Cascade workshop multi-scene robust scheduling method and system under multi-target framework

Abstract

The invention discloses a method and a system for solving cascade workshop multi-scene robust scheduling under a multi-objective framework, and the method comprises the following steps: constructing a mixed integer linear programming model considering the uncertainty of processing time, a robust scheduling problem in multiple scenes is converted into a multi-target problem taking the maximum completion time in each typical disturbance scene as an optimization target; designing a scene-driven heuristic construction method to generate a high-quality initial solution set; iterative search of a scheduling solution is carried out under an evolutionary greedy optimization framework based on scene decomposition, adaptive parameter control, subgroup division, local reconstruction and a variation guide strategy are fused, and the search capability and adaptability of an algorithm are improved; and finally, screening a Pareto optimal solution through an aggregation function and a niche mechanism. According to the method, multi-scene scheduling performance balance optimization is realized in a PCB manufacturing cascade production system, the method has the advantages of high modeling precision, high search efficiency, excellent solution set quality and the like, and the robustness and practicability of a scheduling scheme under a multi-scene disturbance condition are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of intelligent manufacturing and production scheduling technology, and specifically to a cascade workshop multi-scenario robust scheduling method and system based on a multi-objective optimization framework. The method belongs to the production planning and optimization control technology for dynamic disturbance environments in manufacturing systems, and is particularly suitable for production systems with a cascade structure. Background Art

[0002] In modern manufacturing systems, the production environment is often disrupted by uncertainties such as new order insertions, processing time fluctuations, equipment failures, and shipping delays. This creates challenges for scheduling systems that dynamically adapt to multiple scenarios. This is especially true in cascaded workshop structures, where upstream and downstream processes are tightly coupled. Any disruption can easily disrupt production, impacting overall completion time and resource utilization efficiency.

[0003] Existing scheduling methods often optimize based on a single objective or specific disturbance scenario, failing to comprehensively measure scheduling robustness across a wide range of possible scenarios. To improve the adaptability of scheduling solutions under diverse disturbance scenarios, it is necessary to consider scheduling performance under a variety of typical disturbance scenarios. However, traditional robust scheduling strategies often rely on heuristic rules or modeling approaches based on single-objective robustness metrics, making it difficult to simultaneously address scheduling optimality and balance across multiple disturbance scenarios.

[0004] To address these issues, constructing a multi-objective optimization model by using the maximum completion time under multiple typical disturbance scenarios as independent optimization objectives is a key approach to improving scheduling robustness. This approach not only effectively reflects the scheduling quality under each scenario but also achieves multi-objective collaborative optimization through a scenario-driven subpopulation strategy and an evolutionary greedy optimization framework, thereby generating a highly adaptable scheduling solution with excellent overall performance.

[0005] Therefore, there is an urgent need for a multi-objective robust scheduling method that is suitable for cascade workshop structures and can simultaneously optimize the maximum completion time under multiple disturbance scenarios. Summary of the Invention

[0006] In light of this, the present invention aims to address the issues of poor scheduling stability and feasibility in actual manufacturing systems due to uncertainty in processing time. To address the joint scheduling needs of cascaded workshops under various possible disturbance scenarios, the present invention proposes a multi-objective optimization framework, taking the maximum completion time under each typical disturbance scenario as an independent optimization objective to construct a multi-objective robust scheduling model. On this basis, a scenario-decomposition-based evolutionary greedy algorithm is designed, which is both heuristic and convergent. This algorithm achieves comprehensive optimization of scheduling solutions under multiple scenarios, thereby improving the adaptability and robustness of scheduling strategies in changing environments.

[0007] The technical solutions of the present invention are as follows:

[0008] A method for solving multi-scenario robust scheduling of cascaded workshops under a multi-objective framework includes the following steps:

[0009] Step 1: Build a mixed-integer linear programming model to accurately describe the scheduling problem of a cascade flow shop under the condition of uncertainty in workpiece processing time in a printed circuit board (PCB) manufacturing scenario. A scenario set is constructed based on typical disturbance scenarios. The robust joint scheduling problem is then transformed into a multi-objective optimization problem, with the maximum completion time in each scenario as an independent objective.

[0010] Step 2: Based on the structural characteristics of the scenario-based cascaded shop robust joint scheduling problem, a scenario-driven heuristic solution construction method is designed to generate an initial solution set and improve the distribution quality and diversity of the initial population in the multi-objective space.

[0011] Step 3: Iteratively optimize the scheduling solution within a scenario-based evolutionary greedy optimization framework. Multi-objective decomposition and parallel solution are used to improve the multi-scenario balancing performance and robustness of the scheduling solution. Subgroup partitioning and co-evolution mechanisms, local reconstruction search, and mutation guidance mechanisms are employed to continuously improve the Pareto optimality and global exploration capabilities of the solution set.

[0012] In step 4, the non-dominated environment selection strategy based on the fusion aggregation function and the niche retention mechanism is used to screen non-dominated solutions to improve population diversity and convergence, and finally to construct an elite solution set with both robustness and scheduling performance, thus achieving a closed-loop solution for scheduling optimization.

