A multi-objective fuzzy scheduling method for ship pipe machining based on improved hyper-heuristic algorithm

Abstract

This invention discloses a multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm. The improved hyperheuristic algorithm solves the fuzzy production batch scheduling problem in the ship pipe fitting processing workshop. This problem includes process constraints under grouped technology constraints and machine constraints, with the dual objectives of minimizing the maximum fuzzy completion time and minimizing the total fuzzy energy consumption. The improved hyperheuristic algorithm utilizes an adaptive evolutionary mechanism and a hybrid local search strategy to obtain the final scheduling scheme. This invention addresses the technical problems in existing ship pipe fitting processing scheduling technologies, such as difficulty in adapting to the time uncertainty of the production process, wasted equipment auxiliary time due to neglecting grouped processes, and difficulty in effectively balancing completion efficiency and production energy consumption, achieving synergistic optimization of production efficiency and energy saving.

Description

Technical Field

[0001] This invention relates to a method for scheduling the processing of ship pipe fittings, and in particular to a multi-objective fuzzy scheduling method for the processing of ship pipe fittings based on an improved hyperheuristic algorithm. Background Technology

[0002] As one of the most important systems in a ship, the piping system is the main part of the entire ship. Its manufacturing accounts for a large proportion of the workload in the shipbuilding process, and the task of the ship pipe processing workshop is heavy. The progress of ship pipe processing will seriously affect the progress of ship section manufacturing.

[0003] Shipbuilding pipe fitting processing workshops commonly employ a hybrid flow shop production model. However, existing scheduling technologies typically assume a deterministic production environment, meaning that the processing and setup times for all processes are fixed. In actual shipbuilding production, however, uncontrollable factors such as differences in worker skill levels, minor equipment malfunctions, and fluctuations in raw material supply often result in highly uncertain and ambiguous processing times. Scheduling schemes calculated using existing technologies are prone to deviations during actual implementation, leading to frequent changes in production plans and disrupting production order. Furthermore, shipbuilding pipe fittings are diverse, and switching between different types requires changing fixtures or adjusting equipment parameters, resulting in significant sequence-dependent setup times. Existing technologies often treat pipe fittings as independent entities and randomly sequence them, leading to frequent equipment adjustments and wasted setup time, severely reducing the overall production efficiency of the workshop.

[0004] Existing ship pipe fitting scheduling technologies mostly focus on a single time efficiency indicator (such as minimizing the maximum completion time), often sacrificing the energy efficiency ratio of equipment. Currently, there is a lack of a dual-objective optimization scheduling scheme that can effectively balance the two conflicting goals of "completion efficiency" and "production energy consumption," making it difficult to achieve green and low-carbon operation of the workshop while ensuring delivery time.

[0005] Furthermore, for NP-hard problems such as mixed flow shop scheduling, existing technologies typically employ metaheuristic algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), or Non-Dominated Sorting Genetic Algorithm (NSGA-II) for solution. However, these traditional algorithms have significant drawbacks when dealing with complex solution spaces, such as those in shipbuilding pipe fitting processing, which have large-scale characteristics and multiple constraints (group constraints, fuzzy constraints): First, the parameters of traditional algorithms (such as crossover rate and mutation rate) are usually statically fixed and cannot be adaptively adjusted according to the state of the population during the evolutionary process (such as crowding distance and diversity feedback). This leads to the algorithm easily getting trapped in local optima in the early stages of the search, or having a slow convergence speed in the later stages, making it difficult to find a high-quality global optimum. Second, although existing hyperheuristic algorithms introduce high-level strategies to select low-level operators, their selection mechanisms are often relatively simple (such as based on simple random selection or greedy strategies), lacking the ability to deeply mine the local features of the solution space. The lack of an effective local search mechanism makes it difficult for the algorithm to perform a fine-grained search in the neighborhood of excellent solutions, resulting in insufficient accuracy of the final scheduling scheme and making it difficult to meet high production standards. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, this invention provides a multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm. This method solves the technical problems in the existing technologies, such as poor model adaptability to fuzzy environments and grouped processes, neglect of energy consumption optimization, and the tendency of traditional algorithms to get trapped in local optima and have low search efficiency. It achieves coordinated optimization of completion time and production energy consumption.

[0007] The technical solution of the present invention is as follows:

[0008] A multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm includes: solving the fuzzy production batch scheduling problem in the ship pipe fitting processing workshop using an improved hyperheuristic algorithm. The fuzzy production batch scheduling problem in the ship pipe fitting processing workshop has two objectives: minimizing the maximum fuzzy completion time and minimizing the total fuzzy energy consumption, under process constraints including grouped technical constraints and machine constraints. The maximum fuzzy completion time and the total fuzzy energy consumption are both calculated based on the processing time of the pipe fitting, which is represented by the triangular fuzzy number of the minimum processing time, the most likely processing time, and the maximum processing time.

