Multi-objective optimization method and system for material layout beside production line based on evolutionary optimization

Abstract

The present invention provides a multi-objective optimization method and system for production line material layout based on evolutionary optimization, relating to the fields of intelligent manufacturing and industrial engineering optimization technology. The method first obtains the basic information data required for optimizing the production line material layout and performs data preprocessing and standardization. A multi-objective optimization mathematical model for the production line material layout is then established, and the objective function and constraints are determined. Based on the multi-objective optimization mathematical model for the production line material layout, a heuristic initialization strategy and a dynamic Thompson sampling mechanism are used to improve the MOEA / D algorithm, resulting in a heuristically initialized MOEA / D algorithm. Finally, the heuristically initialized MOEA / D algorithm is used to solve the multi-objective optimization mathematical model for the production line material layout. Through iterative optimization, a Pareto optimal solution set is obtained, i.e., the optimal layout of the production line materials. This method can effectively improve the rationality and efficiency of material layout.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent manufacturing and industrial engineering optimization, and in particular to a multi-objective optimization method and system for material layout along a production line based on evolutionary optimization. Background Art

[0002] Optimizing material placement alongside production lines involves rationally planning and arranging material storage areas adjacent to production lines in manufacturing workshops to improve production efficiency and reduce material handling costs. This involves comprehensive consideration of multiple factors, including production cycle time, material demand frequency, storage space limitations, handling distances, and ergonomics. Material placement alongside production lines directly impacts production line efficiency, worker convenience, and overall production costs, making it a critical issue that urgently needs to be addressed in modern manufacturing.

[0003] In real-world production environments, material layout along production lines requires considering multiple conflicting objectives. On the one hand, material handling distances and times must be minimized to improve distribution efficiency; on the other hand, frequently used materials must be easily accessible to minimize worker fatigue. Finally, material storage space utilization must be considered to avoid congestion and chaos on the production floor. These objectives often present trade-offs, giving the problem typical characteristics of multi-objective optimization.

[0004] Traditional methods for arranging materials alongside production lines rely primarily on empirical rules and simple heuristics, such as the ABC classification method and the proximity principle. While simple and easy to implement, these methods struggle to fully consider the balance between multiple optimization objectives and are ill-suited to complex and changing production environments. With the development of intelligent manufacturing, the requirements for arranging materials alongside production lines are becoming increasingly stringent, necessitating a more scientific and systematic optimization approach.

[0005] Evolutionary algorithms, a class of optimization algorithms that mimic natural evolutionary processes, excel at solving complex optimization problems. Multi-objective evolutionary algorithms, in particular, can simultaneously optimize multiple conflicting objectives, generating a set of equilibrium solutions (Pareto optimal solutions), providing decision makers with a variety of options. Evolutionary algorithms offer advantages such as strong global search capabilities, low mathematical requirements, and ease of handling discrete variables. They are particularly well-suited for solving combinatorial optimization problems such as material layout along production lines. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to address the deficiencies of the above-mentioned existing technologies and provide a multi-objective optimization method and system for material layout along the production line based on evolutionary optimization. By establishing a multi-objective optimization model that considers material ratio, ergonomics and space utilization, and designing a heuristically initialized MOEA / D algorithm, scientific optimization of the material layout along the production line is achieved to improve production efficiency, protect worker health and make full use of space resources.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0008] In one aspect, the present invention provides a multi-objective optimization method for production line material layout based on evolutionary optimization, comprising:

[0009] Obtain the basic information data required for optimizing material layout along the production line; obtain the demand information for each type of material, shelf structure parameters, material specifications and worker operation parameters;

[0010] Perform data preprocessing and standardization on the acquired basic information data;

[0011] Establish a mathematical model for multi-objective optimization of material layout beside production lines, and determine the objective function and constraints of multi-objective optimization of material layout beside production lines;

[0012] The decision variables of the multi-objective optimization mathematical model for material layout along the production line include:

[0013] materials On the shelf level Quantity placed in the upper horizontal direction , vertical placement quantity , material placement direction ,in Taking 0 means the long side is horizontal to the shelf. Taking 1 means the short side is horizontal to the shelf;

[0014] The objectives of the multi-objective optimization of material layout along the production line include minimizing material ratio deviation, minimizing worker workload, and maximizing shelf space utilization. The optimization direction of the two minimization objectives and the one maximization objective is unified, transforming the multi-objective optimization problem into a minimization optimization problem with a consistent direction.