[0013] Step 5: Adaptively adjust the population restart strategy according to the population evolution process, increase population diversity and avoid premature convergence through a dynamic restart mechanism.

[0014] Before executing step 2, preferably, key parameters such as the reference vector and subpopulation capacity required by the scheduling system and the number of individuals in the external elite archive set can be pre-set.

[0015] Furthermore, step 2 includes the following sub-steps:

[0016] Step 2.1, design four heuristic strategies and one random strategy to generate the initial individuals of the scheduling solution of stage 1. v , where the first four individuals are initialized using four different heuristic strategies, and the remaining individuals are initialized using random strategies;

[0017] Step 2.2: For each individual generated stage 1 scheduling solution, calculate the optimal solution in the corresponding optimization scenario ω. vThen, the workpieces are reordered according to the "first come first served" (FCFS) and "parallel machine idle first" rules to generate the initial scheduling solution for the second stage until all individuals are initialized.

[0018] In step 2.3, the population is re-divided according to the Tchebycheff distance between individuals and the reference vector to achieve single-objective focused optimization of the sub-population.

[0019] Furthermore, the step 2.1 may specifically include the following sub-steps:

[0020] Step 2.11: For each subpopulation P v , and its corresponding optimization scenario is ω v For the first individual, based on the production information of the workpiece in the stage 1 of the scenario, the total processing time of each workpiece in all processes is calculated, and the scheduling priority is formed in the non-ascending order of the total time. Then the workpieces are scheduled in sequence, and the current workpiece to be scheduled is inserted into all feasible pipeline scheduling sequences, and the workpiece in the scenario ω is selected. v The sequence with the smallest maximum completion time is used as the optimal scheduling sequence for the current step until all workpieces are scheduled;

[0021] In step 2.12, for the second individual in the subpopulation, generate a random sequence of workpieces and schedule them sequentially. Using the same evaluation method as in step 2.11, select the scheduling sequence with the smallest maximum completion time at each step until the scheduling is complete.

[0022] Step 2.13: For the third individual in the subpopulation, determine its scheduling priority in non-ascending order of the total processing time of the workpiece, and schedule the workpieces in sequence, each time assigning the current workpiece to the v The production line with the smallest current completion time is selected until all workpieces are scheduled;

[0023] Step 2.14: Generate a random sequence of workpieces for the fourth individual in the subpopulation and schedule them sequentially, assigning them to the assembly line using the rule that minimizes the current completion time until the scheduling is complete.

[0024] Step 2.15: For the remaining SPSize-4 individuals in the subpopulation, each pipeline h k Randomly generate a non-repeating workpiece sequence to initialize the scheduling solution;

[0025] Repeat steps 2.11 to 2.15 until all subpopulation individuals corresponding to the optimization scenarios have completed the construction of the initial solution of stage 1.

[0026] Furthermore, before executing step 3, all individuals in the population are first sorted by non-domination according to the Pareto dominance relationship based on the crowding distance, the non-dominated solutions are stored as elite individuals in the external elite archive set EP, and the parameter values ​​in the destruction length list D are initialized.

[0027] Furthermore, step 3 includes the following sub-steps:

[0028] Step 3.1: In each iteration, perform parallel computation evolution for each subpopulation.

[0029] Step 3.2: Perform a local improvement mechanism based on destruction and reconstruction on the current parent individual in the subpopulation to improve the solution quality;

[0030] Step 3.3: Based on the current individual’s fitness value, determine whether to execute the mutation operator according to the adaptive strategy to achieve a balance between search pioneering and solution diversity;

[0031] Step 3.4: If the conditions in step 3.3 are met, perform mutation operations on the offspring individuals to improve solution diversity, thereby generating offspring individuals; otherwise, jump to step 3.5;

[0032] Step 3.5: For the offspring after mutation, determine whether to retain the current offspring individual or the parent individual based on the Tchebycheff distance, and the retained individual will be used as the parent individual in the second stage;

[0033] Step 3.6: For the current parent generation individual, the first-come-first-served and parallel machine idle priority rules are used to determine the workpiece order, and the corresponding stage 2 scheduling solution is generated as the parent generation information of stage 2;

[0034] Step 3.7, again calculate the execution probability of refined improvement strategy 2 based on the parent fitness, so that individuals with lower fitness have a higher probability of improvement, thus obtaining new offspring individuals;

[0035] Step 3.8, merge the solutions of the two stages of the offspring individuals, so as to place the complete individuals into their subpopulation;

[0036] Step 3.9: If the offspring is Pareto-dominated by the parent or has the same target value, then the parameter G = G + 1;

[0037] Step 3.10: Repeat steps 3.2 to 3.9 until the evolution operation of all individuals in the subpopulation is completed;

[0038] Furthermore, step 3.2 specifically includes the following sub-steps:

[0039] Step 3.21, randomly select a value d from the set of damage lengths D;

[0040] Step 3.22, identify the critical pipeline H of the current individual in stage 1 * , and randomly remove d / 2 workpieces from the assembly line to form a preliminary destruction sequence τ;

[0041] ·Step 3.23, except H * Randomly select d / 2 workpieces from other production lines except , remove them, and add them to the destruction sequence τ;

[0042] Step 3.24: Based on the scheduling index of the current optimization scenario, the workpieces in the destruction sequence τ are reinserted into the current scheduling solution in order to complete the reconstruction operation and generate new individuals.

