Flexible job shop scheduling optimization method based on double-objective imperialist competitive algorithm

Abstract

The invention provides a flexible job shop scheduling optimization method based on a double-target empire competition algorithm. In order to improve the efficiency of the core equipment in the flexible job shop scheduling problem FJSP, a mathematical model is established, which takes the minimization of the maximum completion time and the maximization of the core equipment utilization as the target. An improved empire competition algorithm IICA is designed to solve the model. In the algorithm, a left shift decoding rule is proposed to solve the scheduling integration problem. Two heuristic search strategies are used for global search of the empire competition algorithm. On this basis, the adaptive number revolution algorithm is used to improve the convergence speed in the later stage to improve the local search efficiency. Simulation experiments verify the feasibility of the optimization model. The experimental results show that the algorithm has higher efficiency and effectiveness than the existing algorithm.

Description

Technical Field

[0001] This invention relates to the field of flexible job shop scheduling technology, and specifically to a flexible job shop scheduling optimization method based on a bi-objective empire competition algorithm. Background Technology

[0002] Flexible job shop scheduling, first proposed and proven by Brucker and Schlie in 1990 to be an NP-hard problem, is further extended by the traditional job shop scheduling problem. Its flexibility is mainly reflected in the multiple choices of manufacturing resources, meaning that the cost and time of manufacturing resources differ for different workpieces and different processes. In recent years, influenced by factors such as energy constraints, environmental protection, and energy conservation and emission reduction, how to improve production efficiency, reduce energy consumption, and increase equipment utilization has become a focus of attention for many scholars.

[0003] Current research mainly focuses on different objectives, different problem models, and different algorithms. Existing technologies typically employ multi-objective simulated annealing algorithms to solve the MOFJSP problem with the objectives of minimizing total workshop energy consumption and minimum completion time; multi-objective evolutionary optimization algorithms to solve the MOFJSP problem with the optimization objectives of maximum completion time and interval machine load; NSGA-II to solve the MOFJSP problem with the optimization objectives of minimizing carbon emissions, energy costs, and maximum completion time; migratory bird optimization algorithms to solve the MOFJSP problem under firmware low-carbon strategies; and teaching optimization algorithms based on optimization mechanisms to solve the MOFJSP problem with the objective of minimizing carbon emissions. Addressing the uncertainty of actual production delivery times, a quantum particle swarm optimization algorithm based on chaotic theory has been proposed to solve the multi-objective flexible job shop problem by incorporating a chaotic mechanism into the particle swarm optimization algorithm.

[0004] As mentioned above, significant progress has been made in the study of the Flexible Job Shop (FJSP) problem, but in-depth research on core equipment is lacking. With increasing customization, issues such as delivery time, energy consumption, and large product volumes make production planning and scheduling more complex. Simultaneously, due to equipment limitations, long processing cycles, and high energy consumption, certain processing equipment becomes the core equipment of the entire production process. To reduce energy consumption and improve delivery rates, enterprises urgently need a bi-objective algorithm based on improving the utilization rate of core equipment to solve practical production problems. Summary of the Invention

[0005] This invention proposes a flexible job shop scheduling optimization method based on a bi-objective empire competition algorithm to solve the efficiency problem of core equipment in flexible job shop scheduling.

[0006] To address the aforementioned technical problems, this invention provides a distributed intelligent manufacturing scheduling method based on an improved gray wolf optimization algorithm, comprising the following steps:

[0007] Step S1: Set preset conditions, basic parameters and constraints for the target flexible work workshop, and set an optimization objective function based on minimizing the completion time and maximizing the utilization rate of core equipment to construct a production scheduling model;

[0008] Step S2: Perform two-stage integer encoding and decoding operations on the process sequencing and equipment selection parts of the workpiece processing;

[0009] Step S3: Based on the Empire Competition algorithm, various population initialization strategies are used to generate the initial population;

[0010] Step S4: Calculate the fitness of the initial population, sort them, select dominant individuals and assign subordinate individuals to generate the initial race;

[0011] Step S5: Select multiple assimilation strategies to assimilate the initial race to obtain an assimilated race;

[0012] Step S6: Optimize the assimilation race using an optimization strategy that combines priority selection and adaptive parameters to generate an optimized race;

[0013] Step S7: Calculate the total cost of the optimized race, conduct race competition, and output the optimal solution when the set maximum number of iterations is met; otherwise, repeat steps S3 to S7.

