Multi-objective job shop scheduling optimization method and system based on double-layer elite evolution

Abstract

The application discloses a multi-objective job shop scheduling optimization method and system based on double-layer elite evolution, constructs a dynamic self-adaptive mutation operator, realizes dynamic balance of global exploration and local development through an exponential decay mechanism and population diversity feedback, designs a double-layer elite reservation strategy, uses an internal elite pool to guarantee convergence, uses a historical elite pool to maintain diversity, and effectively alleviates a high-dimensional solution space degradation problem, introduces an entropy weight method dynamic weighting model, automatically adjusts weight distribution based on objective function information entropy, and realizes multi-objective optimization trade-off. In the standard test set and automobile parts production line industrial verification, compared with NSGA-II and SPEA2, the convergence index HV is increased by more than 10%, the solution set distribution breadth IGD is reduced by more than 25%, and the calculation time is shortened by more than 60%, and the optimization performance and engineering practicability of the multi-objective job shop scheduling are significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing and production scheduling technology, specifically involving a multi-objective job shop scheduling optimization method based on two-layer elite evolution, and also involving a multi-objective job shop scheduling optimization system based on two-layer elite evolution. Background Technology

[0002] With the deepening of Industry 4.0 and intelligent manufacturing, manufacturing systems are facing unprecedented challenges of complexity and dynamism. As a core issue in manufacturing system optimization, the job shop scheduling problem directly impacts a company's production efficiency, resource utilization, energy consumption, and operating costs. Traditional single-objective scheduling methods focus only on single indicators such as completion time, making it difficult to meet the comprehensive optimization needs of modern manufacturing for multiple dimensions such as efficiency, energy consumption, cost, and delivery time. Therefore, multi-objective job shop scheduling problems have emerged and become a research hotspot in operations research, computer science, and industrial engineering.

[0003] The essence of the multi-objective job shop scheduling problem is to seek a dynamic balance among multiple conflicting optimization objectives. For example, minimizing the maximum completion time often requires increasing machine operating speed, but this may lead to increased energy consumption; while reducing energy consumption may require reducing processing speed or increasing idle time, thereby extending the completion time. This non-cooperative game-like characteristic between objectives makes the problem highly complex and challenging.

[0004] Currently, the mainstream algorithms for solving multi-objective job shop scheduling problems can be divided into three categories: The first category is exact algorithms based on mathematical programming, such as branch and bound and dynamic programming. These methods can find the optimal solution for small-scale problems, but as the problem size increases, the computational complexity grows exponentially, making them difficult to apply to real-world production scenarios. The second category is heuristic algorithms based on problem characteristics, such as priority scheduling rules and neighborhood search algorithms. These methods are computationally efficient, but the quality of the solution depends on the quality of the rule design and is prone to getting trapped in local optima. The third category is metaheuristic algorithms based on population evolution, such as genetic algorithms, particle swarm optimization, and evolutionary algorithms. These methods have good global search capabilities and are currently the mainstream research and application direction.

[0005] In the field of multi-objective evolutionary algorithms, the non-dominated sorting genetic algorithm NSGA-II and the intensity Pareto evolutionary algorithm SPEA2 are the two most representative classic algorithms. NSGA-II was proposed by Kalyanmoy Deb in 2002. It achieves a good balance between convergence and diversity of solution set through non-dominated sorting and crowding comparison mechanism. This algorithm performs well in low-dimensional multi-objective optimization problems and is widely used in industrial scheduling, path planning, resource allocation and other fields. However, NSGA-II has the following inherent defects: (1) It adopts a fixed mutation probability and cannot dynamically adjust the search strategy according to the population evolution state. It is prone to premature convergence in complex multimodal problems; (2) The crowding comparison mechanism fails in high-dimensional objective space and it is difficult to maintain the uniform distribution of solution set; (3) It lacks a local search mechanism for problem characteristics and has limited convergence accuracy.

[0006] The SPEA2 algorithm, proposed by Zitzler et al. in 2001, improves convergence accuracy by introducing external archiving and density estimation techniques. This algorithm utilizes the dominance of strength-based solutions and controls the solution set distribution using k-nearest neighbor density estimation. Compared to NSGA-II, SPEA2 performs better on complex Pareto front problems, but its computational complexity is as high as O(MN²), where M is the number of targets and N is the population size. When dealing with large-scale, high-dimensional problems, the computational cost of SPEA2 increases significantly, making it difficult to meet the real-time requirements of industrial applications. Furthermore, SPEA2 is highly sensitive to parameters such as the archive size; improper parameter settings can lead to a severe deterioration in solution set quality.

[0007] In recent years, researchers have proposed a series of improved methods to address the above problems. For example, hybrid genetic algorithms incorporate local search operators into the evolutionary framework, enhancing local exploitation capabilities; adaptive parameter adjustment methods dynamically adjust crossover and mutation probabilities according to the evolutionary stage; and the decomposition-based multi-objective evolutionary algorithm MOEA / D decomposes the multi-objective problem into several single-objective sub-problems for parallel solution. However, existing methods still suffer from the following technical bottlenecks: (1) The problem of balancing global exploration and local development: The mutation probability of existing methods is usually fixed or only changes monotonically with the number of generations. It cannot be adaptively adjusted according to the actual diversity state of the population, resulting in the loss of population diversity in the later stage of evolution and the algorithm stagnation in local optima.

[0008] (2) Degeneration problem of high-dimensional solution space: As the objective dimension and the number of decision variables increase, the solution set distribution of the Pareto front becomes sparse. The traditional elite preservation mechanism is difficult to guarantee convergence and diversity at the same time, and high-quality solutions are easily lost in the evolution process.

[0009] (3) Static limitations of multi-objective trade-offs: Existing methods rely on static rules for objective weight allocation or diversity maintenance strategies, such as preset weight vectors or fixed density estimation. This makes it difficult to adapt to changes in high-dimensional dynamic data, resulting in an uneven distribution of the solution set across different objective dimensions.

[0010] (4) Real-time constraints in industrial scenarios: Existing algorithms have high time and space complexity, which makes it difficult to meet the requirements of actual production for the speed of generating scheduling schemes in scenarios such as automotive parts processing and semiconductor manufacturing that require minute-level response.

[0011] Therefore, designing a multi-objective job shop scheduling optimization method that can adaptively balance global exploration and local development, effectively maintain the diversity of high-dimensional solution sets, intelligently weigh multi-objective conflicts, and meet the real-time requirements of industry is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0012] The purpose of this invention is to provide a multi-objective job shop scheduling optimization method based on two-layer elite evolution, which solves the problems of insufficient solution set diversity and low computational efficiency of existing NSGA-II and SPEA2 algorithms when dealing with high-dimensional complex job shop scheduling problems.

[0013] The first technical solution adopted in this invention is a multi-objective job shop scheduling optimization method based on two-layer elite evolution. The core innovative mechanisms include a dynamic adaptive mutation operator, a two-layer elite retention strategy, and an entropy weighting dynamic weighting model. The three mechanisms work together to achieve breakthroughs in three dimensions: convergence speed, solution set distribution, and computational efficiency.

[0014] I. Dynamic Adaptive Mutation Operator Traditional evolutionary algorithms use a fixed mutation probability, resulting in a lack of adaptability in the search behavior. This invention designs a dynamic adaptive mutation operator that introduces an evolutionary state awareness mechanism, establishing a dynamic mapping relationship between mutation probability and population diversity, enabling intelligent switching between global exploration and local development.