[0009] The improved hyperheuristic algorithm includes: setting a low-level heuristic rule base in the domain layer, which contains several deterministic scheduling rules; encoding each gene position of each chromosome individual with an integer and mapping it to a deterministic scheduling rule in the low-level heuristic rule base; adjusting the crossover probability based on the average crowding distance of the population and using different mutation methods for different population individuals for adaptive evolution; adding local search and using three neighborhood structures—single-point mutation, rule block exchange, and rule clustering—to generate candidate solutions; and using a probabilistic acceptance strategy to accept solutions and inject them into the population.

[0010] This invention uses triangular fuzzy numbers to represent the uncertainty of processing time and introduces grouping constraints to reduce the sequence-dependent preparation time caused by switching between different types of pipe fittings. This solves the problems of poor robustness and low production continuity of existing deterministic models. It incorporates the maximum completion time and total production energy consumption into the optimization objective, solving the problem of excessive energy waste caused by traditional single-objective scheduling methods when pursuing efficiency. In addition, by improving the hyperheuristic algorithm, it effectively overcomes the shortcomings of traditional metaheuristic algorithms in solving large-scale multi-objective scheduling problems, such as slow convergence speed, loss of population diversity, and easy getting trapped in local optima, thereby obtaining a high-quality Pareto optimal solution set.

[0011] Furthermore, the process constraints and machine constraints that include grouped technical constraints are as follows: the processing order of each group is determined; each machine can only produce one pipe fitting; each workpiece can only be processed on one machine; the completion time of each stage of fuzzy processing of the pipe fitting is the sum of the fuzzy start time and the fuzzy processing time of that stage; for the same pipe fitting, the start time of the next process must be greater than the end time of the previous process; on the same machine, according to the processing order, the fuzzy start time of the later pipe fitting is not earlier than the end time of the previous pipe fitting; in each group, the first processing stage of the pipe fitting that is ranked earlier starts processing before the pipe fitting that is ranked later.

[0012] Furthermore, the rules in the low-level heuristic rule base include: shortest processing time priority, longest processing time priority, first-come-first-served, earliest deadline priority, minimum remaining workload priority, minimum remaining processes priority, minimum slack time priority, critical ratio priority, and earliest start time priority.

[0013] Furthermore, the adaptive evolution includes a crossover operation with a crossover probability. The crossover operation is performed by randomly generating two different position indices within the chromosome length range, and exchanging the middle segment located between the two position indices between the two parent individuals to produce two new offspring individuals.

[0014] Furthermore, during the crossover operation, the crossover probability is increased when the average crowding distance of the population is below a threshold, and decreased when the average crowding distance of the population is above the threshold.

[0015] Furthermore, the improved hyperheuristic algorithm employs an improved binary tournament selection strategy for high-level evolutionary search, which includes randomly selecting two individuals from the current population as candidate solutions and performing non-dominated ranking comparisons: for two individuals at different Pareto front levels, the individual at the higher level is selected; for two individuals at the same Pareto front level, the individual with the larger crowding distance is selected; and for two individuals at the same Pareto front level with the same crowding distance, random selection is performed.

[0016] Furthermore, the mutation methods include randomly replacing each gene position with a deterministic scheduling rule, mutating to a deterministic scheduling rule with similar performance, and mutating to an arbitrary deterministic scheduling rule.

[0017] Furthermore, the mutation of the current deterministic scheduling rule is performed with a mutation probability of 0.15. Individuals located at the first Pareto front are mutated to deterministic scheduling rules with similar performance. Individuals that appear repeatedly in the population are mutated to arbitrary deterministic scheduling rules with a mutation probability of 0.3.

[0018] Furthermore, the candidate solution generation for the local search includes: selecting a subset of individuals from the top 50% of Pareto levels in the current population, and for each selected individual, applying three neighborhood structures in parallel to generate candidate solutions.

[0019] Furthermore, the crowding distance is calculated using an adaptive grid method: each target dimension is divided to form a multidimensional grid. For each individual, the crowding distance is the sum of the inverse of the individual density of the individual's grid and the individual density of adjacent grids, where the individual density is the number of individuals in each grid.

