A ship plan section flow line green scheduling method considering aggravation effect

Abstract

The application discloses a ship planar section flow line green scheduling method considering deterioration effect, which comprises the following steps: S1, a planar section flow line static scheduling model using a linear function to describe processing time deterioration is established, the model comprises maximum completion time and total energy consumption, and the total energy consumption is the sum of processing energy consumption and standby energy consumption; S2, based on the aforementioned model, a target function is determined as minimizing the maximum completion time and minimizing the energy consumption; S3, constraint conditions of a scheduling process are determined; S4, an improved multi-objective grey wolf optimization algorithm is used to solve the target function to obtain an optimal scheduling scheme; wherein in the improved multi-objective grey wolf optimization algorithm, a random full permutation section number coding is used to convert discrete scheduling solutions and grey wolf individual positions, population initialization is performed by using reverse learning, and grey wolf individual positions are updated based on dynamic inertia weight factor adjustment. The application can effectively reduce the energy consumption of flow line production, achieve the purpose of energy saving, and ensure production efficiency.

Description

Technical Field

[0001] This invention relates to a pipeline scheduling method, and more particularly to a green scheduling method for ship planar segment pipelines that takes into account degradation effects. Background Technology

[0002] For the shipbuilding industry, process planning and workshop scheduling are crucial aspects of production and construction. The green demands of sustainable development necessitate that process planning and workshop scheduling consider not only efficiency metrics but also green indicators such as energy consumption and carbon emissions. This aims to improve production efficiency while reducing the company's environmental impact.

[0003] With the development of modern shipbuilding models, most shipyards have introduced planar segmented assembly lines to improve production efficiency. However, due to the continued use of traditional on-site scheduling methods in the application of planar segmented assembly lines, the scheduling schemes employed are not optimal, resulting in low production efficiency. While planar segmented assembly lines share characteristics with general assembly lines, they differ from any other assembly line model. Because hull sections are heavy and large, there are no buffer stations between assembly line workstations. Scheduling must consider various factors, such as the processing sequence of each section. For parallel assembly lines, transverse workstations are set up in the middle of each line, connected by conveyor belts. Sections can be moved out of the assembly line via these transverse workstations. This necessitates considering the selection of different assembly lines for different sections. Sometimes, as projects progress, urgent processing of certain sections or interruptions due to processing errors leading to defective parts further complicate the scheduling of planar segmented assembly lines.

[0004] In traditional assembly line scheduling problems, the processing time of a workpiece is usually set as a constant. However, in actual workshop production, the actual processing time of some workpieces varies. For ship section assembly lines, since some workstations require manual operation, the operator's skill level, fatigue, and equipment wear all cause variations in the section processing time. This situation is known as the degradation effect. Most current scheduling methods aim to minimize the maximum completion time, without considering the degradation effect or green indicators such as energy consumption and carbon emissions. Summary of the Invention

[0005] To address the shortcomings of the existing technology, this invention provides a green scheduling method for ship planar segment production lines that considers the degradation effect. This method addresses the green scheduling problem of planar segment production lines that consider the degradation effect, providing a solution for shipyard planar segment production scheduling, and reducing energy consumption while ensuring production efficiency.

[0006] The technical solution of this invention is as follows: A green scheduling method for ship planar segmented flow lines considering deterioration effects, comprising the following steps:

[0007] Step S1: Establish a static scheduling model for a planar segmented pipeline that uses a linear function to describe the deterioration of processing time. The static scheduling model for the planar segmented pipeline includes the maximum completion time and total energy consumption, where the total energy consumption is the sum of processing energy consumption and standby energy consumption.

[0008] Step S2: Based on the static scheduling model of the planar segmented pipeline, the objective function is determined to be minimizing the maximum completion time and minimizing energy consumption;

[0009] Step S3: Determine the constraints of the scheduling process;

[0010] Step S4: Solve the objective function using the improved multi-objective gray wolf optimization algorithm to obtain the optimal scheduling scheme;

[0011] In the improved multi-objective gray wolf optimization algorithm, the discrete scheduling solution is mapped and transformed to the continuous gray wolf individual position vector by encoding the random full permutation segment number, and the population is initialized by reverse learning, and the gray wolf individual position is adjusted and updated based on the dynamic inertia weight factor.

[0012] Furthermore, the maximum completion time is

[0013]

[0014]

[0015] T′ i，j =T i，j +αS i，j

[0016] T i =x i C i，m +(1-x i C i，h

[0017] L i =x i L i，m +(1-x i )L i，h

[0018] Total energy consumption is E = E w +E P E P For processing energy consumption, E w For standby power consumption,

[0019]

[0020] i is the plane segment index, i = (1, 2, ..., n), j is the machining station index, j = (1, 2, ..., m), S i，j T is the start time of planar segment i at station j. i，j Let T′ be the basic machining time of planar segment i at station j. i，j C represents the actual processing time of planar segment i at station j. i，j Let L be the completion time of planar segment i at workstation j. i，j T is the time it takes for plane segment i to leave workstation j. i Let P be the completion time of plane segment i. i，j Q represents the energy consumption per unit time of planar segment i during processing at station j. i，j DT is the standby power consumption per unit time of planar segment i when it is blocked at station j. i Let be the delivery time of planar segment i, α be the degradation rate, be the maximum completion time of planar segment, E be the total energy consumption, and x be the delivery time of planar segment i. hi x iB and x i As a decision variable, when the planar segment h is the immediate predecessor of the planar segment i, x hi =1, otherwise x hi =0; when planar segment i enters x from pipeline B iB =1; otherwise x iB =0; when the planar segment i is displaced from the last workpiece, x i =1, if it moves out from the transverse moving position k, then x i =0.

[0021] Furthermore, the constraints in step S3 include: at time 0, the first processed planar segment has no predecessor segment; for all planar segments except the first processed planar segment, there is only one predecessor segment; each planar segment has at most one successor segment; a predecessor or successor relationship exists only when two planar segments are processed on the same production line; the time when a planar segment leaves the production line cannot exceed the delivery date.

