A scheduling method for distributed manufacturing based on an imperialist competitive algorithm

Abstract

The application discloses a kind of scheduling method of distributed manufacturing based on empire competition algorithm, comprising the following steps: establishing the objective function including minimizing maximum completion time, minimizing maximum machine load and minimizing total energy consumption, and setting the constraint condition of objective function according to the assembly process of product;Set coding and decoding rules, encode process sequencing and machine selection to obtain process sequencing vector OSV and machine selection vector MAV;Set the hybrid initialization rule of OSV and MAV, generate initial solution set;Calculate the objective function value of all initial solutions in initial solution set, select the better solution as the colony from it, the remaining initial solution is as the colony, adopt OX cross to realize the assimilation between colony, adopt POX cross to realize the assimilation between colony and colony, generate new solution set;Design the neighborhood of OSV and MAV, carry out variable neighborhood descent search to colony, obtain the optimal production scheduling scheme.

Description

Technical Field

[0001] This invention relates to the field of workshop scheduling technology, and specifically to a scheduling method for distributed manufacturing based on the Empire Competition algorithm. Background Technology

[0002] The product manufacturing industry is undergoing a transformation from a centralized to a distributed manufacturing model. In distributed manufacturing, product production is no longer limited to a single production unit but is completed through the collaborative work of multiple units, encompassing both workpiece processing and product assembly. The advantage of this model lies in its ability to integrate resources from multiple workshops, thereby significantly improving production capacity, shortening production cycles, and ensuring on-time delivery. However, this model also presents challenges: on the one hand, manually formulating production plans and scheduling workshops becomes extremely complex, easily leading to errors in scheduling schemes, and the traditional method of manually distributing work orders is inefficient; on the other hand, there is a close constraint between component processing plans and product assembly plans, and any change in processing stages can affect the assembly plan, thus impacting the stability of the entire production process.

[0003] To address the complexity of distributed assembly shop scheduling, current manufacturing enterprises employ a variety of technologies, such as heuristic algorithms, scheduling rules and prioritization methods, and advanced planning and scheduling systems (APS). Heuristic algorithms, based on experience and intuition, provide an efficient way to search the solution space; scheduling rules and prioritization methods assign priorities to jobs and schedule them according to these priorities; and APS integrates various algorithms and models to optimize production planning and scheduling.

[0004] These technologies typically simplify the assembly process, assuming all steps for a workpiece are completed within a single workshop, without considering the transfer of steps between workshops. This simplified approach has limitations in practice because in real-world production environments, different manufacturing units may be geographically close, such as multiple factories within the same enterprise or collaborative factories between different enterprises. Transferring and processing workpieces between them is common and necessary. Furthermore, existing optimization objectives primarily focus on reducing completion time, lowering total cost, and balancing machine load, neglecting crucial indicators in the context of green and distributed manufacturing, such as processing and transportation energy consumption. Therefore, existing technologies struggle to fully meet the practical needs of cross-workshop collaboration and multi-objective optimization. Summary of the Invention

[0005] This invention proposes a scheduling method for distributed manufacturing based on the Empire Competition algorithm, which solves the problems of existing technologies that do not consider cross-workshop process transfer and ignore processing and transportation energy consumption.

[0006] To address the aforementioned technical problems, this invention provides a scheduling method for distributed manufacturing based on the Empire Competition Algorithm, comprising the following steps:

[0007] Step S1: Establish an objective function that includes minimizing the maximum completion time, minimizing the maximum machine load, and minimizing the total energy consumption, and set the constraints of the objective function according to the product's assembly process;

[0008] Step S2: Set encoding and decoding rules, encode the process sorting and machine selection to obtain the process sorting vector OSV and the machine selection vector MAV. The elements in the process sorting vector are the workpiece numbers, and the elements in the machine selection vector represent the index of the processing machine selected by the workpiece number at the corresponding position in the process sorting vector.

[0009] Step S3: Set the mixed initialization rules for OSV and MAV, and generate the initial solution sets for OSV and MAV;

[0010] Step S4: Calculate the objective function values ​​of all initial solutions in the initial solution set. Initial solutions with objective function values ​​greater than a set objective function threshold are designated as colonies, and the remaining initial solutions are designated as colonies. Assimilation between colonies is achieved using OX crossover, and assimilation between colonies and colonies is achieved using POX crossover, generating a new solution set.

[0011] Step S5: Design the neighborhoods of OSV and MAV, obtain multiple neighborhood search combinations, perform variable neighborhood descent search on the colony countries, and obtain the optimal production scheduling scheme.

[0012] Preferably, the expression for the objective function in step S1 is:

[0013] minf1 = E n,1 ;

[0014]

[0015]

[0016] In the formula, f1, f2, and f3 represent the completion time of the scheduling scheme, the machine load of the scheduling scheme, and the total machine energy consumption of the scheduling scheme, respectively; E n,1 The completion time for the final assembly process; W k m is the working time of the k-th machine; k is the machine number; m f Let F be the total number of machines in workshop f; F be the total number of processing workshops; E ... p Energy consumption for machine operation; E i E represents the idle energy consumption of the machine. t Energy consumption of transportation equipment; n is the total number of workpieces; u i pe is the total number of operations for workpiece i;f,k Let k be the operating power of the kth machine in workshop f; Let be the processing time of the j-th process of workpiece i on the k-th machine in workshop f; For the decision variable, it is 1 when the j-th process of workpiece i is processed on the k-th machine in workshop f, and 0 otherwise; f,k S represents the idle power of the k-th machine in workshop f; i,j Let be the start time of the j-th process for workpiece i; The completion time of the first process for the first workpiece; The variable is 1 when the first process of the first workpiece on the kth machine in workshop f is processed before the jth process of workpiece i, and 0 otherwise; te is the working power of the transportation equipment. The variable is 1 when the j-th process of workpiece i is processed on machine k1 and the (j-1)-th process of workpiece i is processed on machine k2, and 0 otherwise. Let be the transportation time of workpiece j between machine k1 and machine k2.

