that: In Step S14, a multi-objective genetic programming method is used for the solution, including the following steps: Step S21: Complete the population initialization according to the workpiece processing information and the encoding and decoding strategies; Step S22: Perform grafting, mutation, and elite selection operations; Step S23: When the running time of the algorithm reaches the maximum number of runs, the algorithm terminates and a planning plan is obtained.

4. The production scheduling method considering multi - cavity imbalance and machine failure according to claim 3, wherein: The encoding strategy in Step S21 includes: setting the workpiece arrangement sequence and the machine arrangement sequence; the workpiece arrangement sequence and the machine arrangement sequence are encoded using a binary tree; the elements in the binary tree are all terminator set rules; the terminator set uses "+", "-", "x", and " / " as the function set for connection; The terminator set rules of the workpiece arrangement sequence include: 1) NAPT: The average processing time of the next process; 2) NOR: The remaining number of processes; 3) NAO: The average number of available machines for the next process of the workpiece; 4) NCO: The number of operations completed by the current workpiece; 5) EAT: The earliest available processing time of the workpiece; 6) TS: The time the workpiece has been processed; 7) PTC: The processing time of the current process workpiece; 8) EER: The energy efficiency ratio, that is, the ratio of the energy required to complete the task to the processing time; 9) WT The waiting time of the workpiece; 10) ECN The average energy consumption of the next process; The terminator set rules of the machine arrangement sequence include: 1) MLU: The machine with the lowest utilization rate; 2) MSPT: The earliest available time of the machine; 3) SWT: The shortest processing time of the machine for the next component.

5. The production scheduling method considering multi - cavity imbalance and machine failure according to claim 4, characterized in that: The decoding strategy described in step S21 includes: input workpiece terminator set rules, machine terminator set rules, function symbol sets, population size, and binary tree depth; perform individual decoding, select workpieces and machines for allocation one by one; record the processing time of each machine, the processed status of workpieces, and the current maximum completion time during allocation, wait until all workpiece processes are arranged, and determine the completion time E of each workpiece ij , the maximum completion time of production is , the current individual decoding is completed; determine the operation time window and the maximum completion time of all tasks arranged by all binary tree rules in the population, and the decoding is completed.

6. The production scheduling method considering multi - cavity imbalance and machine failure according to claim 5, wherein: The grafting operation in Step S22 includes: replacing branches by pruning the binary tree and comparing the quality of the resulting binary tree after grafting; according to the greedy rule, taking the better new binary tree as the winning tree; if the quality of the binary tree does not improve, keep the original binary tree unchanged.

7. A production scheduling method considering multi - cavity imbalance and machine failures according to claim 6, characterized in that: The mutation operation described in step S22 includes: selecting a binary tree, mutating it into other rules in the set by pruning the terminal rules or function symbols in the branches; according to the greedy rule, if the mutated binary tree is excellent, it is used as the winning tree, and if the quality of the binary tree has not improved, the original binary tree remains unchanged; among them, the mutated category is subjected to high-quality mutation according to the mutation probability of the terminal symbol in the high-quality binary tree species.

8. A production scheduling method considering multi - cavity imbalance and machine failures according to claim 7, characterized in that: The elite selection operation described in step S22 includes: evaluating the multi-objective machining binary tree scheduling result through the hypervolume index. Let the reference point be , then the HV value is the hypervolume between the binary tree scheduling result x and the reference point , and its expression is: ； Calculating the selection probability of a binary tree P ( x i ) is as follows: ； In the formula, represents the makespan; represents the total production energy consumption of all machines; N represents the set of parts; After that, non-dominated sorting is used for elite selection, and those with a higher sorting rank are used as the new binary tree population, and the frequency of occurrence of terminal symbols in the new binary tree population is counted as the mutation probability. The non-dominated sorting includes: 1) Calculate the crowding degree of the new population; 2) Determine the mutation probability of the terminal symbol according to the combination scheduling rule with a higher domination level; 3) Select the population individuals with a higher domination level according to the set number of populations to form a new population.

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