[0015] The core of this operator lies in the dual dynamic factor regulation: the first is the time decay factor, which adopts the Logistic function model to make the mutation probability decrease non-linearly with the number of iterations, ensuring that the algorithm has a high exploration ability in the early stage of the search and focuses on local fine search in the later stage; the second is the diversity compensation factor, which is based on the ratio of the population's average Euclidean distance to the historical maximum distance. When the population diversity is lower than the threshold, the mutation probability is actively increased to prevent premature convergence.

[0016] In its implementation, this invention constructs a multi-level mutation operator pool: when the mutation probability is high, Gaussian mutation is used to generate random perturbations conforming to a normal distribution, enabling a wide-range search; when the mutation probability is moderate, non-uniform mutation is used to perform offset operations in the boundary regions of the solution space, enhancing local fine-grained search; when the mutation probability is low, bit-flip mutation is used to maintain the basic diversity of the population. This hierarchical strategy enables the algorithm to automatically select the most suitable mutation operation according to the current search stage.

[0017] II. Two-tiered elite retention strategy A single elite pool is prone to losing high-quality solutions due to capacity limitations when processing high-dimensional data. The two-layer elite retention strategy proposed in this invention constructs a dual guarantee mechanism for convergence and diversity through the collaborative work of an internal elite pool and a historical elite pool.

[0018] An internal elite pool stores non-dominated solutions from the current generation, with a maximum capacity of 20% of the population size. This pool employs a strict Pareto dominance update rule: a replacement operation is triggered only when a new individual is superior to an existing elite in the pool in terms of Pareto dominance. This mechanism ensures that the internal elite pool always represents the current optimal search direction, providing stable guidance for algorithm convergence.

[0019] A historical elite pool records high-quality solutions across generations, with a capacity of 5% to 10% of the population size. Each historical solution carries a time decay weight, whose influence gradually decreases with each generation to avoid the excessive influence of outdated solutions. Individuals in the HEP with low overlap with the current solution space are selected using cosine similarity. These solutions represent historically superior patterns that differ from the current search direction and can inject new genetic information into the population.

[0020] Elite-guided crossover is a crucial step in the collaborative work of the two elite pools: with a 30% probability, a parent is selected from the HEP (Higher Elite Pool) and crossover is performed with elites from the IEP (Independent Elite Pool). This knowledge reuse mechanism injects historically superior patterns into the current population, effectively mitigating the risk of losing high-quality solutions while maintaining the diversity of the solution set.

[0021] III. Dynamic Weighting Model Using Entropy Weighting Method Traditional multi-objective algorithms rely on static rules for weight allocation or diversity maintenance strategies, making them ill-suited for adapting to high-dimensional dynamic data. This invention introduces an information entropy-driven weight allocation mechanism, dynamically adjusting weights by calculating the information entropy of the objective function in real time, thereby achieving multimodal adaptive focusing.

[0022] The core of this mechanism lies in the fact that information entropy reflects the degree of disorder in a system. The larger the entropy value, the smaller the discreteness of the objective function and the less information it contains, and its weight should be reduced accordingly. The algorithm recalculates the information entropy of each objective at regular intervals and allocates weights based on the reciprocal of the entropy value, so that search resources are automatically tilted towards objectives with low information content and sparse distribution.

[0023] To prevent search oscillations caused by sudden weight changes, this invention introduces an inertia factor to smooth out weight variations. Compared to the static weight strategy of traditional methods, this mechanism enables the algorithm to dynamically adjust multi-objective trade-offs based on the actual distribution of the solution set, significantly improving convergence accuracy in complex Pareto front scenarios.

[0024] Based on the above objectives, the technical solution adopted in this invention is as follows: A multi-objective job shop scheduling optimization method based on two-layer elite evolution is used to construct a dynamic adaptive mutation operator, achieving a dynamic balance between global exploration and local development through an exponential decay mechanism and population diversity feedback; a two-layer elite retention strategy is designed, utilizing an internal elite pool to ensure convergence and a historical elite pool to maintain diversity; an entropy weight method dynamic weighting model is introduced, automatically adjusting the weight allocation based on the information entropy of the objective function to achieve an optimal trade-off between multiple objectives; the specific process is as follows: Step 1: Problem Modeling and Population Initialization Construct a mathematical model for the multi-objective job shop scheduling problem and determine the optimization objectives (including but not limited to minimizing the maximum completion time). and minimize total energy consumption The system includes constraints (including process sequence constraints, machine exclusivity constraints, transport time constraints, and machine availability constraints). A two-stage real-number encoding strategy is adopted, with each chromosome representing a scheduling scheme. The initial population is generated using the Latin hypercube sampling method to ensure the uniformity of the initial coverage of the solution space.

[0025] Step 2: Dynamic Adaptive Mutation A dynamic adaptive mutation operator is constructed based on the population evolution state. A time decay factor and a diversity compensation factor are introduced to dynamically adjust the mutation probability. The corresponding operator is selected from the multi-level mutation operator pool to perform the mutation operation and generate the offspring population. Step 3: Non-dominated sorting and crowding calculation The parent and offspring populations are merged into a temporary population, and a fast non-dominated sort is performed to divide the Pareto front hierarchy. Then, for individuals within the same front hierarchy, their crowding distance is calculated to measure the distribution density of individuals in the target space. Step 4: Construct a two-tiered elite retention strategy The non-dominated solution set of the current generation is stored in the internal elite pool IEP, and the high-quality solutions of previous generations are stored in the historical elite pool HEP. Individuals in HEP ​​with an overlap of less than 0.3 with the current population are selected by cosine similarity. Parents are selected from them with a 30% probability and cross-crossed with the elites in IEP, thereby injecting the historical good patterns into the current population. Step 5: Dynamic weighting using entropy weight method The objective function value of the current population is normalized, the information entropy of each objective is calculated, dynamic weights are allocated according to the entropy value, and the weights of the previous generation and the newly calculated weights are weighted and averaged by the inertia factor to smooth weight changes and prevent search oscillations. Step 6: Environmental Selection and Population Regeneration By combining elite retention with weighted crowding comparison, the next generation of individuals is selected from the temporary population. Individuals with higher non-dominant levels are prioritized; within the same level, a comprehensive density estimate is calculated using dynamic weights, and individuals with higher comprehensive density are selected to maintain diversity. Step 7: Determine the termination condition.

[0026] Step 7: Determine if the termination condition is met. If yes, output the Pareto optimal solution set as the optimal scheduling scheme; otherwise, return to step 2.

[0027] The invention is further characterized in that, The population is initialized using a two-stage real number encoding strategy as follows: Each chromosome represents a scheduling scheme. The first segment is the process sequence code (OS), with a length equal to the total number of processes. Each position represents a process, and its value is the job number. The order in which the same job number appears indicates which process it is. The second segment is the machine allocation code (MS), with the same length as the OS. Each position's value is the machine number selected for the corresponding process, and this machine must belong to the candidate machine set for that process. The initial population is generated using the Latin hypercube sampling method, and the population size is... N Adjust dynamically based on the complexity of the problem.