[0014] Furthermore, the objective function to be optimized includes:

[0015] 1) Maximize the utilization rate of core equipment:

[0016]

[0017] 2) Minimize completion time:

[0018] C max =max{C ijk}

[0019] In the formula, C ijk B represents the completion time of the i-th process of the j-th workpiece on equipment k. ijk This indicates the start time of the i-th process of the j-th workpiece on equipment k;

[0020] Furthermore, the decoding operation arranges its process sequence from left to right.

[0021] Furthermore, the various population initialization strategies include:

[0022] 1) Random initialization strategy: Randomly generates the order of processes and resources;

[0023] 2) The core equipment power-on / off strategy prioritizes core equipment that is already powered on;

[0024] 3) The maximum completion time strategy selects individuals whose maximum completion time is less than the average maximum completion time;

[0025] 4) Core equipment utilization strategy: Select individuals whose core equipment utilization rate is greater than the average core equipment utilization rate.

[0026] Furthermore, the ratio of the population initialization strategy is set to 0.3:0.3:0.3:0.1.

[0027] Furthermore, the population size of the initial population and the number of dominant individuals of the initial species were calculated through orthogonal experiments.

[0028] Furthermore, the various assimilation strategies include:

[0029] 1) An assimilation strategy based on improved sequential crossover OX;

[0030] 2) Assimilation strategy based on improved sub-path cross SEC.

[0031] Furthermore, the steps of the assimilation strategy based on the improved sequential crossover OX include:

[0032] Step S3411: Construct temporary individuals based on the subordinate individuals assigned to the dominant individual;

[0033] Step S3412: Randomly replace the process segment of the temporary individual to form a new solution;

[0034] Step S3412: If the new solution is better than the temporary individual, then assimilate and replace the subordinate individual;

[0035] Step S3414: Repeat steps S3412 to S3413 until all subordinate individuals have been assimilated and replaced.

[0036] Furthermore, the steps of the assimilation strategy based on the improved sub-path cross-SEC include:

[0037] Step S3421: Construct temporary individuals based on the subordinate individuals assigned to the dominant individual;

[0038] Step S3422: Based on the core equipment utilization rate, sort the subordinate individuals and select the subordinate individual with the highest utilization rate as the optimized individual;

[0039] Step S3423: Select a core device code segment from the optimized individual and assign it to the temporary individual to form a new solution.

[0040] Step S3424: If the new solution is better than the temporary individual, then use the new solution to assimilate and replace the subordinate individual;

[0041] Step S3425: Repeat steps S3422 to S3424 until all subordinate individuals have been assimilated and replaced.

[0042] Furthermore, the method for generating the optimized race in step S6 includes the following steps:

[0043] Step S61: Perform a non-dominant ranking on the subordinate individuals, and set an initial revolution rate r based on the ranking results from largest to smallest. original ;

[0044] Step S62: Set the iteration coefficients, and based on the iteration coefficients and the initial revolution rate r original Calculate the current revolution rate r current ;

[0045] Step S63: Based on the current revolution rate r current The subordinate individual g is selected using a roulette wheel.

[0046] Step S64: Optimize the subordinate individual g to generate a new solution z;

[0047] Step S65: When the new solution z is better than the subordinate individual g, then the new solution z is used to replace the subordinate individual g.

[0048] The advantage of this invention is that it proposes a flexible job shop scheduling optimization method based on a bi-objective empire competition algorithm to solve the efficiency problem of core equipment in flexible job shop scheduling.

