A steam turbine shop layout optimization method, system, device and medium
By using Sobol sequence initialization, dynamically adjusted crossover and mutation probabilities, and a non-dominated sorting strategy, the problem of poor initial solution quality in the traditional NSGA-II algorithm for multi-period reconfigurable layouts in turbine workshops is solved, achieving more efficient layout optimization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHENYANG UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2025-09-22
- Publication Date
- 2026-06-16
AI Technical Summary
The traditional NSGA-II algorithm has poor initial solution quality in multi-period reconfigurable layouts of steam turbine workshops, low optimization efficiency, and is prone to getting trapped in local optima, failing to meet the requirements for efficient and accurate layout.
The population is initialized using Sobol sequences, local search is performed by combining crossover and mutation probabilities of different sizes, and optimization is achieved through a non-dominated sorting strategy to finally determine the optimal layout scheme.
It improves the quality of the initial solution, accelerates the convergence speed of the algorithm, enhances the dynamic adjustment capability of the search strategy, avoids getting trapped in local optima, and yields a faster and more accurate optimal layout scheme.
Smart Images
Figure CN121189168B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of workshop layout optimization technology, and in particular to a method, system, equipment and medium for optimizing the layout of a steam turbine workshop. Background Technology
[0002] The workshop is the core of a manufacturing system, and its layout directly impacts the efficiency of numerous activities during production, such as manufacturing, assembly, and material handling. When producing complex, customized products, the flexibility and adaptability of the workshop layout are crucial due to the characteristics of high variety, small batches, and rapid customization. A well-designed workshop layout can significantly reduce production waste, improve equipment utilization and production process continuity, and adapt to rapidly changing market demands, thereby enhancing the overall competitiveness of the enterprise. Furthermore, a rational workshop layout provides a solid foundation for subsequent automation upgrades and intelligent manufacturing, laying a competitive advantage for the enterprise's long-term development.
[0003] Multi-period reconfigurable layouts belong to the dynamic shop floor layout optimization problem with multiple optimization objectives. Solving this type of problem is highly complex, with key challenges including: the large scale and numerous variables of the shop floor layout problem, leading to computational difficulties; potential conflicts between objectives during multi-objective optimization, making it difficult to find the optimal solution; and the dynamic reconfiguration of the shop floor based on production order changes further increasing the complexity. Furthermore, this is a combinatorial optimization problem, with solution time increasing exponentially with problem size. Therefore, advanced intelligent algorithms are commonly used to improve efficiency and quality in solving this type of problem. Currently, commonly used algorithms include multi-objective particle swarm optimization, simulated annealing, multi-objective differential evolution, and multi-objective ant colony optimization. The NSGA-II algorithm maintains population diversity and a uniform Pareto front distribution through mechanisms such as crowding distance and tournaments to ensure comprehensive solutions. Moreover, NSGA-II exhibits strong robustness and stability in solving multi-objective optimization problems, making it widely applicable to various types of multi-objective optimization problems.
[0004] Although NSGA-II has global search capabilities and diversity maintenance capabilities when handling multi-period reconfigurable layouts, the initial solution quality of the traditional NSGA-II algorithm is poor, the optimization efficiency is low, and it is easy to get trapped in local optima, which cannot meet the needs of the turbine workshop for efficient and accurate optimization of multi-period reconfigurable layouts. Summary of the Invention
[0005] Therefore, it is necessary to provide a method, system, equipment, and medium for optimizing the layout of a steam turbine workshop to address the aforementioned technical problems.
[0006] This invention provides a method for optimizing the layout of a steam turbine workshop, comprising:
[0007] Obtain production information from the steam turbine workshop;
[0008] Taking production information and multiple production cycles in the production process as inputs, and minimizing the logistics cost, reconfiguration cost and production unit area of the turbine workshop layout as objective functions, and the equipment layout scheme of each production cycle as output, a multi-cycle reconfigurable equipment layout problem model of the turbine workshop is constructed.
[0009] Based on the multi-period reconfigurable equipment layout problem model of the steam turbine workshop, Sobol sequence is used for population initialization to uniformly generate multiple initial populations representing the initial layout scheme of the steam turbine workshop.
[0010] Local searches were performed on all initial populations using crossover and mutation probabilities of different magnitudes to obtain subpopulations corresponding to each initial population; then the initial populations and their corresponding subpopulations were merged to obtain multiple intermediate populations representing candidate layout schemes for steam turbine workshops.