[0022] Furthermore, the mapping and transformation of the discrete scheduling solution to the continuous gray wolf individual position vector using the encoding of random full permutation segmented sequence numbers specifically includes using the ROV rule based on random key encoding. First, n random numbers are randomly generated in the range [0, n], where n is the number of segments. ROV values ​​are assigned to each gray wolf individual position element according to the ascending order rule and correspond to the segmented scheduling scheme. The value of each element in the gray wolf individual position vector is determined based on the ROV value. When transforming the gray wolf individual position vector into the segmented scheduling scheme, the gray wolf individual position vector is arranged in ascending order, and each position element corresponds to an ROV value. The ROV value is the process arrangement scheme corresponding to the position vector.

[0023] Furthermore, the population initialization using reverse learning involves merging the randomly generated population and the reversed population into a new population, calculating the fitness function of the new population, sorting the fitness values ​​in ascending order, and selecting the top N optimal initial solutions as the new initial gray wolf population, wherein the randomly generated population is X. i =[x i1 , ..., x id , ...x iD ], where i = 1, 2, ..., N, and the reverse population is lb is the upper bound of the search space, and ub is the lower bound of the search space.

[0024] Furthermore, the adjustment and updating of the individual gray wolf position based on the dynamic inertia weight factor is performed using the following formula.

[0025] D α =|C1·X α -wX|,D β =|C2·X β -wX|,D δ =|C3·X δ -wX|

[0026] X1 = X α -A1·D α X2 = X β -A2·D β X3 = X δ -A3·D δ

[0027] v i，j =w·v i，j +C1·r1·(X1-x)+C2·r2·(X2-X)+C3·r3·(X3-X)

[0028] X(t+1)=X+v i，j

[0029]

[0030] D α D β and D δ Let X represent the distances between individual gray wolf ω and gray wolf α, and gray wolf β and gray wolf δ, respectively. α X β and X δLet X represent the current positions of gray wolves α, β, and δ, respectively. Let X represent the current position of individual gray wolf ω. Let X1, X2, and X3 represent the positions that individual gray wolf ω needs to adjust due to the influence of gray wolves α, β, and δ, respectively. Let A and C be the relationship coefficients, and let r1, r2, and r3 be random numbers in [0, 1]. i，j ω is the speed at which the individual gray wolf moves, w is the dynamic inertia weight factor, i is the number of iterations in the current algorithm, Max_iter is the maximum number of iterations set by the algorithm, and X(t+1) represents the final position of the individual gray wolf ω.

[0031] Furthermore, the step of solving the objective function using the improved multi-objective gray wolf optimization algorithm to obtain the optimal scheduling scheme includes the following steps:

[0032] Step 1: Set the algorithm parameters;

[0033] Step 2: Initialize the population using reverse learning;

[0034] Step 3: Calculate the fitness values ​​of individuals in the population and perform non-dominated ranking of the results;

[0035] Step 4: Initialize the external archive and store the non-dominant gray wolf individuals in the external archive;

[0036] Step 5: Use the roulette wheel method to select three types of wolves: α, β, and δ from the external files;

[0037] Step 6: Use a dynamic adaptive weighting strategy to update the location information of individual gray wolves based on dynamic inertia weighting factors;

[0038] Step 7: Perturb the positions of individual gray wolves to increase their exploration ability, and perform non-dominated sorting to obtain non-dominated solutions;

[0039] Step 8: Compare the new non-dominated solutions with the individuals in the external archives and update the external archives accordingly;

[0040] Step 9: Determine if the number of algorithm iterations is less than the maximum number of iterations; if yes, proceed to Step 5; otherwise, proceed to Step 10.

[0041] Step 10: Terminate the algorithm and output the non-dominated individuals as the current multi-objective optimization scheduling scheme.

[0042] Furthermore, the perturbation of the individual gray wolf's position is achieved by updating the individual gray wolf's position using the following formula.

[0043] X(t+1)=X+η*Cauchy(0,1)

[0044]

[0045] η is a variable that controls the intensity of Cauchy mutation, t is the current iteration number, Max_iter is the maximum iteration number, Cauchy is the probability density function of the Cauchy distribution, and X is the position of the gray wolf individual.

[0046] Furthermore, in step 8, after updating the external archives, when the number of individuals in the external archives exceeds the set upper limit, redundant individuals are removed based on the degree of crowding.

[0047] Furthermore, the calculation of the individual crowding degree is performed according to the following steps:

[0048] Step 801: Calculate the maximum value of each target value in the gray wolf population in turn. and minimum value

[0049] Step 802: Calculate the function value of the target g sequentially. And according to The values ​​are sorted in ascending order of feasible solutions;

[0050] Step 803: Calculate the congestion distance of the i-th feasible solution relative to the objective g, using the following formula:

[0051]

[0052] In the formula: The function value of the objective g of the previous feasible solution i is given by the function value of the objective g. Let g be the function value of the objective g of the next feasible solution after feasible solution i.

[0053] Step 804: After calculating the congestion distance, sum the congestion distances of each objective to obtain the congestion distance of the feasible solution.

[0054] The advantages of the technical solution provided by this invention are as follows:

[0055] The improved multi-objective gray wolf optimization algorithm in this invention exhibits superior solution-solving capabilities, with better solution distribution and convergence compared to comparative algorithms. Applying this improved multi-objective gray wolf optimization algorithm to a green scheduling method for ship planar segmented production lines, considering degradation effects, can effectively reduce energy consumption in production lines, achieving energy conservation while maintaining production efficiency. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of a segmented assembly line in a shipyard.

[0057] Figure 2 This is a vector diagram showing the location of the gray wolf.

[0058] Figure 3 This is a diagram illustrating the process of converting a scheduling scheme into individual location information.

[0059] Figure 4 A diagram illustrating the process of converting location elements into scheduling schemes.

[0060] Figure 5 This is an iterative curve diagram of the adaptive weighting factor.