[0028] Step 2, which involves constructing the dynamic adaptive mutation operator, specifically includes: The mutation probability is jointly regulated by introducing a time decay factor and a diversity compensation factor. The mutation probability is calculated using the following formula:

[0029] in, t For the current generation, T This represents the total number of iterations. The maximum mutation probability, This is the attenuation rate control coefficient. This marks a mid-evolutionary turning point, where D(t) represents the average Euclidean distance of the current population. This is the highest average distance in history. This is the diversity compensation coefficient; Based on the calculated probability of variation The corresponding operator is selected from the multi-level mutation operator pool to perform the mutation operation, and the offspring population is obtained, as follows: when Gaussian mutation is used to generate random perturbations that conform to a Gaussian distribution and add them to the current individual; When 0.2 < When the value is ≤0.5, non-uniform variation is used, with probability... The individual dimensions are perturbed, with the perturbation amplitude decreasing with the number of iterations, as shown in the formula. ;in, The result is a uniformly random number, taking values ​​in the range [0,1]. To control the disturbance decay rate for system parameters, This represents the range of values ​​that the variable can take in the current dimension, i.e., the difference between the upper and lower bounds of the variable. when When the value is ≤0.2, random flipping mutations are performed on the binary encoded gene loci.

[0030] In step 3, the parent and offspring populations are merged into a temporary population, and a fast non-dominated sort is performed on the temporary population to define the Pareto front hierarchy. The specific process for performing the fast non-dominated sort on the temporary population is as follows: (1) For each individual in the population The number of other individuals who dominate this individual is denoted as . (i.e., how many individuals are compared to) (better), and record the The set of individuals under control ; (2) All optimal solutions that are not dominated by any other individual, i.e. Individuals with a value of 0 constitute the first Pareto front layer. ; (3) For Each individual in traverse its dominated set Individuals in ,Will of Decrease the value by 1; if after decrementing by 1 of If it becomes 0, it means It is no longer dominated by any unprocessed individuals, and is placed into the next frontier layer. ; (4) Repeat step (3) until all individuals have been assigned to the corresponding front layer; After stratification, the crowding distance is calculated for individuals within the same frontal layer, using the following method: For each objective function (such as completion time or energy consumption), individuals within that layer are sorted in ascending order of their objective function values. The individuals at the beginning and end of the sorted layer, i.e., those with the smallest and largest values ​​for that objective function, are called boundary individuals. Their crowding distance is set to an infinite number to ensure that they can be retained in subsequent selections, thereby maintaining the boundary coverage of the Pareto front. For the i-th individual in the middle, its position at the 1st... k The congestion component on each target is calculated as follows: That is, the difference in function values ​​of two adjacent individuals on the target, divided by the difference between the maximum and minimum values ​​of the target across the entire frontier layer; An individual's total congestion distance is equal to the sum of the congestion components in all target directions.

[0031] The two-tiered elite retention strategy in step 4 specifically includes: An internal elite pool (IEP) and a historical elite pool (HEP) are constructed. The capacity of the internal elite pool (IEP) is 10% to 20% of the population size, and it is used to store the non-dominated solution set F1 of the current generation. The update rules of the internal elite pool (IEP) are as follows: when the number of individuals in the pool has not reached the capacity limit, all non-dominated solutions F1 can be added; when the pool is full and a new non-dominated solution is added, if the new individual Pareto dominates an old individual in the pool, the new individual replaces the old individual; if the new individual does not dominate any individual in the pool, their crowding distance is compared, and the individual with the higher crowding distance is retained. The historical elite pool (HEP) has a capacity of 5% to 10% of the population size and is used to record high-quality solutions across generations. Each high-quality solution across generations carries a time decay weight. ,in To solve the existing algebra, The attenuation coefficient; Using cosine similarity Individuals in the historical elite pool (HEP) with an overlap of less than 0.3 with the current solution space are selected. Parents from the HEP are chosen with a 30% probability to participate in elite-guided crossover. The crossover formula is as follows:

[0032] in, These are vector representations of two individuals. This is the mixing coefficient, which is dynamically adjusted during evolution and ranges from 0.1 to 0.5. The parent generation is represented by the above capacity ratio and crossover probability values, which were determined through parameter sensitivity experiments: when the HEP capacity is below 5%, historical superior patterns are lost too quickly, and the diversity of the solution set decreases; when it is above 10%, old solutions cause interference and convergence, and the overall HV index decreases by 2% to 3%. A crossover probability of 30% corresponds to the balance point between elite guidance strength and population diversity (experimental data are shown in Example 5).

[0033] The entropy weighting method dynamic weighting model in step 5 specifically includes: In the current population N individual m The objectives (m=2 in this embodiment, i.e., maximum completion time and total energy consumption) are normalized using the following formula:

[0034] in, Indicates the first in the population i The individual in the first j Function values ​​on each target; Calculate the first j Information entropy of a target, information entropy The value range is [0,1]:

[0035] Calculate the first based on information entropy. j Dynamic weights of each objective :

[0036] Each interval The weights are updated once, and the inertia factor is used. Smoothing weight mutations:

[0037] in, This represents the total number of iterations.

[0038] Step 6 is as follows: (1) Prioritize individuals with higher non-dominant levels, i.e., select from F1, F2, ... in sequence; (2) When individuals are selected sequentially according to the Pareto front layer order (from F1, F2, ...), if a certain front layer F k If the number of individuals in a layer exceeds the remaining capacity of the next generation population, meaning that not all individuals in that layer can be added, then the overall density estimate for those individuals in that layer is calculated using dynamic weights: ,in For individuals i In the jCrowding distance on each target; select individuals with higher overall density to join the new population in order to maintain the diversity of the solution set.

[0039] The second technical solution adopted in this invention is a multi-objective job shop scheduling optimization system based on two-layer elite evolution, comprising: The data acquisition module is used to obtain workpiece information, machine information, processing time data, and energy consumption parameters for workshop scheduling issues. The population initialization module is used to generate the initial population using a two-stage real number encoding strategy; The dynamic mutation module is used to dynamically adjust the mutation probability and perform adaptive mutation operations based on the population's evolutionary state. The non-dominated sorting module is used for fast non-dominated sorting and crowding calculation of the population; The dual-layer elite pool module includes an internal elite pool and a historical elite pool, used to store and filter elite individuals; The dynamic weighting module is used to calculate the dynamic weights of each objective function based on the entropy weighting method. The environment selection module is used to select the next generation of population by combining elite retention and weighted crowding comparison; The output module is used to output the Pareto optimal solution set and the corresponding Gantt chart scheduling scheme.

[0040] The system is integrated into a manufacturing execution system or industrial internet platform to achieve data interconnection with the shop floor digital twin system and supports real-time rescheduling triggered by dynamic events.

[0041] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0042] Compared with the prior art, the present invention has the following beneficial effects: (1) Significantly improved convergence performance. Through the global exploration and local development balance mechanism of the dynamic adaptive mutation operator, and the stable guidance of the convergence direction by the two-layer elite retention strategy, the experiment on the standard test function set of this invention shows that the hypervolume index HV is improved by more than 8.7% on average compared with NSGA-II, and the reverse generation distance IGD is reduced by more than 25.3% on average, proving that the algorithm can more accurately approximate the real Pareto front.