[0020] Compared with the prior art, the present invention has the following advantages:

[0021] 1. Significantly improves the robustness and executability of the scheduling scheme in actual production. This invention, by constructing a scheduling model based on triangular fuzzy numbers, can effectively accommodate time uncertainties caused by differences in manual operation and minor equipment malfunctions. Simultaneously, this invention incorporates group technology constraints, mandating continuous processing of pipe fittings of the same family, effectively reducing the ineffective downtime caused by frequent fixture changes and equipment adjustments when switching between different pipe fitting families, thereby improving the utilization rate of workshop equipment and production continuity.

[0022] 2. Achieved synergistic optimization of production efficiency and energy conservation. Existing scheduling methods often only pursue single-time efficiency, leading to prolonged equipment idling or high-load operation, resulting in serious energy waste. This invention simultaneously uses "fuzzy maximum completion time" and "fuzzy total energy consumption" as optimization objectives, providing a set of Pareto optimal solutions. Decision-makers can flexibly choose solutions according to needs, significantly reducing workshop energy consumption while ensuring no delivery delays, achieving green and low-carbon shipbuilding processes, and meeting the sustainable development requirements of modern manufacturing.

[0023] 3. Overcomes premature convergence and improves global optimization capability. Addressing the shortcomings of traditional genetic algorithms or hyperheuristic algorithms, such as fixed parameters and susceptibility to local optima, this invention employs an adaptive evolutionary mechanism based on population crowding distance feedback. This mechanism senses the population state in real time, automatically increasing the mutation probability to escape local traps when the population is clustered, and increasing the crossover probability to accelerate convergence when the population is sparse. This allows the algorithm to maintain good search vitality even in large-scale, complex solution spaces, ensuring the global superiority of the final scheduling scheme.

[0024] 4. Enhanced accuracy in local development of the solution space and improved scheduling quality. This invention employs a hybrid local search within the hyperheuristic algorithm, utilizing multiple neighborhood operators such as single-point swaps, rule block swaps, and rule clustering to deeply mine and refine the elite solutions generated by evolution. Compared to existing technologies relying solely on simple heuristic rules, this invention can find more compact scheduling sequences with smaller gaps, further reducing completion time and improving overall processing quality. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating a multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm, as an example.

[0026] Figure 2 This is a box plot comparing the diffusion index of the method of the present invention and the comparative method.

[0027] Figure 3 This is a box plot comparing the intergenerational distance index between the method of this invention and the comparative method.

[0028] Figure 4 This is a box plot comparing the method of the present invention with a comparative method on the inverse intergenerational distance index. Detailed Implementation

[0029] The present invention will be further described below with reference to embodiments, but these are not intended to limit the scope of the invention.

[0030] Please combine Figure 1As shown in the figure, the multi-objective fuzzy scheduling method for ship pipe fitting processing based on the improved hyperheuristic algorithm in this embodiment is to solve the fuzzy production batch scheduling problem in the ship pipe fitting processing workshop using the improved hyperheuristic algorithm.

[0031] The fuzzy production batch scheduling problem in a ship pipe fitting processing workshop, under process constraints and machine constraints including grouping technical constraints, aims to minimize the maximum fuzzy completion time and minimize the total fuzzy energy consumption. Specifically, the problem is described as follows: N pipe fittings are divided into groups and processed on various machines. Each group contains several pipe fittings. Each pipe fitting has multiple processes, and each process has a fixed number of parallel machines to choose from. Some processes can only be processed using a subset of machines, but the process constraints and machine constraints must be satisfied. The goal is to simultaneously minimize the maximum fuzzy completion time and the total fuzzy energy consumption. The processing time of the pipe fittings is expressed as a triangular fuzzy number. Given in the form of, where Minimum processing time, The most likely processing time, This represents the maximum processing time. The fuzzy preparation time between different pipe fittings is related to the sequence of pipe fittings.

[0032] To facilitate better calculations, the following reasonable assumptions are made:

[0033] (1) When scheduling begins, all current groups have been completed and can start processing, and all machines in all production stages are in operation.

[0034] (2) All pipe fittings in the same group must be processed continuously, and the production of pipe fittings in different groups is not allowed to be carried out in an interleaved manner;

[0035] (3) At any given time, a machine can process at most one pipe fitting to be processed, and a pipe fitting to be processed can be processed at most on one machine.

[0036] (4) The processing of each processing stage shall not be interrupted, and for two adjacent processing stages of the same pipe fitting, the next processing stage may begin only after the previous processing stage is completed;

[0037] (5) The priority of pipe fittings to be processed is the same within the same group, and the priority is also the same between different groups;

[0038] (6) The preparation time between each pipe fitting to be processed is sequentially related to the pipe fittings on the current machine.