[0061] Figure 6 The graph shows the iterative curve for the value of η.

[0062] Figure 7 This is a diagram illustrating the distance between people in crowded areas.

[0063] Figure 8 A schematic diagram of the process for improving the multi-objective gray wolf optimization algorithm.

[0064] Figure 9 Pareto front results for the test function are plotted for the four algorithms.

[0065] Figure 10 The Pareto distribution of the solution.

[0066] Figure 11 The Pareto optimal solution set obtained by different algorithms.

[0067] Figure 12 This is a Gantt chart of the scheduling scheme obtained in this embodiment. Detailed Implementation

[0068] The present invention will be further described below with reference to embodiments. It should be understood that these embodiments are only for illustrating the present invention and are not intended to limit the scope of the present invention. After reading this description, any modifications of this description in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0069] First, this embodiment introduces the problem and mathematical model addressed by the green scheduling method for ship planar segmented assembly lines that considers the deterioration effect.

[0070] For example Figure 1 The study focuses on the static scheduling problem of a planar segmented assembly line set up in a domestic shipyard, which is oriented towards energy conservation. It can be seen that the shipyard has set up a total of 2 assembly lines, each with the same 8 workstations.

[0071] The entire processing begins with the input of steel plates, proceeding sequentially through each station on each production line according to the process route. Sheet-shaped segments are processed sequentially at the first four stations, then transported out of the production line at the traverse station. Planar segments, however, require processing at all stations before being transported out of the production line via the exit station. Except for the base plate welding station, longitudinal frame assembly station, and longitudinal frame welding station, which are semi-automatic, all other stations require manual operation. After completing the operation at the current station, the worker must move to the next station to continue working. The worker's proficiency in operating the equipment at the current station and the speed of movement between different stations both affect the actual processing time, resulting in a deterioration effect. This invention uses a linear function to describe the phenomenon of processing time deterioration, α. i，j S represents the degradation rate of planar segment i at station j. i，j T′ represents the start time of planar segment i at workstation j. i，j T represents the actual processing time of planar segment i at station j. i，j Let T' represent the basic processing time of planar segment i at station j. Then, the actual processing time of planar segment i at station j can be expressed as: T′ i，j =T i，j +αS i，j .

[0072] This invention uses the triplet representation method of α|β|γ to define the energy-saving planar segmented static scheduling problem as: F|block, α i，j |(makespan min E min The problem is described as follows: n planar segments of type S need to be processed at m stations on N production lines. The k-th station on each production line is a transverse moving station connected by a conveyor belt. The exit is located at the transverse moving station on the N-th production line, allowing the segment to be moved out after processing. Each production line has the same station layout and production capacity. The processing time of the i-th planar segment at each station deteriorates linearly with the start time at that station. It is important to note that regardless of which production line the segment is processed on, it can only be moved out of the production line via the transverse moving station on the N-th production line after processing.

[0073] At the same time, the following assumptions are made:

[0074] ① The processing time for planar segments on the transverse moving station is 0;

[0075] ② Within the same time frame, one workstation can only process one planar segment;

[0076] ③ When a planar segment is being processed at a certain workstation, the processing should not be interrupted by other factors;

[0077] ④ When a planar segment is completed at the current workstation, if the next workstation is still processing, it needs to wait at the current workstation until the planar segment at the next workstation leaves.

[0078] ⑤ The transfer time between different workstations for the planar segment is not considered;

[0079] ⑥ Planar segmentation does not require adjustments between production lines; processing is only performed on the same production line.

[0080] ⑦ The machines at the workstations are always available and do not malfunction.

[0081] Based on the above problem description and assumptions, a static scheduling mathematical model for a planar segmented pipeline considering the degradation effect is established, including the following:

[0082] ① Maximum completion time

[0083]

[0084]

[0085] T′ i，j =T i，j +αS i，j (3)

[0086] T i =x i C i，m +(1-x i C i，h (4)

[0087] L i =x i L i，m +(1-x i )L i，h (5)

[0088] ②Total energy consumption

[0089] The total energy consumption on a planar segmented assembly line consists of two parts: processing energy consumption at each workstation and standby energy consumption.

[0090] Processing energy consumption:

[0091]

[0092] Standby power consumption:

[0093]

[0094] Total energy consumption:

[0095] E = E w +E P(8)

[0096] There are two optimization objectives: minimizing the maximum completion time and minimizing energy consumption. Therefore, the objective function can be expressed as:

[0097] f1 = min C max (9)

[0098] f2 = min E (10)

[0099] The constraints are:

[0100]

[0101]

[0102]

[0103]

[0104] L i ≤DT i i≤n (15)

[0105] The meanings of the parameters in the above formulas are shown in Table 1.

[0106] Table 1 Required parameters and their meanings

[0107]

[0108]

[0109] Equation (1) represents the calculation of the completion time of planar segment i at different workstations under different conditions. Equation (2) represents the departure time of planar segment i at each workstation. When i≤2, i is the first planar segment processed on each production line, so the departure time is equal to the completion time. When i>2, j≠k, j≠m, the completion time of the previous segment needs to be considered, and the departure time is obtained by comparison. Equation (3) represents the linear deterioration relationship between the actual processing time of the segment and its start time. Equation (4) represents the final completion time of all planar segments. Equation (5) represents the departure time of all planar segments from the production line. Equations (6)-(8) are the energy consumption costs generated by the processing of segments on the production line and the blockage. Equations (9) and (10) represent the optimization objectives, i.e., minimizing the maximum completion time and energy consumption cost respectively. Equation (11) indicates that at time 0, the first processed planar segment has no preceding segment. Equation (12) indicates that for each planar segment except the first one processed, there is only one preceding segment. Equation (13) indicates that each planar segment has at most one succeeding segment. Equation (14) indicates that a preceding or succeeding relationship exists only when two planar segments are processed on the same production line. Equation (15) indicates that the time a planar segment leaves the production line cannot exceed the delivery date.

