Clustering and entropy-guided reentrant hybrid flow shop scheduling method

Abstract

The invention relates to a clustering and entropy-guided reentrant hybrid flow shop scheduling method. The method comprises the following steps: step 1, establishing a problem model; step 2, setting algorithm operation parameters; 3, adopting an initialization strategy to generate an exploration population and a development population; 4, judging whether a first-stage termination condition is met or not, if not, executing a first-stage evolutionary strategy and an updating strategy on the exploration population and the development population, and otherwise, executing the step 5; 5, constructing an elite population; 6, judging whether a second-stage termination condition is met or not, and if not, executing a second-stage evolutionary strategy on the elite population; otherwise, outputting a Pareto solution set; and 7, updating the elite population. According to the method, dynamic balance of global exploration and local development is realized, and the solution distribution can be improved while the solution set convergence is ensured, so that the completion time and the total energy consumption are reduced, the production cost is reduced, and the workshop scheduling efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of job shop scheduling, in particular to a clustering and entropy-guided reentrant hybrid flow shop scheduling method. BACKGROUND

[0002] The core feature of the reentrant hybrid flow shop scheduling problem is that on the one hand, the product needs to go through multiple consecutive processing stages, each stage containing multiple parallel machines; on the other hand, some processes need to repeatedly enter the previous stage for reprocessing or detection repair, resulting in the existence of reentrant characteristics in the workshop. This kind of problem has high complexity and challenge, and is an important research direction in modern production management.

[0003] Taking seamless steel pipe manufacturing as an example, the billet needs to go through the processes of heating, piercing, rough rolling, multi-pass finishing, heat treatment, straightening and detection, etc. in turn. Among them, the multi-pass finishing and detection repair link often needs the product to return to the same stage for processing multiple times, which typically embodies the reentrant characteristic. At the same time, different stages contain multiple optional devices, which belong to the category of hybrid flow shop. In such a production process, the scheduling goal is not only to pursue the shortest completion time, but also to consider the total energy consumption in the production process. For example, the heat treatment furnace and the rolling mill will consume a lot of energy when waiting and idling, and an unreasonable scheduling sequence will cause frequent heating or long-time idling of the equipment, thereby causing an increase in energy consumption and production cost. If the scheduling scheme is unreasonable, it may also cause production bottlenecks, decreased equipment utilization, and even increased rework, thereby seriously affecting the production efficiency and product quality.

[0004] Therefore, in the context of multi-objective optimization, how to reasonably formulate the scheduling strategy of the reentrant hybrid flow shop to minimize the completion time while effectively reducing the energy consumption is a key problem with both practical significance and research value. SUMMARY

[0005] To more effectively address the scheduling problem of multi-objective reentrant hybrid flow shop systems, this application proposes a clustering and entropy-guided scheduling method for reentrant hybrid flow shop systems. This method fully considers the reentrant processing characteristics of workpieces at different stages, constructing a dual-population architecture combining an exploration population and a development population to enhance the algorithm's global search and local development capabilities. Evolutionary operators are integrated into a two-stage strategy, with the optimization objective of minimizing the maximum completion time and total energy consumption. Compared with traditional flow shop scheduling methods, the proposed method offers advantages such as ease of implementation, readily adjustable parameters, and superior performance in solution set convergence and distribution. It can achieve more accurate scheduling results through multiple iterative optimizations, avoiding time and energy waste caused by rework and equipment idleness. Furthermore, this method can effectively coordinate the task allocation of each process according to production needs, ensuring production efficiency while also considering energy conservation and emission reduction; it can also balance the load between different stages and machines, alleviating bottlenecks and blockages in the production process, thereby improving the stability and reliability of the production line. The optimized scheduling scheme can not only reduce equipment idling time and energy consumption, reduce resource waste and lower production costs, but also meet the development needs of green manufacturing and has significant practical application value.

[0006] This invention provides a clustering and entropy-guided reentrant hybrid flow shop scheduling method, comprising the following steps:

[0007] Step 1: Establish a multi-objective reentrant hybrid flow shop scheduling problem model with the optimization objectives of minimizing the maximum completion time and minimizing the total energy consumption;

[0008] Step 2: Set the algorithm running parameters;

[0009] Step 3: Generate the exploration population and the development population using an initialization strategy;

[0010] Step 4: Determine whether the first phase termination condition is met. If not, execute the first phase evolution strategy and update strategy for the exploration population and the development population; otherwise, proceed to step 5.

[0011] Step 5: Select high-performing individuals from the exploration and development populations to build an elite population;

[0012] Step 6: Determine if the termination condition of the second stage is met. If not, execute the second stage evolution strategy on the elite population; otherwise, output the Pareto solution set.

[0013] Step 7: Update the elite population.

[0014] Furthermore, the objective function of the problem model in step 1 is:

[0015]

[0016] wherein, is the maximum makespan, is the total energy consumption.

[0017] Further, the parameters in step 2 include: the size of the exploration population , the size of the elite population , the neighborhood radius

[0018] the termination time of the first phase: ;

[0019] the termination time of the second phase: ;

[0020] wherein, is the number of passes, ; is the number of jobs, ; is the number of phases, .

[0021] Further, step 4 includes:

[0022] determining whether the first phase termination time is reached according to the running time ; if not, entering the first phase evolution strategy; otherwise, executing step 5;

[0023] the first phase evolution strategy; wherein: the first search strategy is executed on the development population, and the job sequence of the development population is updated, the first search strategy including six index-based local search methods;

[0024] the development population individuals are transmitted into the exploration population, the second search strategy is executed on the merged exploration population, and the job sequence and the machine sequence of the exploration population are updated, the second search strategy including: performing priority operation crossover on the job sequence, and performing uniform crossover on the machine sequence.

[0025] Further, step 3 includes:

[0026] the development population adopts a job sequence encoding based on passes, the job sequence is denoted as , and an initial scheduling scheme is generated by a hybrid heuristic method to allocate jobs to each machine;

[0027] the exploration population adopts joint encoding of the job sequence and the machine sequence, the job sequence is denoted as , and the machine sequence is denoted as , and an initial scheduling scheme is generated by a random method; wherein, is the index of the job sequence , For the first One workpiece being processed. For the last workpiece to be processed, For process sequence index, This is the last processing step. Machine sequence index, The machine assigned to the last process.