[0039] (7) The transportation time of the pipe fittings in different processing stages is not considered, and the processing buffer of any processing stage is sufficient.

[0040] Before further describing the present invention, the following explanation is given regarding the various symbol parameters involved:

[0041]

[0042] The mathematical model for solving the aforementioned problem is expressed as follows:

[0043] (1) Maximum fuzzy completion time

[0044] (1)

[0045] (2) Total energy consumption

[0046] (2)

[0047] With the optimization objectives of minimizing the maximum completion time and production energy consumption, the objective function can be expressed as:

[0048] (3)

[0049] (4)

[0050] The constraints are:

[0051] (5)

[0052] (6)

[0053] (7)

[0054] (8)

[0055] (9)

[0056] (10)

[0057] (11)

[0058] (12)

[0059] Equations (3) and (4) represent the optimization objectives, namely minimizing the maximum fuzzy completion time and minimizing the total fuzzy energy consumption; Equations (5) and (6) represent that the processing order of each group is determined; Equation (7) represents that each machine can only process one pipe fitting; Equation (8) represents that each workpiece can only be processed on one machine; Equation (9) represents that the fuzzy processing completion time of each stage of the pipe fitting is the sum of the fuzzy start processing time and the fuzzy processing time of that stage; Equation (10) represents that for the same pipe fitting, the start time of the next process must be greater than the end time of the previous process; Equation (11) represents that on the same machine, if the pipe fitting... The processing sequence in pipe fittings Then, the fuzzy start time of the next pipe fitting is no earlier than the end time of the previous pipe fitting; Equation (12) indicates that the first processing stage of the pipe fitting in each group starts before the pipe fitting in the next group.

[0060] Scheduling in shipbuilding pipe fitting workshops presents unique constraints, such as stringent group technology requirements and a dual-objective trade-off between efficiency (maximum completion time) and sustainability (energy consumption). Traditional single heuristics (such as SPT or EDD) are clearly inadequate in adapting to the typically intricate and evolving bottlenecks in hybrid flow shop environments. Furthermore, standard multi-objective evolutionary algorithms (MOEAs) often face challenges in handling the large-scale discrete search space typical of combinatorial scheduling. Therefore, this invention improves upon the hyperheuristic algorithm and names it the Improved Hyperheuristic Algorithm.

[0061] The improved hyperheuristic algorithm employs a two-layer optimization architecture, which comprises two distinct levels:

[0062] 1. Domain Layer (Low-Level Heuristic, LLH): This is the foundation of the domain layer. This layer contains a set of nine deterministic scheduling rules. These rules act as "atomic operators" for constructing scheduling schemes, ensuring that domain-specific constraints are inherently and strictly adhered to during the scheduling process.

[0063] 2. High-level (Evolutionary Search Strategy): This layer employs an adaptive genetic mechanism to evolve the sequence of heuristic rules. The algorithm's goal is not to seek a static final schedule, but rather to find an optimal set of rules that can be applied sequentially to successive batches of pipe fittings.

[0064] Meanwhile, the hyperheuristic algorithm also designs three adaptation strategies:

[0065] 1. Integer-based batch coding: A custom coding scheme is designed in which each gene corresponds to a specific pipe family, thereby directly mapping decision variables to the physical grouping constraints of the workshop.

[0066] 2. Adaptive Evolution Operator: To prevent the algorithm from stagnating, the crossover and mutation probabilities are dynamically adjusted based on the crowding distance of the population.

[0067] 3. Hybrid Local Search: By employing complementary neighborhood structures in the evolutionary cycle—namely, single-point mutation, rule block exchange, and rule clustering—the algorithm can effectively avoid local optima in the dual-objective solution space.

[0068] Specifically, the low-level heuristic rule set is integrated, comprising nine deterministic scheduling rules with different optimization characteristics. Each rule is designed for a specific scheduling objective, and the rule numbers and names are as follows:

[0069] 1. Rule 0: Shortest Processing Time First (SPT);

[0070] 2. Rule 1: Longest Processing Time First (LPT);

[0071] 3. Rule 2: First Come First Served (FCFS);

[0072] 4. Rule 3: Earliest Due Date First (EDD);

[0073] 5. Rule 4: Minimum Work Remaining (MWR) takes precedence.

[0074] 6. Rule 5: Least Operations Remaining (LOR) takes precedence.

[0075] 7. Rule 6: Least Slack Operation (LSO) takes precedence.

[0076] 8. Rule 7: Critical Ratio (CR) takes precedence.

[0077] 9. Rule 8: Earliest Start Time (EST) takes precedence.