[0017] Preferably, the expression for the constraint condition is:

[0018]

[0019] In the above formula, S i,j Let be the start time of the j-th process for workpiece i; Let be the processing time of the j-th process of workpiece i on the k-th machine in workshop f; The variable is 1 when the j-th process of workpiece i is processed on the k-th machine in workshop f, and 0 otherwise. The variable is 1 when the j-th process of workpiece i is processed on machine k1 and the (j-1)-th process of workpiece i is processed on machine k2, and 0 otherwise. Let be the transportation time of workpiece j between machine k1 and machine k2; For decision variables, E is 1 when the first operation of the first workpiece on the k-th machine in workshop f is processed before the j-th operation of workpiece i; otherwise, it is 0. i,j Let θ be the completion time of the j-th process of the i-th workpiece; θ is a sufficiently large positive number.

[0020] Preferably, the OSV layer encoding hybrid initialization rules set in step S3 include:

[0021] a. Prioritize selecting the component with the smallest sum of average time for the remaining operations of all workpieces under that component on its machineable capacity. If multiple components have the smallest time, randomly select one of them, and then randomly select one unfinished workpiece under that component.

[0022] b. Prioritize selecting the component with the fewest remaining processes among all workpieces under the component. If there are multiple components with the fewest processes, randomly select one of them, and then randomly select one unfinished workpiece under that component.

[0023] c. Randomly select a workpiece according to the process constraint relationship;

[0024] The mixed initialization rules for MAV layer encoding include:

[0025] a. Assign the current process to the machine with the shortest total processing time in the set of selectable processing machines. If there are multiple machines with the shortest total processing time, assign it to one of them randomly. The total processing time is the sum of the processing time of the current workpiece process and the transportation time between the current workpiece process and its previous process.

[0026] b. Assign the current process to the machine with the lowest total energy consumption in the selectable processing machine set. If there are multiple machines with the lowest total energy consumption, assign it to one of them randomly. The total energy consumption is the sum of the processing energy consumption of the current workpiece process and the transportation energy consumption between the current workpiece process and its previous process.

[0027] c. Assign the current process to the machine with the lowest machine load in the selectable processing machine set. If there are multiple machines with the lowest load, randomly select one of them. The machine load is the total processing time of the processing tasks arranged on that machine.

[0028] Preferably, step S4, which uses OX crossover to achieve assimilation between colonial states and POX crossover to achieve assimilation between colonial states and colonies, generating a new solution set, includes the following steps:

[0029] Step S41: Set the learning probability pLearn for the colonizing nation. Treat a colonizing nation and its multiple colonies as an empire, and set col for each colony in the empire. j Assimilation with its colonized countries resulted in offspring colonies. s ;

[0030] Step S42: If the offspring col s It is col j For non-dominated solutions, then col is used. s Update the colony, otherwise proceed to step S43;

[0031] Step S43: Calculate the individual country cost, the standardized cost of an individual country, and the power of an individual country for all colonized countries, and designate the colonized country with the greatest power as the strongest colonized country;

[0032] Step S44: Imp to other colonized countries i Assimilation with the strongest colonial power yields offspring imp.s ;

[0033] Step S45: Generate a random number between 0 and 1. If the child imp s It is imp i If the solution is non-dominated and the random number is not greater than pLearn, then imp is used. s Update the colony; otherwise proceed to step S46.

[0034] Step S46: Repeat steps S41 to S45 until only one empire remains or the set algorithm termination condition is met, then terminate the operation.

[0035] Preferably, the step S41 describes the colonies in each empire... j Assimilation with its colonized countries resulted in offspring colonies. s Includes the following steps:

[0036] Step S411: For OSV: Randomly divide the workpiece set into two subsets J1 and J2. Randomly select two solutions from the initial solution set of OSV as parent P1 and P2. Copy the operations belonging to J1 in parent P1 to child P2. s And keeping the positions of all processes unchanged, insert the processes belonging to J2 in parent generation P2 into child generation P in the relative order in P2. s The gap;

[0037] Step S412: For MAV: Randomly select a number of operations less than the total number of operations from all operations as the number set O. Randomly select two solutions from the initial solution set of MAV as parent M1 and M2. Copy the machine indices belonging to O in parent M1 to child M2. s And keeping the positions unchanged, copy the machine indices that do not belong to 0 in the parent M2 to the child M. s And keep the position unchanged.

[0038] Preferably, the expression for calculating the cost of a single country in step S43 is:

[0039]

[0040] The expression for calculating the standardized cost of the individual country is as follows:

[0041]

[0042] The expression for calculating the power of a single country is:

[0043]

[0044] In the above formula, C i For a single country, n represents the cost; n represents the number of optimization objectives; W represents the cost of a single country.d f represents the weight of the d-th optimization objective; d C is the function value of the d-th optimization objective. i Standardized costs for a single country; P i The power of a single country; N imp The total number of colonized countries.

[0045] Preferably, the imp to other colonial countries described in step S44 i Assimilation with the most powerful colonial power includes the following steps:

[0046] Step S441: Randomly select two solutions from the initial solution set as parents P1 and P2. Randomly select two crossover points in parent P1 to obtain a crossover segment. Copy the gene at the crossover segment position of parent P2 to offspring P. S The corresponding positions are determined, and a mapping set is established based on the crossover genes of parents P2 and P1;

[0047] Step S442: Copy the genes from parent P1, excluding the crossover segment, sequentially to offspring P1. S At the corresponding location, each gene is checked during replication. If the gene is in the mapping set, it is replaced with the mapping value, and the mapping relationship is deleted from the mapping set.