[0028] Furthermore, the hybrid heuristic method is specifically as follows:

[0029] First, calculate the total processing time for each workpiece, and then process all of them. The total processing time of each workpiece is sorted in descending order to obtain the workpiece sequence;

[0030] Based on the sorting results, the workpieces are inserted into the following three types of positions in sequence:

[0031] The insertion position with the goal of minimizing the maximum completion time;

[0032] Insertion position with the goal of minimizing total energy consumption;

[0033] Simultaneously optimize the insertion positions of maximum completion time and total energy consumption;

[0034] After the workpiece is inserted, the machine allocation is performed using the following two methods:

[0035] Prioritize the machine that can complete the processing of the workpiece the earliest; when there are multiple machines that meet the conditions, select the machine with the lowest total energy consumption under this allocation.

[0036] Prioritize the machine that minimizes the total energy consumption of the workpiece; when multiple machines with the same energy consumption exist, select the machine that can complete the processing earliest.

[0037] By combining the above three types of insertion positions with two machine allocation methods, six work sequence sequences can be generated; based on each work sequence and the two machine allocation methods, twelve complete scheduling schemes are finally obtained.

[0038] One of the courses is One workpiece, Each round is One workpiece.

[0039] Furthermore, the first search strategy includes the following steps:

[0040] First, calculate the ideal point-guided expansion of the current development population. ;

[0041] Then, it is compared with the ideal point guiding spread of the previous generation of development population If the current ideal point guiding spread is reduced, one of the index-based local search strategies LS1 to LS4 is randomly selected for execution; otherwise, one of the index-based local search strategies LS5 to LS6 is randomly selected for execution.

[0042] The indexes include ideal proximity, bottom point area spread, nearest neighbor distance deviation, and ideal point guiding spread.

[0043] The index-based local search strategies include the following six types:

[0044] LS1: A workpiece is randomly selected from the workpiece sequence and inserted into the position with the minimum ideal proximity, and the machine allocation mode is to select the machine with the earliest completion time.

[0045] LS2: A workpiece is randomly selected from the workpiece sequence and inserted into the position with the minimum ideal proximity, and the machine allocation mode is to select the machine with the minimum total energy consumption.

[0046] LS3: A workpiece is randomly selected from the workpiece sequence and inserted into the position with the maximum bottom point area spread, and the machine allocation mode is to select the machine with the earliest completion time.

[0047] LS4: A workpiece is randomly selected from the workpiece sequence and inserted into the position with the maximum bottom point area spread, and the machine allocation mode is to select the machine with the minimum total energy consumption.

[0048] LS5: A workpiece is randomly selected from the workpiece sequence and inserted into the position with the minimum nearest neighbor distance deviation, and the machine allocation mode is to select the machine with the earliest completion time.

[0049] LS6: A workpiece is randomly selected from the workpiece sequence and inserted into the position with the minimum nearest neighbor distance deviation, and the machine allocation mode is to select the machine with the minimum total energy consumption.

[0050] Further, the second search strategy includes the following steps:

[0051] First, the weighted evaluation score WES of each individual in the exploration population is calculated, and the formula of the weighted evaluation score WES is as follows:

[0052]

[0053] wherein, is the ideal point,​​​​​​​ is the bottom point, is the ideal point, is the (normalized) objective vector of the i-th non-dominated solution, is the Euclidean distance.

[0054] Then, the exploration population individuals are sorted in descending order of the weighted evaluation score, and are paired: the individual with the highest score is paired with the individual with the lowest score, the individual with the second highest score is paired with the individual with the second lowest score, and so on;

[0055] Finally, the priority operation crossover is performed on the process sequence of the individuals in the exploration population, and the uniform crossover is performed on the machine sequence, to generate new exploration individuals.

[0056] Further, the index is specifically:

[0057] The ideal proximity is used to calculate the Euclidean distance between the solution and the ideal point, and the calculation formula of the ideal proximity is as follows:

[0058]

[0059] The ideal point is composed of the minimum value of each normalized objective, and is used to represent the theoretically optimal solution in the objective space; the smaller the value of the ideal proximity is, the better the convergence performance of the solution is; The bottom point area expansion is used to measure the area of the rectangle formed by the solution and the bottom point, and the calculation formula of the bottom point area expansion is as follows:

[0060] The bottom point is composed of the maximum value of all normalized objectives, and is used to represent the extreme boundary of the objective space; the larger the value of the bottom point area expansion is, the better the solution is in terms of boundary coverage and exploration ability;

[0061] The nearest neighbor distance deviation is used to evaluate the uniformity of the distribution of the solution set, and is calculated by the standard deviation of the Euclidean distance between adjacent solutions, and the formula of the nearest neighbor distance deviation is as follows:

[0062]

[0063] The nearest neighbor distance deviation is used to evaluate the uniformity of the distribution of the solution set, and is calculated by the standard deviation of the Euclidean distance between adjacent solutions, and the formula of the nearest neighbor distance deviation is as follows:

[0064]

[0065] The nearest neighbor distance deviation is used to evaluate the uniformity of the distribution of the solution set, and is calculated by the standard deviation of the Euclidean distance between adjacent solutions, and the formula of the nearest neighbor distance deviation is as follows: ​​​​​​​denotes the Euclidean distance between the th solution and the th solution in the normalized makespan order, denotes the average of the distances; the smaller the nearest neighbor distance deviation value is, the more evenly the solution set is distributed;

[0066] The ideal point guided spread , on the basis of the classical spread indicator, the distance from the boundary solution to the ideal point and the distance deviation of the neighboring solutions in the solution set are introduced for improvement, and the calculation formula is:

[0067]

[0068] wherein, and denote the first solution and the last solution in the non-dominated solution set in descending order of makespan; the smaller the ideal point guided spread value is, the clearer the boundary of the solution set and the more evenly the solution set is distributed.

[0069] Further, the step 7 comprises:

[0070] Firstly, the candidate solution set is de-duplicated to eliminate redundant individuals;

[0071] Then, the fast non-dominated sorting is performed on the remaining individuals, which are divided into several non-dominated levels, and the weighted evaluation score WES is calculated in each level.

[0072] Finally, the individuals are selected in turn according to the non-dominated level order to construct a new generation of population; when the number of individuals in a certain level exceeds the remaining capacity, the individual with a higher weighted evaluation score WES is preferentially retained until the predetermined population size is reached.