[0078] To effectively map the solution space of the scheduling problem to the search space of the genetic algorithm, the population individuals are encoded as follows: each chromosome individual consists of L ordered genes, where L represents the number of groups of components in the production task. Each gene bit corresponds to an integer variable with a value ranging from 0 to 8, which is mapped to deterministic scheduling rules in nine different low-level heuristic rule sets. This encoding method has a clear physical meaning: the integer value on each gene bit determines the sorting rule adopted by the corresponding component group during scheduling. For example, when the third gene bit of an individual is 1, it means that the third group of components will be sorted using the longest processing time first (LPT) rule. This encoding design not only ensures that each individual can represent a complete scheduling strategy, but also allows genetic operations to directly apply to the combinatorial optimization of scheduling rules.

[0079] The corresponding decoding process first parses the individual gene sequence to determine the scheduling rule used for each pipe group. For example, if the i-th gene position of an individual is k, it means that the pipes in the i-th group will be sorted using rule k. Then, the pipe sets within each pipe group are fully sorted according to a comparison function with specified rules. After sorting, the pipe sequences of all groups are concatenated in group order to form a complete processing sequence.

[0080] The hyperheuristic algorithm employs a fully randomized strategy for population initialization to ensure diversity and broad search space coverage in the initial population. Specifically, for an initial population of size N, each gene locus of each individual is independently selected from integers 0 to 8 through uniform random sampling. This initialization method ensures that: each low-level heuristic rule has an equal chance of appearing in the initial population; different rules can form sufficient random combinations; and the population distribution in the search space is uniform and representative. Extensive experimental verification shows that this initialization strategy can provide sufficient genetic diversity for the subsequent evolutionary process and effectively prevent the algorithm from prematurely converging to a local optimum.

[0081] In the high-level evolutionary search phase, an improved binary tournament selection strategy is employed, which achieves a good balance between maintaining selection pressure and population diversity. The specific implementation process is as follows:

[0082] First, two individuals are randomly selected from the current population as candidate solutions. A non-dominated sampling strategy is used for selection to ensure that each individual has an equal chance of being selected. Then, the two candidate solutions are compared using a non-dominated ranking method.

[0083] 1) If two individuals are located at different Pareto front levels, the individual at the higher level (i.e., the solution that has been dominated fewer times) is selected. This mechanism ensures that elite solutions can be preserved to the next generation.

[0084] 2) If two individuals are located at the same Pareto front level, their crowding distances are further compared. The individual with the larger crowding distance is selected, which helps maintain the distribution of the solution set in the target space. The crowding distance is calculated by summing the normalized distances of adjacent solutions in each target dimension.

[0085] 3) When two individuals are at the same crowding distance, one of them is randomly selected to maintain population diversity.

[0086] Because a constraint handling mechanism is introduced during the selection process, individuals that violate hard constraints are given a punitive fitness value to ensure that infeasible solutions are not selected.

[0087] The crowding distance calculation uses an adaptive grid method:

[0088] 1) Target space partitioning: Each target dimension is divided into 10 equal parts to form a multi-dimensional grid.

[0089] 2) Local density estimation: Count the number of individuals in each grid as the density estimate.

[0090] 3) Distance calculation: For each individual, calculate the sum of the reciprocals of the individual densities in its own grid and adjacent grids.

[0091] This method is more stable than the traditional sorting-based crowding distance calculation, especially suitable for the case where the target value distribution is uneven.

[0092] The two-point crossover strategy is used for the crossover operation, and this strategy can dynamically adjust the search intensity according to the evolutionary stage. The detailed process of the crossover operation is as follows:

[0093] 1) Crossover point determination: Randomly generate two different position indexes pt1 and pt2 within the chromosome length range (satisfying 0 ≤ pt1 < pt2 < L), and these two points divide the chromosome into three consecutive segments.

[0094] 2) Crossover execution: Two parent individuals exchange the middle segment between pt1 and pt2 to generate two new offspring individuals. This operation not only retains some excellent patterns of the parents but also generates new rule combinations through segment recombination.

[0095] 3) Adaptive adjustment: The crossover probability Pc is dynamically adjusted according to the population diversity index. When the average crowding distance of the population is lower than the threshold, Pc is increased to 0.95 to enhance the exploration ability; when the average crowding distance of the population is higher than the threshold, Pc is decreased to 0.8 to strengthen the exploitation ability.

[0096] 4) Validity verification: Check whether the newly generated individuals meet all the constraint conditions, and repair or discard the individuals that do not meet the conditions. The time complexity of the crossover operation is O(L), where L is the chromosome length.