[0015] The constraints for the multi-objective optimization of material layout beside the production line include: material demand satisfaction constraint, shelf length constraint, shelf depth constraint, and shelf load-bearing constraint;

[0016] Aiming at the multi-objective optimization mathematical model of material layout along the production line, the MOEA / D algorithm is improved by adopting the heuristic initialization strategy and dynamic Thompson sampling mechanism, and the heuristic initialization MOEA / D algorithm is obtained.

[0017] Based on the heuristic initialization MOEA / D algorithm, the multi-objective optimization mathematical model of material layout beside the production line is solved, and the Pareto optimal solution set is obtained through iterative optimization, that is, the optimal layout of materials beside the production line is obtained.

[0018] Furthermore, the material demand information for each type includes the material number, the demand quantity in each time period, the expected ratio and the maximum demand quantity;

[0019] The shelf structure parameters include the number of shelf layers, the length of each layer, the depth of each layer and the maximum load-bearing capacity;

[0020] The material specification information includes material number, long side dimension, short side dimension and unit weight;

[0021] The worker operation parameters include the energy consumption coefficients of workers picking up and placing materials corresponding to different shelf layer heights.

[0022] Furthermore, the data preprocessing and standardization of the acquired basic information data includes cleaning, verifying and format conversion of the acquired basic information data, specifically:

[0023] Analyze the historical consumption of each type of material demand data and calculate the demand volatility and correlation of each type of material;

[0024] Grid the shelf space and establish a unified spatial coordinate system;

[0025] Standardize material specification data and calculate the actual dimensions occupied by materials in different placement directions.

[0026] Furthermore, the multi-objective optimization mathematical model for material layout along the production line is improved by using a heuristic initialization strategy and a dynamic Thompson sampling mechanism to obtain a specific method for heuristic initialization of the MOEA / D algorithm:

[0027] Step S1: Initialize algorithm parameters; set population size , maximum number of iterations , neighborhood size , mutation probability , crossover probability and the set of weight vectors The Chebyshev decomposition method is used to decompose the multi-objective optimization problem of material layout along the production line into multiple single-objective sub-problems with directional preferences. Each sub-problem is modeled using the maximum weighted deviation function, which effectively guides the heuristically initialized MOEA / D algorithm to find a uniformly distributed Pareto optimal solution in the solution space, as shown in the following formula:

[0028] , ,in, is the Chebyshev decomposition function; is the decision variable; is an ideal point, which represents the vector of the minimum values ​​of the components of the current objective function on the feasible solution set; For the The objective function is The weight vector under the iteration reflects the current The importance of each goal in the iteration; is the objective function value, is the number of targets; is the feasible region, which represents the set of solutions that satisfy all constraints in the decision space; For the An ideal point of the objective function;

[0029] Step S2: Design a heuristic initialization strategy and design a four-stage initialization method based on the characteristics of the multi-objective optimization problem of material layout along the production line:

[0030] Stage 1: Randomize material orientation;

[0031] For each individual, randomly set the placement direction of each material , and calculate the corresponding actual occupied size;

[0032] Phase 2: Sorting the shelf layers;

[0033] The shelf layers are sorted according to the energy consumption coefficient of taking and placing materials on the shelf layers, and materials are allocated to the shelf layers with low energy consumption first, thereby obtaining the shelf layer priority ranking;

[0034] Stage 3: Assigning material priorities;

[0035] Arrange the materials in descending order according to their expected ratio, give priority to materials with high ratio, and thus obtain the material ranking;

[0036] Stage 4: Generate greedy layout;

[0037] Randomly allocate the quantity of materials based on material priority and shelf layer priority, subject to the following constraints:

[0038] , ,in, and For materials under current constraints On the shelf level The maximum number of horizontal and vertical positions that can be placed. and The maximum number of placements for each material in the horizontal and vertical directions is preset during the heuristic initialization phase;

[0039] Step S3: Design an adaptive operator selection mechanism based on Beta distribution and Thompson sampling to dynamically adjust the selection probability of the mutation operator. In each generation, sample once from each Beta distribution and select the operator with the largest sampling value for the mutation operation.

