A multi-modal multi-objective re-entrant hybrid flow shop scheduling method

Abstract

The present application relates to the technical field of workshop scheduling, in particular to a multi-modal multi-objective reentrant hybrid flow shop scheduling method, which is based on a multi-modal multi-objective meme method driven by hierarchical online learning, and comprises the following steps: step 1: establishing a problem model; step 2: setting method running parameters; step 3: generating a population by using an initialization strategy; step 4: judging whether a first-stage termination condition is met, if not, executing a first-stage evolution strategy and an environment selection strategy on the population, otherwise executing step 5; step 5: constructing a multi-modal archive; step 6: judging whether a second-stage termination condition is met; the present application can effectively mine a large number of performance-equivalent but structurally different multi-modal scheduling solutions while guaranteeing the convergence of the target space and maintaining the diversity of the decision space.

Description

Technical Field

[0001] This invention relates to the field of workshop scheduling technology, and in particular to a multimodal, multi-objective, reentrant hybrid flow workshop scheduling method. Background Technology

[0002] The core characteristics of the reentrant hybrid flow shop scheduling problem are: on the one hand, products need to go through multiple consecutive processing stages, each stage containing multiple parallel machines; on the other hand, processes need to return to previous stages for reprocessing, thus forming a reentrant processing flow. Due to the diversity of equipment configuration, process paths, and rework frequency, there are often multiple scheduling schemes with different structures but equivalent performance under the same optimization objective, making this type of problem inherently multimodal. Furthermore, in actual production, it is usually necessary to simultaneously optimize multiple conflicting scheduling objectives, making the problem exhibit complex multimodal and multi-objective characteristics.

[0003] Taking a semiconductor packaging and testing production line as an example, chip products need to go through multiple processing stages in sequence, including die bonding, bonding, packaging, curing, testing, and sorting. Under the requirements of high reliability and high precision manufacturing, in order to meet the strict constraints of performance consistency and quality stability, chips need to undergo multiple rounds of refinement and performance consolidation treatments, thus forming a production path that can re-enter the same processing stage multiple times, demonstrating typical reentrancy characteristics.

[0004] In this process, due to differences in optional equipment combinations, processing sequence arrangements, and multi-round processing path configurations, even with the same objective function values ​​such as maximum completion time and total energy consumption, there may still be multiple process routes and scheduling sequences with significant structural differences, exhibiting obvious multimodal solution structure characteristics. The existence of such multimodal scheduling schemes enables the system to quickly switch to alternative equivalent schemes without sacrificing scheduling performance when faced with sudden changes in customer demand (such as the need for early delivery of individual workpieces) or production disturbances, thereby improving the responsiveness and operational robustness of the production system.

[0005] In this type of production system, the scheduling objective includes not only minimizing the maximum completion time but also reducing the total energy consumption during the production process. For example, packaging equipment, curing ovens, and testing machines all generate significant energy consumption during frequent start-ups, shutdowns, idling, and multiple processing cycles. Different scheduling schemes may perform similarly in terms of completion time and energy consumption, but they differ significantly in equipment load distribution, processing cycle configuration, and process path selection, thus having different impacts on system operational stability, equipment lifespan, and the ability to cope with uncertain disturbances.

[0006] Therefore, how to effectively explore and maintain multiple scheduling schemes with equivalent performance but significant structural differences while ensuring the convergence of the target space, and achieve synergistic optimization of decision space diversity and scheduling performance, is a key challenge with important engineering value and research significance in the scheduling problem of multimodal, multi-objective, reentrant hybrid flow shop. Summary of the Invention

[0007] To more effectively address the multimodal, multi-objective, reentrant hybrid flow shop scheduling problem, this application proposes a hierarchical online learning-driven multimodal, multi-objective, reentrant hybrid flow shop scheduling method, addressing the characteristics of this problem, such as multiple reentrant processes, parallel equipment selection, and the coexistence of performance-equivalent multimodal solutions. This method takes the structural characteristics of the problem as its starting point, fully considers the multimodal distribution characteristics of scheduling solutions in the decision space, constructs a method architecture of co-evolution of the population and multimodal archives, and divides the method evolution process into two stages. This improves the convergence of the objective space while enhancing the diversity of the decision space, thereby more fully exploring and maintaining multiple performance-equivalent but structurally different scheduling schemes.

[0008] Compared with traditional flow shop scheduling methods, the proposed method is designed to meet the actual scheduling needs of reentrant hybrid flow shops. It has advantages such as simple implementation and easy parameter adjustment, and performs well in terms of objective space convergence, decision space diversity, and the ability to discover and maintain multimodal solutions. Through multiple iterative optimizations, the method can obtain more accurate and robust scheduling results, effectively avoiding time waste and increased energy consumption caused by improper multi-round processing arrangements, equipment idling, or stage blockages.

[0009] Furthermore, this method, based on the multi-stage, multi-equipment, and multi-round processing characteristics of this problem, coordinates the task allocation relationship between various processes, ensuring production efficiency while also considering energy conservation and emission reduction. It can also achieve load balancing between different processing stages and parallel equipment, alleviating bottlenecks and congestion in the production process, thereby improving the stability and reliability of the production line operation. The optimized scheduling scheme not only reduces equipment idling time and energy consumption, minimizing resource waste and production costs, but also aligns with the development needs of green manufacturing, demonstrating significant engineering application value.

[0010] This invention provides a multimodal, multi-objective, reentrant hybrid flow shop scheduling method, comprising the following steps:

[0011] Step 1: Establish a multimodal, 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, while maximizing the number of multimodal solutions;

[0012] Step 2: Set the running parameters of the scheduling problem model;

[0013] Step 3: Based on the aforementioned operating parameters, generate a population using an initialization strategy and set the method runtime;

[0014] Step 4: Determine whether the first stage termination condition has been met based on the running time of the method. If not, execute the first stage evolution strategy and the first stage environment selection strategy for the population; otherwise, proceed to step 5.

[0015] Step 5: Extract multimodal solutions from the population and construct a multimodal profile;

[0016] Step 6: Determine whether the second-stage termination condition has been met based on the running time of the method. If not, execute the second-stage evolutionary strategy, environmental selection, energy-saving strategy, and genetic strategy on the population and multimodal archive; otherwise, output the Pareto solution set and Pareto front.