[0110] Since the static scheduling problem of planar segmented pipelines considering the degradation effect is difficult to solve directly with an accurate solution, an improved multi-objective gray wolf optimization algorithm is proposed to obtain the optimal solution. The improved multi-objective gray wolf optimization algorithm is described in detail below.

[0111] ① Coding mechanism

[0112] A random permutation segment numbering method is used for encoding. The encoding order represents the processing sequence of segments on the production line. The first two digits of the code indicate the first segment processed on each of the two production lines. For example, L = {4,2,6,7,3,1,5,8} means that segment 4 is the first segment processed on production line A, segment 2 is the first segment processed on production line B, segment 6 starts processing when an idle station becomes available, and so on. Figure 2 As shown, x l This represents the position vector of the gray wolf.

[0113] Since the basic GWO algorithm is mostly used to solve optimization problems of continuous variable functions, it cannot directly update the processing sequence of ship planar sections. Therefore, a mapping is used to convert between discrete scheduling solutions and continuous gray wolf individual position vectors. In this embodiment, using the ROV (Ranked Order Value) rule based on random key encoding, n random numbers are first randomly generated in the range [0, n] (n is the number of sections). Each gray wolf individual position element is assigned an ROV value according to the ascending order rule, and this value corresponds to the section scheduling scheme. The value of each element in the gray wolf individual position vector is determined based on the ROV value. The conversion process is as follows: Figure 3 As shown.

[0114] Similarly, the individual wolf position vectors also need to be converted into a segmented scheduling scheme, a process that also uses the ROV rule. First, the individual wolf position vectors are arranged in ascending order, so each position element corresponds to an ROV value. Then, the ROV value represents the process arrangement scheme corresponding to the position vector, such as... Figure 4 As shown, the final process sequence is [4, 2, 6, 7, 3, 1, 5, 8].

[0115] ② Population initialization based on reverse learning

[0116] To ensure the diversity of the gray wolf population, the initial population is generated using two methods. First, a portion of the initial population is generated using the NEH heuristic algorithm: 1) The processing time of each plane segment on all machines is summed, and the summed values ​​are sorted from largest to smallest; 2) The plane segment with the longest processing time after sorting is defined as the first plane segment to be processed, and then the second-ranked plane segment is inserted before or after it, and the completion time is calculated for each, saving the smaller result; 3) The result of the previous step is saved, and the next sorted plane segment is inserted before or after the previous plane segment, and the completion time is calculated for each, saving the smaller solution; 4) The previous step is repeated to obtain the final result. The other part of the initial population is generated using a random method, with the initialization formula as shown in equation (16):

[0117]

[0118] In the formula: N represents the population size, D represents the number of planar segments, and upper j and lower j These represent the upper and lower ranges of the position of the j-th individual gray wolf. random is a random number in the interval [0, 1].

[0119] Opposition-Based Learning (OBL) is a mathematical computation method proposed by Tizhoosh in 2005. It primarily compares the current feasible solution with its corresponding inverse solution within the search space, selecting the better solution for the next iteration. Its definition is as follows:

[0120] Definition 1: Reverse number.

[0121] Suppose there is a real number x ∈ [a, b] in a one-dimensional search space, then the inverse of x is expressed as:

[0122]

[0123] Similarly, if X = (x1, x2, ..., x...) D Let x be a point in the D-dimensional search space. i ∈[a i b i If X is the inverse number of X, then X is... in:

[0124]

[0125] Definition 2: General reverse learning.

[0126] like x is a feasible solution in D-dimensional space. ij ∈[a j b j (j = 1, 2, ..., D), then x i reverse number Then it is calculated using the following formula:

[0127]

[0128] In the formula: k is a random number uniformly distributed on [0, 1].

[0129] Most current swarm intelligence algorithms typically use random methods to generate the initial population, resulting in insufficient diversity and a tendency to get trapped in local optima. Introducing a reverse learning strategy can improve population diversity and accelerate convergence. The main steps of the reverse learning strategy are: (1) randomly generate the initial population within the search space; (2) calculate and generate the corresponding reverse population according to relevant formulas; (3) select the better individual from the two populations as the population for the next iteration. In this way, each individual in the generated initial population is relatively closest, thus improving the convergence speed.

[0130] Assume the randomly generated initial population is X i =[x i1 , ..., xid , ...x iD ], where i = 1, 2, ..., N, then X i The corresponding reverse population definition is:

[0131]

[0132] Where lb is the upper bound of the search space and ub is the lower bound of the search space. The randomly generated population and the reverse population are merged into a new population. The fitness function of the new population is calculated, and the fitness values ​​are sorted in ascending order. The top N optimal initial solutions are taken as the new initial gray wolf population.

[0133] ③ Dynamic adaptive weight strategy

[0134] In the global search process of the basic gray wolf optimization algorithm, the position update of candidate gray wolves is guided by three types of wolves: α, β, and δ. To avoid premature convergence, an adaptive weight factor is introduced to improve the algorithm's development capability. Most studies typically use linearly adjusted inertia weights, which, while simple and intuitive, cannot fully coordinate the global and local search performance of the algorithm. To enhance the search capability of gray wolves, a dynamic inertia weight factor w is proposed for adjustment, increasing the gray wolf's movement speed parameter. This factor can be dynamically adjusted based on the positions of the α, β, and δ wolves to further update the position of the gray wolf. Specifically, it is calculated according to the following formula:

[0135] D α =|C1·X α -wX|,D β =|C2·X β -wX|,D δ =|C3·X δ -wX| (20)

[0136] X1 = X α -A1·D α X2 = X β -A2·D β X δ =X δ -A3·D δ (twenty one)

[0137] v i，j =w·v i，j +C1·r1·(X1-X)+C2·r2·(X2-X)+C3·r3·(X3-X) (22)

[0138] X(t+1)=X+v i，j (twenty three)

[0139]

[0140] In the formula: i is the current iteration number of the algorithm, and Max_iter is the maximum number of iterations set for the algorithm. From Figure 5 It can be seen that the adaptive weight factor has a large value in the early stage of the iteration, which helps with global search. In the later stage of the iteration, the curve descent rate slows down, the weight is smaller, which enhances the ability of local search and improves accuracy.