[0049] To optimize the algorithm's performance, an orthogonal method is employed to select the optimal population size, maximum number of iterations, and initial number of empires, taking into account the characteristics of the model. Multiple population initialization strategies are used to generate an initial population, ensuring population diversity while increasing the number of high-quality individuals. Various assimilation strategies are employed to achieve better assimilation results. Furthermore, an optimization strategy combining priority selection and adaptive parameters effectively prevents the algorithm from getting trapped in local optima in early iterations, improving global search capabilities and enhancing convergence in later stages, thus strengthening local search capabilities.

[0050] In summary, the method of the present invention can provide enterprises with more choices, and is more flexible, efficient, and cost-saving. It also makes it convenient for enterprises to change the scheduling plan according to the actual processing and production needs. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the algorithm flow of the present invention;

[0052] Figure 2 This is a schematic diagram of the encoding of the present invention;

[0053] Figure 3 This is a trend diagram of the population size C factor level in the comparative experiment of the preferred embodiment of the present invention;

[0054] Figure 4 This is a trend chart of the maximum number of iterations N in the comparative experiment of the preferred embodiment of the present invention;

[0055] Figure 5 This is a trend chart of the initial dominant individual number E level in the comparative experiment of the preferred embodiment of the present invention;

[0056] Figure 6 These are the comparison results of three IGD algorithms in the comparative experiment of the preferred embodiment of the present invention;

[0057] Figure 7 These are the ER comparison results of three algorithms in the comparative experiment of the preferred embodiment of the present invention;

[0058] Figure 8 These are three algorithms and the real Pareto front in the comparative experiment of the preferred embodiments of the present invention;

[0059] Figure 9 This is one of the improved Empire Competition Algorithm IICA Gantt charts in the comparative experiment of the preferred embodiments of the present invention;

[0060] Figure 10 This is the second improved Empire Competition Algorithm IICA Gantt Chart in the comparative experiment of the preferred embodiment of the present invention. Detailed Implementation

[0061] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0062] like Figure 1 As shown, this embodiment of the invention provides a flexible job shop scheduling optimization method based on a dual-objective empire competition algorithm, specifically including the following steps:

[0063] Step S1: Set preset conditions, basic parameters and constraints for the target flexible work workshop, and set an optimization objective function based on minimizing the completion time and maximizing the utilization rate of core equipment to construct a production scheduling model;

[0064] To effectively describe the scheduling problem, it is now assumed that the core device is a single device. The preset conditions set in this embodiment of the invention include:

[0065] 1) At time t=0, every workpiece and device is available.

[0066] 2) Each machine can only process one workpiece within a fixed time period, and each workpiece can only be processed on one machine at a fixed time.

[0067] 3) The time for installing, unloading, and transporting the workpiece is included in the processing time.

[0068] 4) The equipment must not be interrupted during the fixed processing time.

[0069] 5) The device can operate continuously and has an unlimited buffer.

[0070] The basic parameters to be set include:

[0071] n: Total number of workpieces;

[0072] m: Total number of devices;

[0073] n j The total number of processes for workpiece j;

[0074] η k Equipment utilization rate;

[0075] j,g: workpiece index number, j,g = 1,2,3,4…,n;

[0076] i,h: Work process number index, i,h = 1,2,3,4…;

[0077] k: Device number index, k = 1, 2, 3, 4, ..., m

[0078] O ij The i-th process step for workpiece j;

[0079] O ijk The i-th process of workpiece j is processed on equipment k;

[0080] P ijk Process O ij Choose the time required to process the data on device k;

[0081] B ijk : The start time of the i-th process of the j-th workpiece on equipment k;

[0082] C ij Process O ij Completion time;

[0083] C ijk : The completion time of the i-th process of the j-th workpiece on equipment k;

[0084] Cmax : The maximum completion time of the scheduling plan;

[0085] S ij Process O ij The set of available devices;

[0086]

[0087]

[0088] Set the constraints as follows:

[0089] 1) The next step can only be carried out after the previous step is completed:

[0090] C ij -C (i-1)j ≥P ijk X ijk i = 2, 3, ..., n j

[0091] 2) Two workpieces cannot be processed on the same machine at the same time:

[0092]

[0093] 3) Process O ij It must be completed on the specified device and cannot be done across different devices:

[0094]

[0095] The specific optimization objective function is as follows:

[0096] 1) Maximize the utilization rate of core equipment:

[0097]

[0098] Based on the needs, the utilization rate of different equipment is divided, C ijk B represents the completion time of the i-th process of the j-th workpiece on equipment k. ijk This represents the start time of the i-th process of the j-th workpiece on equipment k. Specifically, it is expressed as the utilization rate of a certain equipment, which is the ratio of the total processing time of all workpieces processed on that equipment to the difference between the completion time of the last processing run and the start time of the first processing run on that equipment.

[0099] 2) Minimize completion time:

[0100] C max =max{C ijk}

[0101] Specifically,

[0102] Step S2: Perform two-stage integer encoding and decoding operations on the process sequencing and equipment selection parts of the workpiece processing;

[0103] Specifically, considering the characteristics of the production scheduling model constructed in this invention, a two-part integer encoding method consisting of a process sequencing part (OS) and a device selection part (MS) is adopted. The length of both the OS and MS parts is equal to the total number of processes. The number in the OS represents the workpiece number, and its frequency in the encoding indicates which processing step this workpiece is in. Each bit in the MS represents the sequence number in the set of processing devices for the corresponding process. The length of each individual bit is twice the total number of processes.

[0104] like Figure 2 As shown, each number in OS on the left represents the workpiece number, and the number of times it appears is equal to the number of processes for that workpiece. When converting to the order of processes, each number is read from left to right, and the order in which the same number appears is the processing order of that process. Figure 2 The right MS represents the processing machine. Each number corresponds to the sequence number in the processing machine set, not the machine number. When converting the processing process part into the process sequence, it is [O11,O21,O12,O22,O23].

[0105] The following example illustrates the coding process using specific embodiments, as shown in Table 1. This example represents the processing of two workpieces across three machines in five steps. Workpiece 1 has two processing steps, and workpiece 2 has three steps. This is a partially flexible job shop scheduling problem. Each step O ij Each has its corresponding set of optional devices S ij The table shows the set of optional equipment for each process step, with the equipment code representing the sequence number of the optional equipment set. Thus, process O... 11 The optional device set includes three devices: M1, M2, and M3. If device code = 1, it means that the first device is selected from the optional device set.

[0106] Table 1

[0107]

[0108] Meanwhile, in order to obtain a feasible scheduling scheme, the decoding in this embodiment of the invention adopts a left-shift strategy, that is, to arrange the processes in the OS from left to right, so that the processes are arranged as early as possible while satisfying various constraints.

[0109] Step S3: Based on the Empire Competition algorithm, various population initialization strategies are used to generate the initial population;

[0110] There are three main parameters affecting the Imperial Competition Algorithm (ICA): population size (C), maximum number of iterations (N), and number of dominant individuals (E). To find the optimal combination of parameters for the ICA algorithm, an orthogonal method is used to optimize these parameters.

[0111] In this embodiment of the invention, the optimal population size C, the maximum number of iterations N, and the number of dominant individuals E are selected using the orthogonal method.