[0043] In step 3.25, if the new individual dominates its parent in the Pareto sense, the current d value is considered valid and is added to the set D.

[0044] Furthermore, step 3.7 specifically includes:

[0045] Step 3.71: scramble the artifact sequence of the current parent individual to generate a reference sequence;

[0046] In step 3.72, the parent individual selects artifacts in the reference sequence in turn, removes them from the original sequence, and tests the scheduling effect of inserting them into all feasible positions under the current optimization objective;

[0047] Step 3.73: Select the location with the best scheduling effect to insert the workpiece and update the current scheduling solution.

[0048] In step 3.74, repeat steps 3.72 to 3.73 until all workpieces are inserted or the scheduling solution is no longer improved.

[0049] Furthermore, step 4 includes the following sub-steps:

[0050] Step 4.1: Delete duplicate individuals in all subpopulations to improve the diversity of the solution set;

[0051] Step 4.2: Calculate the fitness value of each individual and the Tchebycheff distance between it and the guided reference vector, and delete the redundant individuals with poor performance in each subpopulation based on the evaluation results;

[0052] Step 4.3: Sort and rank all individuals based on Pareto dominance relationship and crowding distance;

[0053] Step 4.4: Starting from the first level after sorting, select individuals that do not exceed the upper limit of the elite archive set as the new elite solution;

[0054] In step 4.5, the remaining individuals that have not been selected are supplemented using the niche mechanism until the elite archive set reaches the capacity threshold.

[0055] Furthermore, the step 4.5 specifically includes the following operations:

[0056] Step 4.51: select from the unselected individual set T the individual set with the multi-target distance metric d MOT The individual farthest from the top is called candidate individual z * , and remove it from the set T;

[0057] Step 4.52, search for the set T that matches z * The individual with the smallest angle between them is denoted as q * ;

[0058] Step 4.53, according to z * and q * The convergence value of the individual z with better convergence is selected from it *′ Add to the elite archive collection;

[0059] Step 4.54, based on the newly added individual z *′ , update the d between the remaining individuals in the set T and the current elite set MOT distance;

[0060] In step 4.55, repeat steps 4.51 to 4.54 until the elite archive collection is filled to the preset capacity limit.

[0061] Furthermore, step 5 includes the following sub-steps:

[0062] Step 5.1: Calculate the restart parameter b based on the current number of iterations and parameter G; if G < (1 / 3.0)*Iteration, then b = 10; if G < (2 / 3.0)*Iteration, then b = 20; otherwise, b = 30;

[0063] Step 5.2: Remove the SPSize*(100-b)*0.01 individuals with the lowest ranking in the subpopulation and randomly generate new individuals up to the threshold size SPSize.

[0064] The beneficial effects of the present invention are:

[0065] (1) For the first time, a mixed integer linear programming model for solving multi-scenario robust scheduling in a cascade workshop under a multi-objective framework was established. This model can more accurately characterize the robust scheduling problem under processing time uncertainty in the printed circuit board (PCB) production process, provide a systematic and multi-objective mathematical description of the scheduling problem, and improve the applicability and expressiveness of the model.

[0066] (2) We conducted an in-depth analysis of the structural characteristics of the two-stage PCB production process, fully considering the coupling relationship between the stages and the knowledge of the problem characteristics, and designed a scenario-driven hybrid heuristic initialization method. This method takes into account the optimization objectives in different scenarios, ensures the high quality and diversity of the initial population, and has high algorithm execution efficiency, providing a good foundation for subsequent searches;

[0067] (3) An algorithmic framework integrating adaptive parameter adjustment, scenario partitioning, and subpopulation greedy optimization is proposed, which can more effectively adapt to the robustness requirements of multi-objective and multi-scenario cascaded workshop joint scheduling, significantly improving the algorithm's global search capability and the quality of the Pareto optimal solution set;

[0068] (4) A non-dominated environment selection strategy based on aggregation function and niche mechanism is adopted to optimize the diversity maintenance and convergence performance of the population, effectively enhance the robustness of the system, ensure the closed-loop execution of the scheduling optimization process, and achieve robust and efficient scheduling optimization;

[0069] (5) The present invention is superior to existing multi-objective flow shop scheduling methods (IMOEA / D-LS and LNSGAIII), classic multi-objective optimization algorithms NSGA-III and SPEA2 in terms of solution efficiency and computational performance, and can be faster.