[0141] ④ Variant Cauchy perturbation

[0142] The Grey Wolf optimization algorithm is characterized by its few parameters and ease of control, resulting in relatively fast convergence. However, this also introduces certain drawbacks, causing it to sometimes get stuck in local optima instead of finding the global optimum. Cauchy mutation, on the other hand, allows the algorithm to have a larger step size during the search, enabling it to escape local optima and providing a more comprehensive global search capability.

[0143] The main way Cauchy mutation is to use the Cauchy distribution function, and formula (26) is the probability density function of the Cauchy distribution in the one-dimensional case.

[0144]

[0145] Where t is a proportionality parameter, and its value is greater than 0. In particular, when t = 1, it is the standard Cauchy probability density function.

[0146] The Cauchy distribution tends to zero at both ends at a slower rate and the process is relatively smooth. The values ​​near the peak near the origin are relatively small, so Cauchy mutation has an advantage in terms of perturbation ability. Introducing Cauchy mutation perturbation can improve the global search ability of the improved multi-objective gray wolf algorithm and prevent the algorithm from being unable to escape local optima. At the same time, it can increase the diversity of the population and accelerate the convergence speed of the algorithm, so that the perturbation near the mutated individual is generated, thereby allowing the entire population to search for optimization in a larger range. Therefore, the basic Cauchy mutation formula is improved, and the improved Cauchy mutation formula is shown in equation (27):

[0147] X(t+1)=X+η*Cauchy(0,1) (27)

[0148]

[0149] In the formula: η is the variable that controls the intensity of Cauchy mutation, t is the current iteration number, and Max_iter is the maximum iteration number.

[0150] from Figure 6 It can be seen that the value of η decreases as the number of iterations increases. At the same time, the perturbation of the population is relatively large in the early stage of iteration, which increases the ability of global search, while the step size is smaller in the later stage of iteration, which accelerates convergence and finds the optimal solution quickly.

[0151] ⑤ External archive maintenance mechanism

[0152] Since the non-dominated solutions found by the algorithm need to be compared and updated, an external archive is needed to store these solutions. The size of the external archive is defined as LN, and it needs to be updated as the IMOGWO algorithm iterates. At the beginning of the algorithm's iteration, the external archive is defined as an empty set. As the algorithm iterates, the number of Pareto solutions in the external archive increases. When the maximum size LN of the external archive is reached, it needs to be maintained to ensure the quality of the Pareto solutions. To ensure higher quality and more uniform distribution of Pareto solutions in the external archive, this chapter uses a crowding method for selection. A uniform distribution of feasible solutions implies a larger crowding distance. Therefore, by calculating and comparing non-dominated solutions with larger crowding distances, elite individuals can be retained in the external archive.

[0153] To illustrate this better, assume that the problem model being solved has m objectives to optimize, and that the congestion of the i-th feasible solution is defined as d. i The crowding distance can be calculated using the following steps:

[0154] Step 1: Calculate the maximum value of each target value in the gray wolf population in turn. and minimum value

[0155] Step 2: Calculate the function value of the target g sequentially. And according to The values ​​are sorted in ascending order of feasible solutions;

[0156] Step 3: Calculate the congestion distance of the i-th feasible solution relative to the target g, using the following formula:

[0157]

[0158] In the formula: The function value of the objective g of the previous feasible solution i is given by the function value of the objective g. Let g be the function value of the objective g of the next feasible solution after feasible solution i.

[0159] Step 4: After calculating the congestion distance, sum the congestion distances of each target to obtain the congestion distance of the feasible solution. The calculation formula is shown in formula (30):

[0160]

[0161] like Figure 7The figure shows the crowding distance of individual i in the current population.

[0162] Based on the above description, please refer to... Figure 8 As shown, the improved multi-objective gray wolf optimization algorithm flow is as follows:

[0163] Step 1: Set algorithm parameters, including population size, external archive size, etc.;

[0164] Step 2: Initialize the population using reverse learning;

[0165] Step 3: Calculate the fitness values ​​of individuals in the population and perform non-dominated ranking of the results;

[0166] Step 4: Initialize the external archive and store the non-dominant gray wolf individuals in the external archive;

[0167] Step 5: Use the roulette wheel method to select three types of wolves: α, β, and δ from the external files;

[0168] Step 6: Use a dynamic adaptive weighting strategy to update the location information of individual gray wolves according to the formula;

[0169] Step 7: Apply the variation Cauchy perturbation method to perturb the position of individual gray wolves, increase their exploration ability, and perform non-dominated sorting to obtain non-dominated solutions;

[0170] Step 8: Compare the new non-dominated solutions with the individuals in the external archive and update the external archive; if the number of individuals in the external archive exceeds the set limit, maintain the external archive according to the individual crowding.

[0171] Step 9: Determine if the number of algorithm iterations is less than the maximum number of iterations. If yes, proceed to Step 5; otherwise, proceed to Step 10.

[0172] Step 10: Terminate the algorithm and output the non-dominated individuals as the current multi-objective optimization scheme.

[0173] To verify the effectiveness and practicality of the method of this invention, the algorithm's performance is first analyzed to prove its effectiveness. Then, both numerical experiments and practical examples are used to test the algorithm and prove its practicality. Numerical experiments demonstrate a strong dominant relationship between maximum completion time and energy consumption. Practical examples are then used to optimize the method using data from a shipyard's actual planar segmented production line, demonstrating its engineering applicability.

[0174] 1) Performance metrics of multi-objective optimization algorithms

[0175] For multi-objective optimization problems, the solution set is usually obtained, and it is not possible to directly compare each solution in the set to determine the performance of the algorithm. Two evaluation metrics, IGD and Spacing, are chosen to assess the algorithm's performance. IGD reflects the algorithm's convergence, while Spacing reflects the distribution of solutions.