[0043] (2) Excellent ability to maintain solution set diversity. The historical elite pool mechanism in the two-layer elite retention strategy effectively prevents the degradation problem of high-dimensional solution space. Experimental data show that the spacing index and the distribution index Δ decreased by an average of 31.2% and 28.6% in all test cases. Especially in the degradation front scenario, the Δ value dropped sharply from 1.15 to 0.68, which verifies the explicit control effect of the present invention on the solution set distribution.

[0044] (3) Significantly improved computational efficiency. This invention optimizes the non-dominated sorting process through a neighborhood comparison strategy, reducing the time complexity from the traditional O(MN²) to O(MN log N). In a 100-dimensional benchmark test, the CPU time efficiency is improved by 65%-75% compared to NSGA-II, and the peak memory usage is reduced by 52.3%, which can meet the real-time requirements of scheduling scheme generation in industrial settings.

[0045] (4) Excellent adaptability to industrial scenarios. In the industrial verification of automotive parts production lines, the scheduling scheme generated by this invention effectively reduced the production delay rate and energy consumption costs. When faced with dynamic disturbances such as the insertion of urgent orders, the backup scheduling scheme in the two-layer elite pool shortened the system reconfiguration time by 37%, fully verifying the robustness and engineering practicality of the algorithm.

[0046] (5) Multi-objective optimization trade-off capability. The entropy weight method dynamic weighting model enables the algorithm to adaptively adjust the optimization focus according to the actual distribution of the solution set. In semiconductor manufacturing scheduling, when the load of a certain type of equipment is detected to exceed the threshold, the model automatically increases the weight of the equipment utilization target, guiding the algorithm to generate a more balanced scheduling scheme, and the standard deviation of equipment utilization is reduced by 21.3%.

[0047] In summary, this invention constructs a multi-objective optimization solution for complex industrial scenarios through the synergistic innovation of dynamic adaptive mutation operators, a two-layer elite retention strategy, and an entropy weighting dynamic weighting model, providing methodological support for real-time decision-making in intelligent manufacturing systems. Attached Figure Description

[0048] Figure 1 This is the overall flowchart of the multi-objective job shop scheduling optimization method based on two-layer elite evolution of the present invention.

[0049] Figure 2 This is a schematic diagram illustrating the working mechanism of the dynamic adaptive mutation operator in this invention.

[0050] Figure 3 This is an interactive schematic diagram of the two-layer elite retention strategy in this invention.

[0051] Figure 4 This is a flowchart of the calculation process of the dynamic weighted model using the entropy weight method in this invention.

[0052] Figure 5 This is a comparison chart of the HV index convergence curves of EVNS-NSGAII, NSGA-II, and SPEA2 on the DTLZ test function set in this embodiment of the invention.

[0053] Figure 6This is a Pareto front contrast scatter plot in an embodiment of the present invention, showing the energy consumption distribution of the present invention EVNS-NSGAII and the contrast algorithm in the target space. Detailed Implementation

[0054] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0055] Example 1 The application scenarios of this invention's multi-objective job shop scheduling optimization method based on two-layer elite evolution are as follows: Step S1: Problem Modeling and Population Initialization This step first constructs a mathematical model of the multi-objective job shop scheduling problem. Consider a flexible job shop scheduling scenario involving n jobs and m machines. Each job... (i=1,...,n) contains The process has strict sequential constraints, and each process... (j=1,..., It can be processed on any machine in its candidate machine set, and the processing time and energy consumption may vary on different machines.

[0056] This embodiment sets two optimization objectives: minimizing the maximum completion time ( And minimizing total energy consumption. Maximum completion time is defined as the time required to complete the last operation of all workpieces, calculated using the following formula: ,in Let be the completion time of workpiece i.

[0057] Total energy consumption comprises four components: processing energy consumption, idle energy consumption, transportation energy consumption, and standby energy consumption. Processing energy consumption is the energy actually consumed by each process on the selected machine; idle energy consumption is the energy consumed when the machine is working but not processing; transportation energy consumption is generated by automated guided vehicles (AGVs) transporting workpieces between machines; and standby energy consumption is the basic energy consumption of the machine when it is idle. The formula for calculating total energy consumption is:

[0058] The constraints include: (1) Process sequence constraint: The processes for the same workpiece must be executed in a predetermined order, that is, the processes... Must be in the process You can only begin after this is completed; (2) Machine exclusivity constraint: A machine can only process one operation at a time; (3) Transportation time constraints: There must be sufficient transportation time interval between consecutive processes of the same workpiece so that the AGV can transport the workpiece from the previous machine to the next machine; (4) Machine availability constraint: Each machine is available at the initial moment and can only process one process at a time.

[0059] A two-segment real-number encoding strategy is adopted, with each chromosome representing a scheduling scheme. The first segment is the Operation Sequence Code (OS), with a length equal to the total number of operations. Each position represents an operation, and its value is the job number. The order in which the same job number appears indicates which operation the job is in. The second segment is the Machine Assignment Code (MS), with the same length as the OS. The value at each position is the machine number selected for the corresponding operation, and this machine must belong to the candidate machine set for that operation.

[0060] The initial population is generated using the Latin hypercube sampling method. The population size N is dynamically adjusted according to the problem complexity; in this embodiment, it is set to 200. Latin hypercube sampling can ensure the uniformity of the initial coverage of the solution space, and compared with random initialization, it can effectively avoid excessive clustering of initial solutions in local regions.

[0061] Step S2: Dynamic Adaptive Mutation Operation Please see Figure 2 This step performs an adaptive mutation operation on each individual in the current population Pt. Mutation probability. The calculation formula is as follows, which is regulated by two dynamic factors:

[0062] in: t The current generation number is T, and the maximum number of iterations is T (set to 500 in this example). The maximum mutation probability is set to 0.3 in this embodiment; β is the decay rate control coefficient, which is set to 0.1 in this embodiment; γ is the mid-evolutionary turning point. In this embodiment, it is set to 0.5, which means that the mutation probability is maintained at a high level in the first 50% of the evolutionary stage and gradually decreases in the latter 50%. The average Euclidean distance of the current population reflects the degree of dispersion of the population. The historical maximum average distance is used for normalization; The diversity compensation coefficient is set to 0.05 in this embodiment.

[0063] Population diversity When the diversity compensation factor is below a certain threshold of its historical maximum value, The time decay factor increases, actively raising the mutation probability to increase population diversity and prevent premature convergence. Conversely, when population diversity is sufficient, this factor is smaller, and the mutation probability is mainly determined by the time decay factor.

[0064] Based on the calculated probability of variation Select the corresponding operator from the multi-level mutation operator pool to perform the mutation operation: when When the value is greater than 0.5, Gaussian mutation is used to generate a result that conforms to... A random perturbation of the distribution is added to the current individual, where δ decreases dynamically with the number of iterations. δ0 is the initial standard deviation, which is set to 0.1 in this embodiment; When 0.2 < When the variance is ≤0.5, non-uniform variation is used: using probability... The individual dimensions are perturbed, with the perturbation amplitude decreasing with the number of iterations, as shown in the formula. Where r is a uniformly random number in the range [0,1]. b To control the disturbance decay rate for system parameters; when When the value is ≤0.2, bit flipping mutation is used: the binary encoded gene bits are randomly flipped to maintain the basic diversity of the population.

[0065] The offspring population is generated through the above dynamic adaptive mutation operation. .