[0017] Furthermore, step 3 includes:

[0018] The first phase of population adoption is based on The workpiece sequence code for each pass, wherein the workpiece sequence is: And an initial scheduling scheme is generated using a diversity heuristic method to allocate workpieces to each machine;

[0019] in, For workpiece sequence index, For the first One workpiece being processed. The last workpiece to be processed; The number of times the Tao is mentioned.

[0020] Furthermore, step 6 includes:

[0021] Determine whether the second phase termination time has been reached based on the running time. ;

[0022] If the target is not met, a second-stage evolutionary strategy is implemented for the population, and a second-stage environmental selection strategy is adopted to update the population and multimodal profile. Then, an energy-saving strategy is adopted for the population and multimodal profile to further reduce energy consumption.

[0023] Every five iterations, a second-stage genetic operation is performed, and a second-stage environmental selection strategy is used to update the population and multimodal profile.

[0024] The second-stage population and multimodal archives employ joint encoding of process sequences and machine sequences, wherein the process sequences are as follows: The machine sequence is ;

[0025] in, For process sequence index, This is the last processing step. Machine sequence index, The machine assigned to the last process, and the end time of the second stage. ;in, For the number of workpieces, For the number of times, This refers to the number of stages.

[0026] Furthermore, the diversity heuristic method in step 3 is as follows:

[0027] The workpieces are first arranged in non-ascending order according to the total processing time to generate a seed sequence. ;

[0028] Then, three workpiece insertion rules are used to generate a workpiece sequence. The three types of workpiece insertion rules include: an insertion rule aimed at minimizing the maximum completion time; an insertion rule aimed at minimizing total energy consumption; and an insertion rule that simultaneously optimizes both the maximum completion time and total energy consumption.

[0029] After the workpiece is inserted, five methods are used for machine allocation, namely:

[0030] (1) Select the machine that can complete the processing of the workpiece earliest; when there are multiple machines that meet the conditions, select the machine with the lowest total energy consumption under this allocation.

[0031] (2) Select the machine that can make the workpiece finish processing the earliest; when there are multiple machines that meet the conditions, randomly select one machine.

[0032] (3) Select the machine that minimizes total energy consumption; when there are multiple machines with the same energy consumption, select the machine that can complete the processing earliest.

[0033] (4) Select the machine that minimizes total energy consumption; if there are multiple machines with the same energy consumption, randomly select one machine.

[0034] (5) Select the machine with the lowest total load; when there are multiple machines with the same energy consumption, randomly select one machine.

[0035] By combining the above three insertion rules with five machine allocation methods, 15 individuals can be generated; the remaining... Each individual randomly generates a sequence of workpieces, which is then combined with the five machine allocation rules mentioned above; among them, Indicates population size.

[0036] Furthermore, the first-stage environment selection strategy in step 4 is specifically as follows:

[0037] First, regarding the solution set Perform deduplication; the first stage uses the first deduplication method, and the second stage uses the second deduplication method;

[0038] Specifically:

[0039] The first deduplication method is based on the objective function value, removing individuals with the same objective function value; the second deduplication method is based on the scheduling sequence, removing individuals with the same scheduling sequence.

[0040] Then, min-max normalization is performed on each individual in the deduplicated solution set to obtain the normalized solution set. ;

[0041] Next, the set of unified solutions Perform a non-dominated sort and select individuals to join the population layer by layer according to the dominance level; if joining is done at the current dominance level... This led to the population size exceeding If so, the sub-region filtering strategy will be executed;

[0042] The sub-region filtering strategy includes the following steps:

[0043] The first quadrant of the target space [0, 90°] is uniformly divided into... Sub-regions The number of sub-regions , Indicates a region. Indicates the first There are regions; for the i-th individual within a region... , and Let these represent the first and second target values ​​of the i-th individual, respectively; based on their polar angles in the target space... The sub-region to which it belongs is determined, and the polar angle and region division formula are as follows:

[0044]

[0045]

[0046] For individuals in each subregion Calculate their distance to the ideal point respectively. European distance The best time to completion European distance And to the optimal total energy consumption Euclidean distance They are respectively:

[0047]

[0048]

[0049]

[0050] The minimum value among the above distances is taken as the individual. Comprehensive evaluation indicators ,for:

[0051]

[0052] Each sub-region is based on the aforementioned comprehensive evaluation indicators The size is used to select representative individuals.

[0053] Furthermore, the second-stage evolutionary strategy in step 6 includes an adaptive local search strategy based on online learning, specifically:

[0054] (1) Target space partitioning and mapping

[0055] First, using the same target space partitioning method as the first-stage environmental selection, the first quadrant of the target space is divided into three characteristic sub-regions: the low total energy consumption region. Balanced optimization region and areas with low completion time Furthermore, an external non-dominated solution archive A is introduced as a knowledge base for online learning, providing real-time data support for subsequent regional potential assessment and adaptive decision-making.

[0056] (2) Regional selection layer decision

[0057] The region selection layer guides search resources to adaptively allocate to sub-regions with higher potential by evaluating the evolutionary value of each feature sub-region online; a spatial distribution sparsity index is introduced. With regional uncertainty measurement This is used to comprehensively measure the evolutionary potential of a subregion, as follows:

[0058]

[0059]

[0060] in, Indicates that it is located in a sub-region Non-dominated solution set within; spatial sparsity Used to characterize the distribution density of solutions within a region, the larger the value, the sparser the distribution of solutions within that region, and thus the higher the potential for replenishment; Indicates the number of global searches. Subregion Number of times selected; regional uncertainty measure This value is used to characterize the degree of exploration of the area. The larger the value, the lower the degree of exploration of the area and the higher its exploration value. To explore weighting coefficients used to adjust the strength of the influence of uncertainty in the region selection process;

[0061] The region selection layer selects the target sub-region with the greatest evolutionary potential based on the following criteria:

[0062]

[0063] (3) Operator selection layer

[0064] In determining the target sub-region Subsequently, the operator selection layer, based on the accumulated historical search feedback online, selects from the multimodal local search operator set. Select the local search operator that performs best within the target sub-region; where Represents an operator;

[0065] The set of multimodal local search operators is designed based on the structural characteristics of critical and non-critical processes. The critical path is defined as the longest processing sequence from the start to the end of the operation; processes located on the critical path are defined as critical processes; and the remaining processes are defined as non-critical processes. The multimodal local search operators specifically include:

[0066] Randomly select a non-critical process and compare it with... After exchanging randomly selected non-critical processes to generate candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained.