[0097] A specific example of the crossover operation is as follows:

[0098] The parent individual 1 is [0, 1, 2, 3, 4], the parent individual 2 is [5, 6, 7, 8, 0], and the position indexes are (2, 3). Therefore, 1, 2 of the parent individual 1 and 6, 7 of the parent individual 2 are the middle segments, and after they are exchanged, two offspring individuals are obtained. The offspring individual 1 is [0, 6, 7, 3, 4], and the offspring individual 2 is [5, 1, 2, 8, 0].

[0099] The mutation operation is a key mechanism to maintain population diversity. The mutation operation strategy of this invention is as follows:

[0100] 1) Basic Mutation: Each gene locus mutates with a probability Pm=0.15. During mutation, the current rule number is randomly replaced with one of the other 8 rules. This uniform mutation ensures that all rules have a chance to be explored.

[0101] 2) Directed mutation: For high-performing individuals (located at the first Pareto front), a local mutation strategy is employed, allowing mutation only to rules with similar performance. For example, the SPT rule may only mutate into time-related rules such as LPT or EDD.

[0102] 3) Enhanced mutation: Apply stronger mutation pressure to individuals that appear repeatedly in the population, increasing the mutation probability to 0.3 and allowing for larger rule jumps.

[0103] 4) Constraint Preservation: Immediately after mutation, check whether the new individual satisfies all constraints, and make corrections if necessary. The average time complexity of the mutation operation is O(Pm×N×L).

[0104] After adaptive crossover and mutation, a local search is performed, the specific steps of which are as follows:

[0105] 1) Initial solution selection: Select 30% of the best individuals (located in the top 50% of the Pareto level) from the current population as the starting point for the local search.

[0106] 2) Neighborhood generation: For each selected individual, three neighborhood structures are applied in parallel to generate candidate solutions. Each neighborhood structure generates 5 neighborhood solutions, for a total of 15 candidates.

[0107] 3) Candidate evaluation: The target value of the candidate solution is calculated using a fast evaluation method (simplified scheduling simulation).

[0108] 4) Solution acceptance criteria: A probability acceptance strategy is adopted, with an improved solution accepted with a probability of 0.7 and an inferior solution accepted with a probability of 0.3 (simulated annealing idea).

[0109] 5) Termination condition: No improvement after 10 consecutive iterations, or reaching the maximum number of evaluations (100×L).

[0110] 6) Elite retention: Reinject the improved solution into the population, replacing the corresponding number of the worst individuals.

[0111] The three neighborhood structures are:

[0112] 1) Single-point mutation neighborhood: Randomly select a gene locus in an individual and replace the current rule with another rule. This neighborhood structure is simple to implement and suitable for fine-tuning. Its neighborhood size is 8×L, where L is the chromosome length.

[0113] 2) Neighborhood swapping of rule blocks: Select two different rule blocks (contiguous gene segments) and swap their positions. This operation can change the order in which rules are applied, making it suitable for adjusting inter-group scheduling strategies. The neighborhood size is approximately O(L²).

[0114] 3) Rule-based clustering neighborhood: Cluster rules with similar functions (such as time-oriented SPT / LPT / EDD) and perform rule replacement within the cluster. This strategy can effectively explore while maintaining scheduling characteristics.

[0115] Finally, the Pareto front management mechanism adopted in this invention uses a fast non-dominated sorting algorithm for its non-dominated sorting, and its optimized implementation includes:

[0116] 1) Parallel computing: Utilizing multithreading technology to compute the dominance relationships between individuals in parallel.

[0117] 2) Incremental update: Between generations, only the new individuals are compared with the complete dominance comparison, while the existing individuals are updated using an incremental update strategy.

[0118] 3) Memoization technique: Cache the calculated dominance relationships to avoid duplicate calculations.

[0119] The time complexity of the sorting process is optimized from the traditional O(MN²) to an average of O(MNlogN), where M is the target number and N is the population size.

[0120] Elite retention employs a tiered strategy:

[0121] 1) First level: Unconditionally retain all individuals at the first non-dominant frontier.

[0122] 2) Second level: Select a subset of individuals based on crowding distance to ensure population diversity.

[0123] 3) Third and lower levels: Only a small number of special individuals (such as solutions with extreme objective values) are retained.

[0124] This strategy ensures both the preservation of elite solutions and the maintenance of sufficient population diversity. The proportion of elite solutions is adaptively adjusted, ranging from 20% to 40%.

[0125] After the search iteration is completed, the Pareto optimal solution set is finally output, generating a scheduling scheme for ship pipe fitting processing.