[0066] Step S3: Non-dominated sorting and crowding calculation This step will involve the parent generation. with offspring The populations are merged into a temporary population Rt with a size of 2N=400. A fast non-dominated sort is then performed on Rt, and Pareto fronts are defined.

[0067] The specific process of non-dominated sorting is as follows: (1) Initialization: for each individual Calculate two parameters: (Dominate (number of individuals) and (quilt (The set of dominant individuals); (2) Find all Individuals with a value of 0 are placed in the first frontier layer F1; (3) For each individual in F1 traverse its dominated set Individuals in ,Will of Subtract 1, if If it becomes 0, then... Place it into the next leading edge layer F2; (4) Repeat the above process until all individuals have been stratified.

[0068] To reduce time complexity, this invention employs a neighborhood comparison strategy: when comparing the dominance relationship between two individuals, comparisons are only made within the set of individuals that are neighbors of the current individual in the target space, rather than traversing the entire population. This strategy reduces the traditional O(MN²) time complexity to O(MN log N), where M is the target number (M=2 in this embodiment) and N is the population size.

[0069] For individuals within the same frontal layer, their crowding distance is calculated. The crowding distance reflects the distribution density of that individual with its neighbors in the target space. For the k-th target of the i-th individual, its crowding component is calculated as the difference between neighboring individuals on that target divided by the difference between the maximum and minimum values ​​of that target. The overall crowding distance of individual i is the sum of the crowding components along all target directions. Boundary individuals (those that take extreme values ​​on all targets) have their crowding set to infinity to ensure they are preserved.

[0070] Step S4: Two-tier elite retention strategy Please see Figure 3 This step constructs a two-layer elite retention strategy, which ensures the convergence and diversity of the solution set through the collaborative work of the internal elite pool and the historical elite pool.

[0071] Internal Elite Pool (IEP): With a maximum capacity of 20% of the population size (40 individuals), it stores the non-dominated solution set F1 from the current generation Rt. This pool employs a strict Pareto dominance update rule: a replacement operation is triggered when a new individual is superior to an existing elite in the pool in terms of Pareto dominance; if the new individual and existing individuals are not mutually dominant, crowding is compared, and the individual with greater crowding is retained. This mechanism ensures that the internal elite pool always represents the current optimal search direction.

[0072] Historical Elite Pool (HEP): This pool comprises 5% to 10% of the population size; in this example, it contains 15 individuals and records high-quality solutions across generations. Each high-quality solution carries a time-decay weight. , where g is the generation number of the solution and λ is the decay coefficient (set to 0.1 in this embodiment). As the generation increases, the influence of old solutions gradually decreases, avoiding the excessive influence of outdated solutions.

[0073] The elite solution interaction mechanism includes three stages: (1) Similarity matching: through cosine similarity Individuals in the HEP with an overlap of less than 0.3 with the current solution space are selected. These solutions represent historically superior patterns that differ from the current search direction and can inject new genetic information into the population.

[0074] (2) Elite-guided crossover: With a 30% probability, a parent is selected from the HEP and crossover is performed with the elites in the IEP. The crossover formula is:

[0075] in, θ This is the mixing coefficient, which is dynamically adjusted during the evolution process. The initial value is 0.5, and it gradually decreases to 0.1 as the number of generations increases, indicating that in the later stages, it relies more on the patterns in the historical elite pool for fine-tuning.

[0076] (3) Restarting stagnant individuals: For individuals that have not improved for 5 consecutive generations, a restart operation is applied, that is, a new individual is randomly generated in the neighborhood of the individual in order to escape the local optimum.

[0077] Step S5: Dynamic weighted model using entropy weight method Please see Figure 4 This step dynamically calculates the weights of each optimization objective based on the information entropy theory, thereby achieving intelligent trade-offs among multiple objectives.

[0078] Suppose the current population P contains N individuals (N=200), and there are m optimization objectives (m=2 in this example). The dynamic weight calculation process is as follows: Step S5.1: Target Space Normalization Normalize the j-th objective function value: in Let be the function value of the i-th individual on the j-th objective.

[0079] Step S5.2: Information Entropy Calculation The information entropy of the j-th target is: Information entropy The value of entropy ranges from [0,1]. The larger the entropy value, the smaller the dispersion of the objective function, the smaller the individual differences in the objective, and the less information it contains; conversely, the smaller the entropy value, the greater the information content.

[0080] Step S5.3: Dynamic weight allocation Weight of the j-th objective for: This formula gives higher weight to targets with greater information (lower entropy), guiding the algorithm to tilt search resources toward targets with sparse current distribution.

[0081] Step S5.4: Weight Smoothing Update. To avoid search oscillations caused by sudden weight changes, the weights are updated every τ generations and smoothed using an inertia factor: in = max(10, 0.1T) = 50, =0.9. This mechanism gives the weight changes a certain degree of memory, maintaining the stability of the search direction.

[0082] Step S6: Environmental Selection and Population Renewal This step selects N=200 individuals from the temporary population Rt (size 2N=400) to form the next generation population Pt+1.

[0083] The environment selection strategy combines the advantages of elite retention and tournament selection: (1) Prioritize individuals with higher non-dominant levels, i.e., select from F1, F2, ... in sequence; (2) When a certain frontier layer cannot be fully incorporated, the overall density estimate of the individuals within that layer is calculated using dynamic weights: in Let be the crowding distance of individual i on the j-th objective. Individuals with higher overall density are selected to join the new population to maintain the diversity of the solution set.

[0084] This selection strategy ensures both the convergence of the Pareto front (by prioritizing higher-level fronts) and the uniformity of distribution within the front through weighted crowding.

[0085] Step S7: Termination condition determination The algorithm terminates if any of the following conditions are met: (1) Reaching the maximum number of generations =500; (2) The quality of the solution set has not improved significantly for 20 consecutive generations, that is, the rate of change of the hypervolume index HV is less than the threshold. .

[0086] After the algorithm terminates, the non-dominated solution set in the final population is output as the Pareto optimal scheduling scheme. At the same time, a corresponding Gantt chart is generated to intuitively show the processing sequence and time arrangement of each machine.

[0087] Example 2: Detailed Implementation of the Dynamic Adaptive Mutation Operator This embodiment provides a detailed description of the specific implementation of the dynamic adaptive mutation operator.

[0088] The core of the dynamic adaptive mutation operator lies in the real-time calculation of mutation probability and the collaborative work of multi-level mutation operators. The values ​​of the parameters in the mutation probability calculation formula are as follows: = 0.3: Maximum mutation probability, used in the early stages of evolution or when population diversity is severely insufficient; = 0.01: Minimum mutation probability, used in the later stages of evolution to maintain basic exploration capabilities; = 0.1: Decay rate control coefficient, which controls the rate at which the mutation probability decreases from its maximum value to its minimum value; = 0.5: Mid-evolutionary turning point, indicating that when t / T = 0.5, the time decay factor takes the median value; = 0.05: Diversity compensation coefficient, which controls the contribution of diversity compensation factor.

[0089] Time decay factor It is a sigmoid function (Logistic function), when t / T < hour, ≈ The mutation probability remains at a high level; when t / T > hour, It rapidly decreases to near zero. This non-linear decay characteristic allows the algorithm to have ample exploratory capabilities in the early stages, while focusing on local development in the later stages.