[0011] A non-dominated sorting strategy is used to sort multiple intermediate populations, and the intermediate population with the highest non-dominated sorting level is taken as the optimal population. The optimal layout scheme of the turbine workshop is determined based on the optimal population.
[0012] Alternatively, a multi-cycle reconfigurable device layout problem model can be constructed based on the following formula:
[0013] ;
[0014] ;
[0015] ;
[0016] in, Logistics costs during the production process, for Unit logistics handling cost during the production cycle for Equipment during the production cycle and equipment The transport distance between them for Equipment during the production cycle and equipment The frequency of material handling between them Indicates the cost of reconstruction. As decision variables, , , They are respectively the period Inside The cost of installing, moving, and dismantling various types of equipment. For period The profit generated per unit time in an internal production unit. For period Internal reconfiguration equipment Time required Indicates the area of the production unit. , for The horizontal and vertical coordinates of the equipment's location during the production cycle. , This refers to the lateral and longitudinal distances between the equipment and the unit boundary. This represents the number of production cycles.
[0017] Optionally, the model for the multi-cycle reconfigurable device layout problem satisfies model constraints, which specifically include:
[0018] The equipment location coordinates are determined based on the following formula. Relevant constraints:
[0019] ;
[0020] ;
[0021] ;
[0022] The relevant constraints for safety clearance are determined based on the following formula:
[0023]
[0024] The element boundary constraints are determined based on the following formula:
[0025] ;
[0026] ;
[0027] The following formula is used to determine the longitudinal constraints of equipment in the same row or equipment:
[0028] ;
[0029] ;
[0030] in, For peer equipment and The net distance between them As decision variables, This is the distance from the center of the first row of devices to the edge of the unit; This represents the center-to-center distance between two adjacent rows of devices.
[0031] Optionally, based on the following formula, a local search is performed on all initial populations using different crossover and mutation probabilities to obtain the subpopulations corresponding to each initial population:
[0032] ;
[0033] in, For crossover probability, For the maximum crossover probability, To minimize the crossover probability, ; To specify the maximum fitness of an individual, For individual fitness before crossover, The average fitness value of the population. This represents the maximum fitness value of the population.
[0034] ;
[0035] in, The mutation probability, The maximum mutation probability, The minimum mutation probability, ;
[0036] In this study, different crossover and mutation probabilities were used for individuals with different fitness levels in different initial populations.
[0037] Optionally, the non-dominated sorting strategy uses a hybrid encoding of floating-point encoding and binary encoding, encoding movable devices as 1 and non-movable devices as 0;
[0038] The non-dominated sorting strategy is used to sort multiple intermediate populations in a non-dominated manner, so that all mobile devices coded as 1 are removed from their current positions. The mobile devices coded as 1 are then selected from the existing vacant positions in descending order of their individual floating-point numbers, thus obtaining the optimal population.
[0039] This invention provides a turbine workshop layout optimization system, comprising:
[0040] The data acquisition module is used to acquire production information from the steam turbine workshop;
[0041] The model building module is used to construct a multi-cycle reconfigurable equipment layout problem model for the steam turbine workshop, taking production information and multiple production cycles in the production process as inputs, minimizing the logistics cost, reconfiguration cost and production unit area of the steam turbine workshop layout as objective functions, and taking the equipment layout scheme of each production cycle as output.
[0042] The initial layout module is used for the multi-period reconfigurable equipment layout problem model based on the turbine workshop. It uses the Sobol sequence for population initialization to uniformly generate multiple initial populations representing the initial layout scheme of the turbine workshop.
[0043] The intermediate layout module is used to perform local searches on all initial populations using crossover and mutation probabilities of different sizes to obtain subpopulations corresponding to each initial population; and to merge the initial populations and their corresponding subpopulations to obtain multiple intermediate populations representing candidate layout schemes for the turbine workshop.
[0044] The final layout module is used to perform non-dominated sorting on multiple intermediate populations using a non-dominated sorting strategy, and to select the intermediate population with the highest non-dominated sorting level as the optimal population, and to determine the optimal layout scheme of the turbine workshop based on the optimal population.
[0045] This invention provides a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the above-described turbine workshop layout optimization method.
[0046] This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described turbine workshop layout optimization method.