[0126] To evaluate the performance of the method of this invention (Enhanced HH algorithm) in solving the production scheduling problem of a ship pipe processing workshop, 10 computational examples were generated based on actual production data obtained from a survey of the ship pipe processing workshop of a large shipyard, and with appropriate scaling. The relevant data settings are: the total number of each ship pipe processing stage... The number of parallel machines in the stages of material cutting, pipe bending, pipe straightening, welding, cleaning and grinding, and pump pressure testing. Processing time Total number of pipe fittings Number of groups .

[0127] The comparison algorithms are the original hyperheuristic algorithm (Original HH), NSGA-II, and MOPSO. To provide a consistent evaluation of algorithm performance, 10 independent experiments were conducted on all examples using the three algorithms, and the following evaluation metrics were set:

[0128] 1. Inverse intergenerational distance (IGD): Measures both convergence and diversity. A lower value indicates better performance.

[0129] 2. Generational Distance (GD): Primarily measures the degree of convergence between the obtained Pareto front and the true Pareto front.

[0130] 3. Spread: Measures the uniformity of the solution distribution on the Pareto front.

[0131] Since the true solution to the multi-objective production scheduling problem in a ship pipe processing workshop with resource constraints is difficult to obtain, the Pareto front of the solutions obtained by all algorithms in all experiments of a certain example is used to replace the true solution of the problem. At the same time, since the objective values ​​of different objectives differ in magnitude, which will introduce errors into the calculation indicators, the objective values ​​are normalized before evaluation to eliminate errors unrelated to algorithm performance.

[0132] The experimental results of each algorithm for solving each set of examples under the three evaluation indicators of Spread, GD, and IGD are shown in the table below.

[0133]

[0134] The case studies were divided into three groups based on the number of pipe fittings (N): Small-scale: N < 50; Medium-scale: Large-scale: N>150, plot box plots of diffusion, GD, and IGD indices obtained by different algorithms on computational examples of various scales, such as... Figures 2 to 4 As shown.

[0135] It can be seen that, for the diffusion index, the improved hyperheuristic algorithm has the lowest box position and the smallest box height, indicating that the algorithm performs best and is most stable in terms of solution set distribution uniformity. The median of NSGA-II is about 0.65, which is significantly better than MOPSO and Original HH, but there are a few outliers. Original HH: The box is the highest (median > 0.9) and the range of the upper and lower whiskers is the largest, indicating that the solution set distribution is the most uneven.

[0136] In small-scale problems (N<50), the improved hyperheuristic algorithm has the smallest difference from NSGA-II (median difference of about 0.1); in large-scale problems (N>150), the advantage of the improved hyperheuristic algorithm is more significant (median difference of about 45% compared to the original HH).

[0137] For the GD metric, the improved hyperheuristic algorithm maintains a median value in the range of 0.15 to 0.2 and can still maintain low volatility (IQR < 0.1) in large-scale problems; although MOPSO has a median value (about 0.3) that is better than the original HH, it has obvious high outlier points (the maximum GD value reaches 0.6); NSGA-II performs close to the improved hyperheuristic algorithm on medium-sized problems, but its performance degrades faster as the problem size increases.

[0138] Regarding the IGD metric, the best performance is that the median IGD of the improved hyperheuristic algorithm is stable between 0.3 and 0.4, and the bins within each size group are compact (standard deviation < 0.1); the worst performance is that Original HH exhibits extreme values ​​(maximum IGD > 1.2) in large-scale problems, reflecting unstable solution set quality; the algorithm difference is that the median difference between Enhanced HH and NSGA-II (approximately 0.15) is smaller than the difference between NSGA-II and MOPSO (approximately 0.2).

[0139] Therefore, overall, the improved hyperheuristic algorithm demonstrates significant advantages in solution quality, stability, and scalability, making it particularly suitable for complex large-scale scheduling scenarios. NSGA-II can be considered as an alternative for small- to medium-scale problems, while the traditional method (Original HH) requires further optimization to adapt to modern production needs.

[0140] The invention was rigorously validated through large-scale experiments using examples (sample size N=10 to 200) generated from real shipyard data. The experimental results lead to the following conclusions:

[0141] (1) Superior solution quality: Comparative analysis shows that the present invention is significantly superior to NSGA-II, MOPSO and standard hyperheuristic algorithms (diffusion) in terms of convergence (IGD / GD) and diversity distribution.

[0142] (2) Statistical significance: The Wilcoxon signed-rank test confirmed that the performance advantage of the present invention was statistically significant at all problem sizes (p<0.05).

[0143] (3) Strategy effectiveness: Ablation studies have verified the key contributions of the adaptive mechanism and the local search module to the algorithm's escape from local optima.