[0090] Diversity compensation factor In this context, the average Euclidean distance D(t) of the population is calculated as follows:

[0091] in, For individuals and The Euclidean distance between them; The maximum value of D(t) from generation 1 to the current generation is used for normalization.

[0092] When population diversity declines Decrease Increasing the size of the population enhances the effect of the compensating factor, leading to a higher overall mutation probability. This actively introduces new genetic variations, preventing the population from falling into local optima.

[0093] The detailed implementations of the three mutation operators in the multi-level mutation operator pool are as follows: Gaussian mutation: applicable The high probability of variation stage. For individual x = ( , , ..., Perform the following for each component:

[0094] in, For the first i Standard deviation of dimension , The initial coefficient is 0.1. and The first i The upper and lower bounds of a dimension.

[0095] Non-uniform variation: applicable to 0.2 < The intermediate variation probability stage is ≤ 0.5. For each component, a probability is given. implement:

[0096] Where τ is a random value that can be 0 or 1. r is a uniformly random number in the range [0,1], and b is a system parameter (taken as 2). This function can generate a large perturbation in the early stages of evolution, and the perturbation amplitude decreases in the later stages of evolution, achieving a local fine-grained search. This represents the range of values ​​that the variable can take in the current dimension, i.e., the difference between the upper and lower bounds of the variable.

[0097] Bit flip mutation: applicable The low mutation probability stage is ≤ 0.2. For binary-coded individuals, with probability... Flip each gene position: 0 becomes 1, 1 becomes 0.

[0098] Example 3: Detailed Implementation of a Two-Layer Elite Retention Strategy This embodiment provides a detailed description of the specific implementation of the two-layer elite retention strategy.

[0099] Maintenance of the internal elite pool (IEP): The maximum capacity of the IEP is NIEP = 0.2N = 40. After the non-dominated sorting is completed in each generation, all individuals in the front layer F1 are added to the IEP. If the number of individuals in the IEP exceeds the number of individuals in the NIEP, they are retained according to the following priority: (1) individuals with lower non-dominated levels are given priority; (2) when the non-dominated levels are the same, individuals with higher crowding are given priority. When a new individual is added to the IEP, its Pareto dominance relationship with existing individuals in the pool is checked: if the new individual dominates an individual in the pool, it is replaced; if it is dominated, it is not added; if they do not dominate each other, the crowding is compared, and the individual with higher crowding is retained.

[0100] Maintenance of the Historical Elite Pool (HEP): The maximum capacity of the HEP is NHEP = 0.05N = 10. At the end of each generation, the top 10% of the most fit individuals in the current population are added to the HEP. Each individual in the HEP carries a time-decay weight. , where g is the generation number of an individual in the HEP, and λ is the decay coefficient (taken as 0.1). When the number of individuals in the HEP exceeds that in the NHEP, the individual with the lowest weight is eliminated.

[0101] Elite-guided cross-disciplinary approach: With probability = 0.3 Parents are selected from HEP and cross-referenced with elites from IEP. The selection of HEP parents is based on cosine similarity:

[0102] Calculate the cosine similarity between each individual in the HEP and the current population centroid (mean of each dimension), and select individuals with a similarity of less than 0.3 as candidate parents. These individuals represent historically superior patterns that differ significantly from the current population.

[0103] The elite-guided cross-fertilization formula is:

[0104] in θ The mixing coefficient is initially 0.5, and decreases linearly to 0.1 with increasing generations.

[0105] Stall restart mechanism: For each individual, record its consecutive unimproved generations, `stagnation_generation`. If `stagnation_generation` ≥ 5, perform a restart operation on that individual: randomly generate a new individual within its neighborhood, specifically by adding uniformly distributed values ​​to each dimension of the individual. random perturbations, of which After restarting, stagnation_generation is reset to 0.

[0106] Example 4: Industrial Scenario Verification This embodiment demonstrates the industrial application of the method of the present invention in a real-world automotive parts production line setting.

[0107] Experimental scenario setting: The gearbox housing processing workshop of an automotive parts manufacturing company contains 8 processing equipment (including CNC milling machines, drilling machines, heat treatment furnaces, grinding machines, cleaning machines, coordinate measuring machines, etc.), and needs to process 5 different types of gearbox housing workpieces. Each workpiece contains 6 processes, for a total of 30 processes. The optimization objective is: (1) Minimize the maximum completion time. (2) Minimize total energy consumption, including equipment processing energy consumption, idle energy consumption and AGV transportation energy consumption.

[0108] Comparison algorithm settings: - NSGA-II: Population size 200, number of iterations 500, crossover probability 0.9, fixed mutation probability 1 / 30; - SPEA2: Population size 200, archive size 200, number of iterations 500, crossover probability 0.9, mutation probability 1 / 30; - EVNS-NSGAII (this invention): population size 200, number of iterations 500, crossover probability 0.9, dynamic mutation probability pm(t)∈[0.01,0.3].

[0109] Please see Figure 5 The figure shows the HV convergence curves of the three algorithms during the iteration process. As can be seen from the figure, NSGA-II experiences premature convergence around generation 200, with the HV value stabilizing around 0.71; SPEA2 converges more slowly, reaching HV=0.76 around generation 350; while the present invention, EVNS-NSGAII, reaches HV=0.79 at generation 150 and continues to improve to 0.83 at generation 450. Compared to NSGA-II and SPEA2, the present invention improves the HV index by 16.9% and 9.2%, respectively.

[0110] In the time-optimal solution, machine utilization is high and the process arrangement is compact. The total operating time is 42.5 hours, but the total energy consumption is 385 kWh. In the optimal energy consumption scheme, the machine load is balanced, and idle periods are set between processes to reduce peak power. The time required is 51.2 hours, with a total energy consumption of 312 kWh, representing a 19.0% energy saving compared to the optimal time-based solution. Users can weigh the options between the two based on their actual production needs.

[0111] Please see Figure 6 This paper compares the Pareto front distribution of three algorithms in the target space. As can be seen from the figure, the solution set of NSGA-II is mainly distributed in the central region of the target space, with fewer solutions at the two boundary points, exhibiting obvious "solution set gaps"; the solution set of SPEA2 is more evenly distributed, but its convergence is insufficient, with some solutions being far from the true front; the solution set of the present invention, EVNS-NSGAII, has both good convergence and distribution, with the Pareto front completely covering the entire target space, and even at the inflection point region (…). The higher distribution density (around 45h, Energy ≈340kWh) provides decision-makers with a wider range of choices.

[0112] Table 1 presents the statistical results (mean ± standard deviation) of the performance metrics of the three algorithms in 10 independent runs: Table 1. Comparison of Performance Metrics of Three Algorithms

[0113] As shown in Table 1, this invention improves the HV index by 16.9% and 9.8% compared to NSGA-II and SPEA2, respectively; reduces the IGD index by 38.5% and 27.3%, respectively; reduces the Spacing index by 38.0% and 23.2%, respectively; and shortens the runtime by 36.9% compared to NSGA-II and 71.2% compared to SPEA2. All indicators are statistically significant (Wilcoxon rank-sum test, p<0.05).

[0114] Example 5: Sensitivity Analysis of Algorithm Parameters This embodiment performs sensitivity analysis on key parameters in the algorithm of the present invention, providing guidance on parameter setting for practical applications.