[0040] Step S4: With probability Select parent individuals in the neighborhood with probability Randomly select from the entire population to balance neighborhood search and global search;

[0041] Step S5: Check and repair constraints on the new solution generated after the mutation operation:

[0042] Fix 1: Depth constraint fix, if the number of items of type i in the depth direction of the k-th shelf If the total depth of the rack exceeds the maximum allowable depth of the rack layer, it needs to be restricted as shown in the following formula:

[0043] ,in, is the quantity of the i-th type of material after repair in the depth direction of the k-th shelf, is the depth of the shelf layer, For materials Actual occupied depth;

[0044] Fix 2: Fix the length constraint to ensure that the total horizontal length of all materials on each shelf does not exceed the maximum length of that shelf, as shown in the following formula:

[0045] like , then the placement quantity of the i-th type of material is scaled proportionally:

[0046] ,in, is the length of the shelf layer, For materials The actual occupied length, is the number of material types;

[0047] Fix 3: Requirement constraint fix;

[0048] like , For materials If the demand is less than the total amount of the i-th material allocated on all shelf layers, it means that the total amount of the i-th material allocated on all shelf layers is less than the production demand, and the material is added to the shelf layers where there is still available space;

[0049] Step S6: Population update and ideal point maintenance; use Chebyshev distance to evaluate the quality of the solution, update the solution in the neighborhood, and dynamically update the ideal point based on the newly generated individuals in each generation of evolution .

[0050] Furthermore, the specific method of solving the multi-objective optimization mathematical model of material layout beside the production line based on the heuristic initialization MOEA / D algorithm and obtaining the Pareto optimal solution set through iterative optimization is as follows:

[0051] Step C1: Use a hybrid coding method to design a coding scheme for the material position and placement, and obtain the coding vector of the material position and placement: the horizontal placement quantity and the vertical placement quantity are both coded as integer codes, and the dimensions are , is the number of material types, is the number of shelves; the placement direction is coded in binary, and the dimension ;

[0052] Step C2: For each subproblem in the multi-objective optimization mathematical model for material layout along the production line, loop through steps S3-S6 until all subproblems have been processed and the number of loops reaches the set maximum number of loops. In each loop, select a subproblem to be optimized, use the dynamic Thompson sampling mechanism to select a suitable mutation operator to generate a new solution, and perform repair processing on the new solution. Then, evaluate the new solution to determine whether its quality is better than the current population and update it accordingly. At the same time, update the performance statistics of the ideal point and operator. Periodically adjust the utility value of each subproblem to dynamically optimize the overall search strategy.

[0053] Step C3: When the heuristically initialized MOEA / D algorithm meets the termination condition, the final Pareto solution set is output.

[0054] On the other hand, the present invention also provides a multi-objective optimization system for material layout beside a production line based on evolutionary optimization, comprising a data acquisition module, a model building module, an algorithm design module, a model solving module and a result output module;

[0055] The data acquisition module obtains production line material demand information, shelf structure parameters, material specification information and worker operation energy consumption data, and pre-processes and standardizes these basic data;

[0056] The model building module establishes a multi-objective optimization mathematical model that takes into account material ratio balance, worker workload and space utilization, and designs constraints to ensure the feasibility of the solution;

[0057] The algorithm design module designs a heuristic initialization MOEA / D algorithm, adopts a heuristic initialization strategy to improve the quality of the initial solution, and realizes adaptive operator selection through dynamic Thompson sampling;

[0058] The model solving module solves the multi-objective optimization mathematical model of the material layout beside the production line based on the heuristic initialization MOEA / D algorithm, and obtains the Pareto optimal solution set through iterative optimization, that is, the optimal layout of the materials beside the production line;

[0059] The result output module analyzes and evaluates the model solution optimization results, generates material layout plans and provides decision support information.