[0067] Random selection Each process is processed and then reallocated to other feasible processing machines. After generating candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained.

[0068] Randomly select a process and compare it with... After exchanging processing machines for processes at the same processing stage, and generating candidate solutions, the solution that performs best in terms of maximum completion time, control relationship, and total energy consumption is retained.

[0069] Randomly select a key process and attempt to insert it into... After generating candidate solutions from randomly selected candidate locations, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained.

[0070] Randomly select a process and compare it with... After randomly selecting the positions of each process and exchanging them to generate candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained.

[0071] in, This represents the size of the neighborhood for the local search. This represents the total number of processes.

[0072] For each set of region-operator pairs Maintain the region-operator reward value separately. and operator call count And evaluate the operator online in the region Average performance within and uncertainty measurement ,as follows:

[0073]

[0074]

[0075] in, Operator In the region The number of calls within; The larger the value, the better the historical optimization performance of the operator in that region; The larger the value, the higher the exploration value of the operator in that region; We explore weighting coefficients for operators to adjust the influence of uncertainties in the operator selection process;

[0076] The operator selection layer selects the target region based on the following criteria. The optimal local search operator is as follows:

[0077]

[0078] (4) Online reward mechanism and parameter update

[0079] Based on the selected local search operator The generated candidate solution is relative to the original solution Based on the improvements made and considering the optimization focus of different target sub-regions, an immediate reward function is constructed:

[0080]

[0081] in, These represent the individual with the optimal completion time, the individual with the optimal allocation, and the individual with the optimal total energy consumption, respectively. To maximize the completion time, Represents an individual Maximum completion time Represents an individual Maximum completion time; Total energy consumption, Represents an individual energy consumption Represents an individual Energy consumption; Indicates a dominant relationship;

[0082] Subsequently, the region-operator reward matrix is ​​corrected using an incremental update method:

[0083]

[0084] in, Indicates the area Using operators The region-operator reward value;

[0085] Finally, synchronize and update external files. Statistical information for the region selection layer and the operator selection layer.

[0086] Furthermore, the second-stage environment selection strategy in step 6 is specifically as follows:

[0087] First, from the solution set Extract the multimodal solutions and add them to the multimodal archive;

[0088] Then, for the solution set Perform the first phase of environment selection;

[0089] Next, multimodal environment selection is performed on the multimodal file;

[0090] The multimodal environment selection includes the following steps:

[0091] Non-dominated solutions are extracted from the multimodal archive to form a candidate solution set; when the size of the candidate solution set is smaller than the preset multimodal archive size... When the candidate solution set is not less than the preset multimodal file size, the candidate solution set is used as the updated multimodal file size. At that time, the candidate solution set is divided into groups based on the objective function value. target clusters Each target cluster corresponds to a target vector in the target space; all non-empty target clusters are traversed sequentially, and in each round, a representative solution is selected from one target cluster and added to the updated multimodal archive, until the preset multimodal archive size is reached. Or all target clusters are empty.

[0092] Furthermore, step 5 includes:

[0093] Multimodal solutions are extracted from the first-stage population and incorporated into a multimodal archive. A multimodal solution refers to multiple scheduling schemes with significantly different decision-space structures, assuming identical target space performance and non-dominated behavior. The size of the multimodal archive is specified. .

[0094] Furthermore, the second-stage genetic strategy in step 6 specifically includes:

[0095] First, merge population and multimodal profiles;

[0096] Then, a binary tournament was used to select half of the parent individuals from the merged population to carry out the second-stage genetic strategy;

[0097] The second-stage genetic strategy includes: The probability of performing partial sequential crossover on the OS and uniform crossover on the MS is given by... The probability is used to perform reverse mutation on the OS and random machine replacement mutation on the MS. Otherwise, the Pareto solution set and Pareto front are output; wherein, the crossover probability is... Probability of mutation OS represents process sequence, and MS represents machine sequence.

[0098] Furthermore, the energy-saving strategy in step 6 specifically includes:

[0099] First, using a reverse traversal method, starting from the last process of the last workpiece, each process is shifted to the right sequentially from back to front; the right shift includes the following rules:

[0100] Rule 1: When the process is not the last pass, the start time after shifting to the right must not be later than the start time of the corresponding process in the next stage and the subsequent process on the same machine, and the minimum of the two shall be taken.

[0101] Rule 2 states that when the process is the last one, after shifting to the right, in addition to satisfying the two constraints in Rule 1, it must also be no later than the start time of the first stage of the next process, taking the minimum of the three.

[0102] The present invention has the following technical effects:

[0103] Methodological aspects:

[0104] 1. A population-multimodal archive co-evolutionary framework was constructed to achieve hierarchical management of the target space and decision space. The population is used to maintain the convergence and diversity of the target space, while the multimodal archive is used to store multimodal solutions, thereby enhancing the diversity of the decision space and the ability to preserve multimodal solutions.

[0105] 2. A dual-space environment selection strategy is proposed. In the target space, a decomposition-based multi-reference point environment selection strategy is adopted to enhance convergence performance. In the decision space, a multimodal environment selection mechanism is introduced to maintain the diversity of scheduling structure, thereby achieving a synergistic balance between target space convergence and decision space diversity.

[0106] 3. To address the problem characteristics of MMRHFSP, a set of multimodal local search operators was designed, and a hierarchical online learning architecture consisting of a region selection layer and an operator selection layer was constructed. The region selection layer evaluates the evolutionary potential of each target sub-region from a macroscopic perspective, guiding search resources to migrate to high-potential regions. The operator selection layer, based on historical search feedback, achieves dynamic matching between operator effectiveness and region characteristics, thereby improving the discovery capability of multimodal solutions.

[0107] 4. An improved IGDX index for discrete scheduling problems is proposed. By fusing Kendall tau sequence distance, which measures sequence differences, and Hamming distance, which measures allocation differences, it effectively makes up for the shortcomings of traditional indexes in reflecting the characteristics of discrete scheduling decision structure, thus more accurately evaluating the diversity performance of MMRHFSP in the decision space.

[0108] Application level:

[0109] 1. Compared with traditional flow shop scheduling methods, the method provided by this invention has the advantages of simple implementation, easy parameter adjustment, and excellent performance in terms of target space convergence and distribution, decision space diversity and multimodal solution discovery capability.