[0115] Population size N: Five population settings (N=50, 100, 200, 300, and 500) were tested. Experimental results show that the algorithm achieves optimal performance (HV=0.832) when N=200; HV=0.798 when N=100, a decrease of 4.1%; and HV=0.825 when N=500, comparable to N=200 but with a 120% increase in computation time. It is recommended that the population size be set between 100 and 300.

[0116] Maximum mutation probability : Tested Five settings were provided: 0.1, 0.2, 0.3, 0.4, and 0.5. Experimental results show that... Performance is optimal when the value is 0.3; When the value is too small (0.1), the exploration ability is insufficient, HV=0.761; When the value is too large (0.5), convergence is unstable, HV=0.788. Recommendation: Set it between 0.25 and 0.35.

[0117] Attenuation coefficient : Tested Five settings were provided: 0.05, 0.1, 0.15, 0.2, and 0.25. Experimental results show that... Performance is optimal when the value is 0.1; When the age is too small, the mutation probability decreases slowly, and in the later stages, diversity is maintained excessively. When the size is too large, the mutation probability drops rapidly, leading to insufficient exploration. Recommendation: Set between 0.08 and 0.15.

[0118] Mixing coefficient Initial value: Tested Five settings were provided: 0.3, 0.4, 0.5, 0.6, and 0.7. Experimental results show that... Performance is optimal when the value is 0.5; The impact of the historical elite pool is too great when the time is too short, resulting in unstable convergence. When the pool of historical elites is too large, its contribution is insufficient, leading to a decrease in diversity. Recommendation: Set it between 0.4 and 0.6.

[0119] Example 6: Comparison with other improved algorithms This embodiment compares the present invention with other improved multi-objective evolutionary algorithms proposed in recent years, including: MOEA / D (decomposition-based multi-objective evolutionary algorithm), NSGA-III (reference point-assisted NSGA-II), and RVEA (reference vector-guided evolutionary algorithm).

[0120] The experiment used three standard test problems: DTLZ1, DTLZ3, and DTLZ7. The number of objectives was m=3, the number of decision variables was n=12, the population size was N=100, and the number of iterations was T=500. Each algorithm was run independently 30 times, and the mean HV index was calculated. Table 2 shows the comparison results: Table 2: Comparison of HV metrics for different algorithms on the DTLZ test problem

[0121] As shown in Table 2, the HV index of this invention is superior to the comparative algorithms on all three test problems, with a particularly significant advantage on DTLZ3 (high-dimensional multimodal problem), where it improves by 6.3%, 4.4%, and 2.8% compared to MOEA / D, NSGA-III, and RVEA, respectively. This verifies the effectiveness of the dynamic adaptive mutation operator of this invention in handling multimodal problems, and the advantage of the two-layer elite preservation strategy in maintaining the diversity of high-dimensional solution sets.

[0122] Example 7: System Integration and Application This embodiment describes a specific implementation of integrating the method of the present invention into a manufacturing execution system or an industrial internet platform.

[0123] The multi-objective job shop scheduling optimization system based on two-layer elite evolution provided by this invention includes the following modules: (1) Data acquisition module: It connects to the workshop equipment control system (PLC, SCADA) through the industrial Internet of Things interface to obtain equipment status, processing progress and energy consumption data in real time. At the same time, it reads production data such as work order information, process route and bill of materials from the manufacturing execution system (MES).

[0124] (2) Population initialization module: Based on the collected data, a scheduling problem model is constructed, and an initial population is generated using a two-stage real number encoding strategy. It supports loading high-quality initial solutions from the historical scheduling scheme library to accelerate convergence.

[0125] (3) Dynamic mutation module: Based on the population evolution status, the mutation probability is dynamically adjusted, adaptive mutation operation is performed, and offspring population is generated.

[0126] (4) Non-dominated sorting module: Performs fast non-dominated sorting and crowding calculation on the population, and adopts a neighborhood comparison strategy to reduce time complexity.

[0127] (5) Two-layer elite pool module: It includes an internal elite pool and a historical elite pool, which are used to store and select elite individuals. The internal elite pool ensures the stability of the convergence direction, while the historical elite pool maintains the diversity of solution sets and supports knowledge reuse.

[0128] (6) Dynamic weighting module: The dynamic weights of each objective function are calculated based on the entropy weight method, and the optimization focus is adaptively adjusted according to the actual distribution of the solution set.

[0129] (7) Environmental selection module: Combine elite retention with weighted crowding comparison to screen the next generation of population.

[0130] (8) Output module: Outputs the Pareto optimal solution set and the corresponding Gantt chart scheduling scheme, supporting scheme comparison and visualization.

[0131] In scenarios triggered by dynamic events (such as equipment failure or emergency order insertion), the system obtains real-time status changes through a digital twin interface and triggers incremental rescheduling. Backup scheduling schemes in the historical elite pool can generate alternative schemes within 15 minutes, significantly improving response efficiency compared to manual scheduling.

[0132] Example 8: Storage Medium Implementation The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method of the present invention. The storage medium can be any medium capable of storing program code, such as ROM, RAM, magnetic disk, optical disk, or flash memory.

[0133] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A multi-objective job shop scheduling optimization method based on two-layer elite evolution, characterized in that, A dynamic adaptive mutation operator is constructed to achieve a dynamic balance between global exploration and local development through an exponential decay mechanism and population diversity feedback. A two-layer elite retention strategy is designed, which uses an internal elite pool to ensure convergence and a historical elite pool to maintain diversity. An entropy weight method dynamic weighting model is introduced to automatically adjust the weight allocation based on the information entropy of the objective function to achieve multi-objective optimization.

2. The multi-objective job shop scheduling optimization method based on two-layer elite evolution as described in claim 1, characterized in that, The specific operating steps are as follows: Step 1: Construct a mathematical model for the multi-objective job shop scheduling problem, determine the set of optimization objectives and constraints, and initialize the population using a two-stage real number encoding strategy; Step 2: Construct a dynamic adaptive mutation operator based on the population evolution state, introduce a time decay factor and a diversity compensation factor to dynamically adjust the mutation probability, and perform adaptive mutation operation to generate offspring population; Step 3: Merge the parent and offspring populations into a temporary population, perform fast non-dominated sorting, and divide the individuals in the population into different Pareto front levels; then, for individuals within the same front level, calculate their crowding distance to measure the distribution density of individuals in the target space. Step 4: Construct a two-layer elite retention strategy, storing the selected elite individuals into an internal elite pool and a historical elite pool respectively, and using cosine similarity to select high-quality cross-generational solutions, guiding elite crossover with a preset probability; Step 5: Dynamically calculate the information entropy of the optimization target based on the entropy weight method, automatically assign target weights according to the entropy value, and provide weighted guidance for the crowding comparison in the environment selection process; Step 6: Combining elite preservation with weighted crowding comparison, select the next generation of individuals from the temporary population, prioritizing individuals with higher non-dominant levels; Step 7: Determine if the termination condition is met. If yes, output the Pareto optimal solution set as the optimal scheduling scheme; otherwise, return to step 2.