[0073] Further, the second phase evolution strategy in the step 6 comprises a neighborhood search strategy, specifically:

[0074] Firstly, cluster structure extraction

[0075] The elite solution set is analyzed by clustering using a noisy density-based clustering method to identify the cluster structure and noise points in the solution set, wherein is set to 1 to allow a single solution to form an independent cluster; is the minimum number of sample points;

[0076] Then, entropy calculation and evolution weight distribution

[0077] The target space is divided into × A grid, of which: clusters The solution in is , for , for , , , , , For the size of an elite population, Let i be the number of grid partitions, and i be the index of the cluster. To maximize the completion time, Total energy consumption, The smallest , For the largest , The smallest , For the largest , e is the index of the elite solution, x e For the first An elite solution Value, y e For the first An elite solution value;

[0078] For each solution Assign a unique one-dimensional index The one-dimensional index The calculation formula is as follows:

[0079]

[0080] in, Solution The row in which it is located Representing the solution The column it belongs to;

[0081] Statistics for each cluster Falling into the grid Number of solutions Calculate the corresponding probability The probability The calculation formula is as follows:

[0082]

[0083] in, , Cluster The number of individuals;

[0084] Through the probability Computational clusters normalized entropy of , the normalized entropy of is calculated as follows:

[0085]

[0086]

[0087] where, and represent the minimum and maximum entropy of all clusters, respectively;

[0088] map the entropy to the evolutionary weight , the evolutionary weight is calculated as follows:

[0089]

[0090] Finally, the objective space is divided by the slope

[0091] calculate the average objective slope of each cluster , the average objective slope is calculated as follows:

[0092]

[0093] where, and represent the average normalized and , respectively;

[0094] According to the objective slope, the objective space is divided into four regions, and the corresponding neighborhood search strategy is selected:

[0095] Region , the objective slope : the solution set maximum completion time is too large, prefer to use the strategy to optimize the maximum completion time as the main and take into account the multi-objective coordination, using NS1, NS3, NS5;

[0096] Region , the objective slope : the target is biased to the maximum completion time, using the comprehensive optimization strategy to strengthen the multi-objective coordination and diversity, while optimizing the maximum completion time, using NS1, NS5, NS6;

[0097] Region , the objective slope : the target is biased to the total energy consumption, using the comprehensive optimization strategy to strengthen the multi-objective coordination and diversity, while optimizing the total energy consumption, using NS2, NS5, NS6;

[0098] region for target slope : solution set total energy consumption is large, prefer to adopt to optimize the total energy consumption as the main and give consideration to the multi-objective collaborative strategy, adopt NS2, NS4, NS5;

[0099] The six neighborhood search strategies NS1-NS6 described above are all based on key machines and key processes, wherein the critical path is defined as the longest machining sequence from the starting point to the end point, the processes thereon are key processes, and the assigned machines are key machines; the specific strategies are as follows:

[0100] NS1: randomly select 10% of the machines from the set of key machines, and reassign the workpieces machined thereon to other feasible machines in the same stage, evaluate all feasible machine assignment schemes, and select the scheme that minimizes the maximum completion time to retain;

[0101] NS2: the operation process is similar to NS1, but selects the machine assignment scheme to minimize the total energy consumption as the optimization target;

[0102] NS3: randomly select 10% of the processes from the key processes, and try to reinsert them into all feasible positions, and select the position that minimizes the maximum completion time to perform the insertion operation;

[0103] NS4: the operation process is similar to NS3, but selects the insertion position to minimize the total energy consumption as the optimization target;

[0104] NS5: randomly select 10% of the processes from the key processes, and try to reinsert them into all feasible positions of the current process sequence; if there is an insertion position that makes the new solution Pareto dominate the original solution, select the position to perform the insertion operation;

[0105] NS6: randomly select 10% of the processes from the key processes, and try to exchange them with other processes; if there is an exchange scheme that makes the new solution Pareto dominate the original solution, retain the exchange scheme.

[0106] Further, the second stage evolution strategy in step 6 includes an energy saving strategy, specifically:

[0107] First, for a single-pass reentrant mixed flow shop:

[0108] Identify all machines with shutdown time equal to the maximum completion time, and perform backward shift on all processes on these machines to reduce machine idle energy consumption;

[0109] Traverse each machine in descending order of stage index and descending order of machine index within each stage:

[0110] If the last workpiece of the machine cannot be moved backward, only the other workpieces are moved backward;

[0111] If the last workpiece of the machine can be moved backward, but the workpiece of the first process cannot be moved backward, only the other workpieces are moved backward;

[0112] If the last workpiece of the machine and the first workpiece can be moved backward, all workpieces are moved backward. If the total energy consumption is reduced after adjustment, the adjustment is retained; otherwise, the backward movement of the last workpiece and the workpiece of the first process is cancelled, and only the adjustment of the remaining workpieces is retained.

[0113] Wherein, the "backward movement" refers to delaying the execution of the workpiece on the machine as much as possible, but the completion time of the workpiece after adjustment cannot be later than the start time of the next stage or the first stage process of the next pass;

[0114] Then, for the reentrant mixed flow shop containing multiple passes:

[0115] Identify all machines with shutdown time equal to the maximum completion time, and perform backward movement on all processes on these machines to reduce machine idle energy consumption.

[0116] Traverse each machine in descending order of stage index and descending order of machine index in each stage. For each machine, determine the backward movement feasibility according to the state of the first workpiece of the machine and the last workpiece of the machine:

[0117] If the last workpiece of the machine cannot be moved backward, only the other workpieces are marked as being able to be moved backward;

[0118] If the last workpiece of the machine can be moved backward, further distinguish three cases:

[0119] If the first workpiece of the machine cannot be moved backward, only the other workpieces are marked as being able to be moved backward;

[0120] If the first workpiece of the machine can be moved backward, but there is a workpiece that cannot be moved backward afterwards, only the other workpieces are marked as being able to be moved backward;

[0121] If the first workpiece of the machine can be moved backward, and there is no workpiece that cannot be moved backward afterwards, all workpieces are marked as being able to be moved backward;

[0122] After completing the backward movement feasibility marking of all machines, only the workpieces previously marked as being able to be moved backward are moved rightward.

[0123] The present application has the following technical effects:

[0124] Method level:

[0125] 1. A dual-population architecture consisting of an exploration population and a development population is designed to achieve a dynamic balance between global search ability and local optimization ability. A two-stage evolution strategy is introduced to focus on the joint promotion of global exploration and local development in the early evolution stage, and to further strengthen neighborhood search in the later evolution stage, thereby balancing search efficiency and solution quality.

[0126] 2. Four lightweight internal evaluation indicators are introduced to evaluate convergence, boundary coverage, and distribution uniformity. These indicators provide an extensible and practical alternative to external evaluation indicators and further support the design of six index-based local search strategies to dynamically guide the development population.

[0127] 3. A density-based clustering method is used to identify distribution patterns in the target space, distinguishing between dense and sparse regions. Then, a weighted mechanism based on entropy is used to quantify solution density within each cluster to adaptively allocate search resources.

[0128] 4. Energy-saving strategies for single-pass and multi-pass are designed. By introducing targeted delays to the start time of some processes, idle time is effectively reduced without violating feasibility or extending overall completion time, thereby achieving more energy-efficient scheduling results.