[0110] 2. This invention constructs an iterative scheduling optimization mechanism for the characteristics of reentrant hybrid flow workshops, performs unified modeling and collaborative optimization of rework paths and multiple entry processes in the production process, and mines and retains multimodal scheduling solutions with different structural features during the optimization process. This effectively reduces the time delay and energy consumption redundancy caused by process backflow and equipment waiting, while providing enterprises with diversified and optional scheduling schemes and improving the adaptability and robustness of scheduling results in complex production environments.

[0111] 3. This invention can adapt and dynamically adjust the scheduling scheme according to changes in production status for complex production tasks involving multiple processes and stages. Through the evolution and screening of multimodal solutions, the scheduling results can take into account different production preferences and energy consumption levels while meeting capacity and delivery constraints. This achieves multi-objective and multi-form comprehensive optimization of the scheduling scheme, which is conducive to enterprises maintaining stable and efficient operation and achieving energy conservation and consumption reduction under uncertain production conditions.

[0112] 4. This invention coordinates the load distribution relationship between different processing stages and heterogeneous equipment, and combines multimodal scheduling solutions to make multi-angle optimization decisions on production bottlenecks and resource blockages. This avoids local overload or resource idleness problems caused by a single scheduling structure, and enhances the continuity, stability and anti-disturbance capability of the production line. The diversified scheduling schemes obtained can be flexibly switched under different working conditions, effectively reducing equipment idling time and unnecessary energy consumption, thereby reducing resource waste and lowering overall production costs.

[0113] Therefore, the multimodal, multi-objective reentrant hybrid flow shop scheduling method provided by this invention effectively alleviates the conflict between completion time and energy consumption in complex flow shop scheduling through the collaborative search of multimodal scheduling solutions and multi-objective optimization mechanism. It provides diversified and optional high-efficiency and low-energy-consumption scheduling schemes for reentrant hybrid flow shops, and can improve scheduling efficiency and shorten overall completion time under different production conditions. Attached Figure Description

[0114] Figure 1 A schematic diagram illustrating the implementation process of this invention;

[0115] Figure 2 The method of this invention compares the AIGD index with a violin plot;

[0116] Figure 3 The method of this invention is used to compare violin plots of the AIIGDX index;

[0117] Figure 4 The method of this invention is used to compare the AHV index using a violin plot;

[0118] Figure 5 The method of this invention is compared with the radar chart of ANMOV and ANMS indicators. Detailed Implementation

[0119] Embodiments of the invention will now be described more fully below with reference to the accompanying drawings, which illustrate examples of the invention. However, the invention may be embodied in many different forms and should not be construed as 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 invention to those skilled in the art. Throughout the text, the same numerals denote the same elements.

[0120] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It will be further understood that, unless expressly defined herein, the terms used herein shall be interpreted as having the meaning consistent with their meaning in the context of this specification and the relevant field, and shall not be interpreted in an idealized or overly formal sense.

[0121] The specific implementation process of this invention is as follows:

[0122] A multimodal, multi-objective, reentrant hybrid flow shop scheduling method includes the following steps:

[0123] Step 1: Establish a multimodal, 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, while maximizing the number of multimodal solutions;

[0124] Step 2: Set the running parameters of the scheduling problem model;

[0125] Step 3: Based on the aforementioned operating parameters, generate a population using an initialization strategy and set the method runtime;

[0126] Step 4: Determine whether the first stage termination condition has been met based on the running time of the method. If not, execute the first stage evolution strategy and the first stage environment selection strategy for the population; otherwise, proceed to step 5.

[0127] Step 5: Extract multimodal solutions from the population and construct a multimodal profile;

[0128] Step 6: Determine whether the second-stage termination condition has been met based on the running time of the method. If not, execute the second-stage evolutionary strategy, environmental selection, energy-saving strategy, and genetic strategy on the population and multimodal archive; otherwise, output the Pareto solution set and Pareto front.

[0129] Preferably, the objective function of the problem model in step 1 is:

[0130]

[0131] in, To maximize the completion time, Total energy consumption.

[0132] Preferably, the parameters in step 2 include:

[0133] Population size Multimodal archive scale Crossover probability Probability of mutation Regional exploration coefficient and operator exploration coefficient ;

[0134] End time of Phase 1: ;

[0135] End time of Phase Two: ;

[0136] in, For the number of workpieces, ; For the number of times, ; For the number of stages, .

[0137] Preferably, step 3 includes:

[0138] The first phase of population adoption is based on The workpiece sequence is encoded for each pass, and the workpiece sequence is represented as follows: And an initial scheduling scheme is generated using a diversity heuristic method to allocate workpieces to each machine;

[0139] in, For workpiece sequence index, For the first One workpiece being processed. This is the last workpiece to be processed.

[0140] Preferably, the diversity heuristic method in step 3 is as follows:

[0141] First, the workpieces are arranged in non-ascending order according to the total processing time to generate a seed sequence. ;

[0142] Then, three workpiece insertion rules are used to generate a workpiece sequence. The three workpiece insertion rules include: ① an insertion rule aimed at minimizing the maximum completion time; ② an insertion rule aimed at minimizing total energy consumption; and ③ an insertion rule that simultaneously optimizes both the maximum completion time and total energy consumption.

[0143] After the workpiece is inserted, five machine allocation methods are used, including: ① Prioritizing the machine that allows the workpiece to complete processing earliest; if multiple machines meet the conditions, the machine with the lowest total energy consumption under this allocation is selected; ② Prioritizing the machine that allows the workpiece to complete processing earliest; if multiple machines meet the conditions, one machine is randomly selected; ③ Prioritizing the machine that minimizes total energy consumption; if multiple machines have the same energy consumption, the machine that completes processing earliest is selected; ④ Prioritizing the machine that minimizes total energy consumption; if multiple machines have the same energy consumption, one machine is randomly selected; ⑤ Prioritizing the machine with the lowest total load; if multiple machines have the same energy consumption, one machine is randomly selected.

[0144] By combining the above three insertion rules with five machine allocation methods, 15 individuals can be generated; the remaining... Each individual randomly generates a sequence of workpieces, which is then combined with the five machine allocation rules mentioned above.

[0145] This application uses a diversity heuristic method to maintain the overall diversity of the population while ensuring the quality of the initial solution.

[0146] Preferably, step 4 includes:

[0147] Determine whether the first phase termination time has been reached based on the running time. If the objective is not achieved, proceed to the first stage of evolutionary strategy and environment selection strategy; otherwise, execute step 5.