[0070] The high-quality Pareto optimal solution set can be obtained quickly, which greatly improves the practicality and application value of the actual production scheduling plan. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0072] Figure 1 : Flowchart of the method for solving multi-scenario robust scheduling of cascade workshops under the multi-objective framework of the present invention;

[0073] Figure 2 : Flowchart of scenario-driven heuristic method;

[0074] Figure 3 : Actual scheduling effects under multiple scenarios of cascade workshops: (a) Scenario 1; (b) Scenario 2; (c) Scenario 3; (d) Scenario 4; (e) Scenario 5;

[0075] Figure 4 :The mean value graph of 5 algorithms under HV index;

[0076] Figure 5 : Mean graph of 5 algorithms under IGD index; DETAILED DESCRIPTION

[0077] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0078] In real-world manufacturing environments, scheduling systems often face numerous uncertainties, including new order insertions, equipment failures, processing time fluctuations, and shipping delays. These disturbances can render the original scheduling plan ineffective, leading to reduced resource utilization, disrupted production rhythms, and missed delivery dates. This is particularly true in cascaded workshop systems, where strong dependencies exist between previous and subsequent processes. A disruption in any one link can easily trigger a chain reaction across the entire production system, exacerbating the complexity of scheduling.

[0079] Existing scheduling optimization methods are mostly based on single-objective modeling or designed for specific scenarios, making it difficult to comprehensively evaluate the robustness of scheduling solutions under diverse disturbance conditions. Traditional robust scheduling methods typically employ heuristic rules or model based on a single robustness metric. These methods lack the ability to characterize performance trade-offs across multiple scenarios. This results in scheduling results that excel in some scenarios but underperform in others, making it difficult to meet the dual requirements of "high adaptability" and "high stability" required in industrial practice.

[0080] To improve the overall response capabilities of scheduling systems in complex and uncertain environments, a multi-objective optimization framework has been constructed. This framework collaboratively solves the maximum completion time under multiple typical disturbance scenarios as independent optimization objectives, which has become an effective strategy. This framework not only maintains good scheduling performance across different scenarios but also uses a Pareto front optimization mechanism to obtain a set of well-balanced non-dominated solutions, providing production managers with a diverse and controllable selection of scheduling options.

[0081] However, multi-objective, multi-scenario joint optimization problems are computationally extremely complex, and traditional optimization algorithms struggle to balance global search capabilities and solution quality. Therefore, intelligent optimization algorithms designed using co-evolutionary mechanisms have become a research hotspot. Based on the concept of scenario decomposition, this paper combines multi-objective decomposition with a parallel solution strategy to construct a co-evolutionary optimization framework suitable for robust scheduling of cascaded workshops in multiple scenarios. This method integrates a subgroup co-evolutionary mechanism under reference vector partitioning, an adaptive parameter control strategy, a local reconstruction search, and a mutation guidance mechanism, effectively improving the algorithm's exploration depth and diversity maintenance capabilities in the solution space. During the population iteration process, a non-dominated environment selection strategy driven by the aggregation function value and the fusion of the aggregation function and the niche retention mechanism effectively screens high-quality non-dominated solution sets in multiple scenarios. At the same time, a dynamic restart mechanism based on evolutionary state judgment is introduced to adaptively enhance population diversity and suppress premature convergence. This optimization framework ensures that the generated solution sets are reasonably distributed and converge well across multi-objective tasks, significantly enhancing the robustness and practical application value of the scheduling system in complex and uncertain environments.

[0082] This application proposes a method for solving multi-scenario robust scheduling in cascade workshops under a multi-objective framework. This method aims to optimize the scheduling problem in the printed circuit board (PCB) production process, especially in complex environments with multiple uncertainties and disturbances. Its core optimization goal is to minimize the maximum completion time as much as possible under various typical disturbance scenarios, thereby ensuring the efficiency and robustness of production. Figure 1 As shown in Figure 2, the optimization goal is to maximize the completion time under various typical disturbance scenarios. Specifically, it includes the following steps:

[0083] (1) For the cascaded shop floor scheduling problem in the printed circuit board (PCB) production process, a mixed integer linear programming model for multiple scenarios was first constructed. This model comprehensively considers the uncertainty of workpiece processing time under different scenarios and the coupling constraints in the two-stage production process to achieve the coordinated optimization of scheduling robustness and production efficiency. Through this model, the robust scheduling problem under multiple scenarios can be systematically described and optimized, achieving the coordinated optimization of scheduling robustness and production efficiency.

[0084] (2) Design a scenario-driven hybrid heuristic initialization strategy. By intelligently constructing the workpiece processing sequence and equipment allocation under various typical scenarios, a set of initial solutions with both quality and diversity is generated, providing a good foundation for subsequent evolutionary optimization.

[0085] (3) An evolutionary greedy optimization framework based on scenario decomposition is introduced, which combines multi-objective decomposition with a parallel solution mechanism, and uses an adaptive parameter control strategy to dynamically adjust the search behavior. This effectively balances the diversity and robustness of the solution while improving the convergence speed of the multi-objective solution.

[0086] (4) A non-dominated environment selection method that integrates aggregation function and niche mechanism is adopted to screen and retain non-dominated individuals in the evolutionary process, improve the distribution uniformity and stability of the elite solution set, enhance the overall robust performance of the system in different scenarios, and realize a closed-loop scheduling optimization process.