[0129] Application level:

[0130] 1. Compared with traditional flow shop scheduling methods, the method provided by the present application has the advantages of simple implementation, easy parameter adjustment, and excellent performance in solution set convergence and distribution;

[0131] 2. It can perform multiple iterative optimization on the reentrant mixed flow shop scheduling process to obtain a more accurate scheduling scheme and avoid time and energy waste due to rework and equipment idling;

[0132] 3. It can dynamically schedule and optimize multi-process, multi-stage tasks according to production needs, helping enterprises to balance energy saving and production efficiency;

[0133] 4. It can balance the load between different stages and machines, avoid bottlenecks and blockages in the production process, and improve the stability and reliability of the production line. The optimized scheduling scheme can reduce idle time and energy consumption of equipment, reduce resource waste, and effectively reduce production cost.

[0134] Therefore, the optimization method for multi-objective reentrant mixed flow shop scheduling problem provided by the present application can better solve the time and energy conflict problem in complex shop scheduling, provide an efficient and low-energy scheduling scheme for reentrant mixed flow shop, improve scheduling efficiency, and shorten completion time. BRIEF DESCRIPTION OF DRAWINGS

[0135] Figure 1 Schematic diagram of the implementation process of the present application

[0136] Figure 2 Comparison box plot of GD index of the algorithm of the present application under small-scale examples

[0137] Figure 3 Comparison box plot of IGD index of the algorithm of the present application under small-scale examples

[0138] Figure 4 Comparison box plot of HV index of the algorithm of the present application under small-scale examples

[0139] Figure 5 Comparison box plot of GD index of the algorithm of the present application under large-scale examples

[0140] Figure 6 Comparison box plot of IGD index of the algorithm of the present application under large-scale examples

[0141] Figure 7 Comparison box plot of HV index of the algorithm of the present application under large-scale examples DETAILED DESCRIPTION

[0142] Embodiments of the present application will now be described in greater detail below with reference to the accompanying drawings, in which embodiments of the present application are illustrated. The present application may, however, be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art. Throughout the specification, like reference numerals refer to like elements.

[0143] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0144] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing other processes. Other programmable devices provide steps for implementing the functions / acts specified in the flowchart diagrams and / or block diagrams.

[0145] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing other processes. Other programmable devices provide steps for implementing the functions / acts specified in the flowchart diagrams and / or block diagrams.

[0146] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing other processes. Other programmable devices provide steps for implementing the functions / acts specified in the flowchart diagrams and / or block diagrams.

[0147] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing other processes. Other programmable devices provide steps for implementing the functions / acts specified in the flowchart diagrams and / or block diagrams.

[0148] A clustering and entropy-guided re-entrant hybrid flow shop scheduling method, as shown in Figure 1 includes the following steps:

[0149] Step 1: Establish a multi-objective re-entrant hybrid flow shop scheduling problem model with the optimization objectives of minimizing the maximum completion time and minimizing the total energy consumption;

[0150] Step 2: Set the algorithm running parameters;

[0151] Step 3: Generate an exploration population and a development population using an initialization strategy;

[0152] Step 4: judging whether the first stage termination condition is met, if not, executing the first stage evolution strategy and the update strategy on the exploration population and the development population, otherwise executing Step 5;

[0153] Step 5: screening the individuals with excellent performance from the exploration population and the development population to construct an elite population;

[0154] Step 6: judging whether the second stage termination condition is met, if not, executing the second stage evolution strategy on the elite population, otherwise outputting the Pareto solution set;

[0155] Step 7: updating the elite population.

[0156] Preferably, the objective function of the problem model in Step 1 is:

[0157]

[0158] wherein, is the maximum completion time, is the total energy consumption.

[0159] Preferably, the parameters in Step 2 include: the exploration population size , the elite population size , the neighborhood radius .

[0160] The termination time of the first stage: ;

[0161] The termination time of the second stage: ;

[0162] wherein, is the number of passes, ; is the number of workpieces, ; is the number of stages, .

[0163] Preferably, Step 4 includes:

[0164] judging whether the first stage termination time is reached according to the running time ; if not, entering the first stage evolution strategy, otherwise executing Step 5;

[0165] the first stage evolution strategy; wherein: executing the first search strategy on the development population and updating the workpiece sequence of the development population, the first search strategy including six index-based local search methods;

[0166] The individual of the development population is transmitted into the exploration population, a second search strategy is performed on the combined exploration population, and the process sequence and the machine sequence of the exploration population are updated, the second search strategy comprising: performing priority operation crossover on the process sequence, and performing uniform crossover on the machine sequence.

[0167] Preferably, the step 3 comprises:

[0168] The development population adopts a process sequence based on The workpiece sequence is represented as and an initial scheduling scheme is generated by a hybrid heuristic method to allocate workpieces to each machine.

[0169] The exploration population adopts a combined coding of process sequence and machine sequence, the workpiece sequence is represented as and the machine sequence is represented as and an initial scheduling scheme is generated by a random method.

[0170] wherein, is the index of the workpiece sequence is the workpiece processed in the th position, is the last workpiece processed, is the index of the process sequence is the last process, is the index of the machine sequence is the last machine allocated. Preferably, the hybrid heuristic method is specifically as follows:

[0171] Firstly, the total processing time of each workpiece is calculated, and the total processing time of all workpieces is sorted in descending order to obtain a workpiece sequence;

[0172] According to the sorting result, the workpieces are sequentially inserted into the following three types of positions:

[0173] the insertion position aiming to minimize the maximum completion time;

[0174] the insertion position aiming to minimize the total energy consumption;

[0175] the insertion position simultaneously optimizing the maximum completion time and the total energy consumption;

[0176]

[0177] After the workpiece insertion is completed, the following two ways are adopted for machine allocation:

[0178] ​​​The machine which can make the workpiece finish processing earliest is selected preferentially; when there are multiple machines meeting the condition, the machine with the lowest total energy consumption under the distribution is selected;

[0179] The machine which can make the workpiece finish processing earliest is selected preferentially; when there are multiple machines meeting the condition, the machine with the lowest total energy consumption under the distribution is selected;

[0180] Through the combination of the above three types of insertion positions and two machine distribution modes, six workpiece sequences can be generated; based on each workpiece sequence, two machine distribution modes are combined, and finally 12 complete scheduling schemes are obtained;

[0181] Among them, one pass is workpieces, one pass is workpieces.