[0047] The turbine workshop layout optimization method, system, equipment, and medium provided in this invention have the following advantages compared with the prior art:
[0048] In solving the multi-period reconfigurable equipment layout problem model, this invention not only uniformly generates an initial population in the algorithm space to improve the quality of the initial solution and accelerate the convergence speed of the algorithm, but also dynamically adjusts the search strategy to improve the uniformity and diversity of the solution set distribution. This process avoids the problems of low optimization efficiency and easy getting trapped in local optima in the traditional NSGA-II algorithm, and obtains the optimal turbine workshop layout scheme faster and more accurately. Attached Figure Description
[0049] Figure 1 This is a flowchart illustrating a turbine workshop layout optimization method provided in one embodiment;
[0050] Figure 2 This is a material flow-distance analysis diagram of a turbine workshop layout optimization method provided in one embodiment;
[0051] Figure 3 This is a framework diagram of an improved NSGA-II algorithm for a turbine workshop layout optimization method provided in one embodiment;
[0052] Figure 4 A U-shaped layout illustration of a turbine workshop layout optimization method provided in one embodiment;
[0053] Figure 5 This is an optimal layout diagram of one embodiment of a turbine workshop layout optimization method. Figure 5 (a) in the text represents production cycle 1. f 1. Optimal layout Figure 5 (b) in the text represents production cycle 2. f 1. Optimal layout;
[0054] Figure 6 This is an optimal layout diagram of Scheme 2 for a turbine workshop layout optimization method provided in one embodiment;
[0055] Figure 7 This is the optimal layout diagram of Scheme 3 of a turbine workshop layout optimization method provided in one embodiment. Figure 5 (a) in the text represents production cycle 1. f 3. Optimal layout Figure 5 (b) in the text represents production cycle 2. f 3. Optimal layout;
[0056] Figure 8 This is a population distribution diagram of a turbine workshop layout optimization method provided in one embodiment.
[0057] Figure 9 This is a Pareto compromise layout diagram of production unit 3 in a turbine workshop layout optimization method provided in one embodiment. Figure 9 (a) in the diagram is the Pareto compromise layout of production unit 3 under production cycle 1. Figure 9 (b) is the Pareto compromise layout of production unit 3 under production cycle 2. Detailed Implementation
[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0059] This invention provides a method for optimizing the layout of a steam turbine workshop, such as... Figure 1 As shown, the method includes:
[0060] Obtain production information from the steam turbine workshop.
[0061] Taking production information and multiple production cycles in the production process as inputs, and minimizing the logistics cost, reconfiguration cost and production unit area of the turbine workshop layout as objective functions, and taking the equipment layout scheme of each production cycle as output, a multi-cycle reconfigurable equipment layout problem model of the turbine workshop is constructed.
[0062] Based on the multi-period reconfigurable equipment layout problem model of the turbine workshop, Sobol sequence is used for population initialization to uniformly generate multiple initial populations representing the initial layout scheme of the turbine workshop.
[0063] Local searches were performed on all initial populations using crossover and mutation probabilities of varying magnitudes to obtain subpopulations corresponding to each initial population. The initial populations and their corresponding subpopulations were then merged to obtain multiple intermediate populations representing candidate layout schemes for the turbine workshop.
[0064] A non-dominated sorting strategy is used to sort multiple intermediate populations, and the intermediate population with the highest non-dominated sorting level is taken as the optimal population. The optimal layout scheme of the turbine workshop is determined based on the optimal population.
[0065] In this study, an improved non-dominated sorting genetic algorithm was obtained by replacing the random initialization of the non-dominated sorting genetic algorithm with Sobol sequences, using different crossover and mutation probabilities as search strategies, and employing the non-dominated sorting strategy as the reconstruction strategy. This improved algorithm was then used to perform multi-objective optimization on a multi-period reconfigurable equipment layout problem model in a steam turbine workshop, yielding the optimal layout scheme for the steam turbine workshop.
[0066] A Sobol sequence is used to initialize the multi-period reconfigurable equipment layout problem model, uniformly generating multiple initial populations representing initial layout schemes for the turbine workshop in the algorithm space. Local searches are performed on the initial populations using different crossover and mutation probabilities to obtain subpopulations corresponding to each initial population. The initial populations and their corresponding subpopulations are then merged to obtain multiple intermediate populations representing candidate layout schemes for the turbine workshop. A non-dominated sorting strategy is used to non-dominate these intermediate populations, and the intermediate population with the highest non-dominated sorting level is selected as the optimal population. The optimal layout scheme for the turbine workshop is determined based on the optimal population.
[0067] The specific implementation process is as follows:
[0068] Step 1: Collect relevant production information for the turbine workshop, including but not limited to material flow between equipment rooms, production processes, and current layout.
[0069] Step 2: Analyze the layout problems of the turbine workshop. Workshop layout problems include, but are not limited to, long material handling routes, large material flow, and low material handling efficiency.