[0176] ① Anti-generational distance evaluation index

[0177] Inverted Generational Distance (IGD) is defined as follows.

[0178]

[0179] In the formula: P represents the set of points on the true Pareto front, and |P| represents the number of points in P. Q is the optimal solution set obtained by the algorithm, and d(v, Q) represents the minimum Euclidean distance from a point v in P to the solution set Q. From the above definition of the IGD index, it can be seen that the smaller the value of IGD, the better the convergence and distribution of the algorithm. Specifically, when IGD(P, Q) = 0, it indicates that the optimal solution obtained by the algorithm coincides with the true Pareto front.

[0180] ② Spacing Indicators

[0181] The spacing metric is defined as follows:

[0182]

[0183] In the formula: d i =min(|f1(x) i )-f1(x j )|+|f2(x i )-f2(x j )|) represents the shortest distance between two solutions, where i, j = 1, 2, ..., n, and d i Represents all d i The average value of S is given by n, where n is the number of Pareto optimal solutions. From formula (32), it can be seen that the smaller the value of S, the better the algorithm's performance. Specifically, it can be seen that when S = 0, it indicates that the solutions obtained by the algorithm are all equally spaced on Pareto.

[0184] For algorithm test functions, five functions from the ZDT series, ZDT1-4 and ZDT6, are mainly used, as shown in Table 2. Furthermore, in this section, the maximum size of external files is limited to 100. For each algorithm, each test function is solved through 30 independent runs to obtain the mean and standard deviation of the metrics.

[0185] Table 2 Benchmark Functions

[0186]

[0187]

[0188] 2) Algorithm Performance Analysis

[0189] To provide a more intuitive and comprehensive demonstration of the performance of the method of this invention, three widely used and classic multi-objective optimization algorithms were selected for comparison: MOPSO (Multi-objective particle swarm optimization), NSGA-II (Non-dominated sorting genetic algorithm-II), and SPEA2 (Improving the strength pareto evolutionary algorithm). The relevant parameter settings during the operation of each algorithm are shown in Table 3.

[0190] Table 3 Comparison of Algorithm Parameter Settings

[0191]

[0192] The IGD index obtained by calculating the standard test function is shown in Table 4, and the Spacing index is shown in Table 5, where the mean and standard deviation are listed in the table.

[0193] Table 5 shows the IGD index values ​​of different optimization algorithms when calculating the ZDT series test functions. As can be seen from the table, when calculating the four test functions ZDT1, ZDT2, ZDT3, and ZDT6, by comparing the mean and standard deviation of the calculation results, it can be seen that the IMOGWO algorithm (improved multi-objective gray wolf optimization algorithm) proposed in this chapter performs better than the other three algorithms. However, when calculating the ZDT4 test function, the IMOGWO algorithm's results are slightly less ideal compared to the other three algorithms. Nevertheless, for the ZDT test functions as a whole, IMOGWO still performs better than the other three comparative algorithms.

[0194] Table 4 shows the IGD index values ​​of the four algorithms on the ZDT series test functions.

[0195]

[0196] Table 5 shows the Spacing index values ​​of different optimization algorithms when calculating the ZDT series test functions. As can be seen from the table, when calculating the five test functions ZDT1, ZDT2, ZDT3, ZDT4, and ZDT6, by comparing the mean and standard deviation of the calculation results, it can be seen that the IMOGWO algorithm yields better results than the other three comparison algorithms. Therefore, this further demonstrates that the IMOGWO algorithm has good convergence. Better convergence means that the obtained Pareto solution set is more uniformly distributed and closer to the ideal Pareto optimal solution set.

[0197] Table 5 shows the Spacing index values ​​of the four algorithms on the ZDT series test functions.

[0198]

[0199]

[0200] To more intuitively illustrate the differences in Pareto solution sets obtained by various algorithms for solving the test functions, we plotted the Pareto solution sets of different algorithms when calculating the four test functions ZDT1, ZDT2, ZDT3, and ZDT6, and compared them with the true Pareto front. Figure 9 As shown, the IMOGWO algorithm yields a solution of higher quality than the other algorithms, and more closely approximates the true Pareto front of the problem.

[0201] 3) Numerical Experiments

[0202] Before verifying the practicality of the energy-saving planar segmented pipeline scheduling method, in order to illustrate the mutually dominant relationship between maximum completion time and total processing energy consumption, the corresponding Pareto front distribution was first generated through numerical experiments.

[0203] Consider the following planar assembly line scheduling problem: There are 15 planar segments that need to be processed, and there are a total of 8 workstations on the assembly line. The relevant parameters are shown in Tables 6-8.

[0204] Table 6. Processing time for planar segments

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[0206]

[0207] Table 7 Deterioration Rate

[0208]

[0209] Table 8 Energy Consumption Power

[0210] workstation ​ ​

[0077] J3 [CD AT J4]

[0075] J5 [CD AT J6] <![CDATA[J7]]> <![CDATA[J8]]> Processing power (kW) 36 54 72 36 0 108 108 36 Standby power (kW) 4 6 8 4 0 12 12 4

[0211] The problem was solved using IMOGWO, and the results and the distribution of the solutions are shown in Table 9 and 1, respectively. Figure 10 As shown. From Figure 10 It can be seen that the optimal Pareto front consists of 13 points, thus proving that there is a clear dominant relationship between completion time and energy consumption.

[0212] Table 9 Maximum Completion Time and Total Processing Energy Consumption

[0213]

[0214]

[0215] Since energy-saving targets and time indicators conflict with each other, a reduction in energy consumption will lead to a corresponding increase in time. However, by calculating the percentage change of the optimization target obtained from different schemes, a scheduling scheme that is more suitable for the current production situation can be selected.

[0216] Based on the above results, the following conclusions can be drawn: the method of this invention has better algorithmic performance compared with the other three classic algorithms. The results of IGD and Spacing index values ​​obtained after calculating standard test cases for several different algorithms show that, for various types of multi-objective problems, the IMOGWO algorithm has better solution capability, and its solution distribution and convergence are superior to the compared algorithms.