[0182] Preferably, the first search strategy comprises the following steps:

[0183] First, calculate the ideal point guided expansion degree of the current development population ;

[0184] Then, compare it with the ideal point guided expansion degree of the last generation development population : if the current ideal point guided expansion degree decreases, then randomly select one from the index-based local search strategies LS1 to LS4; otherwise, randomly select one from the index-based local search strategies LS5 to LS6;

[0185] The index includes ideal proximity, bottom point area expansion, nearest neighbor distance deviation and ideal point guided expansion degree;

[0186] The index-based local search strategy includes the following six types:

[0187] LS1: randomly select a workpiece from the workpiece sequence and insert it into the position with the smallest ideal proximity , and the machine distribution mode is to select the machine with the earliest completion time.

[0188] LS2: randomly select a workpiece from the workpiece sequence and insert it into the position with the smallest ideal proximity , and the machine distribution mode is to select the machine with the smallest total energy consumption.

[0189] LS3: randomly select a workpiece from the workpiece sequence and insert it into the position with the largest bottom point area expansion , and the machine distribution mode is to select the machine with the earliest completion time.

[0190] LS4: Randomly select one job from the job sequence and insert it into the bottom area expansion The machine assignment mode is to select the machine with the minimum total energy consumption at the position with the maximum distance.

[0191] LS5: Randomly select one job from the job sequence and insert it into the nearest neighbor distance deviation The machine assignment mode is to select the machine with the earliest completion time at the position with the minimum distance.

[0192] LS6: Randomly select one job from the job sequence and insert it into the nearest neighbor distance deviation The machine assignment mode is to select the machine with the minimum total energy consumption at the position with the minimum distance.

[0193] Preferably, the second search strategy comprises the following steps:

[0194] First, the weighted evaluation score WES of each individual in the exploration population is calculated, and the formula of the weighted evaluation score WES is as follows:

[0195]

[0196] wherein, is an ideal point, is a bottom point, is the (normalized) objective vector of the i-th non-dominated solution, is the Euclidean distance.

[0197] Then, the individuals in the exploration population are sorted in descending order of the weighted evaluation score, and are paired: the individual with the highest score is paired with the individual with the lowest score, the individual with the second highest score is paired with the individual with the second lowest score, and so on.

[0198] Finally, the priority operation crossover is performed on the process sequence of the individuals in the exploration population, and the uniform crossover is performed on the machine sequence to generate new exploration individuals.

[0199] Preferably, the index is specifically:

[0200] The ideal proximity is used to calculate the Euclidean distance between the solution and the ideal point , and the formula of the ideal proximity is as follows:

[0201]

[0202] wherein, the ideal point is composed of the minimum value of each normalized objective, and is used to represent the theoretically optimal solution in the objective space; when the ideal proximity ​The smaller the value is, the better the convergence performance of the solution is;

[0203] The bottom point area expansion , for measuring the solution and the bottom point The area of the formed rectangle, the calculation formula of the bottom point area expansion is:

[0204]

[0205] Among them, the bottom point Composed of the maximum value of all normalized objectives, for representing the extreme boundary of the objective space; when the bottom point area expansion The larger the value is, the better the boundary coverage and exploration ability of the solution is;

[0206] The nearest neighbor distance deviation , for evaluating the uniformity of the solution set distribution, which is calculated by the standard deviation of the Euclidean distance between adjacent solutions, the formula of the nearest neighbor distance deviation is:

[0207]

[0208] Among them, The Euclidean distance between the i-th solution and the i+1-th solution sorted by normalized completion time, The average value of the distance; when the nearest neighbor distance deviation The smaller the value is, the more uniform the solution set distribution is;

[0209] The ideal point guiding expansion degree On the basis of the classical expansion degree index, the distance from the boundary solution to the ideal point and the distance deviation of the adjacent solutions in the solution set are introduced for improvement, and the calculation formula is:

[0210]

[0211] Among them, And Respectively represent the first solution and the last solution sorted in descending order of completion time in the non-dominated solution set The smaller the ideal point guiding expansion degree The value is, the clearer the solution set boundary is, and the more uniform the distribution is.

[0212] Preferably, the step 7 comprises:

[0213] Firstly, the candidate solution set is de-duplicated to eliminate redundant individuals;

[0214] Then, a fast non-dominated ranking is performed on the remaining individuals, dividing them into several non-dominated levels, and a weighted evaluation score (WES) is calculated within each level.

[0215] Finally, individuals are selected sequentially according to the non-dominant level to construct the next generation of population; when the number of individuals in a certain level exceeds the remaining capacity, individuals with higher weighted evaluation scores (WES) are retained first until the predetermined population size is reached.

[0216] Preferably, the second-stage evolutionary strategy in step 6 includes a neighborhood search strategy, specifically:

[0217] First, cluster structure extraction

[0218] A density-based clustering method with noise is used to perform cluster analysis on the elite solution set to identify cluster structures and noise points within the solution set. Set to 1 to allow individual solutions to form independent clusters; Minimum number of sample points;

[0219] Then, entropy calculation and evolution weight allocation.

[0220] target space Equal width division into × A grid, of which: clusters The solution in is , for , for , , , , , For the size of an elite population, Let i be the number of grid partitions, and i be the index of the cluster. To maximize the completion time, Total energy consumption, The smallest , For the largest , The smallest , For the largest , e is the index of the elite solution, x e For the first An elite solution Value, y e For the first An elite solution value;

[0221] For each solution Assign a unique one-dimensional index , the one-dimensional index The calculation formula is as follows:

[0222]

[0223] wherein, indicates the row where the solution is located, indicates the column where the solution is located;

[0224] The number of solutions falling into the grid in each cluster is counted, the corresponding probability is calculated, the calculation formula is as follows:

[0225]

[0226] wherein, , indicates the number of individuals of the cluster ;

[0227] The normalized entropy of the cluster is calculated by the probability , the calculation formula is as follows:

[0228]

[0229]

[0230] wherein, and respectively indicate the minimum entropy and the maximum entropy of all clusters;

[0231] The entropy is mapped into the evolutionary weight , the calculation formula is as follows:

[0232]

[0233] Finally, the target space is divided by the slope

[0234] The average target slope of each cluster is calculated, the calculation formula is as follows:

[0235]

[0236] ​​​​​wherein, and respectively represent the average normalized and ;

[0237] According to the target slope, the target space is divided into four regions, and the corresponding neighborhood search strategy is selected:

[0238] Region , the target slope : the solution set is large in maximum completion time, and the strategy is preferentially adopted to mainly optimize the maximum completion time and consider the multi-objective coordination, NS1, NS3, and NS5 are adopted;

[0239] Region , the target slope : the target is inclined to the maximum completion time, the comprehensive optimization strategy is adopted to strengthen the multi-objective coordination and diversity, and the maximum completion time is simultaneously optimized, NS1, NS5, and NS6 are adopted;