[0112] Initializing the population has a significant impact on the algorithm's solution speed and quality. To improve the algorithm's search efficiency and avoid premature entrapment in local optima, this embodiment of the invention employs four population initialization strategies applied alternately, ensuring population diversity while increasing the number of high-quality individuals. The random initialization strategy effectively improves population diversity; based on the core device power-on / off strategy, when initializing the MS portion of an individual, priority is given to selecting from already powered-on core devices to improve the core device utilization rate of the population; the maximum completion time strategy compares the maximum completion time of the initialized individual with the average maximum completion time: after initialization, the maximum completion time C of that individual is calculated. makespan ,like If the new individual is retained, it will be regenerated; otherwise, a new individual will be generated. To reduce the average maximum completion time of individuals in the initialization strategy, choosing individuals with shorter completion times can effectively decrease the maximum completion time of the population. The core equipment utilization-based strategy compares an individual's core equipment utilization rate with its average utilization rate: after initializing an individual, the core equipment utilization rate η for that individual is calculated. CorEquipment ,like If the new individual is retained, it will be regenerated; otherwise, a new individual will be generated. To optimize the average core equipment utilization rate of individuals in the initialization strategy, a higher utilization rate is selected to improve the overall core equipment utilization rate of the population. Furthermore, through experiments and calculations, the ratio of these four initialization strategies in this embodiment of the invention is 0.3:0.3:0.3:0.1.

[0113] Step S4: Calculate the fitness of the initial population, sort them, select dominant individuals and assign subordinate individuals to generate the initial race;

[0114] The Imperial Competitive Algorithm (ICA) searches the solution space on an individual basis, with each individual representing a feasible solution. Individuals with higher fitness are initially designated as dominant individuals, and the remaining individuals are assigned to dominant individuals as subordinates, forming the initial race. To prevent premature convergence and improve global search capabilities, the original method of partitioning by dominant individuals is changed to an equal allocation method, as follows:

[0115] Step 1: Perform non-dominated sorting on the randomly generated population to obtain the Rank value of each individual and use it as the initial power;

[0116] Step 2: Rank the individuals according to their power, and let the top N be... im If a country is the dominant individual, then the N that follows... ck A nation is a subordinate entity; in this embodiment of the invention, N im Equal to the number of dominant individuals, E;

[0117] Step 3: Distribute subordinate individuals equally among dominant individuals to prevent decimals. The number of subordinate individuals of the last dominant individual is determined by subtracting the number already distributed from the total number of individuals. In this embodiment of the invention, the total number of individuals is equal to the population size C.

[0118] Step 4: Randomly assign subordinate individuals to dominant individuals based on the allocation quantity.

[0119] Step S5: Select multiple assimilation strategies to assimilate the initial race to obtain an assimilated race;

[0120] Dominant individuals transfer their customs, culture, and political ideologies to subordinate individuals, while subordinate individuals gravitate towards their dominant counterparts, enhancing their search capabilities within racial regions. Because dominant individuals are superior to their subordinates, assimilation produces solutions of higher quality. This invention employs two heuristic strategies to achieve assimilation between subordinate individuals and their dominant counterparts, using a two-stage approach. When subordinate and dominant individuals exchange information, operations are performed on both parts separately, ensuring that the assimilated individual remains feasible.

[0121] The two strategies employed in this embodiment of the invention are as follows:

[0122] 1) Assimilation strategy based on improved sequential crossover OX:

[0123] Step S511: Construct temporary individuals based on the subordinate individuals assigned to the dominant individual;

[0124] Step S512: Randomly replace the process segment of the temporary individual to form a new solution;

[0125] Step S512: If the new solution is better than the temporary individual, then assimilate and replace the subordinate individual;

[0126] Step S514: Repeat steps S512 to S513 until all subordinate individuals have been assimilated and replaced.

[0127] 2) Assimilation strategy based on improved sub-path cross-SEC:

[0128] Step S521: Construct temporary individuals based on the subordinate individuals assigned to the dominant individual;

[0129] Step S522: Based on the core equipment utilization rate, sort the subordinate individuals and select the subordinate individual with the highest utilization rate as the optimized individual;

[0130] Step S523: Select a core device code segment from the optimized individual and assign it to the temporary individual to form a new solution.

[0131] Step S524: If the new solution is better than the temporary individual, then use the new solution to assimilate and replace the subordinate individual;

[0132] Step S525: Repeat steps S522 to S524 until all subordinate individuals have been assimilated and replaced.