[0048] Step S443: If the mapping set is not empty at this time, then for the child P S The process iterates through all genes and performs mapping transformations until the mapping set is empty, at which point it terminates.

[0049] Preferably, in step S5, a neighborhood is designed based on the critical path and the critical machine. The critical path is the path that takes the longest time from the start of the first process to the completion of the last process, and the critical machine is the machine with the highest load. The neighborhood includes:

[0050] Neighborhood N1: In the OSV layer, randomly select two processes on the critical path and swap the two processes; in the MAV layer, randomly select two machines on the critical path and swap the two machines.

[0051] Neighborhood N2: In OSV, randomly select two processes on the critical path and insert the process that is ranked later before the process that is ranked earlier; in MAV, randomly select two machines on the critical path and insert the machine that is ranked later before the machine that is ranked earlier.

[0052] Neighborhood N3: Randomly select a process from the process set of the critical path and assign the selected process to the machine in the optional machine set that takes the least time;

[0053] Neighborhood N4: Randomly select a process from the process set of the critical path and assign the selected process to the machine with the least energy consumption in the optional machine set;

[0054] Neighborhood N5: Randomly select a process from the process set of the critical machine and assign the selected process to a random machine outside the critical machine.

[0055] Preferably, step S5 employs a reinforcement learning algorithm to perform a variable neighborhood descent search for the colonized countries, including the following steps:

[0056] Step S51: Initialize all values ​​in table Q to 0;

[0057] Step S52: Calculate the average ideal distance (MID) and the reverse generation distance (IGD) for all solutions. Set the state space S according to the relationship between the magnitudes of MID and IGD before and after the iteration. Denote the state of the external environment at the t-th iteration as S. t ;

[0058] The expression for calculating the average ideal distance MID is:

[0059]

[0060] The expression for calculating the anti-generation distance IGD is:

[0061]

[0062] In the above formula, f ji Let j be the objective value of the i-th solution; The minimum value of the j-th objective value among all solutions; n is the number of non-dominated solutions; d i Let be the Euclidean distance between the first front solution i and the nearest globally optimal Pareto first front solution; N is the number of globally optimal Pareto first front solutions;

[0063] Step S53: Combine neighborhoods N1 and N2 with neighborhoods N3, N4, and N5 to obtain 6 neighborhood combinations, and use these neighborhood combinations as the action set A. t Select an action from the action set and execute it, updating the state to S. t+1 ;

[0064] Step S54: Calculate the current reward value R, update the Q table, and perform a variable neighborhood descent search based on the optimal neighborhood combination in the current iteration;

[0065] The expression for calculating the current reward value R is:

[0066] R = R1 + R2;

[0067]

[0068] The expression for updating the Q table is:

[0069] Q(S t A t )=(1-α)Q(S t A t )+α[R t+1 +γ·max(Q(S t+1 ,:))];

[0070] In the above formula, R1 is the reward value of the average ideal distance; R2 is the reward value of the reverse generation distance; α is the learning rate; and γ is the discount rate.

[0071] The advantages of this invention include at least the following:

[0072] 1. By simultaneously considering the three objectives of minimizing the maximum completion time, minimizing the maximum machine load, and minimizing total energy consumption, it is possible to balance production efficiency, equipment utilization, and energy consumption, and more comprehensively meet the needs of production scheduling.

[0073] 2. By setting encoding rules based on process sequencing and machine selection, complex scheduling problems can be accurately represented, and the encoded solutions can be converted into executable scheduling plans through decoding rules, which helps the algorithm to search the solution space more effectively;

[0074] 3. Using OX crossover and POX crossover to implement assimilation operations can effectively combine the advantages of different solutions, promote the exchange of genetic information, increase population diversity, and thus improve the algorithm's global search capability and convergence speed.

[0075] 4. By designing neighborhoods for OSV and MAV and performing variable neighborhood descent search, the solution space can be explored more meticulously, avoiding premature convergence of the algorithm and increasing the probability of finding a better solution. This helps the algorithm to make more precise adjustments when it is close to the optimal solution. Attached Figure Description

[0076] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0077] Figure 2 This is a schematic diagram illustrating the gene encoding of workpiece information in an embodiment of the present invention;

[0078] Figure 3 This is a Gantt chart of the workpiece information after gene decoding in an embodiment of the present invention;

[0079] Figure 4 This is a schematic diagram of the POX intersection in an embodiment of the present invention;

[0080] Figure 5 This is a schematic diagram of the OX intersection in an embodiment of the present invention;

[0081] Figure 6 This is an example diagram of the critical path and critical machine in an embodiment of the present invention;

[0082] Figure 7 This is a schematic diagram of the framework of the reinforcement learning algorithm in an embodiment of the present invention;

[0083] Figure 8 This is a Gantt chart of the Pareto first front solution for the first example in this embodiment of the invention;

[0084] Figure 9 This is the Gantt chart of the Pareto first frontier solution for the second example in this embodiment of the invention. Detailed Implementation

[0085] 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.

[0086] This invention provides a scheduling method for distributed manufacturing based on the Empire Competition algorithm, such as... Figure 1 As shown, it includes the following steps:

[0087] Step S1: Based on the parallelism between the processing and assembly stages in the distributed assembly manufacturing process and the constraints of the processing stage on the assembly stage, a series of assumptions are made about the distributed assembly manufacturing scheduling environment, including:

[0088] (1) At any given time, a machine can only process or assemble one process. Once a process has started, it cannot be interrupted.

[0089] (2) At any given time, a machine can only process one workpiece, and an assembly team can only assemble one product.

[0090] (3) All machines can be processed and assembled at time “0”.