[0240] Region , the target slope : the target is inclined to the total energy consumption, the comprehensive optimization strategy is adopted to strengthen the multi-objective coordination and diversity, and the total energy consumption is simultaneously optimized, NS2, NS5, and NS6 are adopted;

[0241] Region , the target slope : the solution set is large in total energy consumption, and the strategy is preferentially adopted to mainly optimize the total energy consumption and consider the multi-objective coordination, NS2, NS4, and NS5 are adopted;

[0242] The six neighborhood search strategies NS1-NS6 described above are all based on the key machine and the key process design, wherein the critical path is defined as the longest processing sequence from the starting point to the terminal point, the processes thereon are the key processes, and the assigned machines are the key machines; the specific strategies are as follows:

[0243] NS1: 10% of the machines in the key machine set are randomly selected, the workpieces processed thereon are re-assigned to other feasible machines in the same stage, all feasible machine assignment schemes are evaluated, and the solution that minimizes the maximum completion time is reserved;

[0244] NS2: the operation process is similar to NS1, but the machine assignment scheme is selected as the optimization target to minimize the total energy consumption;

[0245] NS3: 10% of the processes in the key process are randomly selected, and the processes are tried to be re-inserted into all feasible positions, and the insertion operation is performed in the position that minimizes the maximum completion time;

[0246] NS4: the operation process is similar to NS3, but the insertion position is selected as the optimization target to minimize the total energy consumption;

[0247] NS5: randomly select 10% of the key processes, try to reinsert them into all feasible positions of the current process sequence; if there is an insertion position that makes the new solution Pareto dominate the original solution, select this position to perform the insertion operation;

[0248] NS6: randomly select 10% of the key processes, try to exchange with other processes; if there is an exchange scheme that makes the new solution Pareto dominate the original solution, keep the exchange scheme.

[0249] Further, the second stage evolution strategy in step 6 includes energy saving strategy, specifically:

[0250] First, for the reentrant mixed flow shop containing only single pass:

[0251] Identify all machines with shutdown time equal to the maximum completion time, and perform backward shift on all processes on these machines to reduce machine idle energy consumption;

[0252] Traverse each machine in descending order of phase index and descending order of machine index within each phase:

[0253] If the last job of the machine cannot be backward shifted, only the backward shift of other jobs is performed;

[0254] If the last job of the machine can be backward shifted, but the job of the first process cannot be backward shifted, only the backward shift of other jobs is performed;

[0255] If the last job and the first job of the machine can be backward shifted, backward shift is performed on all jobs. If the total energy consumption after adjustment decreases, the adjustment is retained; otherwise, the backward shift of the last job and the first process job is cancelled, and only the adjustment of the remaining jobs is retained;

[0256] Wherein, the "backward shift" refers to delaying the execution of the job on the machine as much as possible, but the completion time of the job after adjustment cannot be later than the start time of the next stage or the first stage process of the next pass;

[0257] Then, for the reentrant mixed flow shop containing multiple passes:

[0258] Identify all machines with shutdown time equal to the maximum completion time, and perform backward shift on all processes on these machines to reduce machine idle energy consumption.

[0259] Traverse each machine in descending order of phase index and descending order of machine index within each phase, and for each machine, determine the backward shift feasibility according to the state of the first job of the machine and the last job of the machine:

[0260] If the last workpiece of the machine cannot be moved backward, only the other workpieces are marked as movable backward;

[0261] If the last workpiece of the machine can be moved backward, three cases are further distinguished:

[0262] If the first workpiece of the machine cannot be moved backward, only the other workpieces are marked as movable backward;

[0263] If the first workpiece of the machine can be moved backward, but there is a workpiece that cannot be moved backward later, only the other workpieces are marked as movable backward;

[0264] If the first workpiece of the machine can be moved backward, and there is no workpiece that cannot be moved backward later, all workpieces are marked as movable backward;

[0265] After marking the backward movement feasibility of all machines, only the workpieces previously marked as movable backward are executed rightward movement operations.

[0266] The application further reduces energy consumption and improves solution convergence by the energy-saving strategy for the elite population in the second-stage evolution strategy.

[0267] The application realizes dynamic balance of local development and global exploration through the first-stage evolution strategy, and realizes further enhancement of solution quality through the second-stage evolution strategy. The application is further described and explained below through specific embodiments:

[0268] The simulation experiment uses 275 standard examples. All example parameters are randomly generated according to uniform distribution. The specific settings are as follows: in small-scale examples, the number of workpieces , the number of stages , the number of passes , the number of machines in each stage , processing time ; in large-scale examples, the number of workpieces , the number of stages , the number of passes , the number of machines in each stage , processing time . Among them, represents uniform distribution in the interval .

[0269] To verify the effectiveness of the clustering and entropy-guided unsupervised learning multi-objective evolutionary algorithm (CEUL-MOEA) proposed in the present application, a variety of high-performance optimization algorithms proposed in recent years are selected as comparison objects, including: multi-objective genetic algorithm combined with Lorenz dominance relationship (L-NSGA), genetic algorithm combined with Minkowski distance and local search (MLPGA), improved multi-objective evolutionary algorithm based on decomposition (IMOEA / D), enhanced version combined with local search (IMOEA / D-LS), non-dominated sorting genetic algorithm combined with Q-learning and variable neighborhood search (QVNS-NSGA-II), and non-dominated sorting algorithm combined with double-chain encoding, variable neighborhood search and greedy insertion-based (VNS-NSGA-II). To reduce the randomness of experimental results and enhance the reliability of statistical conclusions, each example is independently run 5 times, and the statistical results are taken as the final performance evaluation basis. In terms of performance indicators, three types of indicators commonly used in the field of multi-objective optimization are used: generational distance (GD), inverted generational distance (IGD), and hyper volume (HV) as performance evaluation indicators. The calculation formulas of the three evaluation indicators are as follows:

[0270] (1) Generational Distance (GD)

[0271] GD is used to evaluate the convergence of the solution set , which calculates the average Euclidean distance from each solution in the solution set to the nearest reference point on the true Pareto front :

[0272]

[0273] where denotes the non-dominated solution set generated by the th algorithm, denotes the union of all normalized non-dominated solution sets generated by the algorithm (i.e., the reference set). and are solutions in and , respectively, denotes the point of solution in the normalized target space, denotes the Euclidean distance between point and in the target space, is the size of the solution set. The smaller the GD value, the closer the solution set is to the true Pareto front, and the better the convergence.