[0133] Meanwhile, in this embodiment of the invention, a selection strategy is set for the choice between the two assimilation strategies. First, a random number r is generated, r∈(0,1). If r≥0.3, the improved ox assimilation is selected; otherwise, the improved SEC assimilation is selected.

[0134] Step S6: Optimize the assimilation race using an optimization strategy that combines priority selection and adaptive parameters to generate an optimized race;

[0135] Optimization is another way for the Imperial Competition Algorithm (ICA) to generate new solutions. Optimization causes unexpected changes in subordinate individuals; by optimizing, a subordinate individual can escape or even surpass its dominant counterpart, resulting in a position swap between the subordinate and dominant individuals. This process is similar to mutation in genetic algorithms, effectively preventing the algorithm from getting trapped in local optima in early iterations, thus enhancing the algorithm's exploration capabilities. It also has some impact on the convergence of the algorithm in later stages, thereby strengthening its local search ability.

[0136] Optimizing weaker subordinates is less likely to produce a better solution than optimizing stronger ones, and it also wastes computational resources. Therefore, the probability of a subordinate participating in optimization is determined based on its non-dominated ranking; that is, the more powerful the subordinate, the higher its probability of participating. Furthermore, to improve the algorithm's convergence speed in later stages, the optimization probability decreases with increasing iterations. This invention designs a new optimization strategy that prioritizes selection combined with adaptive parameters. Based on the non-dominated ranking results from largest to smallest, an initial optimization rate *r* is set. Original The optimization rate for each generation is calculated as follows:

[0137] r current =0.99 n ×r Original

[0138] In the formula, r current represents the current optimization rate, n represents the current iteration number, and 0.99 represents the iteration coefficient, indicating that the probability of optimization decreases as the number of iterations increases.

[0139] Based on the current optimization rate r mentioned above current The process involves selecting a subordinate individual g using a roulette wheel approach, and then optimizing g to generate a new solution z. If g is not selected by the roulette wheel, the process continues with the optimization of the next subordinate individual. If the new solution z is superior to the subordinate individual g, then the new solution z replaces the subordinate individual g. This process is repeated until all subordinate individuals have completed the above steps.

[0140] Step S7: Calculate the total cost of the optimized race, conduct race competition, and output the optimal solution when the set maximum number of iterations is met; otherwise, repeat steps S3 to S7.

[0141] Specifically, the racial competition mechanism causes the weaker dominant individuals to continuously weaken and even perish. Subordinate individuals of the weaker dominant individuals are constantly taken over by other dominant individuals. Ultimately, this leads to the unification of dominant individuals or the coexistence of a few dominant individuals. This mechanism breaks through the limitation that subordinate individuals can only move to their own dominant group, thus increasing the algorithm's global search capability and group diversity to a certain extent. In this process, the power of dominant individuals is calculated based on their total cost.

[0142] First, calculate the cost of each subordinate individual using the following formula: the higher the cost, the lower the power.

[0143]

[0144] The total cost of the dominant individual is calculated using the following formula:

[0145]

[0146] Among them, rank i The rank value of solution i is determined by non-dominated sorting. It is the average crowding distance between solution i and its two adjacent solutions. Let L represent the set of values ​​with rank L, where α is a positive number approaching 0 to prevent the denominator from being 0 during calculation. k This indicates the number of subordinate individuals that the dominant individual k possesses.

[0147] The weakest subordinate of the dominant individual with the least power is selected as the competition object between dominant individuals. The greater the power, the greater the possibility of occupying this subordinate individual, thereby improving search efficiency.

[0148] Example 1:

[0149] In a certain scheduling task, there are 10 pieces of equipment, 6 workpieces, and 6 processes for each workpiece, totaling 36 processes. The sterilization cabinet is the core equipment in this workshop, with equipment number 4. The equipment set corresponding to the workpiece processes is shown in Table 2, and the corresponding processing time is shown in Table 3.