[0087] (5) Finally, the population restart strategy is adaptively adjusted according to the population evolution state, and a dynamic restart mechanism is introduced to enhance population diversity, effectively suppress the risk of premature convergence, and improve the algorithm's global search capability and solution efficiency.

[0088] Specifically, the following steps are included:

[0089] Step 1: Construct a scenario-based multi-objective mixed-integer linear programming model for robust scheduling. This model aims to accurately describe the robust scheduling problem under multiple scenarios in a cascaded workshop and transform it into a multi-objective optimization problem. This model systematically characterizes the completion time constraints of the production process under different scenarios, thereby achieving effective control and optimization of the production schedule. The specific form of the established mixed-integer linear programming model is as follows:

[0090] Objective function: minF={f1,f2,...,f υ ,...,f γ}(1)

[0091] Constraints:

[0092]

[0093]

[0094] The relevant symbols are defined as follows:

[0095]

[0096]

[0097] The constraints in the model are as follows:

[0098] Constraint (2): defines the maximum completion time of the workpiece in each uncertain scenario to clarify the upper limit of the total production time and provide a basis for robust performance evaluation.

[0099] Constraints (3) and (4): ensure that each workpiece can only be arranged in a unique position in its assigned pipeline, thereby avoiding the situation where the same workpiece is repeatedly arranged in multiple positions during scheduling, and ensuring the uniqueness and rationality of scheduling.

[0100] Constraint (5): Allowing each workpiece to serve as both a predecessor and a successor to other workpieces in its pipeline, building a flexible structure of the processing sequence, which helps to adapt to the scheduling needs in different scenarios.

[0101] Constraint (6): restricts virtual workpiece 0 to have only one successor workpiece as the starting node for starting the processing sequence, thereby standardizing the generation logic of the initial schedule and preventing multiple concurrent starting paths.

[0102] Constraints (7) and (8): are used to avoid the cross-processing order of workpieces and ensure that each workpiece strictly follows a single predecessor and successor structure during the processing process, thereby avoiding logical conflicts and scheduling deadlocks.

[0103] Constraints (9) and (10): In each scenario ω υ In the process, the exclusive use of workpieces and machines is constrained, stipulating that a workpiece can only be processed in the next process after the previous process is completed, and the same machine can only process one workpiece at a time, thus reflecting the physical reality constraints of the processing process.

[0104] Constraint (11): Ensures that each workpiece can enter the next stage of processing only after it is transported to stage two by a designated automatic guided vehicle (AGV), effectively describing the scheduling logic under transportation constraints.

[0105] Constraints (12) and (13): Ensure that the scheduling of each workpiece on the parallel machine also meets the requirements of unique predecessor and successor, prevent cross-interference of multiple processing paths, and improve the scheduling controllability of the model for the parallel environment.

[0106] Constraints (14) and (15): define the continuous processing rules of parallel machines, requiring each machine to complete the processing of the current workpiece before starting the next task, reflecting the actual operation rhythm and equipment utilization sequence of stage two.

[0107] Constraints (16) to (19): are used to clarify the value range and domain of each type of decision variable, ensuring the validity of the model variables and the logical consistency of the variable status during the solution process.

[0108] Step 2.1: Initialize individual generation in stage 1; for each optimization scenario ω υ The corresponding subpopulation P υ , use the following strategy to initialize individuals:

[0109] Step 2.11: The first individual adopts heuristic strategy 1 and calculates the total processing time of each job j in stage 1:

[0110]

[0111] Press TPTj Determine the scheduling priority in non-ascending order, insert each workpiece into the scheduling sequence of all feasible pipelines, and select v The solution with the shortest maximum completion time under the scenario;

[0112] Step 2.12: The second individual uses a random sequence of workpieces and inserts the schedule with the criterion of minimizing the maximum completion time;

[0113] Step 2.13: The third individual presses TPT j Sort in non-ascending order and assign each job to the assembly line with the shortest completion time.

[0114] Step 2.14: The fourth individual is scheduled based on a random sequence using the same minimum completion time allocation strategy as in step 2.12;

[0115] Step 2.15: The remaining SPSize-4 individuals are initialized by randomly generating a non-repeating workpiece sequence for each pipeline;

[0116] Repeat steps 2.11 to 2.15 to complete the construction of the initial solutions for all subpopulations in stage 1.

[0117] Step 2.2: Construction of initial solution in stage 2; υ The maximum completion time of the scenarios is sorted in ascending order, and the "first come, first served" (FCFS) and "parallel machine idle first" rules are combined to sort the workpieces in the second stage to generate the initial scheduling solution;

[0118] In step 2.3, the population is re-divided according to the Tchebycheff distance between individual fitness and the reference vector to achieve single-objective focused optimization of the sub-population.

[0119] Step 2.31, normalize the objective function of the first stage and calculate the fitness (f1′(π [1] ),f′2(π [1] ),…,f′ Υ (π [1] )),in:

[0120]

[0121] In step 2.32, the population is divided according to the Tchebycheff between the fitness of each individual and each reference vector. The individual belongs to the reference vector to which it is closest.