[0070] Step 3: Make the following assumptions about the reconfigurable turbine workshop layout:
[0071] (1) All equipment is rectangular in shape;
[0072] (2) The equipment in the reconfigurable production unit adopts a U-shaped layout, and the safety distance between each piece of equipment is known;
[0073] (3) The sum of the absolute values of the differences between the horizontal and vertical coordinates of the center coordinates of each equipment is the handling distance. When handling materials, they all start from the center of the equipment and reach the target center.
[0074] (4) When a production unit is reconfigured, all equipment in that production unit is shut down;
[0075] (5) The product types remain unchanged in different production cycles, only the demand for each product changes.
[0076] Step 4: Construct a multi-cycle reconfigurable device layout problem model. The objective function of the model is:
[0077] ;
[0078] ;
[0079] ;
[0080] In the formula, This represents the logistics costs in the production process. for Unit logistics handling cost during the production cycle for Equipment during the production cycle and equipment The transport distance between them for Equipment during the production cycle and equipment The frequency of material handling between them Indicates the cost of reconstruction. As decision variables, , , They are respectively the period Inside The cost of installing, moving, and dismantling various types of equipment, in terms of cycle time. The profit generated per unit time in an internal production unit. For period Internal reconfiguration equipment Time required Indicates the area of the production unit. , for The horizontal and vertical coordinates of the equipment's location during the production cycle. , This refers to the lateral and longitudinal distances between the equipment and the unit boundary. This represents the number of production cycles.
[0081] Model constraints:
[0082] (1) Equipment position coordinate related constraints:
[0083] ;
[0084] ;
[0085] ;
[0086] In the formula, For peer equipment and The net distance between them. As a decision variable, when the equipment Located in the The value is 1 if the row is in the row, and 0 otherwise. This is the distance from the center of the first row of devices to the edge of the unit; This represents the center-to-center distance between two adjacent rows of devices. x i The x-coordinate represents the location of the device. y i The vertical coordinate represents the location of the device.
[0087] (2) Prevent equipment overlap and ensure safe spacing between equipment.
[0088] ;
[0089] (3) Ensure that the equipment does not exceed the relevant constraints of the unit boundary:
[0090] ;
[0091] ;
[0092] (4) Ensure that equipment in the same row or equipment in the longitudinal direction does not overlap or interfere with each other:
[0093] ;
[0094] ;
[0095] Step 5: Based on the mathematical model in Step 4, design the improved NSGA-II algorithm. The specific steps are as follows:
[0096] Step 5.1: Input initial data such as unit logistics handling cost and handling distance between equipment, and set relevant algorithm parameters including population size. Maximum number of iterations Crossover probability Probability of mutation ;
[0097] Step 5.2: Initialize the population using the Sobol sequence, and simultaneously set the iteration number. ;
[0098] Step 5.3: Determine if a first-generation subpopulation has been generated. If a first-generation subpopulation has been generated, then the iteration count is... Otherwise, the first generation of offspring is generated using operations such as non-dominated sorting, crowding calculation, binary tournament selection, adaptive crossover, mutation, and local search, while setting the number of iterations. ;
[0099] Step 5.4: Merge the parent and offspring populations; the population size is... ;
[0100] Step 5.5: Determine if a new parent population has been generated. If a new parent population has been generated, proceed to Step 5.6; otherwise, use a non-dominant ranking and elite preservation strategy to retain the top individuals in the population ranked from highest to lowest fitness. Individuals represent a new parent population;
[0101] Step 5.6: Perform binary tournament selection, adaptive crossover, mutation, and local search on the new parent population to generate a new child population;
[0102] Step 5.7: Determine if the number of iterations gen is less than the maximum number of iterations. If the result is less than 1, return to step 5.4; otherwise, output the result.
[0103] Step 6: Based on the improved NSGA-II algorithm from Step 5, confirm the initial parameters of the algorithm, run the improved NSGA-II code, and solve the turbine workshop layout problem. Assign equal weights to the optimization objectives of logistics cost, reconfiguration cost, and production unit area. Calculate the normalized weighted value of each solution in the Pareto front, and select the compromise solution with the smallest weighted value as the optimal layout scheme. Furthermore, compare the algorithm with the unimproved NSGA-II algorithm to verify its feasibility.
[0104] Furthermore, since the demand for each product may fluctuate during different production cycles, the equipment layout within the production unit may change accordingly. The goal is to minimize logistics costs, reconfiguration costs, and production unit area to create a reconfigurable layout within the production unit.