[0091] (4) The parts required for product production, the components assembled from the parts, and the final assembled products are all regarded as workpieces. For components and products, there is only one process.

[0092] (5) Workpieces can be transferred and processed across workshops, and each workpiece is immediately transported directly to the assembly workshop after completion.

[0093] Step S2: Establish an objective function that includes minimizing the maximum completion time, minimizing the maximum machine load, and minimizing the total energy consumption, and set the constraints of the objective function according to the product's assembly process.

[0094] Specifically, the expression for the constructed objective function is:

[0095] minf1 = E n,1 ;

[0096]

[0097]

[0098] In the formula, f1, f2, and f3 represent the completion time of the scheduling scheme, the machine load of the scheduling scheme, and the total machine energy consumption of the scheduling scheme, respectively; E n,1 The completion time for the final assembly process; W k m is the working time of the k-th machine; k is the machine number; m f Let F be the total number of machines in workshop f; F be the total number of processing workshops; E ... p Energy consumption for machine operation; E i E represents the idle energy consumption of the machine. t Energy consumption of transportation equipment; n is the total number of workpieces; u i The total number of operations for workpiece i; pe f,k Let k be the operating power of the kth machine in workshop f; Let be the processing time of the j-th process of workpiece i on the k-th machine in workshop f; For decision variables, the value is 1 when the j-th process of workpiece i is processed on the k-th machine in workshop f, and 0 otherwise; f,k S represents the idle power of the k-th machine in workshop f; i,j Let be the start time of the j-th process for workpiece i; The completion time of the first process for the first workpiece; The variable is 1 when the first process of the first workpiece on the kth machine in workshop f is processed before the jth process of workpiece i, and 0 otherwise; te is the working power of the transportation equipment. The variable is 1 when the j-th process of workpiece i is processed on machine k1 and the (j-1)-th process of workpiece i is processed on machine k2, and 0 otherwise. Let be the transportation time of workpiece j between machine k1 and machine k2.

[0099] Then, based on the actual situation on site, constraints are imposed on some parameters of the three objective functions, including:

[0100] (1) Workpiece process constraints: Workpiece processes must be carried out in the process sequence.

[0101]

[0102] (2) Machine constraints: a machine can only perform a single processing or assembly task at a time.

[0103]

[0104] (3) Start and finish time constraints: The start and finish times of all operations on the workpiece must be greater than 0.

[0105]

[0106] (4) Assembly process start time constraint: The start time of the assembly process must be greater than the maximum sum of the completion time and transportation time of its required components:

[0107]

[0108] (5) Constraints on the range of values ​​for decision variables:

[0109]

[0110] In the above formula, S i,j Let be the start time of the j-th process for workpiece i; Let be the processing time of the j-th process of workpiece i on the k-th machine in workshop f; The variable is 1 when the j-th process of workpiece i is processed on the k-th machine in workshop f, and 0 otherwise. The variable is 1 when the j-th process of workpiece i is processed on machine k1 and the (j-1)-th process of workpiece i is processed on machine k2, and 0 otherwise. Let be the transportation time of workpiece j between machine k1 and machine k2; For decision variables, E is 1 when the first operation of the first workpiece on the k-th machine in workshop f is processed before the j-th operation of workpiece i; otherwise, it is 0. i,j Let θ be the completion time of the j-th process of the i-th workpiece; θ is a sufficiently large positive number.

[0111] Step S3: Set encoding and decoding rules to encode the process sequencing and machine selection, obtaining the process sequencing vector (OSV) and the machine selection vector (MAV). The elements in the process sequencing vector are the workpiece numbers, and the elements in the machine selection vector represent the indices of the processing machines selected for the corresponding workpiece number in the process sequencing vector.

[0112] Specifically, the OSV (Operational Search Vector) and MAV (Machine Selection Vector) are actively decoded. The length of the encoded OSV and MAV is m×n, representing the total number of operations. Each encoded solution is represented by an integer code of n+2×m×n, simplifying the encoding and reducing the algorithm's complexity. During decoding, the workpiece operations in the OSV layer are sequentially arranged onto the machines in the corresponding MAV layer, while allowing idle processes to be inserted as early as possible to satisfy process constraints. A possible encoded solution is as follows: Figure 2 As shown, each element in the OSV vector is the workpiece number, and the j-th occurrence indicates the j-th operation of that workpiece. Each element in the MAV vector is the machine index, representing the processing machine selected for the corresponding operation in the OSV vector. m represents the m-th machine in the set of machines available for that operation. The corresponding decoded Gantt chart is shown in the diagram below. Figure 3 As shown.

[0113] Step S3: Set the mixed initialization rules for OSV and MAV, and generate the initial solution sets for OSV and MAV.

[0114] Specifically, the mixed initialization rules for OSV layer encoding include:

[0115] a. Prioritize selecting the component with the smallest sum of average time for the remaining operations of all workpieces on their machineable machines. If multiple components have the smallest time, randomly select one of them, and then randomly select one unfinished workpiece under that component.

[0116] b. Prioritize selecting the component with the fewest remaining processes among all workpieces under the component. If multiple components have the fewest processes, randomly select one of them, and then randomly select an unfinished workpiece under that component.

[0117] c. Randomly select a workpiece according to the process constraint relationship.

[0118] The mixed initialization rules for MAV layer encoding include:

[0119] a. Assign the current process to the machine with the shortest total processing time in the set of selectable processing machines. If there are multiple machines with the shortest total processing time, assign it to one of them randomly. The total processing time is the sum of the processing time of the current workpiece process and the transportation time between the current workpiece process and its previous process.

[0120] b. Assign the current process to the machine with the lowest total energy consumption in the selectable processing machine set. If there are multiple machines with the lowest total energy consumption, assign it to one of them randomly. The total energy consumption is the sum of the processing energy consumption of the current workpiece process and the transportation energy consumption between the current workpiece process and its previous process.