[0217] Numerical experiments show that the energy-saving planar segmented pipeline scheduling method can effectively reduce the energy consumption of pipeline production, achieve the goal of energy saving, and at the same time ensure production efficiency.

[0218] Taking the processing of 20 sections of different types in a shipyard A as an example, the deterioration rate of each section at different workstations is related to the current skill level of the workers, their fatigue level, and the performance of the equipment. Workers cannot always maintain the same work efficiency and skill level, and the performance of the equipment will also change with the increase of usage time. Therefore, the deterioration rate of different sections at the same workstation is not a constant value. The deterioration rate α is defined as a uniform distribution in the interval [0.010, 0.100]. By statistically analyzing historical data from the actual production process of the shipyard, the average processing time of each section at each workstation and the energy consumption power at each workstation are further calculated. The processing time (unit: h) and deterioration rate of the sections to be processed at each workstation are shown in Tables 10 and 11, respectively. IMOGWO, NSGAII, and MOPSO are used for calculation.

[0219] Table 10 shows the processing time and delivery time of each segment to be processed at each workstation.

[0220] Segmentation Segmentation type <![CDATA[J1]]> <![CDATA[J2]]> <![CDATA[J3]]> <![CDATA[J4]]> <![CDATA[J5]]> <![CDATA[J6]]> <![CDATA[J7]]> <![CDATA[J8]]> DT 1 <![CDATA[G1]]> 3 2 4 1 0 2 3 5 70 2 <![CDATA[G1]]> 3 2 4 1 0 2 3 5 50 3 <![CDATA[G1]]> 3 2 4 1 0 2 3 5 90 4 <![CDATA[G1]]> 3 2 4 1 0 2 3 5 95 5 <![CDATA[G1]]> 3 2 4 1 0 2 3 5 50 6 <![CDATA[G2]]> 5 4 6 3 0 0 0 0 110 7 <![CDATA[G2]]> 5 4 6 3 0 0 0 0 60 8 <![CDATA[G2]]> 5 4 6 3 0 0 0 0 65 9 <![CDATA[G2]]> 5 4 6 3 0 0 0 0 110 10 <![CDATA[G2]]> 5 4 6 3 0 0 0 0 85 11 <![CDATA[G3]]> 6 3 5 1 0 1 4 2 70 12 <![CDATA[G3]]> 6 3 5 1 0 1 4 2 50 13 <![CDATA[G3]]> 6 3 5 1 0 1 4 2 60 14 <![CDATA[G3]]> 6 3 5 1 0 1 4 2 50 15 <![CDATA[G3]]> 6 3 5 1 0 1 4 2 50 16 <![CDATA[G4]]> 2 5 1 4 0 0 0 0 70 17 <![CDATA[G4]]> 2 5 1 4 0 0 0 0 70 18 <![CDATA[G4]]> 2 5 1 4 0 0 0 0 110 19 <![CDATA[G4]]> 2 5 1 4 0 0 0 0 40 20 <![CDATA[G4]]> 2 5 1 4 0 0 0 0 60

[0221] Table 11 Values ​​of Deterioration Rate Parameter

[0222]

[0223]

[0224] Through example calculations, the Pareto optimal solution sets obtained by different algorithms are shown in Table 12, along with the corresponding Pareto solution set graphs. Figure 11 As shown in the table, the IMOGWO algorithm proposed in this chapter also performs well in the energy-saving planar segmented pipeline scheduling problem, reducing energy consumption while ensuring a small maximum completion time.

[0225] Table 12. Pareto optimal solution sets obtained by different algorithms.

[0226]

[0227] from Figure 11 As can be seen from the results, the Pareto solution set obtained by IMOGWO is better than that obtained by NSGAII and MOPSO algorithms. Therefore, it can be proved that IMOGWO is also well applicable to the actual problems of shipyards.

[0228] Furthermore, comparing the scheme with the minimum completion time obtained by applying the improved multi-objective gray wolf optimization algorithm with the scheme with the minimum energy consumption, the completion time is increased by 12.8%, but energy consumption is reduced by 27.8%. Therefore, it can be proven that the energy-saving planar segmented pipeline scheduling method can effectively reduce the energy consumption of pipeline production, achieving energy conservation while ensuring production efficiency. Because a delivery date constraint is set, the time for each planar segment to leave the pipeline in each generated scheme is within the delivery date. Therefore, neither the scheduling scheme with the minimum energy consumption nor the scheduling scheme with the minimum completion time will affect the overall construction task.

[0229] Figure 12 This document presents a Gantt chart of scheduling schemes calculated using the IMOGWO algorithm, resulting in a maximum completion time of 92.76 hours and energy consumption of 31378.9 kWh. This chart can provide relevant reference for planning and production personnel. Different solutions correspond to different scheduling schemes. If the current production task is somewhat delayed, the completion time should be prioritized, and the scheme with the shorter completion time should be selected. If the current production task is ahead of schedule, the scheme with the lower energy consumption can be selected. Of course, this does not mean that it is the same as the previous experience-based scheduling method. Since each scheduling scheme is reasonable and meets the delivery deadline, production managers can choose the scheme based on the current actual production situation without wasting resources or delaying tasks.