[0105] Transport distance The calculation method is as follows:
[0106] ;
[0107] express Equipment during the production cycle To determine whether a move has occurred, and to confirm whether production units in different production cycles have been reconfigured, the formula is as follows:
[0108] ;
[0109] Furthermore, the improvements to the NSGA-II algorithm are as follows:
[0110] (1) In step 5.2, the population is initialized using the Sobol sequence to improve the quality of the initial population. Randomly generating the initial population using the NSGA-II algorithm may result in an uneven distribution of the initial population, with some areas having dense populations and others having no populations. The Sobol sequence is a low-discrepancy sequence that is more evenly distributed in space, and it can better cover the entire search space, thus improving the solution efficiency and convergence speed.
[0111] (2) In step 5.3, a smaller crossover and mutation probability is used for individuals with higher fitness, and a larger crossover and mutation probability is used for individuals with lower fitness, as shown in the following formula:
[0112] ;
[0113] in, The crossover probability; For the maximum crossover probability, The minimum crossover probability; To specify the maximum fitness of an individual; For individual fitness before crossover; The average fitness value of the population. This represents the maximum fitness value of the population.
[0114] ;
[0115] in, The mutation probability; The maximum mutation probability; This represents the minimum probability of mutation.
[0116] Specifically, for individuals with different fitness levels in the initial population, different crossover and mutation probabilities are used.
[0117] For individuals in the initial population with a maximum fitness greater than a set threshold, a large crossover probability and a large mutation probability are used; for individuals in the initial population with a maximum fitness less than a set threshold, a small crossover probability and a small mutation probability are used.
[0118] (3) In step 5.5, the non-dominated sorting strategy is used to improve the quality of the solution. Local search is performed on the points with a non-dominated sorting level of 1 and the top 4 points in terms of crowding distance, and the individuals after the search are compared to retain the better solution, thereby improving the uniformity of solution distribution and preventing the solution from getting trapped in local optima.
[0119] The encoding method employs a hybrid approach of floating-point and binary encoding, with mobile devices encoded as 1 and non-mobile devices encoded as 0. During reconstruction, devices encoded as 1 are first removed from their current positions, creating vacant spaces in the existing layout. Subsequently, devices encoded as 1 are repositioned according to their individual floating-point numbers, from largest to smallest, selecting suitable locations from the existing vacant spaces to complete the repositioning.
[0120] Here is a specific example:
[0121] Step 1: Collect relevant production information from the steam turbine workshop, as shown below:
[0122] The turbine workshop in this embodiment of the invention is equipped with various processing equipment, including: 8 lathes, 3 vertical machining centers, 3 grinding machines, 4 drilling machines, 3 milling machines, 3 boring machines, 1 sawing machine, 2 welding machines, 7 semi-fixed fitter's benches, and a heat treatment furnace. A total of 21 types of main self-made parts are used. To facilitate subsequent logistics and layout analysis, the equipment and parts are coded, as shown in Table 1.
[0123] Table 1 Equipment and Part Coding Information
[0124]
[0125] The processing routes for the 21 types of parts are shown in Table 2:
[0126] Table 2 Product Processing Routes
[0127]
[0128] The turbine workshop has a total of 6 production units. The specific production resource information for each production unit is shown in Table 3.
[0129] Table 3 Production Unit Information Table
[0130]
[0131] In addition, the distances between the devices and the parameters of each device are shown in Tables 4 and 5, respectively:
[0132] Table 4 Distance between working equipment
[0133]
[0134] Table 5 Equipment Parameters
[0135]
[0136] Step 2: Analyze the layout of the steam turbine workshop.
[0137] Based on the processing procedures of each product in Table 2, the location distances of the work pairs in Table 4, and the material flow rates of the work pairs in Table 6, a scatter plot of material flow rate and distance analysis for the turbine workshop in this embodiment was plotted using MATLAB R2022b software.
[0138] Table 6 Material Flow in the Equipment Room
[0139]
[0140] The horizontal axis represents the distance between work pairs, and the vertical axis represents the material flow rate between work pairs.
[0141] Problem Analysis:
[0142] Depend on Figure 2 It can be seen that most work pairs have relatively small material volumes and short handling distances, but there are also some work pairs with large material volumes and long handling distances. This results in a significant amount of handling waste, as well as employee fatigue, which directly affects overall logistics and production efficiency, making it difficult to meet the ever-increasing order demand.