[0274] (2) Inverted Generational Distance (IGD)

[0275] IGD comprehensively measures the convergence and distribution of the solution set, and its method is to calculate the reference set. From each point in the generated solution set The average distance between the nearest solutions:

[0276]

[0277] in, This indicates the number of solutions in the reference set. The smaller the IGD value, the closer the generated solution set is to the true front, and the more uniformly it is distributed in the target space.

[0278] (3) Hypervolume (HV)

[0279] HV simultaneously characterizes the convergence and diversity of the solution set, and is defined as the sum of the convergence and diversity of the solution set. Dominated and referenced by Defined target space volume:

[0280]

[0281] in, Let represent the Lebesgue measure, i.e., volume. Let To solve The corresponding point in the normalized objective space. The larger the HV value, the better the solution set performs in terms of convergence and distribution (i.e., it is closer to the true Pareto front and the distribution is more uniform).

[0282] Figures 2-7 The optimization results of each comparison algorithm are presented intuitively on different computational examples. Specifically, from... Figures 2-7 The GD, IGD, and HV indices show that CEUL-MOEA consistently has a lower GD value in both small-scale and large-scale tests, indicating that it performs better in terms of convergence. At the same time, CEUL-MOEA has a lower IGD value and a higher HV value, which shows that the proposed method also has significant advantages in terms of the distribution and diversity of solution sets.

[0283] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Any modifications or changes made to the present invention by those skilled in the art after reading this application and referring to the above embodiments are within the scope of protection claimed in the pending claims of this application.

Claims

1. A clustering and entropy-guided reentrant hybrid flow shop scheduling method, characterized in that... Includes the following steps: Step 1: Establish a multi-objective reentrant hybrid flow shop scheduling problem model with the optimization objectives of minimizing the maximum completion time and minimizing the total energy consumption; Step 2: Set the algorithm running parameters; Step 3: Generate the exploration population and the development population using an initialization strategy; Step 4: Determine whether the first phase termination condition is met. If not, execute the first phase evolution strategy and update strategy for the exploration population and the development population; otherwise, proceed to step 5. Step 5: Select high-performing individuals from the exploration and development populations to build an elite population; Step 6: Determine whether the termination condition of the second stage is met. If not, execute the second stage evolution strategy on the elite population. Otherwise, output the Pareto solution set; Step 7: Update the elite population.

2. The method according to claim 1, characterized in that, The parameters in step 2 include: the size of the exploratory population. Elite population size Neighborhood radius ; End time of Phase 1: ; End time of Phase Two: ; in, For the number of times, ; For the number of workpieces, ; For the number of stages, .

3. The method according to claim 2, characterized in that, Step 4 includes: Determine whether the first phase termination time has been reached based on the running time. If the goal is not achieved, proceed to the first stage of the evolutionary strategy; otherwise, execute step 5. The first stage evolutionary strategy includes: executing a first search strategy on the development population and updating the artifact sequence of the development population. The first search strategy includes six index-based local search methods. The individuals from the development population are transferred to the exploration population. A second search strategy is executed on the merged exploration population, and the process sequence and machine sequence of the exploration population are updated. The second search strategy includes: performing priority operation crossover on the process sequence and performing uniform crossover on the machine sequence.

4. The method according to claim 1, characterized in that, Step 3 includes: Population development adopts a method based on The workpiece sequence is encoded for each pass, and the workpiece sequence is represented as follows: An initial scheduling scheme is generated using a hybrid heuristic approach to allocate workpieces to each machine. The population was explored using a joint encoding of process sequences and machine sequences, wherein the process sequences are denoted as... The machine sequence is denoted as An initial scheduling scheme is generated using a random method; in, For workpiece sequence index, For the first One workpiece being processed. For the last workpiece to be processed, For process sequence index, This is the last processing step. Machine sequence index, The machine assigned to the last process.

5. The method according to claim 4, characterized in that, The hybrid heuristic method is as follows: First, calculate the total processing time for each workpiece, and then process all of them. The total processing time of each workpiece is sorted in descending order to obtain the workpiece sequence; Based on the sorting results, the workpieces are inserted into the following three types of positions in sequence: The insertion position with the goal of minimizing the maximum completion time; Insertion position with the goal of minimizing total energy consumption; Simultaneously optimize the insertion positions of maximum completion time and total energy consumption; After the workpiece is inserted, the machine allocation is performed using the following two methods: Prioritize the machine that can complete the processing of the workpiece the earliest; when there are multiple machines that meet the conditions, select the machine with the lowest total energy consumption under this allocation. Prioritize the machine that minimizes the total energy consumption of the workpiece; when multiple machines with the same energy consumption exist, select the machine that can complete the processing earliest. By combining the above three types of insertion positions with two machine allocation methods, six work sequence sequences can be generated; based on each work sequence and the two machine allocation methods, twelve complete scheduling schemes are finally obtained. One of the courses is One workpiece, Each lane is One workpiece.

6. The method according to claim 3, characterized in that, The first search strategy includes the following steps: First, calculate the ideal point-guided expansion of the current development population. ; Then, guide the expansion by comparing it with the ideal point of the previous generation of the development population. Comparison: If the current ideal point guides the expansion degree If the value decreases, an execution strategy is randomly selected from LS1 to LS4 based on metrics; otherwise, an execution strategy is randomly selected from LS5 to LS6 based on metrics. The metrics include ideal proximity, bottom point area expansion, nearest neighbor distance deviation, and ideal point guided expansion. The indicator-based local search strategies include the following six categories: LS1: Randomly select a workpiece from the workpiece sequence and insert it into the position with the minimum ideal proximity IP. The machine allocation method is to select the machine with the earliest completion time. LS2: Randomly select a workpiece from the workpiece sequence and insert it into the position with the minimum ideal proximity IP. The machine allocation method is to select the machine with the minimum total energy consumption. LS3: Randomly select a workpiece from the workpiece sequence and insert it into the position with the largest bottom point area expansion (NAE). The machine allocation method is to select the machine with the earliest completion time. LS4: Randomly select a workpiece from the workpiece sequence and insert it into the position with the largest bottom point area expansion NAE. The machine allocation method is to select the machine with the smallest total energy consumption. LS5: Randomly select a workpiece from the workpiece sequence and insert it into the position with the smallest nearest neighbor distance deviation NNDD. The machine allocation method is to select the machine with the earliest completion time. LS6: Randomly select a workpiece from the workpiece sequence and insert it into the position with the smallest nearest neighbor distance deviation NNDD. The machine allocation method is to select the machine with the smallest total energy consumption.