[0060] In a third aspect, the present application proposes an electronic device comprising: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the multi-objective optimization method for production line material layout based on evolutionary optimization.

[0061] In a fourth aspect, the present application proposes a computer-readable storage medium storing executable instructions, which, when executed, enable a processor to execute the multi-objective optimization method for production line material layout based on evolutionary optimization.

[0062] In a fifth aspect, the present application proposes a computer program product, comprising a computer program or instructions, which, when executed by a processor, implements the multi-objective optimization method for production line material layout based on evolutionary optimization.

[0063] The beneficial effects of adopting the above-mentioned technical solution are as follows: the multi-objective optimization method and system for material layout beside the production line based on evolutionary optimization provided by the present invention first obtains the basic information required for optimizing the material layout beside the production line, including material demand, shelf structure, material specifications and worker operating parameters, and pre-processes and standardizes these data to provide standardized input for model establishment. Subsequently, a multi-objective optimization mathematical model is constructed, taking into account the balance of material ratios, worker workload and space utilization, and setting corresponding constraints to ensure the feasibility of the solution. On this basis, a heuristic initialization MOEA / D algorithm is designed, which combines heuristic initialization and dynamic Thompson sampling mechanism to realize the adaptive selection of mutation operators. Finally, the multi-objective optimization model is solved by the improved algorithm to obtain the Pareto optimal solution set and form a reasonable material layout solution.

[0064] This method solves the multi-objective optimization problem of material layout along production lines using an improved heuristically initialized MOEA / D algorithm. This method can more efficiently and accurately output an optimization solution that balances material ratios, worker workload, and space utilization. Experimental verification has shown that the method can effectively improve the rationality and efficiency of material layout in actual production environments, reduce operational energy consumption, and improve space utilization, thereby saving labor and space management costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A flowchart of a multi-objective optimization method for material layout along a production line based on evolutionary optimization provided by an embodiment of the present invention;

[0066] Figure 2 Flowchart of the heuristic initialization MOEA / D algorithm provided in an embodiment of the present invention;

[0067] Figure 3 This is a structural framework diagram of a multi-objective optimization system for material layout along a production line based on evolutionary optimization provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0068] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0069] Example 1:

[0070] In this embodiment, the present invention provides a multi-objective optimization method for material layout along the production line based on evolutionary optimization, such as Figure 1 Shown, including:

[0071] Step 1: Obtain the basic information data required for optimizing the material layout along the production line; obtain material demand information, shelf structure parameters, material specifications, and worker operation parameters;

[0072] Step 1.1: Obtain the demand information for each type of material, including the material number, demand quantity in each time period, expected ratio, and maximum demand quantity;

[0073] Step 1.2: Obtain the shelf structure parameters, including the number of shelves, the length of each shelf, the depth of each shelf, and the maximum load-bearing capacity;

[0074] Step 1.3: Obtain material specification information. Each type of material specification information includes material number, long side dimension, short side dimension, and unit weight.

[0075] Step 1.4: Obtain worker operation parameters, including the energy consumption coefficients of workers picking and placing materials corresponding to different shelf heights;

[0076] Step 2: Preprocess and standardize the acquired basic information data; clean, verify, and convert the acquired basic information data into a format to provide standardized input for the optimization model;

[0077] Step 2.1: Analyze the historical consumption of each material demand data and calculate the demand volatility and correlation of each type of material;

[0078] Step 2.2: Grid the shelf space and establish a unified spatial coordinate system;

[0079] Step 2.3: Standardize the material specification data and calculate the actual size occupied by the material in different placement directions;

[0080] Step 3: Establish a multi-objective optimization mathematical model for the material layout beside the production line; determine the objective function and constraints for the multi-objective optimization of the material layout beside the production line, and establish a complete mathematical optimization model;

[0081] Step 3.1: Define decision variables; set materials On the shelf level The number of horizontal placements is , the number of vertical placements is , the material placement direction is ,in Taking 0 means the long side is horizontal to the shelf. Taking 1 means the short side is horizontal to the shelf;

[0082] Step 3.2: Establish the objective function for multi-objective optimization of material layout along the production line;

[0083] Three optimization objectives are defined for the multi-objective layout optimization problem of materials along the production line:

[0084] Goal 1: Minimize the material ratio deviation, as shown in the following formula:

[0085] ,in, is the material ratio deviation, is the number of material types; For materials The actual ratio, ; For materials The expected ratio is determined by the material consumption plan; is the number of shelf layers;

[0086] Goal 2: Minimize the workload of workers, as shown in the following formula:

[0087] ,in, For workers' workload, For materials On the shelf level The operating frequency, ; For materials Unit weight; For the shelf level Pick and place materials Energy consumption coefficient, which is estimated based on comprehensive handling energy consumption, pick-and-place difficulty, and historical experience;

[0088] Goal 3: Maximize shelf space utilization, as shown in the following formula:

[0089] ,in, is the shelf space utilization, and are the length and depth of the shelf layer respectively; and Materials The actual occupied length and depth are calculated as follows:

[0090] , ,in, and Materials The long and short side dimensions;

[0091] Step 3.3: Establish constraints for multi-objective optimization of material layout along the production line;

[0092] Constraint 1: Material requirements meet the constraint, as shown in the following formula:

[0093] ,in, For materials demand;

[0094] Constraint 2: Shelf length constraint, as shown in the following formula:

[0095] ;

[0096] Constraint 3: Shelf depth constraint, as shown in the following formula:

[0097] ;

[0098] Constraint 4: Shelf load-bearing constraint, as shown in the following formula:

[0099] ,in, For shelf layer Maximum load-bearing capacity;

[0100] Step 3.4: To facilitate the optimization algorithm, unify the optimization directions of the two minimization objectives (Objective 1 and Objective 2) and the one maximization objective (Objective 3), and transform the multi-objective optimization problem into a minimization optimization problem with the same direction:

[0101] ;

[0102] Step 4: For the multi-objective optimization mathematical model of material layout beside the production line, the MOEA / D algorithm is improved by using the heuristic initialization strategy and dynamic Thompson sampling mechanism to obtain the heuristic initialization MOEA / D algorithm, which improves the search efficiency and solution quality of the MOEA / D algorithm. The specific process of the algorithm is as follows: Figure 2 As shown;

[0103] Step 4.1: Initialize algorithm parameters; set population size , maximum number of iterations , neighborhood size , mutation probability , crossover probability and the set of weight vectors The Chebyshev decomposition method is used to decompose the multi-objective optimization problem of material layout along the production line into multiple single-objective sub-problems with directional preferences. Each sub-problem is modeled using the maximum weighted deviation function, which effectively guides the heuristically initialized MOEA / D algorithm to find a uniformly distributed Pareto optimal solution in the solution space, as shown in the following formula:

[0104] , ,in, is the Chebyshev decomposition function; is the decision variable; is an ideal point, which represents the vector of the minimum values ​​of the components of the current objective function on the feasible solution set; For the The objective function is The weight vector under the iteration reflects the current The importance of each goal in the iteration; is the objective function value, is the number of targets; is the feasible region, which represents the set of solutions that satisfy all constraints in the decision space; For the An ideal point of the objective function;

[0105] Step 4.2: Design a heuristic initialization strategy and design a four-stage initialization method based on the characteristics of the multi-objective optimization problem of material layout along the production line:

[0106] Stage 1: Randomize material orientation;

[0107] For each individual, randomly set the placement direction of each material , and calculate the corresponding actual occupied size;

[0108] Phase 2: Sorting the shelf layers;

[0109] Shelf layers are sorted according to the energy consumption coefficient of taking and placing materials on the shelf layer, and materials are allocated to the shelf layers with low energy consumption first. This results in a shelf layer priority ranking. Shelf layer priority means that when the algorithm assigns locations to materials, it gives priority to assigning them to the shelf layers with higher levels:

[0110] ,in, is the shelf layer priority order, sort() is the sorting function;

[0111] Stage 3: Assigning material priorities;

[0112] Arrange the materials in descending order according to their expected ratio, giving priority to materials with high ratios, and thus obtain the material sorting:

[0113] ,in, Sort materials;

[0114] Stage 4: Generate greedy layout;

[0115] Randomly allocate the quantity of materials based on material priority and shelf layer priority, subject to the following constraints:

[0116] , ,in, and For materials under current constraints On the shelf level The maximum number of horizontal and vertical positions that can be placed. and The maximum number of placements for each material in the horizontal and vertical directions is preset during the heuristic initialization phase;

[0117] Step 4.3: Design an adaptive operator selection mechanism based on Beta distribution and Thompson sampling to dynamically adjust the selection probabilities of the five mutation operators. In each generation, sample once from each Beta distribution and select the operator with the largest sample value for the mutation operation.