[0143] Step 3: Make the following assumptions about the reconfigurable turbine workshop layout:
[0144] (1) All equipment is rectangular in shape;
[0145] (2) The equipment in the reconfigurable production unit adopts a U-shaped layout, and the safety distance between each piece of equipment is known;
[0146] (3) The sum of the absolute values of the differences between the horizontal and vertical coordinates of the center coordinates of each equipment is the handling distance. When handling materials, they all start from the center of the equipment and reach the target center.
[0147] (4) When a production unit is reconfigured, all equipment in that production unit is shut down;
[0148] (5) The product types remain unchanged in different production cycles, only the demand for each product changes.
[0149] Step 4: Construct a multi-cycle reconfigurable device layout problem model.
[0150] Since the demand for each product may fluctuate during different production cycles, the equipment layout within the production unit may change accordingly. The reconfigurable layout within the production unit is designed with logistics costs, reconfiguration costs, and average unit area as objective functions.
[0151] Step 5: Based on the mathematical model in Step 4, design an improved NSGA-II algorithm.
[0152] Improved encoding method for the NSGA-II algorithm:
[0153] This invention employs a U-shaped layout to improve production flow. Ensuring that the dimensions and safety distances of each piece of equipment meet requirements, the equipment is arranged counter-clockwise in sequence. Taking a U-shaped production unit with 11 pieces of equipment as an example, the U-shaped layout within the unit is explained as follows: Figure 4 As shown.
[0154] To address the layout reconfiguration problem of U-shaped unit devices, this invention employs a hybrid encoding method combining floating-point and binary encoding. Assume there are 11 machines, and their relevant information is known. Floating-point numbers for the 11 machines are randomly generated and placed sequentially from position 1 to position 11 in descending order (with the device center coinciding with the position center), thus determining the position of each machine. During the reconfiguration phase, binary encoding is used, with movable devices encoded as 1 and non-movable devices encoded as 0. When reconfiguring, firstly, all devices encoded as 1 are removed from their current positions, creating vacant positions in the existing layout. Then, for each device encoded as 1, its individual floating-point number is used to select a suitable position from the existing vacant positions in descending order to complete the position reconfiguration.
[0155] Step 6: Based on the improved NSGA-II algorithm from Step 5, confirm the initial parameters of the algorithm, run the improved NSGA-II code, and solve the turbine workshop layout problem. Assign equal weights to the optimization objectives of logistics cost, reconfiguration cost, and production unit area. Calculate the normalized weighted value of each solution in the Pareto front, and select the compromise solution with the smallest weighted value as the optimal layout scheme. Furthermore, compare the algorithm with the unimproved NSGA-II algorithm to verify its feasibility.
[0156] This embodiment has two production cycles, as shown in Table 7. Therefore, the reconfigurable layout is only considered based on the order changes in the two cycles.
[0157] Table 7 Product Demand in Each Production Cycle
[0158]
[0159] When designing a reconfigurable production unit, practical production constraints related to the ease of equipment movement must be considered. Table 8 shows the equipment within the turbine workshop that can be moved within a limited area and the associated costs.
[0160] Table 8 Equipment relocation costs
[0161]
[0162] This invention uses production unit 3, which has the largest number of mobile devices, as an example to illustrate in detail the layout process within a multi-cycle reconfigurable unit. The transfer frequency between devices within production unit 3 during each production cycle is shown in Tables 9 and 10.
[0163] Table 9 Equipment Handling Frequency in Production Cycle 1
[0164]
[0165] Table 10 Equipment Handling Frequency in Production Cycle 2
[0166]
[0167] Regarding the algorithm parameter settings, the INSGA-II algorithm parameters are determined as follows: maximum number of iterations T=200, population size N=50, crossover probability is 0.8, and mutation probability is 0.3.
[0168] Running the improved NSGA-II code, the layout of each production cycle in production cell 3 was solved. The results are shown in Table 11. The layout diagrams of the three schemes are as follows: Figure 5 , Figure 6 , Figure 7 As shown.
[0169] Table 11 INSGA-II Layout Optimization Results
[0170]
[0171] The algorithm yields three alternative solutions, each representing the optimal solution for one of the three objective functions. However, due to the mutual constraints between objective functions in multi-objective optimization problems, it is difficult to simultaneously achieve the optimal solution. Therefore, this invention addresses this issue based on population distribution conditions, such as... Figure 8 The Pareto front, i.e. the Pareto optimal solution set, is determined.