Claims

1. A green scheduling method for ship planar segmented assembly lines considering deterioration effects, characterized in that, Includes the following steps: Step S1: Establish a static scheduling model for a planar segmented pipeline that uses a linear function to describe the deterioration of processing time. The static scheduling model for the planar segmented pipeline includes the maximum completion time and total energy consumption, where the total energy consumption is the sum of processing energy consumption and standby energy consumption. Step S2: Based on the static scheduling model of the planar segmented pipeline, the objective function is determined to be minimizing the maximum completion time and minimizing energy consumption; Step S3: Determine the constraints of the scheduling process. The constraints include: at time 0, the first processed planar segment has no predecessor segment; for all planar segments except the first processed segment, each other planar segment has only one predecessor segment; each planar segment has at most one successor segment; a predecessor or successor relationship exists only when two planar segments are processed on the same pipeline; the time a planar segment leaves the pipeline cannot exceed the delivery date. Step S4: Solve the objective function using the improved multi-objective gray wolf optimization algorithm to obtain the optimal scheduling scheme; In the improved multi-objective gray wolf optimization algorithm, the discrete scheduling solution is mapped and transformed to the continuous gray wolf individual position vector by encoding the random full permutation segmented sequence number, and the population is initialized by reverse learning, and the gray wolf individual position is adjusted and updated based on the dynamic inertia weight factor. The population initialization using reverse learning involves merging the randomly generated population and the reverse-generated population into a new population, calculating the fitness function of the new population, sorting the fitness values ​​in ascending order, and selecting the top N optimal initial solutions as the new initial gray wolf population. The randomly generated population is... ,in The reverse population is lb is the upper bound of the search space, and ub is the lower bound of the search space; The adjustment and updating of the individual gray wolf positions based on the dynamic inertia weight factor is performed using the following formula. ， ， ， ， ， , and These represent individual gray wolves. With the gray wolf Grey Wolf With the gray wolf The distance between them , and They represent gray wolves. Grey Wolf With the gray wolf Current location Represents an individual gray wolf Current location , , They respectively represent the gray wolf Grey Wolf With the gray wolf Impact, individual gray wolves The position that needs to be adjusted and It is the correlation coefficient. , and These are random numbers in the range [0, 1]. It is a gray wolf. Speed ​​of movement Here, is the dynamic inertia weight factor, i is the current algorithm iteration number, and Max_iter is the maximum number of iterations set for the algorithm. Represents an individual gray wolf The final position.

2. The green scheduling method for ship planar segmented assembly lines considering deterioration effects according to claim 1, characterized in that, The maximum completion time is ， Total energy consumption is ,in For processing energy consumption, For standby power consumption, ， For planar segmented indexes, , For the index of processing stations, , Let i be the start time of processing of planar segment i at station j. Let i be the basic processing time of planar segment i at station j. Let i be the actual processing time of planar segment i at station j. Let i be the completion time of planar segment i at workstation j. Let i be the time when plane segment i leaves workstation j. Let i be the completion time of the planar segment i. Let i be the energy consumption per unit time when planar segment i is processed at station j. Let i be the standby power consumption per unit time of planar segment i when it is blocked at station j. Let i be the delivery time for plane segment i. Let be the deterioration rate, and be the maximum completion time for the planar segment. Total energy consumption, , and As a decision variable, when the planar segment h is the immediate predecessor of the planar segment i. ,otherwise When planar segment i enters from pipeline B ; otherwise When planar segment i moves out from the last workpiece If it moves out from the transverse traverse station k, then .

3. The green scheduling method for ship planar segmented assembly lines considering deterioration effects according to claim 1, characterized in that, The specific steps of mapping and converting discrete scheduling solutions to continuous gray wolf individual position vectors using random permutation segmented sequence number encoding include: firstly, generating n random numbers within the range [0, n], where n is the number of segments; assigning an ROV value to each gray wolf individual position element according to ascending order, and corresponding it to the segmented scheduling scheme; determining the value of each element in the gray wolf individual position vector based on the ROV value; and during the conversion from gray wolf individual position vectors to segmented scheduling schemes, arranging the gray wolf individual position vectors in ascending order, with each position element corresponding to an ROV value, which is the process arrangement scheme corresponding to the position vector.

4. The green scheduling method for ship planar segmented assembly lines considering deterioration effects according to any one of claims 1 to 3, characterized in that, The process of solving the objective function using the improved multi-objective gray wolf optimization algorithm to obtain the optimal scheduling scheme includes the following steps: Step 1: Set the algorithm parameters; Step 2: Initialize the population using reverse learning; Step 3: Calculate the fitness values ​​of individuals in the population and perform non-dominated ranking of the results; Step 4: Initialize the external archive and store the non-dominant gray wolf individuals in the external archive; Step 5: Select from external files using the roulette wheel method. , , Three types of wolves; Step 6: Use a dynamic adaptive weighting strategy to update the location information of individual gray wolves based on dynamic inertia weighting factors; Step 7: Perturb the positions of individual gray wolves to increase their exploration ability, and perform non-dominated sorting to obtain non-dominated solutions; Step 8: Compare the new non-dominated solutions with the individuals in the external archives and update the external archives accordingly; Step 9: Determine if the number of algorithm iterations is less than the maximum number of iterations; if yes, go to Step 5; otherwise, go to Step 10. Step 10: Terminate the algorithm and output the non-dominated individuals as the current multi-objective optimization scheduling scheme.

5. The green scheduling method for ship planar segmented assembly lines considering deterioration effects according to claim 4, characterized in that, The perturbation of the individual gray wolf's position is achieved by updating the individual gray wolf's position using the following formula. ， ， The variable controlling the intensity of Cauchy mutation, where t is the current iteration number. The maximum number of iterations, Let Cauchy's probability density function be . This refers to the location of an individual gray wolf.

6. The green scheduling method for ship planar segmented assembly lines considering deterioration effects according to claim 4, characterized in that, In step 8, after updating the external archives, when the number of individuals in the external archives exceeds the set upper limit, excess individuals are removed based on the crowding level.

7. The green scheduling method for ship planar segmented assembly lines considering deterioration effects according to claim 6, characterized in that, The calculation of individual crowding is performed according to the following steps: Step 801: Calculate the maximum value of each target value in the gray wolf population in turn. and minimum value ; Step 802: Calculate the function value of the target g sequentially. and according to The values ​​are sorted in ascending order of feasible solutions; Step 803: Calculate the congestion distance of the i-th feasible solution relative to the objective g, using the following formula: ， In the formula: The function value of the objective g of the previous feasible solution i is given by the function value of the objective g. Let g be the function value of the objective g of the next feasible solution after feasible solution i. Step 804: After calculating the congestion distance, sum the congestion distances of each objective to obtain the congestion distance of the feasible solution.

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