[0118] Operator 1: DE / rand / 1;

[0119] ;

[0120] Operator 2: DE / rand / 2;

[0121] ;

[0122] Operator 3: DE / current-to-rand / 1;

[0123] ;

[0124] Operator 4: DE / current-to-rand / 2;

[0125] ;

[0126] Operator 5: Random search;

[0127] ;

[0128] in, Represents the current individual, represents the individual after mutation, represents different individuals randomly selected from the population, represents a uniform random variable in the interval [0, 1], is the scaling factor, and They are the lower and upper bounds of the decision variables in the multi-objective optimization mathematical model of material layout beside the production line;

[0129] Each operator Maintaining Beta distribution parameters and , operator The probability of being selected for the next mutation for:

[0130] ;

[0131] In each generation, a sample is taken from each Beta distribution, and the operator with the largest sample value is selected for mutation operation; the Beta distribution parameters are dynamically updated according to the operator performance:

[0132] , ,in, Indicates the The parameter value of the generation time, is the number of times operator j successfully participates in the mutation operation (meaning the offspring has better fitness than the parent), is the number of times operator j fails in the mutation operation (meaning the offspring is worse or has no improvement).

[0133] Step 4.4: With probability Select parent individuals in the neighborhood with probability Randomly select from the entire population to balance neighborhood search and global search;

[0134] Step 4.5: Check and repair the constraints of the new solution generated after the mutation operation in step 4.3:

[0135] Fix 1: Depth constraint fix, if the number of items of type i in the depth direction of the k-th shelf If the total depth of the rack exceeds the maximum allowable depth of the rack layer, it needs to be restricted as shown in the following formula:

[0136] ,in, The quantity of the i-th type of material after repair in the depth direction of the k-th shelf;

[0137] Fix 2: Fix the length constraint to ensure that the total horizontal length of all materials on each shelf does not exceed the maximum length of that shelf, as shown in the following formula:

[0138] like , then the placement quantity of the i-th type of material is scaled proportionally:

[0139] ;

[0140] Fix 3: Requirement constraint fix;

[0141] like , it means that the total amount of the i-th material allocated on all shelf layers is less than the production demand, and it is necessary to add this material on the shelf layer where there is still available space;

[0142] Step 4.6: Population update and ideal point maintenance; use Chebyshev distance to evaluate the quality of the solution, update the solution in the neighborhood, and dynamically update the ideal point based on the newly generated individuals in each generation of evolution ;

[0143] Step 5: Solve the multi-objective optimization mathematical model of the material layout beside the production line based on the heuristic initialization MOEA / D algorithm, and obtain the Pareto optimal solution set through iterative optimization, that is, the optimal layout of the materials beside the production line;

[0144] Step 5.1: Use mixed coding to design a coding scheme for material location and placement: the horizontal placement quantity and vertical placement quantity are both coded as integers, and the dimensions are ; The placement direction is coded as binary code, and the dimension ; The final encoding vector of material position and placement is: ;

[0145] Step 5.2: For each subproblem in the multi-objective optimization mathematical model for material layout along the production line, loop through steps 4.3-4.6 until all subproblems have been processed and the maximum number of loops has been reached. In each loop, select a subproblem to be optimized, use the dynamic Thompson sampling mechanism to select a suitable mutation operator to generate a new solution, and perform repair processing on the new solution. Then, evaluate the new solution to determine whether its quality is better than the current population and update it accordingly. At the same time, update the performance statistics of the ideal point and operator. To improve the global search effect, periodically adjust the utility value of each subproblem to dynamically optimize the overall search strategy.