[0150] Table 2

[0151]

[0152] Table 3

[0153]

[0154] To find the optimal combination of operating parameters for the ICA algorithm, an orthogonal method was used to optimize the parameters. The factor level table is shown in Table 4.

[0155] Table 4

[0156]

[0157] Based on the number of factors and levels, orthogonal arrays were used to design orthogonal experiments. Each parameter combination was run independently 20 times, with a maximum run time of 5 minutes. The non-dominated solution sets obtained under each parameter combination were aggregated to obtain a reference set. The inverse generation distance (IGD) for each experimental group was calculated; a smaller IGD value indicates a better result for that group. The experimental results are shown in Table 5, where I, II, III, and IV represent the average values ​​of the current factor at the four different levels.

[0158]

[0159]

[0160] To more intuitively see the impact of the horizontal values ​​on the results, corresponding trend charts are drawn, such as... Figures 3-5 As shown. The conclusion is that the algorithm in this embodiment of the invention exhibits optimal performance when C=300, N=400, and E=8.

[0161] To verify the effectiveness of the algorithm improvement, a comparative experiment was conducted using the improved non-dominated sorting genetic algorithm NSGA-II and the improved artificial bee colony algorithm ABC. The parameters for NSGA-II were: population size 100, maximum number of iterations 100, crossover probability 0.8, and mutation probability 0.1. The parameters for the improved ABC algorithm were: population size 500, maximum number of iterations 10, and file set size 20. The reverse generation distance (IGD) and error rate (ER) were selected as performance evaluation metrics. Smaller metrics indicate better algorithm performance. The IGD and ER values ​​were calculated using the following formulas.

[0162]

[0163]

[0164] N *d represents the size of the set of true Pareto front points. i Let N represent the nearest Euclidean distance from the i-th actual front to the true Pareto front, and let N represent the optimal solution set. i This indicates whether the i-th solution in the optimal solution set lies on the true Pareto front; if so, then e i =0; otherwise e i =1.

[0165] Each algorithm was run independently 20 times under each set of test data. Since the increase in the number of workpieces and processes will increase the algorithm running time, the running time for each run was set to 5 minutes, and the average value of the 20 experiments was taken as the final test result, as shown in Table 6.

[0166] Table 6

[0167]

[0168] Comparison of IGD and ER evaluation metrics for the three algorithms, for example Figure 6 and Figure 7 As shown in the figure, the improved Empire Competition algorithm IICA of this invention exhibits superior IGD and ER metrics compared to the other two algorithms. Figure 8 As shown in the comparative experiments, within the same test time, the improved IICA algorithm obtains an approximate Pareto front that is closer to the real Pareto front in solving the shop floor scheduling problem, with better convergence and diversity.

[0169] The scheduling scheme obtained by the flexible job shop scheduling optimization method based on the bi-objective empire competition algorithm is as follows: Figure 9 and Figure 10 As shown in the figure, the horizontal axis represents time, and the vertical axis represents machine number. In the Gantt chart, the hundreds digit represents the workpiece type, and the units digit represents the process number. The utilization rate of the sterilizer with equipment number 4 is 93.88%, and the completion time is 56 hours; the utilization rate of the other sterilizer is 86.95%, and the completion time is 46 hours. It can be seen that the utilization rate of the core equipment sterilizer has reached a high level, which provides enterprises with more and more flexible options. This also proves the rationality and effectiveness of the improved Empire Competition algorithm in solving this type of problem.