[0122] First, all individuals in the population are sorted according to the Pareto dominance relationship based on crowding distance, the non-dominated solutions are stored as elite individuals in the external elite archive set EP, and the parameter values ​​in the destruction length list D are initialized.

[0123] Step 3.1: In each iteration, perform parallel computation evolution for each subpopulation.

[0124] Step 3.2: Perform a local improvement mechanism based on destruction and reconstruction on each individual in the subpopulation to improve the solution quality;

[0125] Step 3.21, randomly select a value d from the set of damage lengths D;

[0126] Step 3.22: Determine the critical pipeline H of the current individual in stage 1 according to formula (23) * , and randomly remove d / 2 workpieces from the assembly line to form a preliminary destruction sequence τ;

[0127]

[0128] Step 3.23: Remove H * Randomly select d / 2 workpieces from other production lines except , remove them, and add them to the destruction sequence τ;

[0129] Step 3.24: Based on the scheduling index of the current optimization scenario, reinsert the artifacts in the destruction sequence τ into the current scheduling solution in order to complete the reconstruction operation and generate new individuals;

[0130] Step 3.25: If the new individual dominates its parent individual in the Pareto sense, then the current d value is considered valid and is added to the set D.

[0131] Step 3.3: Determine whether to perform the mutation operation based on the fitness. The probability of generating offspring is:

[0132]

[0133] Step 3.4 Randomly generate a random number in the range (0,1) Then perform mutation operation on the current parent individual to improve the diversity of solutions; otherwise, jump to step 3.6; randomly select an operator from the mutation operator set to execute, where the mutation operator set is:

[0134] O1: Randomly swap the positions of two different workpieces in the scheduling sequence;

[0135] O2: Randomly select a workpiece and reinsert it into a new position on the same assembly line;

[0136] O3: Randomly select two positions in the same assembly line and reverse the workpiece sequence between the two positions;

[0137] O4: Select a workpiece from the key virtual assembly line identified by the system and reposition it;

[0138] Step 3.5: For the offspring after mutation, determine whether to retain the current offspring individual or the parent individual based on the Tchebycheff distance, and the retained individual will be used as the parent individual in the second stage;

[0139] Step 3.6: For the newly generated individuals, the "first come, first served" and "parallel machine idle first" rules are used to determine the order of the workpieces, and the corresponding stage 2 scheduling solution is generated as the parent information of stage 2;

[0140] Step 3.7: Again determine the fitness of the parent individuals in the second production phase according to formula (24), and then calculate the execution probability of the refined improvement strategy 2 according to formula (25), so that individuals with lower fitness have a higher improvement probability:

[0141]

[0142] Step 3.71: Generate a random number in the range (0,1) Scramble the artifact sequence of the current parent individual to generate a reference sequence; otherwise, jump to step 3.8;

[0143] Step 3.72: The parent individual selects the workpieces in the reference series in turn, removes them from the original sequence, and tests the scheduling effect of inserting them into all feasible positions under the current optimization objective;

[0144] Step 3.73: Select the location with the best scheduling effect to insert the workpiece and update the current scheduling solution;

[0145] Step 3.74: Repeat steps 3.72 to 3.73 until all workpieces are inserted or the scheduling solution no longer improves.

[0146] Step 3.8: Combine the solutions of the two stages of the offspring individuals to place the complete individuals into their subpopulations;

[0147] Step 3.9: If the offspring is Pareto-dominated by the parent or has the same target value, then the parameter G = G + 1;

[0148] Step 3.10: Repeat steps 3.2 to 3.9 until the evolution operation of all individuals in the subpopulation is completed;

[0149] Step 4.1: Merge the individuals in all subpopulations and delete the duplicate individuals to improve the diversity of the solution set and the efficiency of the algorithm;

[0150] Step 4.2: Calculate the overall fitness value of each individual x (with the maximum completion time of stage 2 as the overall objective function value) and calculate its Tchebycheff distance to the guided reference vector; based on this, delete the redundant individuals with the worst performance in each subpopulation so that the number of individuals in each subpopulation does not exceed the set subpopulation size upper limit SPSize;

[0151] Step 4.3: Sort and grade all individuals based on Pareto dominance and crowding distance to construct a multi-level solution structure;

[0152] Step 4.4: Starting from the first level after sorting, select individuals that do not exceed the upper limit of the elite file set as the new elite solution;

[0153] Step 4.5: For the remaining individuals that have not been selected, the niche mechanism is used to supplement them until the elite archive set reaches the capacity threshold NA.

[0154] Step 4.51: Select from the unselected individual set T the individual set with the multi-target distance metric d MOT The individual farthest from the top is called candidate individual z * , and remove it from the set T, where the distance d MOT Defined as:

[0155]

[0156] Step 4.52: Search the set T for the value corresponding to z * The individual with the smallest angle between them is denoted as q * ;

[0157] Step 4.53: According to z * and q * The convergence value of , from which the individual z with better convergence CV is selected *′ is added to the elite archive set, where the convergence degree is defined as:

[0158]

[0159] Step 4.54: Based on the newly added individual z *′ , update the d between the remaining individuals in the set T and the current elite set MOT distance;

[0160] Step 4.55: Repeat steps 4.51 to 4.54 until the Elite Archive Collection is filled to the preset capacity limit.