[0144] (4) Robustness: Sensitivity analysis shows that the present invention is highly robust to uncertainty. Even under high ambiguity conditions (δ=30%), its performance degradation (18.7%) is still significantly lower than that of the comparative algorithm (>37%), making it particularly suitable for the highly volatile shipyard environment.

Claims

1. A multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm, characterized in that, include: An improved hyperheuristic algorithm is used to solve the fuzzy production batch scheduling problem in a ship pipe fitting processing workshop. The fuzzy production batch scheduling problem in a ship pipe fitting processing workshop has dual objectives: minimizing the maximum fuzzy completion time and minimizing the total fuzzy energy consumption, under process constraints including grouped technical constraints and machine constraints. The maximum fuzzy completion time and the total fuzzy energy consumption are both calculated based on the processing time of the pipe fitting, which is represented by the triangular fuzzy number of the minimum processing time, the most likely processing time, and the maximum processing time. The improved hyperheuristic algorithm includes: setting a low-level heuristic rule base in the domain layer, which contains several deterministic scheduling rules; encoding each gene position of each chromosome individual with an integer and mapping it to a deterministic scheduling rule in the low-level heuristic rule base; adjusting the crossover probability based on the average crowding distance of the population and using different mutation methods for different population individuals for adaptive evolution; adding local search and using three neighborhood structures—single-point mutation, rule block exchange, and rule clustering—to generate candidate solutions; and using a probabilistic acceptance strategy to accept solutions and inject them into the population.

2. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm as described in claim 1, characterized in that, The process constraints and machine constraints, which include grouped technical constraints, are as follows: the processing order of each group is determined; each machine can only produce one pipe fitting; each workpiece can only be processed on one machine; the completion time of each stage of fuzzy processing of the pipe fitting is the sum of the fuzzy start time and the fuzzy processing time of that stage; for the same pipe fitting, the start time of the next process must be greater than the end time of the previous process; on the same machine, according to the processing order, the fuzzy start time of the later pipe fitting is not earlier than the end time of the previous pipe fitting; in each group, the first processing stage of the pipe fitting that is ranked earlier starts processing before the pipe fitting that is ranked later.

3. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm as described in claim 1, characterized in that, The rules in the low-level heuristic rule base include: shortest processing time priority, longest processing time priority, first-come-first-served, earliest deadline priority, minimum remaining workload priority, minimum remaining processes priority, minimum slack time priority, critical ratio priority, and earliest start time priority.

4. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm as described in claim 1, characterized in that, The adaptive evolution includes a crossover operation with a crossover probability. The crossover operation is performed by randomly generating two different position indices within the chromosome length range, and exchanging the middle segment between the two position indices between the two parent individuals to produce two new offspring individuals.

5. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm according to claim 1, characterized in that, During the crossover operation, the crossover probability is increased when the average crowding distance of the population is below a threshold, and decreased when the average crowding distance of the population is above the threshold.

6. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm according to claim 1, characterized in that, The improved hyperheuristic algorithm employs an improved binary tournament selection strategy for high-level evolutionary search, which involves randomly selecting two individuals from the current population as candidate solutions and performing non-dominated ranking comparisons: for two individuals at different Pareto front levels, the individual at the higher level is selected; for two individuals at the same Pareto front level, the individual with the larger crowding distance is selected; and for two individuals at the same Pareto front level with the same crowding distance, random selection is performed.

7. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm according to claim 1, characterized in that, The mutation methods include randomly replacing each gene position with a deterministic scheduling rule, mutating to a deterministic scheduling rule with similar performance, and mutating to any deterministic scheduling rule.

8. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm as described in claim 7, characterized in that, Mutation is performed to randomly replace the current deterministic scheduling rule with a mutation probability of 0.

15. Individuals located at the first Pareto front are mutated to deterministic scheduling rules with similar performance. Individuals that appear repeatedly in the population are mutated to arbitrary deterministic scheduling rules with a mutation probability of 0.

3.

9. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm according to claim 1, characterized in that, The candidate solution generation for the local search includes: selecting a subset of individuals from the top 50% of Pareto levels in the current population, and for each selected individual, applying three neighborhood structures in parallel to generate candidate solutions.

10. The multi-objective fuzzy scheduling method for ship pipe fitting processing based on an improved hyperheuristic algorithm according to any one of claims 1 to 9, characterized in that, The crowding distance is calculated using an adaptive grid method: each target dimension is divided into a multi-dimensional grid. For each individual, the crowding distance is the sum of the inverse of the individual density of the individual's grid and the individual density of adjacent grids, where the individual density is the number of individuals in each grid.

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