[0170] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0171] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A flexible job shop scheduling optimization method based on a bi-objective empire competition algorithm, characterized in that: Includes the following steps: Step S1: Set preset conditions, basic parameters and constraints for the target flexible work workshop, and set an optimization objective function based on minimizing the completion time and maximizing the utilization rate of core equipment to construct a production scheduling model; Step S2: Perform two-stage integer encoding and decoding operations on the process sequencing and equipment selection parts of the workpiece processing; Step S3: Based on the Empire Competition algorithm, various population initialization strategies are used to generate the initial population; Step S4: Calculate the fitness of the initial population, sort them, select dominant individuals and assign subordinate individuals to generate the initial race; Step S5: Select multiple assimilation strategies to assimilate the initial race to obtain an assimilated race; Step S6: Optimize the assimilation race using an optimization strategy that combines priority selection and adaptive parameters to generate an optimized race; Step S7: Calculate the total cost of the optimized race, conduct race competition, and output the optimal solution when the set maximum number of iterations is met; otherwise, repeat steps S3 to S7. The various assimilation strategies include: 1) An assimilation strategy based on improved sequential crossover OX; 2) Assimilation strategy based on improved sub-path cross-SEC; The steps of the assimilation strategy based on improved sequential crossover OX include: Step S511: Construct temporary individuals based on the subordinate individuals assigned to the dominant individual; Step S512: Randomly replace the process segment of the temporary individual to form a new solution; Step S513: If the new solution is better than the temporary individual, then assimilate and replace the subordinate individual; Step S514: Repeat steps S512 to S513 until all subordinate individuals have been assimilated and replaced; The steps of the assimilation strategy based on improved sub-path cross-SEC include: Step S521: Construct temporary individuals based on the subordinate individuals assigned to the dominant individual; Step S522: Based on the core equipment utilization rate, sort the subordinate individuals and select the subordinate individual with the highest utilization rate as the optimized individual; Step S523: Select a core device code segment from the optimized individual and assign it to the temporary individual to form a new solution. Step S524: If the new solution is better than the temporary individual, then use the new solution to assimilate and replace the subordinate individual; Step S525: Repeat steps S522 to S524 until all subordinate individuals have been assimilated and replaced.

2. The flexible job shop scheduling optimization method based on the bi-objective empire competition algorithm according to claim 1, characterized in that: The optimization objective function includes: 1) Maximize the utilization rate of core equipment: ； 2) Minimize the completion time; In the formula, C ijk B represents the completion time of the i-th process of the j-th workpiece on equipment k. ijk η represents the start time of the i-th process of the j-th workpiece on equipment k. k This represents the equipment utilization rate, where n represents the total number of workpieces. j This represents the total number of processes for workpiece j.

3. The flexible job shop scheduling optimization method based on the bi-objective empire competition algorithm according to claim 1, characterized in that: The decoding operation arranges its process sequence from left to right.

4. The flexible job shop scheduling optimization method based on the bi-objective empire competition algorithm according to claim 1, characterized in that: The various population initialization strategies include: 1) The random initialization strategy randomly generates the order of processes and resources; 2) The core equipment power-on / off strategy prioritizes core equipment that is already powered on; 3) The maximum completion time strategy selects individuals whose maximum completion time is less than the average maximum completion time; 4) Core equipment utilization strategy: Select individuals whose core equipment utilization rate is greater than the average core equipment utilization rate.

5. The flexible job shop scheduling optimization method based on the bi-objective empire competition algorithm according to claim 4, characterized in that: The ratio of the population initialization strategy is set to 0.3:0.3:0.3:0.

1.

6. The flexible job shop scheduling optimization method based on the bi-objective empire competition algorithm according to claim 1, characterized in that: The population size of the initial population and the number of dominant individuals of the initial species were calculated through orthogonal experiments.

7. The flexible job shop scheduling optimization method based on the bi-objective empire competition algorithm according to claim 6, characterized in that: Step S6, which generates the optimized race, includes the following steps: Step S61: Perform a non-dominated sort on the subordinate individuals, and set an initial optimization rate r based on the sorting results from largest to smallest. original ; Step S62: Set the iteration coefficients, and based on the iteration coefficients and the initial revolution rate r original Calculate the current optimization rate r current ; Step S63: Based on the current optimization rate r current The subordinate individual g is selected using a roulette wheel. Step S64: Optimize the subordinate individual g to generate a new solution z; Step S65: When the new solution z is better than the subordinate individual g, then the new solution z is used to replace the subordinate individual g.

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