[0148] Preferably, the first-stage evolutionary strategy in step 4 is as follows:

[0149] A binary tournament is used to select half of the parent individuals from the population, and a first-stage genetic strategy is implemented on the population. The first-stage genetic strategy includes: performing partial sequential crossover on the workpiece sequence, performing reverse mutation on the workpiece sequence, and performing random replacement mutation on the machine allocation rule.

[0150] Preferably, the first-stage environment selection strategy in step 4 is as follows:

[0151] First, regarding the solution set Perform deduplication. The first stage uses the first deduplication method, and the second stage uses the second deduplication method.

[0152] The two deduplication methods are as follows:

[0153] The first deduplication method is based on the objective function value, removing individuals with the same objective function value; the second deduplication method is based on the scheduling sequence, removing individuals with the same scheduling sequence.

[0154] Then, min-max normalization is performed on each individual in the deduplicated solution set to obtain the normalized solution set. ;

[0155] Next, the set of unified solutions Perform a non-dominated sort and select individuals to join the population layer by layer according to the dominance level. If joining is done at the current dominance level... This led to the population size exceeding If so, the sub-region filtering strategy will be executed;

[0156] The sub-region filtering strategy includes the following steps:

[0157] The first quadrant of the target space [0, 90°] is uniformly divided into... Sub-regions ,in For any individual within the region Based on its polar angle in the target space The sub-region to which it belongs is determined, and the polar angle and region division formula are as follows:

[0158]

[0159]

[0160] For individuals in each subregion Calculate their distance to the ideal point respectively. The best time to completion And to the optimal total energy consumption The Euclidean distances are denoted as:

[0161]

[0162]

[0163]

[0164] The minimum value among the above distances is taken as the individual. Comprehensive evaluation indicators The calculation formula is as follows:

[0165]

[0166] Finally, each sub-region is evaluated based on the aforementioned comprehensive evaluation indicators. The size of the population is used to select representative individuals, thereby controlling the population size while maintaining the convergence of the target space and the balance of the distribution.

[0167] This application guides the population to converge faster through a first-stage evolutionary strategy, thereby enhancing the convergence and distribution of the target space.

[0168] Preferably, step 5 includes:

[0169] Multimodal solutions are extracted from the population in the first stage and incorporated into a multimodal archive. A multimodal solution refers to multiple scheduling schemes that, while having the same objective space performance and being non-dominated, exhibit significant differences in their decision space structure.

[0170] This application improves the ability of the method to preserve multimodal solutions by using multimodal archives.

[0171] Preferably, step 6 includes:

[0172] Determine whether the second phase termination time has been reached based on the running time. ;

[0173] If the target is not met, a second-stage evolutionary strategy is implemented for the population, and a second-stage environmental selection is used to update the population and multimodal profile. Then, an energy-saving strategy is adopted for the population and multimodal profile.

[0174] Finally, after every five iterations, the method performs a second-stage genetic operation and updates the population using a second-stage environmental selection strategy.

[0175] The second-stage population and multimodal archives employ joint encoding of process sequences and machine sequences, wherein the process sequences are denoted as... The machine sequence is denoted as ;

[0176] in, For process sequence index, This is the last processing step. Machine sequence index, The machine assigned to the last process.

[0177] Preferably, the second-stage evolutionary strategy in step 6 includes an adaptive local search strategy based on online learning, specifically:

[0178] (I) Target Space Partitioning and Mapping

[0179] First, using the same target space partitioning method as the first-stage environmental selection, the first quadrant of the target space is divided into three characteristic sub-regions: the low total energy consumption region. Balanced optimization region and areas with low completion time And introduce external non-dominated solution archives. It serves as a knowledge base for online learning, providing real-time data support for subsequent regional potential assessments and adaptive decision-making.

[0180] (ii) Regional selection layer decision-making

[0181] The region selection layer guides the adaptive allocation of search resources to sub-regions with higher potential by evaluating the evolutionary value of each feature sub-region online. To this end, a spatial distribution sparsity index is introduced. With regional uncertainty measurement This is used to comprehensively measure the evolutionary potential of a subregion, and its calculation method is as follows:

[0182]

[0183]

[0184] in, Indicates that it is located in a sub-region Non-dominated solution set within; spatial sparsity Used to characterize the distribution density of solutions within a region, the larger the value, the sparser the distribution of solutions within that region, and thus the higher the potential for replenishment; Indicates the number of global searches. Subregion Number of times selected; regional uncertainty measure This value is used to characterize the degree of exploration of a region. The higher the value, the lower the degree of exploration of the region and the higher its exploration value. To explore the weighting coefficients used to adjust the influence of uncertainty in the region selection process.

[0185] The region selection layer selects the target sub-region with the greatest evolutionary potential based on the following criteria:

[0186]

[0187] (III) Operator Selection Layer

[0188] In determining the target sub-region Subsequently, the operator selection layer, based on the accumulated historical search feedback online, selects from the multimodal local search operator set. Then select the local search operator that performs best within the target sub-region.

[0189] The set of multimodal local search operators is designed based on the structural characteristics of critical and non-critical processes. The critical path is defined as the longest processing sequence from the start to the end of the operation; processes located on the critical path are defined as critical processes; and the remaining processes are defined as non-critical processes. The multimodal local search operators specifically include:

[0190] Randomly select a non-critical process and compare it with... After exchanging randomly selected non-critical processes to generate candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained.

[0191] Random selection Each process is processed and then reallocated to other feasible processing machines. After generating candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained.

[0192] Randomly select a process and compare it with... After exchanging processing machines for processes at the same processing stage, and generating candidate solutions, the solution that performs best in terms of maximum completion time, control relationship, and total energy consumption is retained.

[0193] Randomly select a key process and attempt to insert it into... After generating candidate solutions from randomly selected candidate locations, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained.

[0194] Randomly select a process and compare it with... After randomly selecting the positions of each process and exchanging them to generate candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained.

[0195] in, This represents the size of the neighborhood for the local search. This represents the total number of processes.

[0196] For each set of region-operator pairs Maintain the region-operator reward value separately. and operator call count And evaluate the operator online in the region Average performance within and uncertainty measurement The calculation formula is as follows:

[0197]

[0198]

[0199] in, Operator In the region The number of calls within; The larger the value, the better the historical optimization performance of the operator in that region; The larger the value, the higher the exploratory value of the operator in that region. We explore weighting coefficients for operators to adjust the influence of uncertainty terms in the operator selection process.