3. The multi-objective job shop scheduling optimization method based on two-layer elite evolution as described in claim 2, characterized in that, The optimization objectives of the multi-objective job shop scheduling problem in step S1 include minimizing the maximum completion time. and minimize total energy consumption Total energy consumption This includes processing energy consumption, idle energy consumption, transportation energy consumption, and standby energy consumption; constraints include process sequence constraints, machine exclusivity constraints, and automated guided vehicle (AGV) transportation time constraints. The population is initialized using a two-stage real number encoding strategy as follows: Each chromosome represents a scheduling scheme. The first segment is the process sequence code (OS), with a length equal to the total number of processes. Each position represents a process, and its value is the job number. The order in which the same job number appears indicates which process it is. The second segment is the machine allocation code (MS), with the same length as the OS. Each position's value is the machine number selected for the corresponding process, and this machine must belong to the candidate machine set for that process. The initial population is generated using the Latin hypercube sampling method, and the population size is... N Adjust dynamically based on the complexity of the problem.

4. The multi-objective job shop scheduling optimization method based on two-layer elite evolution according to claim 2, characterized in that, Step 2, which involves constructing the dynamic adaptive mutation operator, specifically includes: The mutation probability is jointly regulated by introducing a time decay factor and a diversity compensation factor. The mutation probability is calculated using the following formula: in, t For the current generation, T This represents the total number of iterations. The maximum mutation probability, This is the attenuation rate control coefficient. This marks a mid-evolutionary turning point, where D(t) represents the average Euclidean distance of the current population. This is the highest average distance in history. This is the diversity compensation coefficient; Based on the calculated probability of variation The corresponding operator is selected from the multi-level mutation operator pool to perform the mutation operation, and the offspring population is obtained, as follows: when Gaussian mutation is used to generate random perturbations that conform to a Gaussian distribution and add them to the current individual; When 0.2 < When the value is ≤0.5, non-uniform variation is used, with probability... The individual dimensions are perturbed, with the perturbation amplitude decreasing with the number of iterations, as shown in the formula. ;in, The result is a uniformly random number, taking values ​​in the range [0,1]. To control the disturbance decay rate for system parameters, This represents the range of values ​​that the variable can take in the current dimension, i.e., the difference between the upper and lower bounds of the variable. when When the value is ≤0.2, random flipping mutations are performed on the binary encoded gene loci.

5. The multi-objective job shop scheduling optimization method based on two-layer elite evolution according to claim 2, characterized in that, In step 3, the parent and offspring populations are merged into a temporary population, and a fast non-dominated sort is performed on the temporary population to define the Pareto front hierarchy. The specific process of performing the fast non-dominated sort on the temporary population in step 3 is as follows: (1) For each individual in the population The number of other individuals who dominate this individual is denoted as . and record The set of individuals under control ; (2) All optimal solutions that are not dominated by any other individual, i.e. Individuals with a value of 0 constitute the first Pareto front layer. ; (3) For Each individual in traverse its dominated set Individuals in ,Will of Decrease the value by 1; if after decrementing by 1 of If it becomes 0, it means It is no longer dominated by any unprocessed individuals, and is placed into the next frontier layer. ; (4) Repeat step (3) until all individuals have been assigned to the corresponding front layer; After stratification, the crowding distance is calculated for individuals within the same frontal layer, using the following method: For each objective function, individuals within that layer are sorted in ascending order of their objective function values. The individuals at the beginning and end of the sorted layer, i.e., those with the smallest and largest values ​​for that objective function, are called boundary individuals. Their crowding distance is set to an infinite number to ensure that they can be retained in subsequent selections, thereby maintaining the boundary coverage of the Pareto front. For the i-th individual in the middle, its position at the 1st... k The congestion component on each target is calculated as follows: An individual's total congestion distance is equal to the sum of the congestion components in all target directions.

6. The multi-objective job shop scheduling optimization method based on two-layer elite evolution according to claim 2, characterized in that, The two-tiered elite retention strategy in step 4 specifically includes: An internal elite pool (IEP) and a historical elite pool (HEP) are constructed. The capacity of the internal elite pool (IEP) is 10% to 20% of the population size, and it is used to store the non-dominated solution set F1 of the current generation. The update rules of the internal elite pool (IEP) are as follows: when the number of individuals in the pool has not reached the capacity limit, all non-dominated solutions F1 can be added; when the pool is full and a new non-dominated solution is added, if the new individual Pareto dominates an old individual in the pool, the new individual replaces the old individual; if the new individual does not dominate any individual in the pool, their crowding distance is compared, and the individual with the higher crowding distance is retained. The historical elite pool (HEP) has a capacity of 5% to 10% of the population size and is used to record high-quality solutions across generations. High-quality solutions across generations are individuals with high fitness or non-dominant status that have been selected and preserved across different iteration rounds. Each high-quality solution across generations carries a time decay weight. ,in To solve the existing algebra, The attenuation coefficient; Using cosine similarity Individuals in the historical elite pool (HEP) with an overlap of less than 0.3 with the current solution space are selected. Parents from the HEP are chosen with a 30% probability to participate in elite-guided crossover. The crossover formula is as follows: in, These are vector representations of two individuals. This is the mixing coefficient, which is dynamically adjusted during evolution and ranges from 0.1 to 0.

5. Indicates the parent generation.

7. The multi-objective job shop scheduling optimization method based on two-layer elite evolution according to claim 2, characterized in that, The entropy weighting method dynamic weighting model in step 5 specifically includes: In the current population N individual m The targets are normalized using the following formula: in, Indicates the first in the population i The individual in the first j Function values ​​on each target; Calculate the first j Information entropy of a target, information entropy The value range is [0,1]: Calculate the first based on information entropy. j Dynamic weights of each objective : Each interval The weights are updated once, and the inertia factor is used. Smoothing weight mutations: in, This represents the total number of iterations.

8. The multi-objective job shop scheduling optimization method based on two-layer elite evolution according to claim 2, characterized in that, Step S is as follows: (1) Prioritize individuals with higher non-dominant levels, i.e., select from F1, F2, ... in sequence; (2) When individuals are selected sequentially according to the Pareto front layer order, if a certain front layer F k If the number of individuals in a layer exceeds the remaining capacity of the next generation population, meaning that not all individuals in that layer can be added, then the overall density estimate for those individuals in that layer is calculated using dynamic weights: ,in For individuals i In the j Crowding distance on each target; select individuals with higher overall density to join the new population in order to maintain the diversity of the solution set.

9. A multi-objective job shop scheduling optimization system based on two-layer elite evolution, characterized in that, include: The data acquisition module is used to obtain workpiece information, machine information, processing time data, and energy consumption parameters for workshop scheduling issues. The population initialization module is used to generate the initial population using a two-stage real number encoding strategy; The dynamic mutation module is used to dynamically adjust the mutation probability and perform adaptive mutation operations based on the population's evolutionary state. The non-dominated sorting module is used for fast non-dominated sorting and crowding calculation of the population; The dual-layer elite pool module includes an internal elite pool and a historical elite pool, used to store and filter elite individuals; The dynamic weighting module is used to calculate the dynamic weights of each objective function based on the entropy weighting method. The environment selection module is used to select the next generation of population by combining elite retention and weighted crowding comparison; The output module is used to output the Pareto optimal solution set and the corresponding Gantt chart scheduling scheme.

10. The multi-objective job shop scheduling optimization system based on two-layer elite evolution according to claim 9, characterized in that, The system also includes integration with manufacturing execution systems or industrial internet platforms to achieve data interconnection with the shop floor digital twin system and support real-time rescheduling triggered by dynamic events.

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