[0172] This invention employs a normalized weighted method to determine the optimal Pareto solution. Consulting with enterprise experts confirmed that the three optimization objectives have equal importance. Therefore, this invention assigns equal weights to the three optimization objectives, calculates the normalized weighted value of each solution in the Pareto front, and selects the compromise solution with the smallest weighted value as the optimal layout scheme for production unit 3. This scheme has a logistics cost of 67,754.72 yuan, a reconfiguration cost of 8,625 yuan, and an average unit area of 123.76 square meters. The specific layout scheme is as follows... Figure 9 As shown.
[0173] The effectiveness of the improved multi-objective genetic algorithm proposed in this invention is verified by solving the problem model using the multi-objective genetic algorithm and the multi-objective particle swarm optimization algorithm, and calculating the Pareto front. Figure 8 It can be seen that INSGA-II has multiple points that strongly dominate the other two algorithms, and its Pareto front performance is superior. In addition, compared with the unmodified NSGA-II, the improved algorithm has a faster convergence speed, stronger optimization ability, and a smaller and more uniform solution set range, as shown in Table 12.
[0174] Table 12 Comparison of Algorithm Convergence Speed
[0175]
[0176] Using the same method, the layout schemes for the remaining 5 production units were solved, and the Pareto optimal layout results for each production unit are shown in Table 13.
[0177] Table 13 Layout Results of Each Unit
[0178]
[0179] This invention offers at least the following advantages: Considering production order disturbances within production equipment, a multi-period reconfigurable equipment layout problem model is established with logistics costs, reconfiguration costs, and average unit area as objective functions. An improved NSGA-II algorithm is designed, incorporating Sobol sequences to enhance initial population quality, adaptive crossover and mutation strategies to improve search efficiency and convergence speed, and local search strategies to enhance the uniformity and diversity of the solution set distribution. A Pareto front compromise layout scheme is selected based on population distribution and actual production needs. Furthermore, this invention utilizes multiple algorithms to solve the reconfigurable layout optimization model. The final results validate the effectiveness of the improved NSGA-II algorithm.
[0180] Based on the same inventive concept, embodiments of the present invention also provide a turbine workshop layout optimization system, comprising:
[0181] The data acquisition module is used to acquire production information from the steam turbine workshop.
[0182] The model building module is used to construct a multi-cycle reconfigurable equipment layout problem model for the turbine workshop, taking production information and multiple production cycles in the production process as inputs, minimizing the logistics cost, reconfiguration cost and production unit area of the turbine workshop layout as objective functions, and outputting the equipment layout scheme of each production cycle.
[0183] The initial layout module is used for the multi-period reconfigurable equipment layout problem model based on the turbine workshop. It uses Sobol sequence for population initialization to uniformly generate multiple initial populations representing the initial layout scheme of the turbine workshop.
[0184] The intermediate layout module is used to perform local searches on all initial populations using different crossover and mutation probabilities to obtain subpopulations corresponding to each initial population. The initial populations and their corresponding subpopulations are then merged to obtain multiple intermediate populations representing candidate layout schemes for the turbine workshop.
[0185] The final layout module is used to perform non-dominated sorting on multiple intermediate populations using a non-dominated sorting strategy, and to select the intermediate population with the highest non-dominated sorting level as the optimal population, and to determine the optimal layout scheme of the turbine workshop based on the optimal population.
[0186] Based on the same inventive concept, this invention also provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of a turbine workshop layout optimization method.
[0187] Based on the same inventive concept, embodiments of the present invention also provide a computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the steps of a turbine workshop layout optimization method.
[0188] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.