[0121] c. Assign the current process to the machine with the lowest machine load in the selectable processing machine set. If there are multiple machines with the lowest load, randomly select one of them. The machine load is the total processing time of the processing tasks arranged on that machine.

[0122] The first two rules of OSV layer encoding are combined with the first three rules of MAV layer encoding to generate an initial solution equal to the set number. The remaining initial solutions are generated by other mixed rules of OSV layer encoding and MAV layer encoding.

[0123] Step S4: Calculate the objective function values ​​of all initial solutions in the initial solution set. Select the solutions with better quality from the initial solutions as colonizing countries and the remaining initial solutions as colonies. Use OX crossover to achieve assimilation between colonizing countries and POX crossover to achieve assimilation between colonizing countries and colonies, and generate a new solution set.

[0124] Specifically, N individuals, or nations, are constructed from the initial population, and the N individuals with better quality are selected. imp One initial solution is designated as the colonial state, and the remaining initial solutions are designated as colonies. A colonial state and its multiple colonies constitute an empire. Assimilation between colonial states is achieved using OX crossover, and assimilation between colonial states and colonies is achieved using POX crossover. The process includes the following steps:

[0125] Step S41: Set the learning probability pLearn for each colony in the empire, and for each colony col... j Assimilation with its colonized countries resulted in offspring colonies. s This includes the following steps:

[0126] Step S411: For the OSV layer: Randomly divide the workpiece set into two subsets J1 and J2. Randomly select two solutions from the initial solution set of the OSV as parent P1 and P2. Copy the operations belonging to J1 in parent P1 to the child P2. s And keeping the positions of all processes unchanged, insert the processes belonging to J2 in parent generation P2 into child generation P in the relative order in P2. s The vacancy.

[0127] like Figure 4 The example shown is the POX crossover method. The workpiece set is randomly divided into two subsets, J1 and J2, where J1 = {1, 2} and J2 = {3, 4, 5}. The operations belonging to J1 in the parent P1 are copied to the child set while maintaining their positions in P1. The operations belonging to J2 in the parent P2 are inserted into the child set in the order they appear in P2. s The missing part was eventually filled by the offspring P. s .

[0128] Step S412: For the MAV layer: Randomly select a number of processes less than the total number of processes from all processes as the number set O. Randomly select two solutions from the initial solution set of MAV as parent M1 and M2. Copy the machine indices belonging to O in parent M1 to child M2. s And keeping the positions unchanged, copy the machine indices that do not belong to 0 in the parent M2 to the child M. s And keep the position unchanged.

[0129] Step S42: If the offspring col s It is col j For non-dominated solutions, then col is used. s Update the colony, or proceed to step S43.

[0130] Step S43: Calculate the individual country cost, the standardized cost of an individual country, and the power of an individual country for all colonized countries, and designate the colonized country with the greatest power as the strongest colonized country.

[0131] The expression for calculating the cost of a single country is:

[0132]

[0133] The expression for calculating the standardized cost of a single country is:

[0134]

[0135] The expression for calculating the power of a single country is:

[0136]

[0137] In the above formula, C i For a single country, denoted by ; n represents the number of optimization objectives; W represents the cost. d f represents the weights for the d-th optimization objective, with an initial weight ratio of 1:1; d C is the function value of the d-th optimization objective. i Standardized costs for a single country; P i The power of a single country; N imp The total number of colonized countries.

[0138] Step S44: Imp to other colonized countries i Assimilation with the strongest colonial power yields offspring imp. s This includes the following steps:

[0139] Step S441: Randomly select two solutions from the initial solution set of OSV layer encoding as parents P1 and P2. Randomly select two crossover points in parent P1 to obtain crossover segments. Copy the gene at the crossover segment position of parent P2 to offspring P. SThe corresponding positions are determined, and a mapping set is established based on the crossover genes of parents P2 and P1;

[0140] Step S442: Copy the genes from parent P1, excluding the crossover segment, sequentially to offspring P1. S At the corresponding location, each gene is checked during replication. If the gene is in the mapping set, it is replaced with the mapping value, and the mapping relationship is deleted from the mapping set.

[0141] Step S443: If the mapping set is not empty at this time, then for the child P S The process involves iterating through all genes and performing mapping transformations until the mapping set is empty.

[0142] Step S444: Perform synchronous transformation on the MAV layer encoding to obtain M s .

[0143] like Figure 5 The diagram shows an example of the OX crossover method. Two crossover points, 13 and 17, are selected from the OSV layer encoding. The crossover gene segment in the parent P2 is copied to the offspring P. S At the corresponding positions, a mapping set {[2,1],[3,4],[4,3][4,2],[2,1} is established for this gene segment in parents P2 and P1. The genes in parent P1, excluding the crossover segment, are sequentially copied to the offspring P. S At the corresponding location, each gene is checked during replication. If the gene is in the mapping set, it is replaced with the mapping value, and the mapping relationship is deleted from the mapping set. If the mapping set is not empty at this time, then for the offspring P... S The process iterates through all genes and performs mapping transformations until the mapping set is empty, at which point it terminates. The MAV layer encoding is simultaneously transformed to obtain M. s Since the OX crossover method may produce infeasible solutions, it is necessary to consider the offspring M. s Error correction was performed. The offspring P was ultimately obtained. S and offspring M s .

[0144] Step S45: Generate a random number between 0 and 1. If the child imp s It is imp i If the solution is non-dominated and the random number is not greater than pLearn, then imp is used. s Update the colony; otherwise proceed to step S46.

[0145] Step S46: Repeat steps S41 to S45. The operation terminates when the weaker empire loses all its colonies and the empire is destroyed, until only one empire remains or the algorithm's termination condition is met.