[0161] Step 5.1: Calculate the restart parameter b based on the current number of iterations and parameter G; if G < (1 / 3.0)*Iteration, then b = 10; if G < (2 / 3.0)*Iteration, then b = 20; otherwise, b = 30;

[0162] Step 5.2: Remove the SPSize*(100-b)*0.01 individuals with the lowest ranking in the subpopulation and randomly generate new individuals up to the threshold size SPSize.

[0163] In summary, the beneficial effects of this application are:

[0164] (1) For the first time, a multi-objective mixed-integer linear programming model for the multi-scenario robust scheduling problem in a cascaded workshop was established, systematically describing the impact of processing time uncertainty on scheduling results during PCB production. This model not only covers complex scheduling characteristics such as multi-stage, multi-scenario, and multi-constraint, but also takes into account multiple optimization objectives such as robustness, scheduling efficiency, and resource utilization. It can more accurately describe the impact of uncertain disturbances in the actual production environment on scheduling performance, providing a formalized and scalable modeling framework for the robust scheduling problem, significantly improving the adaptability and expressiveness of the model.

[0165] (2) We deeply analyze the structural coupling relationship between the surface mount technology (SMT) stage and the plug-in process (DIP) stage in the PCB production process, and design a scenario-driven hybrid heuristic initialization strategy based on the process constraints and task characteristics in production practice. This method integrates rule heuristics, scheduling knowledge, and a multi-scenario trade-off mechanism to generate an initial population with high feasibility, high fitness, and structural diversity under different disturbance scenarios. This not only improves the algorithm execution efficiency, but also provides a stable and reliable search starting point for subsequent evolutionary search, strengthening the robustness of the algorithm.

[0166] (3) An evolutionary greedy optimization framework (MSEGA) that integrates an adaptive parameter adjustment mechanism and scenario decomposition is proposed. This algorithm can dynamically adjust the search intensity and direction according to different evolutionary stages. Combining multi-objective decomposition with a parallel solution mechanism, it effectively balances the diversity and robustness of solutions while improving the convergence speed of multi-objective solutions. Then, through a local greedy mechanism, potential optimal solutions in the solution space are explored to achieve a synergistic enhancement of global search capabilities and local optimization capabilities. This framework is highly suitable for multi-objective, multi-scenario cascade workshop joint scheduling problems, significantly improving the convergence efficiency and the breadth and accuracy of the Pareto solution set.

[0167] (4) A non-dominated solution environment selection strategy based on aggregation function and niche mechanism was constructed, which effectively balanced the diversity maintenance and convergence speed of the population. This strategy can effectively avoid the local optimal trap while ensuring search stability, enhance the distribution balance and robustness of the solution, and provide theoretical and algorithmic support for the continuous optimization of the scheduling system in complex environments. It realizes the transition from single-scenario optimality to multi-scenario robust optimality, and improves the dynamic adaptability of the system in the actual manufacturing process.

[0168] (5) The present invention is superior to existing mainstream scheduling algorithms in terms of solution efficiency and optimization performance, including effective multi-objective scheduling algorithms (IMOEA / D-LS), enhanced local search NSGAIII algorithm (LNSGAIII), and classic multi-objective evolutionary algorithms (such as SPEA2 and MOEA / D). A large number of comparative experiments show that the model and algorithm proposed in this invention can obtain a more advantageous Pareto front solution set in a shorter time, and is superior in terms of the number, distribution balance and quality of solutions.

[0169] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A multi-scenario robust scheduling method for cascaded workshops under a multi-objective framework, characterized by: The following steps are involved: Step 1: Construct a mixed integer linear programming model that considers processing time uncertainty and transforms the robust scheduling problem under multiple scenarios into a multi-objective problem with the maximum completion time under each typical disturbance scenario as the optimization objective. Step 2: Design a scenario-driven heuristic solution construction method to generate an initial solution set and perform population division based on the reference vector; Step 3: Iteratively optimize the scheduling solution within a scenario-based evolutionary greedy optimization framework. Multi-objective decomposition and parallel solution are used to improve the multi-scenario balancing performance and robustness of the scheduling solution. This involves employing subgroup partitioning and co-evolution mechanisms, local reconstruction search, and mutation guidance mechanisms. Step 4: Use the aggregation function value to update the subpopulation and the non-dominated environment selection strategy based on the niche retention mechanism to screen the non-dominated solutions and construct a robust elite solution to achieve a closed-loop solution for scheduling optimization; Step 5: Adaptively adjust the population restart strategy according to the population evolution process, increase population diversity and avoid premature convergence through a dynamic restart mechanism.

2. The method according to claim 1, characterized in that The mixed integer linear programming model constructed in step 1 specifically includes: The objective function is to minimize the maximum completion time under each scenario; The constraints include workpiece processing sequence constraints, machine exclusivity constraints, and inter-stage transportation constraints; Introduce scene index variables to achieve joint modeling of multiple scenes.