Claims
1. A method for optimizing the layout of a steam turbine workshop, characterized in that, include: Obtain production information from the steam turbine workshop; Taking production information and multiple production cycles in the production process as inputs, and minimizing the logistics cost, reconfiguration cost and production unit area of the turbine workshop layout as objective functions, and the equipment layout scheme of each production cycle as output, a multi-cycle reconfigurable equipment layout problem model of the turbine workshop is constructed. Among them, a multi-cycle reconfigurable device layout problem model is constructed based on the following formula: ； ； ； in, Logistics costs during the production process, for Unit logistics handling cost during the production cycle for Equipment during the production cycle and equipment The transport distance between them for Equipment during the production cycle and equipment The frequency of material handling between them Indicates the cost of reconstruction. As decision variables, , , They are respectively the period Inside The cost of installing, moving, and dismantling various types of equipment. For period The profit generated per unit time by the internal production unit. For period Internal reconfiguration equipment Time required Indicates the area of the production unit. , for The horizontal and vertical coordinates of the equipment's location during the production cycle. , This refers to the lateral and longitudinal distances between the equipment and the unit boundary. This refers to the number of production cycles. Based on the multi-period reconfigurable equipment layout problem model of the steam turbine workshop, Sobol sequence is used for population initialization to uniformly generate multiple initial populations representing the initial layout scheme of the steam turbine workshop. Local searches were performed on all initial populations using crossover and mutation probabilities of different magnitudes to obtain subpopulations corresponding to each initial population; then the initial populations and their corresponding subpopulations were merged to obtain multiple intermediate populations representing candidate layout schemes for steam turbine workshops. Specifically, based on the following formula, different crossover and mutation probabilities are used to perform local searches on all initial populations to obtain the subpopulations corresponding to each initial population: ； in, For crossover probability, For the maximum crossover probability, To minimize the crossover probability, ; To specify the maximum fitness of an individual, For individual fitness before crossover, The average fitness value of the population. This represents the maximum fitness value of the population. ； in, The mutation probability, The maximum mutation probability, The minimum mutation probability, ; Among them, different crossover probabilities and mutation probabilities are used for individuals with different fitness in different initial populations; A non-dominated sorting strategy is used to sort multiple intermediate populations, and the intermediate population with the highest non-dominated sorting level is taken as the optimal population. The optimal layout scheme of the turbine workshop is determined based on the optimal population.
2. The turbine workshop layout optimization method as described in claim 1, characterized in that, The method of employing a non-dominated sorting strategy to perform non-dominated sorting on multiple intermediate populations, and selecting the intermediate population with the highest non-dominated sorting level as the optimal population, specifically includes: The non-dominated sorting strategy uses a hybrid encoding of floating-point and binary codes, encoding movable devices as 1 and non-movable devices as 0. The non-dominated sorting strategy is used to perform non-dominated sorting on multiple intermediate populations, so that all mobile devices coded as 1 are removed from their current positions. The mobile devices coded as 1 are then selected from the existing vacant positions in descending order of their individual floating-point numbers to obtain the optimal population.
3. A steam turbine workshop layout optimization system, characterized in that, include: The data acquisition module is used to acquire production information from the steam turbine workshop; The model building module is used to construct a multi-cycle reconfigurable equipment layout problem model for the steam turbine workshop, taking production information and multiple production cycles in the production process as inputs, minimizing the logistics cost, reconfiguration cost and production unit area of the steam turbine workshop layout as objective functions, and taking the equipment layout scheme of each production cycle as output. Among them, a multi-cycle reconfigurable device layout problem model is constructed based on the following formula: ； ； ； in, Logistics costs during the production process, for Unit logistics handling cost during the production cycle for Equipment during the production cycle and equipment The transport distance between them for Equipment during the production cycle and equipment The frequency of material handling between them Indicates the cost of reconstruction. As decision variables, , , They are respectively the period Inside The cost of installing, moving, and dismantling various types of equipment, in terms of cycle time. The profit generated per unit time by the internal production unit. For period Internal reconfiguration equipment Time required Indicates the area of the production unit. , for The horizontal and vertical coordinates of the equipment's location during the production cycle. , This refers to the lateral and longitudinal distances between the equipment and the unit boundary. This refers to the number of production cycles. The initial layout module is used for the multi-period reconfigurable equipment layout problem model based on the turbine workshop. It uses the Sobol sequence for population initialization to uniformly generate multiple initial populations representing the initial layout scheme of the turbine workshop. The intermediate layout module is used to perform local searches on all initial populations using crossover and mutation probabilities of different sizes to obtain subpopulations corresponding to each initial population; and to merge the initial populations and their corresponding subpopulations to obtain multiple intermediate populations representing candidate layout schemes for the turbine workshop. Specifically, based on the following formula, different crossover and mutation probabilities are used to perform local searches on all initial populations to obtain the subpopulations corresponding to each initial population: ； in, For crossover probability, For the maximum crossover probability, For the minimum crossover probability, ; To specify the maximum fitness of an individual, For individual fitness before crossover, The average fitness value of the population. This represents the maximum fitness value of the population. ； in, The mutation probability, The maximum mutation probability, For the minimum mutation probability, ; Among them, different crossover probabilities and mutation probabilities are used for individuals with different fitness in different initial populations; The final layout module is used to perform non-dominated sorting on multiple intermediate populations using a non-dominated sorting strategy, and to select the intermediate population with the highest non-dominated sorting level as the optimal population, and to determine the optimal layout scheme of the turbine workshop based on the optimal population.
4. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the turbine workshop layout optimization method according to any one of claims 1-2.
5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the turbine workshop layout optimization method according to any one of claims 1-2.