[0146] Step S5: Design the neighborhoods of OSV and MAV, obtain multiple neighborhood search combinations, perform variable neighborhood descent search on the colony countries, and obtain the optimal production scheduling scheme.

[0147] Specifically, five neighborhoods are designed based on the critical path and the critical machine. The critical path is the path with the longest time from the start of the first process to the completion of the last process, and the critical machine is the machine with the highest load. Three basic elements are set: state space, action selection, and reward setting. The reinforcement learning Q-Learning algorithm is used to determine the optimal neighborhood search combination. A variable neighborhood descent search is performed on the colony countries to find the optimal solution, including the following steps:

[0148] Step S51: Based on the critical path and critical machine, design 5 neighborhoods to enhance the algorithm's local search capability, including:

[0149] Neighborhood N1: In OSV, randomly select two processes on the critical path and swap them; in the MAV layer, randomly select two machines on the critical path and swap them.

[0150] Neighborhood N2: In OSV, randomly select two processes on the critical path and insert the process that is ranked later before the process that is ranked earlier; in MAV, randomly select two machines on the critical path and insert the machine that is ranked later before the machine that is ranked earlier.

[0151] Neighborhood N3: Randomly select a process from the process set of the critical path and assign the selected process to the machine with the least time in the set of available machines. That is, a random mutation is performed on a gene in the MAV layer that belongs to the critical path, while the encoding of the OSV layer remains unchanged.

[0152] Neighborhood N4: Randomly select a process from the process set of the critical path and assign the selected process to the machine with the least energy consumption in the set of available machines. That is, a random mutation is performed on a gene in the MAV layer that belongs to the critical path, while the encoding of the OSV layer remains unchanged.

[0153] Neighborhood N5: Randomly select a process from the process set of the critical machine and assign the selected process to a random machine outside the critical machine. That is, a random mutation is performed on a gene in the MAV layer that belongs to the critical path, while the encoding of the OSV layer remains unchanged.

[0154] Step S52: Introduce the Q-Learning algorithm and initialize all values ​​in the Q table to 0.

[0155] Step S53: Calculate the average ideal distance (MID) and the reverse generation distance (IGD) for all solutions. Set the state space S according to the relationship between the magnitudes of MID and IGD before and after the iteration. Denote the state of the external environment at the t-th iteration as S.t ;

[0156] The expression for calculating the mean ideal distance (MID) is:

[0157]

[0158] The expression for calculating the anti-generation distance IGD is:

[0159]

[0160] In the above formula, f ji Let j be the objective value of the i-th solution; The minimum value of the j-th objective value among all solutions; n is the number of non-dominated solutions; d i Let be the Euclidean distance between the first front solution i and the nearest globally optimal Pareto first front solution; N is the number of globally optimal Pareto first front solutions.

[0161] The constructed state space is shown in Table 2, where MID(g) is the MID value of the g-th iteration and IGD(g) is the IGD value of the g-th iteration.

[0162] Table 1 State Space

[0163]

[0164] Step S53: Combine neighborhoods N1 and N2 with neighborhoods N3, N4, and N5 to obtain 6 neighborhood combinations. Take these neighborhood combinations as the action set A. t The colonizing state selects and executes an action from the action set. Specifically, it performs a variable neighborhood descent search within the neighborhood combination [N1, N3] / [N1, N4] / [N1, N5] / [N2, N3] / [N2, N4] / [N2, N5] and updates the current state to S. t+1 .

[0165] Step S54: Calculate the current reward value R, update the Q table, and perform a variable neighborhood descent search based on the optimal neighborhood combination in the current iteration.

[0166] The expression for calculating the current reward value R is:

[0167] R = R1 + R2;

[0168]

[0169] The expression for updating the Q table is:

[0170] Q(S t A t )=(1-α)Q(S t A t )+α[Rt+1 +γ·max(Q(S t+1 ,:))];

[0171] In the above formula, R1 is the reward value of the average ideal distance; R2 is the reward value of the reverse generation distance; α is the learning rate; and γ is the discount rate.

[0172] This invention designs a hybrid initialization population, a double assimilation strategy using OX crossover and POX crossover, and a variable neighborhood search strategy combined with Q-Learning. To verify its effectiveness, algorithms that do not use the hybrid initialization population strategy, do not use the variable neighborhood search strategy combined with Q-Learning, and do not use the double assimilation strategy are denoted as EICA1, EICA2, and EICA3, respectively, and are compared with the EICA algorithm proposed in this invention.

[0173] The MID values ​​of different strategy algorithms are shown in Table 2, and the IGD values ​​are shown in Table 3. The effectiveness of the three strategies proposed in this invention can be seen from the tables.

[0174] Table 2. MID values ​​of different strategy algorithms with a fixed number of reference points F

[0175]

[0176]

[0177] Table 3. IGD values ​​of different strategy algorithms with a fixed number of reference points F.

[0178]

[0179]

[0180] To demonstrate the practical application of the scheduling results, this invention uses the larger-scale F2MK08 and F3MK09 examples to present the scheduling Gantt charts for a corresponding non-dominated solution obtained by the EICA algorithm, as shown below. Figure 8 , Figure 9 As shown.

[0181] The purpose of this invention is to provide a distributed manufacturing scheduling method based on the Empire Competition algorithm, which improves the algorithm's search efficiency through intelligent scheduling. Furthermore, by combining the existing information systems of the case study company with actual product examples, a distributed assembly manufacturing scheduling system was developed. This system can intelligently schedule and display solutions, and apply the results to production execution, thereby achieving cost reduction and efficiency improvement.

[0182] The specific steps for demonstrating intelligent scheduling are as follows:

[0183] Step S1: Develop a distributed assembly and manufacturing scheduling system.