3. The method according to claim 1 or 2, characterized in that The step 2 includes: Step 2.1: For each subpopulation, three heuristic strategies and one random strategy are used to generate the scheduling solution for the first stage. The first individual adopts a heuristic strategy of non-ascending total processing time; the second individual adopts a random sequence maximum completion time minimum strategy; the third individual adopts a shortest processing time priority allocation strategy; the remaining individuals adopt a random generation strategy; In step 2.2, based on the initial phase one scheduling solution, the solutions are arranged in ascending order by maximum completion time, and the phase two scheduling solution is constructed according to the first-come-first-served and parallel machine idle-first rules. In step 2.3, the population is re-divided according to the Tchebycheff distance between the individual and the reference vector, so that each sub-population focuses on the optimization of a specific scenario.

4. The method according to claim 1, wherein The step 3 comprises: Step 3.1, perform evolution operations on each subpopulation in parallel; Step 3.2, perform destruction-reconstruction local improvement on the solution of the current individual corresponding to stage 1; Step 3.3: Determine whether to perform the mutation operation based on the fitness value and the adaptive strategy. If the conditions are met, proceed to step 3.4; otherwise, jump to step 3.

7. Step 3.4, perform mutation operation on the solution of the current individual corresponding to stage 1 to generate offspring; Step 3.5, individual environment selection based on Tchebycheff distance; Step 3.6: For the retained individuals, the first-come-first-served and idle-machine-first rules are used to generate the scheduling solution for the second stage; Step 3.7: Calculate the execution probability of the refined search improvement strategy based on the individual fitness; if the conditions are met, execute the refined search improvement strategy for the current individual; otherwise, jump to step 3.9; Step 3.8, merge the solutions of the current two stages to construct a complete individual and update the current subpopulation; Step 3.9: If the offspring is Pareto-dominated by the parent or has the same target value, then the parameter G = G + 1; Step 3.10: Repeat the evolution process for all sub-population individuals to complete the evolution.

5. The method according to claim 4, characterized in that The step 3.2 includes: Step 3.21: Randomly select a value d from the set of damage lengths D; Step 3.22: Identify the critical pipeline in stage 1 and remove d / 2 artifacts from it; Step 3.23: Remove d / 2 workpieces from other production lines and add them to the destruction sequence; Step 3.24: Reinsert the destruction sequence artifacts based on the current optimization scenario indicators to form a new solution; Step 3.25: If the new solution dominates the parent individual, append the current d value to the set D.

6. The method according to claim 5, characterized in that The step 3.4 includes: Step 3.41: Randomly select an operation operator from the mutation operator set; Step 3.42: Perform mutation operation on the current individual according to the operator characteristics to enhance diversity and suppress premature maturation.

7. The method according to claim 5, characterized in that The step 3.8 includes: Step 3.81: Disrupt the current parent artifact sequence to generate a reference sequence; Step 3.82: Select the workpieces in sequence according to the reference sequence and test their insertion scheduling effect; Step 3.83: Select the optimal insertion position and update the scheduling solution; Step 3.84: Repeat the insertion operation until all workpieces are inserted or the solution cannot be improved.

8. The method according to claim 1, characterized in that The step 4 comprises: Step 4.1, delete duplicate individuals in all subpopulations; Step 4.2: Calculate the fitness value of each individual and the Tchebycheff distance between it and the guided reference vector, and delete the redundant individuals with poor performance in each subpopulation based on the evaluation results; Step 4.3: Sort and rank all individuals based on Pareto dominance relationship and crowding distance; Step 4.4, starting from the first priority level after sorting, select individuals in sequence until the upper limit of the elite archive set is reached, and the selected individuals constitute the new elite solution set; In step 4.5, for the remaining individuals that have not been selected, the niche mechanism is used for supplementary screening until the elite archive set is completed to the preset capacity threshold.

9. The filtering selection strategy according to claim 8, characterized in that: The step 4.5 includes: Step 4.51: Select from the unselected individuals set T the individuals that are in the same range as the currently selected individuals set. MOT The farthest individual z * , and remove it from the set T; Step 4.52: Determine the value of z in the set T. * The individual q with the smallest angle between * ; Step 4.53: Compare z * With q * The convergence value of the individual z with better convergence is selected from them * 'Added to the elite archive collection; Step 4.54: According to the newly added individual z * ′, update the d between the remaining individuals in the set T and the elite set MOT distance; Step 4.55: Repeat steps 4.51 to 4.54 until the Elite Archives collection reaches the preset capacity limit.

10. The method according to claim 1, characterized in that The step 5 comprises: Step 5.1, calculate the restart parameter b based on the current number of iterations and parameter G; Step 5.2: Remove the SPSize*(100-b)*0.01 individuals with the lowest ranking in the subpopulation and randomly generate new individuals up to the threshold size SPSize.

11. A scheduling system for implementing the method according to any one of claims 1 to 10, characterized in that include: Scenario modeling module, used to construct a set of typical disturbance scenarios; Optimization solution module, which executes multi-objective evolutionary algorithm; Solution evaluation module, analyzing scheduling performance under various scenarios; Visual output module to generate executable scheduling solutions.

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