[0200] The operator selection layer selects the target region based on the following criteria. The optimal local search operator is as follows:

[0201]

[0202] (iv) Online reward mechanism and parameter updates

[0203] Based on the selected local search operator The generated candidate solution is relative to the original solution Based on the improvements made and considering the optimization focus of different target sub-regions, an immediate reward function is constructed:

[0204]

[0205] in, These represent the individual with the optimal completion time, the individual with the optimal allocation, and the individual with the optimal total energy consumption, respectively. To maximize the completion time, Represents an individual Maximum completion time Represents an individual Maximum completion time; Total energy consumption, Represents an individual energy consumption Represents an individual Energy consumption; It indicates a dominant relationship.

[0206] Subsequently, the region-operator reward matrix is ​​corrected using an incremental update method:

[0207]

[0208] Finally, synchronize and update external files. Statistical information for the region selection layer and the operator selection layer.

[0209] This application improves the diversity of the decision space while maintaining the convergence of the target space through a second-stage evolutionary strategy, and enhances the method's ability to discover multimodal solutions.

[0210] Preferably, the second-stage environment selection strategy in step 6 is as follows:

[0211] First, from the solution set Extract the multimodal solutions and add them to the multimodal archive;

[0212] Then, for the solution set Perform the first phase of environment selection;

[0213] Next, multimodal environment selection is performed on the solution set multimodal archive;

[0214] Preferably, the multimodal environment selection includes the following steps:

[0215] Non-dominated solutions are extracted from the multimodal archive to form a candidate solution set; when the size of the candidate solution set is smaller than the preset multimodal archive size... When the candidate solution set is not less than the preset multimodal file size, the candidate solution set is used as the updated multimodal file size. At that time, the candidate solution set is divided into groups based on the objective function value. target clusters Each target cluster corresponds to a target vector in the target space; all non-empty target clusters are traversed sequentially, and in each round, a representative solution is selected from one target cluster and added to the updated multimodal archive, until the preset multimodal archive size is reached. Or all target clusters are empty.

[0216] This application balances the convergence of the objective space and the diversity of the decision space through a second-stage environmental selection strategy.

[0217] Preferably, the energy-saving strategy in step 6 is as follows:

[0218] First, a "reverse traversal" method is used, meaning that starting from the last process of the last workpiece, each process is shifted to the right sequentially from back to front. This right shift includes the following rules:

[0219] Rule 1: When the process is not the last pass, the start time after shifting to the right must not be later than the start time of the corresponding process in the next stage and the subsequent process on the same machine, and the minimum of the two shall be taken.

[0220] Rule 2 states that when the process is the last one, after shifting to the right, in addition to satisfying the two constraints in Rule 1, it must also be no later than the start time of the first stage of the next process, taking the minimum of the three.

[0221] This application further reduces the energy consumption of the solution set through energy conservation.

[0222] This application guides the population to converge faster through a first-stage evolutionary strategy, enhancing the convergence and distribution of the target space. A second-stage evolutionary strategy balances the convergence of the target space with the diversity of the decision space, and uncovers potential multimodal solutions. The invention is further described below with reference to specific embodiments:

[0223] The simulation experiment used 160 standard cases. All case parameters were randomly generated according to a uniform distribution. Specific settings are as follows: For small-scale cases, the number of workpieces... Number of stages Number of times Number of machines at each stage and workpiece processing time For large-scale examples, the range of the above parameters is extended to... , , , and .in, Indicates the interval A uniform distribution on the surface.

[0224] To verify the effectiveness of the hierarchical online learning-driven multimodal multi-objective meme method (HOLM3A) proposed in this invention, this paper selects seven representative multi-objective optimization methods for comparison, covering the following three categories: (1) Classical MOEAs: the genetic method combining Minkowski distance and local search (MLPGA), the improved multi-objective evolutionary method based on decomposition (IMOEA / D), and its improved version combined with local search strategy (IMOEA / D-LS); (2) MMOEAs for discrete scheduling optimization: the affinity propagation hierarchical meme method (APHMA) and the non-dominated sorting genetic method with multimodal solution preservation mechanism (NSGA-MSPM); (3) MMOEAs for continuous optimization: the evolutionary method based on hierarchical sorting method (HREA) and the differential evolution method based on similar niches (SNLSDE). To reduce the randomness of the experimental results and enhance the reliability of the statistical conclusions, each example was run independently 5 times, and its statistical results were used as the basis for the final performance evaluation. In terms of performance metrics, three commonly used metrics in the field of multi-objective optimization were adopted: Inverse Generation Distance (IGD), Hypervolume (HV), Improved Inverse Generation Distance in Decision Space (IIGDX), Average Number of Multimodal Objective Vectors (ANMOV), and Average Number of Multimodal Solutions (ANMS) as performance evaluation metrics. The calculation formulas for the three evaluation metrics are as follows:

[0225] (1) IGD

[0226] IGD is defined as a reference Pareto front. target vector To method Pareto Front The average of the nearest Euclidean distances to the target vector.

[0227]

[0228] in, yes The number of target vectors. The smaller the IGD value, the better the convergence and distribution of the method.

[0229] (2) HV

[0230] HV is defined as Relative to reference point Lebesgue measure of the dominated target space .

[0231]

[0232] A higher HV value indicates better overall performance of the method in the target space.

[0233] (3) IIGDX

[0234] The improved decision space inverse generation distance (IIGDX) is defined as the distance from the reference Pareto solution set. Decision variables in To method Pareto solution set The most recent decision variable =( , The average mixing distance.

[0235]

[0236] A smaller IIGDX value indicates better diversity of the method in the decision space.

[0237] The Kendalltau sequence distance was used to measure structural differences between operating systems (OS). To eliminate scale differences, the Kendalltau sequence distance was normalized.

[0238]

[0239]

[0240] in It is the set of adjacency commutation operators. It is Convert to Minimum number of swaps required; and These represent the minimum and maximum Kendall tau sequence distances between OSes, respectively.

[0241] The Hamming distance is used to measure the difference between MSs, and the corresponding normalized form is as follows:

[0242]

[0243]

[0244] in, It is an indicator function; it returns 1 if the condition is true, and 0 otherwise. and These are the minimum and maximum Hamming distances between MS, respectively.