[0184] Step S2: Production managers import the basic data required for scheduling, such as all material information of the product and process information of each workpiece. They can also adjust the algorithm parameters according to different situations and needs.

[0185] Step S3: Use the above scheduling algorithm to generate a scheduling scheme. After determining the scheduling scheme, schedule production and assign corresponding processing or assembly tasks to the machines and equipment to generate the corresponding scheduling scheme.

[0186] 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.

[0187] 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 scheduling method for distributed manufacturing based on the Empire Competition Algorithm, characterized in that, Includes the following steps: Step S1: Establish an objective function that includes minimizing the maximum completion time, minimizing the maximum machine load, and minimizing the total energy consumption, and set the constraints of the objective function according to the product's assembly process; Step S2: Set encoding and decoding rules, encode the process sorting and machine selection to obtain the process sorting vector OSV and the machine selection vector MAV. The elements in the process sorting vector are the workpiece numbers, and the elements in the machine selection vector represent the index of the processing machine selected by the workpiece number at the corresponding position in the process sorting vector. Step S3: Set the mixed initialization rules for OSV and MAV, and generate the initial solution sets for OSV and MAV; Step S4: Calculate the objective function values ​​of all initial solutions in the initial solution set. Initial solutions with objective function values ​​less than a set objective function threshold are designated as colonies, and the remaining initial solutions are designated as colonies. Assimilation between colonies is achieved using OX crossover, and assimilation between colonies and colonies is achieved using POX crossover, generating a new solution set. Step S5: Based on the critical path and critical machine, design the neighborhoods of OSV and MAV, obtaining multiple neighborhood search combinations. Use a reinforcement learning algorithm to perform variable neighborhood descent search on the colonized countries to obtain the optimal production scheduling scheme. The critical path is the path with the longest time from the start of the first process to the completion of the last process. The critical machine is the machine with the highest load. The neighborhood includes: Neighborhood N1: In the OSV layer, randomly select two processes on the critical path and swap the two processes; in the MAV layer, randomly select two machines on the critical path and swap the two machines. Neighborhood N2: In OSV, randomly select two processes on the critical path and insert the process that is ranked later before the process that is ranked earlier; in MAV, randomly select two machines on the critical path and insert the machine that is ranked later before the machine that is ranked earlier. Neighborhood N3: Randomly select a process from the process set of the critical path and assign the selected process to the machine in the optional machine set that takes the least time; Neighborhood N4: Randomly select a process from the process set of the critical path and assign the selected process to the machine with the least energy consumption in the optional machine set; Neighborhood N5: Randomly select a process from the process set of the critical machine and assign the selected process to a random machine outside the critical machine; The method of using reinforcement learning algorithms to perform variable neighborhood descent search on colonial countries includes the following steps: Step S51: Initialize all values ​​in table Q to 0; Step S52: Calculate the average ideal distance (MID) and the reverse generation distance (IGD) for all solutions. Set the state space S according to the relationship between the magnitudes of MID and IGD before and after the iteration. Denote the state of the external environment at the t-th iteration as S. t ; The expression for calculating the average ideal distance MID is: ； The expression for calculating the anti-generation distance IGD is: ； In the above formula, Let j be the objective value of the i-th solution; Let n be the minimum of the j-th objective value among all solutions; n is the number of non-dominated solutions. Let be the Euclidean distance between the i-th solution and the nearest globally optimal Pareto first front solution; N is the number of globally optimal Pareto first front solutions; Step S53: Combine neighborhoods N1 and N2 with neighborhoods N3, N4, and N5 to obtain 6 neighborhood combinations, and use these neighborhood combinations as an action set. Select an action from the action set and execute it, updating the state to S. t+1 ; Step S54: Calculate the current reward value R, update the Q table, and perform a variable neighborhood descent search based on the optimal neighborhood combination in the current iteration; The expression for calculating the current reward value R is: ； ； ； The expression for updating the Q table is: ； In the above formula, The reward value is the average ideal distance. The reward value is the anti-generation distance; Let MID be the value of the t-th iteration; Let be the IGD value of the t-th iteration; The learning rate; is the discount rate.

2. The scheduling method for distributed manufacturing based on the Empire Competition Algorithm according to claim 1, characterized in that: The expression for the objective function in step S1 is: ； ； ； In the formula, , , These are the completion time of the scheduling plan, the machine load of the scheduling plan, and the total energy consumption of the machine in the scheduling plan; The completion time for the final assembly process; The working time of the k-th machine; Machine serial number; Let f be the total number of machines in workshop f; This represents the total number of processing workshops. Energy consumption for machine operation; This refers to the idle energy consumption of the machine. Energy consumption of transportation equipment; This represents the total number of workpieces. The total number of processes for workpiece i; Let k be the operating power of the kth machine in workshop f; Let be the processing time of the j-th process of workpiece i on the k-th machine in workshop f; The variable is 1 when the j-th process of workpiece i is processed on the k-th machine in workshop f, and 0 otherwise. Let be the idle power of the k-th machine in workshop f; Let be the start time of the j-th process for workpiece i; Let j1 be the completion time of the j1st process of the i1th workpiece; As a decision variable, it is 1 when the j1st process of the i1th workpiece on the kth machine in workshop f is processed before the jth process of workpiece i, and 0 otherwise; The operating power of the transportation equipment; The variable is 1 when the j-th process of workpiece i is processed on machine k1 and the (j-1)-th process of workpiece i is processed on machine k2, and 0 otherwise. Let be the transportation time of workpiece i between machine k1 and machine k2.