7. The method according to claim 3, characterized in that, The second search strategy includes the following steps: First, the weighted evaluation score (WES) of each individual in the exploration population is calculated. The formula for the weighted evaluation score (WES) is as follows: ； in, For the ideal point, As the base point, For the first The (normalized) objective vector of a non-dominated solution. Euclidean distance; Then, the individuals in the exploration population are sorted from highest to lowest according to their weighted evaluation scores and paired up: the individual with the highest score is paired with the individual with the lowest score, the individual with the second highest score is paired with the individual with the second lowest score, and so on. Finally, priority operation crossover is performed on the process sequence of individuals in the exploration population, and uniform crossover is performed on the machine sequence to generate new exploration individuals.

8. The method according to claim 1, characterized in that, Step 7 includes: First, the candidate solution set is deduplicated to eliminate redundant individuals; Then, a fast non-dominated ranking is performed on the remaining individuals, dividing them into several non-dominated levels, and a weighted evaluation score (WES) is calculated within each level. Finally, individuals are selected sequentially according to the non-dominant hierarchy to construct the next generation of population; when the number of individuals in a certain hierarchy exceeds the remaining capacity, individuals with higher weighted evaluation scores (WES) are retained first until the predetermined population size is reached.

9. The method according to claim 1, characterized in that, The second-stage evolutionary strategy in step 6 includes a neighborhood search strategy, specifically: First, cluster structure extraction; A density-based clustering method with noise is used to perform cluster analysis on the elite solution set to identify cluster structures and noise points within the solution set. Set to 1 to allow individual solutions to form independent clusters; Minimum number of sample points; Then, entropy calculation and evolutionary weight allocation; target space Equal width division into × A grid, of which: clusters The solution in is , for , for , , , , , For the size of an elite population, Let i be the number of grid partitions, and i be the index of the cluster. To maximize the completion time, Total energy consumption, The smallest , For the largest , The smallest , For the largest , e is the index of the elite solution, x e For the first An elite solution Value, y e For the first An elite solution value; For each solution Assign a unique one-dimensional index The one-dimensional index The calculation formula is as follows: ； in, Solution The row in which it is located Solution The column it belongs to; Statistics for each cluster Falling into the grid Number of solutions Calculate the corresponding probability The probability The calculation formula is as follows: ； in, , Cluster The number of individuals; Through the probability Computational clusters Normalized entropy The normalized entropy The calculation formula is as follows: ； ； in, and Let represent the minimum and maximum entropy of all clusters, respectively; Entropy Mapped to evolutionary weights The evolution weight The calculation formula is as follows: ； Finally, the target space is divided using slope. Calculate each cluster average target slope The average target slope The calculation formula is as follows: ； in, and They represent the average normalization. and ; The target space is divided into four regions based on the target slope, and corresponding neighborhood search strategies are selected: area , is the target slope The maximum completion time of the solution set is too large. Therefore, we should prioritize strategies that optimize the maximum completion time while also taking into account multi-objective collaboration, such as NS1, NS3, and NS5. area , is the target slope The objective is biased towards the maximum completion time. A comprehensive optimization strategy is adopted to enhance the coordination and diversity of multiple objectives, while optimizing the maximum completion time. NS1, NS5, and NS6 are used. area , is the target slope The objective is biased towards total energy consumption. A comprehensive optimization strategy is adopted to enhance the synergy and diversity of multiple objectives, while optimizing total energy consumption, using NS2, NS5, and NS6. area , is the target slope The total energy consumption of the solution set is too high. Therefore, we should prioritize strategies that optimize the total energy consumption while also taking into account the cooperation of multiple objectives, such as NS2, NS4, and NS5. The six neighborhood search strategies NS1–NS6 described above are all based on critical machines and critical processes. The critical path is defined as the longest processing sequence from the start point to the end point, with the processes along it being critical processes and the assigned machines being critical machines. The specific strategies are as follows: NS1: Randomly select 10% of the machines from the set of critical machines, redistribute the workpieces processed on them to other feasible machines in the same stage, evaluate all feasible machine allocation schemes, and select the solution that minimizes the maximum completion time to retain. NS2: The operation process is similar to NS1, but the machine allocation scheme is selected with the goal of minimizing total energy consumption. NS3: Randomly select 10% of the critical processes and attempt to re-insert them into all feasible positions. Select the position that minimizes the maximum completion time and perform the insertion operation. NS4: The operation process is similar to NS3, but the insertion position is selected with the goal of minimizing total energy consumption. NS5: Randomly select 10% of the key processes and attempt to re-insert them into all feasible positions in the current process sequence; if there is an insertion position where the new solution Pareto dominates the original solution, then select that position to perform the insertion operation; NS6: Randomly select 10% of the key processes and attempt to exchange them with other processes; if there is an exchange scheme that makes the new solution Pareto dominant over the original solution, then retain the exchange scheme.

10. The method according to claim 1, characterized in that, The second-stage evolutionary strategy in step 6 includes an energy-saving strategy, specifically: First, for reentrant mixed flow workshops that only contain a single pass: Identify all machines whose shutdown time equals their maximum completion time and perform a shift operation on these machines to reduce idle energy consumption. Traverse each machine in descending order by stage index and machine index within each stage: If the last workpiece of the machine cannot be moved backward, then only the other workpieces are moved backward; If the last workpiece of the machine can be moved backward, but the workpiece of the first process cannot be moved backward, then only the other workpieces are moved backward. If both the last and first workpieces of the machine can be moved backward, then move all workpieces backward; if the total energy consumption is reduced after the adjustment, then retain the adjustment; otherwise, cancel the backward movement of the last workpiece and the first process workpiece, and only retain the adjustment for the remaining workpieces. The term "postponement" refers to delaying the execution of the workpiece on its assigned machine as much as possible, but the completion time of the adjusted workpiece shall not be later than the start time of the next stage or the next first stage process. Then, for reentrant mixed flow workshops containing multiple passes: Identify all machines whose shutdown time equals their maximum completion time and perform a shift operation on these machines to reduce idle energy consumption. Traverse each machine in descending order of stage index and machine index within each stage. For each machine, determine the feasibility of moving backward based on the state of the machine's first and last workpieces: If the last workpiece of the machine cannot be moved backward, then only the other workpieces are marked as movable backward; If the last workpiece of the machine can be moved backward, then three cases can be further distinguished: If the first workpiece of the machine cannot be moved backward, then only the other workpieces are marked as movable backward; If the first workpiece of the machine can be moved backward, but there is a subsequent workpiece that cannot be moved backward, then only the other workpieces are marked as being able to be moved backward; If the first workpiece of the machine can be moved backward, and there are no subsequent workpieces that cannot be moved backward, then all workpieces are marked as movable backward; After marking all machines as feasible to move backward, only perform the rightward movement operation on the workpieces that were previously marked as feasible to move backward.

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