[0245] (4) ANMOV

[0246] The formulas for calculating ANMOV and ANMS are as follows:

[0247]

[0248]

[0249] in, Indicates the number of cases. Representation method In the The intersection of the Pareto solution set obtained in each example and the reference Pareto solution set. This represents the corresponding set of target vectors. Indicates the first The target vector is shared in each case. The set of decision variables. A larger ANMOV value indicates that the method identifies more multimodal target vectors; a larger ANMS value reflects the method's stronger ability to discover and maintain multimodal solutions.

[0250] Figures 2-5 The optimization results of each comparison method are presented intuitively on different computational examples. Specifically, from... Figures 2-4 The average IGD (AIGD), average HV (AHV), and average IIGDX (AIIGDX) in the data show that HOLM3A has lower AIGD, AHV, and AIIGDX values ​​in all examples, which indicates the superior performance of the proposed method in terms of convergence and distribution in the target space and diversity in the decision space. Figure 5 The ANMOV and ANMS of HOLM3A are significantly higher than those of the comparative methods, indicating that the proposed method has a significant advantage in multimodal solution discovery and preservation capabilities.

[0251] 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 multimodal, multi-objective, reentrant hybrid flow shop scheduling method, wherein the method is based on a hierarchical online learning-driven multimodal, multi-objective meme method, characterized in that... Includes the following steps: Step 1: Establish a multimodal, 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, while maximizing the number of multimodal solutions; Step 2: Set the running parameters of the scheduling problem model; Step 3: Based on the aforementioned operating parameters, generate a population using an initialization strategy and set the method runtime; Step 4: Determine whether the first stage termination condition has been met based on the running time of the method. If not, execute the first stage evolution strategy and the first stage environmental selection strategy on the population; otherwise, execute step 5. The first stage evolution strategy is as follows: select half of the parent individuals from the population using a binary tournament and execute the first stage genetic strategy on the population. The first-stage genetic strategy includes: performing partial sequential crossover on the workpiece sequence, performing reverse mutation on the workpiece sequence, and performing random replacement mutation on the machine allocation rule; the first-stage environment selection strategy specifically includes: firstly, performing partial sequential crossover on the solution set... Deduplication is performed; the first stage uses the first deduplication method, and the second stage uses the second deduplication method. The first deduplication method is based on the objective function value, removing individuals with the same objective function value; the second deduplication method is based on the scheduling sequence, removing individuals with the same scheduling sequence. Then, each individual in the deduplicated solution set is subjected to min-max normalization to obtain the normalized solution set. Next, the normalization solution set Perform a non-dominated sort and select individuals to join the population layer by layer according to the dominance level; if joining is done at the current dominance level... This led to the population size exceeding If so, the sub-region filtering strategy will be executed; Step 5: Extract multimodal solutions from the population and construct a multimodal profile; Step 6: Determine whether the second-stage termination condition has been met based on the running time of the method. If not, execute the second-stage evolutionary strategy, environment selection, energy-saving strategy, and genetic strategy on the population and multimodal archive; otherwise, output the Pareto solution set and Pareto front. The second-stage evolutionary strategy includes an adaptive local search strategy based on online learning. The second-stage environment selection strategy specifically involves: first, from the solution set... Extract the multimodal solutions and add them to the multimodal archive; then, process the solution set... Perform the first-stage environment selection; then, perform multimodal environment selection on the multimodal file.

2. The method according to claim 1, characterized in that, Step 3 includes: The first phase of population adoption is based on The workpiece sequence code for each pass, wherein the workpiece sequence is: And an initial scheduling scheme is generated using a diversity heuristic method to allocate workpieces to each machine; in, For workpiece sequence index, For the first One workpiece being processed. The last workpiece to be processed; The number of times the Tao is mentioned.

3. The method according to claim 1, characterized in that, Step 6 includes: Determine whether the second phase termination time has been reached based on the running time. ; If the target is not met, a second-stage evolutionary strategy is implemented for the population, and a second-stage environmental selection strategy is adopted to update the population and multimodal profile. Then, an energy-saving strategy is adopted for the population and multimodal profile to further reduce energy consumption. Every five iterations, a second-stage genetic operation is performed, and a second-stage environmental selection strategy is used to update the population and multimodal profile. The second-stage population and multimodal profile are jointly encoded using process sequences and machine sequences, wherein the process sequences are... The machine sequence is ; in, For process sequence index, This is the last processing step. Machine sequence index, The machine assigned to the last process, and the end time of the second stage. ; in, For the number of workpieces, For the number of times, This refers to the number of stages.

4. The method according to claim 2, characterized in that, The diversity heuristic method in step 3 is as follows: The workpieces are first arranged in non-ascending order according to the total processing time to generate a seed sequence. ; Then, three workpiece insertion rules are used to generate a workpiece sequence. The three types of workpiece insertion rules include: an insertion rule aimed at minimizing the maximum completion time; an insertion rule aimed at minimizing total energy consumption; and an insertion rule that simultaneously optimizes both the maximum completion time and total energy consumption. After the workpiece insertion is completed, five machine allocation methods are adopted, namely: (1) Select the machine that can complete the processing of the workpiece earliest; when there are multiple machines that meet the conditions, select the machine with the lowest total energy consumption under this allocation. (2) Select the machine that can make the workpiece finish processing the earliest; when there are multiple machines that meet the conditions, randomly select one machine. (3) Select the machine that minimizes total energy consumption; when there are multiple machines with the same energy consumption, select the machine that can complete the processing earliest. (4) Select the machine that minimizes total energy consumption; if there are multiple machines with the same energy consumption, randomly select one machine. (5) Select the machine with the lowest total load; when there are multiple machines with the same energy consumption, randomly select one machine. By combining the above three workpiece insertion rules with five machine allocation methods, 15 individuals can be generated; the remaining... Each individual randomly generates a workpiece sequence, which is then combined with the five machine allocation methods mentioned above; among them, Indicates population size.

5. The method according to claim 1, characterized in that, The sub-region filtering strategy includes the following steps: The first quadrant of the target space [0, 90°] is uniformly divided into... Sub-regions The number of sub-regions , Indicates a region. Indicates the first There are regions; for the i-th individual within a region... , and Let these represent the first and second target values ​​of the i-th individual, respectively; based on their polar angles in the target space... The sub-region to which it belongs is determined, and the polar angle and region division formula are as follows: ； For individuals in each subregion Calculate their distance to the ideal point respectively. European distance The best time to completion European distance And to the optimal total energy consumption Euclidean distance They are respectively: ； ； ； The minimum value among the above distances is taken as the individual. Comprehensive evaluation indicators ,for: ； Each sub-region is based on the aforementioned comprehensive evaluation indicators The size is used to select representative individuals.