3. The scheduling method for distributed manufacturing based on the Empire Competition Algorithm according to claim 1, characterized in that: The expression for the constraint condition is: ； ； ； ； ； ； ； In the above formula, Let be the start time of the j-th process for workpiece i; Let be the processing time of the j-th process of workpiece i on the k-th machine in workshop f; The variable is 1 when the j-th process of workpiece i is processed on the k-th machine in workshop f, and 0 otherwise. The variable is 1 when the j-th process of workpiece i is processed on machine k1 and the (j-1)-th process of workpiece i is processed on machine k2, and 0 otherwise. Let be the transportation time of workpiece i between machine k1 and machine k2; As a decision variable, it is 1 when the j1st process of the i1th workpiece on the kth machine in workshop f is processed before the jth process of workpiece i, and 0 otherwise; Let be the completion time of the j-th process for the i-th workpiece; It is a sufficiently large positive number.

4. The scheduling method for distributed manufacturing based on the Empire Competition Algorithm according to claim 1, characterized in that: The mixed initialization rules for OSV layer encoding set in step S3 include: a. Prioritize selecting the component with the smallest sum of average time for the remaining operations of all workpieces under that component on their machineable capacity. If multiple components have the smallest time, randomly select one of them, and then randomly select one unfinished workpiece under that component. b. Prioritize selecting the component with the fewest remaining processes among all workpieces under the component. If there are multiple components with the fewest processes, randomly select one of them, and then randomly select one unfinished workpiece under that component. c. Randomly select a workpiece according to the process constraints; The mixed initialization rules for MAV layer encoding include: a. Assign the current process to the machine with the shortest total time in the set of selectable processing machines. If there are multiple machines with the shortest total time, assign it to one of them randomly. The total time is the sum of the processing time of the current workpiece process and the transportation time between the current workpiece process and its previous process. b. Assign the current process to the machine with the lowest total energy consumption in the selectable processing machine set. If there are multiple machines with the lowest total energy consumption, assign it to one of them randomly. The total energy consumption is the sum of the processing energy consumption of the current workpiece process and the transportation energy consumption between the current workpiece process and its previous process. c. Assign the current process to the machine with the lowest machine load in the selectable processing machine set. If there are multiple machines with the lowest load, randomly select one of them. The machine load is the total processing time of the processing tasks arranged on that machine.

5. The scheduling method for distributed manufacturing based on the Empire Competition Algorithm according to claim 1, characterized in that: Step S4 describes using OX crossover to achieve assimilation between colonial states and using POX crossover to achieve assimilation between colonial states and colonies, generating a new solution set, and includes the following steps: Step S41: Set the learning probability pLearn for the colonizing nation. Treat a colonizing nation and its multiple colonies as an empire, and for each colony in the empire... Assimilation with its colonized countries and the resulting offspring ; Step S42: If offspring yes If the non-dominated solution is obtained, then adopt Update the colony, otherwise proceed to step S43; Step S43: Calculate the individual country cost, the standardized cost of an individual country, and the power of an individual country for all colonized countries, and designate the colonized country with the greatest power as the strongest colonized country; Step S44: To other colonized countries Assimilate with the most powerful colonial power and obtain offspring ; Step S45: Generate a random number between 0 and 1. If the offspring... yes If the non-dominated solution is found and the random number is not greater than pLearn, then adopt... Update the colony; otherwise proceed to step S46. Step S46: Repeat steps S41 to S45 until only one empire remains or the set algorithm termination condition is met, then terminate the operation.

6. The scheduling method for distributed manufacturing based on the Empire Competition Algorithm according to claim 5, characterized in that: The colonies in each empire described in step S41 Assimilation with its colonized countries, resulting in offspring Includes the following steps: Step S411: For OSV: Randomly divide the workpiece set into two subsets J1 and J2. Randomly select two solutions from the initial solution set of OSV as parent P1 and P2. Copy the operations belonging to J1 in parent P1 to child P2. s And keeping the positions of all processes unchanged, insert the processes belonging to J2 in parent generation P2 into child generation P in the relative order in P2. s The gap; Step S412: For MAV: Randomly select a number of operations less than the total number of operations from all operations as the number set O. Randomly select two solutions from the initial solution set of MAV as parent M1 and M2. Copy the machine indices belonging to O in parent M1 to child M1. s And keeping the positions unchanged, copy the machine indices that do not belong to 0 in the parent M2 to the child M. s And keep the position unchanged.

7. The scheduling method for distributed manufacturing based on the Empire Competition Algorithm according to claim 5, characterized in that: The expression for calculating the cost of the individual country in step S43 is as follows: ； The expression for calculating the standardized cost of the individual country is as follows: ； The expression for calculating the power of a single country is: ； In the above formula, For a single country, the cost is represented by 'n'; 'n' represents the number of optimization objectives; W represents the cost of a single country. d f represents the weight of the d-th optimization objective; d Let d be the value of the objective function for optimization. Standardized costs for individual countries; For the power of a single country; The total number of colonized countries.

8. The scheduling method for distributed manufacturing based on the Empire Competition Algorithm according to claim 5, characterized in that: The steps described in S44 regarding other colonial countries Assimilation with the most powerful colonial power includes the following steps: Step S441: Randomly select two solutions from the initial solution set as parents P1 and P2. Randomly select two crossover points in parent P1 to obtain a crossover segment. Copy the gene at the crossover segment position of parent P2 to offspring P. S The corresponding positions are determined, and a mapping set is established based on the crossover genes of parents P2 and P1; Step S442: Copy the genes from parent P1, excluding the crossover segment, sequentially to offspring P1. S At the corresponding location, each gene is checked during replication. If the gene is in the mapping set, it is replaced with the mapping value, and the mapping relationship is deleted from the mapping set. Step S443: If the mapping set is not empty at this time, then for the child P S The process iterates through all genes and performs mapping transformations until the mapping set is empty, at which point it terminates.

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