6. The method according to claim 2, characterized in that, The second-stage evolutionary strategy in step 6 is as follows: (1) Target space partitioning and mapping; First, using the same target space partitioning method as the first-stage environmental selection, the first quadrant of the target space is divided into three characteristic sub-regions: the low total energy consumption region. Balanced optimization region and areas with low completion time Furthermore, an external non-dominated solution archive A is introduced as a knowledge base for online learning, providing real-time data support for subsequent regional potential assessment and adaptive decision-making. (2) Regional selection layer decision-making; The region selection layer guides search resources to adaptively allocate to sub-regions with higher potential by evaluating the evolutionary value of each feature sub-region online; a spatial distribution sparsity index is introduced. With regional uncertainty measurement This is used to comprehensively measure the evolutionary potential of a subregion, as follows: ； in, Indicates that it is located in a sub-region Non-dominated solution set within; spatial sparsity Used to characterize the distribution density of solutions within a region, the larger the value, the sparser the distribution of solutions within that region, and thus the higher the potential for replenishment; Indicates the number of global searches. Subregion Number of times selected; regional uncertainty measure This value is used to characterize the degree of exploration of the area. The larger the value, the lower the degree of exploration of the area and the higher its exploration value. To explore weighting coefficients used to adjust the strength of the influence of uncertainty in the region selection process; The region selection layer selects the target sub-region with the greatest evolutionary potential based on the following criteria: ； (3) The operator selection layer determines the target sub-region Subsequently, the operator selection layer, based on the accumulated historical search feedback online, selects from the multimodal local search operator set. Select the local search operator that performs best within the target sub-region; where Represents an operator; The set of multimodal local search operators is designed based on the structural characteristics of critical and non-critical processes. The critical path is defined as the longest processing sequence from the start to the end of the operation; processes located on the critical path are defined as critical processes; and the remaining processes are defined as non-critical processes. The multimodal local search operators specifically include: Randomly select a non-critical process and compare it with... After exchanging randomly selected non-critical processes to generate candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained. Random selection Each process is processed and then reallocated to other feasible processing machines. After generating candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained. Randomly select a process and compare it with... After exchanging processing machines for processes at the same processing stage, and generating candidate solutions, the solution that performs best in terms of maximum completion time, control relationship, and total energy consumption is retained. Randomly select a key process and attempt to insert it into... After generating candidate solutions from randomly selected candidate locations, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained. Randomly select a process and compare it with... After randomly selecting the positions of each process and exchanging them to generate candidate solutions, the solution that performs best in terms of maximum completion time, dominance relationship, and total energy consumption is retained. in, This represents the size of the neighborhood for the local search. This represents the total number of processes. For each set of region-operator pairs Maintain the region-operator reward value separately. and operator call count And evaluate the operator online in the region Average performance within and uncertainty measurement ,as follows: ； in, Operator In the region The number of calls within; The larger the value, the better the historical optimization performance of the operator in that region; The larger the value, the higher the exploration value of the operator in that region; We explore weighting coefficients for operators to adjust the influence of uncertainties in the operator selection process; The operator selection layer selects the target region based on the following criteria. The optimal local search operator is as follows: ； (4) Online reward mechanism and parameter updates; Based on the selected local search operator The generated candidate solution is relative to the original solution Based on the improvements made and considering the optimization focus of different target sub-regions, an immediate reward function is constructed: ； in, These represent the individual with the optimal completion time, the individual with the optimal allocation, and the individual with the optimal total energy consumption, respectively. To maximize the completion time, Represents an individual Maximum completion time Represents an individual Maximum completion time; Total energy consumption, Represents an individual energy consumption Represents an individual Energy consumption; Indicates a dominant relationship; Subsequently, the region-operator reward matrix is ​​corrected using an incremental update method: ； in, Indicates the region Using operators The region-operator reward value; Finally, update external files simultaneously. Statistical information for the region selection layer and the operator selection layer.

7. The method according to claim 2 or 6, characterized in that, The multimodal environment selection includes the following steps: Non-dominated solutions are extracted from the multimodal archive to form a candidate solution set; when the size of the candidate solution set is smaller than the preset multimodal archive size... When the candidate solution set is not less than the preset multimodal file size, the candidate solution set is used as the updated multimodal file size. At that time, the candidate solution set is divided into groups based on the objective function value. target clusters Each target cluster corresponds to a target vector in the target space; all non-empty target clusters are traversed sequentially, and in each round, a representative solution is selected from one target cluster and added to the updated multimodal archive, until the preset multimodal archive size is reached. Or all target clusters are empty.

8. The method according to claim 1, characterized in that, Step 5 includes: Multimodal solutions are extracted from the first-stage population and incorporated into a multimodal archive. A multimodal solution refers to multiple scheduling schemes with significantly different decision-space structures, assuming identical target space performance and non-dominated behavior. The size of the multimodal archive is specified. .

9. The method according to claim 2, characterized in that, The second-stage genetic strategy in step 6 is as follows: First, merge population and multimodal profiles; Then, a binary tournament was used to select half of the parent individuals from the merged population to carry out the second-stage genetic strategy; The second-stage genetic strategy includes: The probability of performing partial sequential crossover on the OS and uniform crossover on the MS is given by... The probability of performing reverse mutation on the OS and random machine replacement mutation on the MS is given; otherwise, the Pareto solution set and Pareto front are output; wherein, the crossover probability is given. Probability of mutation OS represents process sequence, and MS represents machine sequence.

10. The method according to any one of claims 1-6, characterized in that, The energy-saving strategy in step 6 is as follows: First, using a reverse traversal method, starting from the last process of the last workpiece, each process is shifted to the right sequentially from back to front; the right shift includes the following rules: Rule 1: When the process is not the last pass, the start time after shifting to the right must not be later than the start time of the corresponding process in the next stage and the subsequent process on the same machine, and the minimum of the two shall be taken. Rule 2 states that when the process is the last one, after shifting to the right, in addition to satisfying the two constraints in Rule 1, it must also be no later than the start time of the first stage of the next process, taking the minimum of the three.

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