[0146] Step 5.3: When the heuristically initialized MOEA / D algorithm meets the termination conditions, the final Pareto solution set is output; each solution clearly describes the quantity distribution and placement direction of each material on the shelf layer, and gives the numerical results of the three optimization objectives, corresponding to shelf space utilization, material ratio deviation, and worker workload, respectively, to facilitate multi-objective trade-offs and decision analysis.

[0147] Example 2:

[0148] In this embodiment, a multi-objective optimization system for material layout beside production lines based on evolutionary optimization is proposed. Figure 3 As shown, it includes data acquisition module, model building module, algorithm design module, model solving module and result output module;

[0149] The data acquisition module obtains production line material demand information, shelf structure parameters, material specification information and worker operation energy consumption data, and pre-processes and standardizes these basic data;

[0150] The model building module establishes a multi-objective optimization mathematical model that takes into account material ratio balance, worker workload and space utilization, and designs corresponding constraints to ensure the feasibility of the solution;

[0151] The algorithm design module designs a heuristic initialization MOEA / D algorithm, adopts a heuristic initialization strategy to improve the quality of the initial solution, and realizes adaptive operator selection through dynamic Thompson sampling;

[0152] The model solving module solves the multi-objective optimization mathematical model of the material layout beside the production line based on the heuristic initialization MOEA / D algorithm, and obtains the Pareto optimal solution set through iterative optimization, that is, the optimal layout of the materials beside the production line;

[0153] The result output module analyzes and evaluates the model solution optimization results, generates material layout plans and provides decision support information.

[0154] Example 3:

[0155] This embodiment proposes an electronic device, comprising: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the multi-objective optimization method for production line material layout based on evolutionary optimization.

[0156] The electronic device can be a mobile phone, computer, or tablet computer, and includes a memory and a processor. The memory stores a computer program that, when executed by the processor, implements the multi-objective optimization method for production line material layout based on evolutionary optimization as described in the embodiments. It is understood that the electronic device may also include an input / output (I / O) interface and a communication component.

[0157] The processor is configured to execute all or part of the steps of the multi-objective optimization method for material layout along the production line based on evolutionary optimization as described in the above-described embodiment. The memory is configured to store various types of data, such as instructions for any application or method in the electronic device, as well as data related to the application.

[0158] The processor can be an application specific integrated circuit (ASIC), a digital signal processor (DSP), a programmable logic device (PLD), a field programmable gate array (FPGA), a controller, a microcontroller, a microprocessor or other electronic components, and is used to execute the multi-objective optimization method for production line material layout based on evolutionary optimization described in the above embodiments.

[0159] Example 4:

[0160] This embodiment provides a computer-readable storage medium storing executable instructions. When the instructions are executed, if they are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0161] The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the multi-objective optimization method for production line material layout based on evolutionary optimization described in each embodiment of the present application.

[0162] The aforementioned storage media include: flash memory, hard disk, multimedia card, card-type memory (for example, SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR abbreviation, memory data register) memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, server, APP (Application, abbreviation of application software) application store and other media that can store program verification codes, on which a computer program is stored. When the computer program is executed by the processor, it can implement the above-mentioned steps of the multi-objective optimization method for material layout along the production line based on evolutionary optimization.

[0163] Example 5:

[0164] This embodiment provides a computer program product, including a computer program or instructions, which, when executed by a processor, implements the multi-objective optimization method for production line material layout based on evolutionary optimization.

[0165] Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution can be embodied in the form of a computer program product.

[0166] The various embodiments in this application are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

[0167] The scope of protection of this application is not limited to the above-described embodiments. Obviously, those skilled in the art may make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of this application and its equivalents, the disclosure is intended to include such modifications and variations.

[0168] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A multi-objective optimization method for material layout along a production line based on evolutionary optimization, characterized by: include: Obtain basic information data required for optimizing material layout along the production line; Obtain information on material demand, shelf structure parameters, material specifications, and worker operation parameters for each type of material; Perform data preprocessing and standardization on the acquired basic information data; Establish a mathematical model for multi-objective optimization of material layout beside production lines, and determine the objective function and constraints of multi-objective optimization of material layout beside production lines; The decision variables of the multi-objective optimization mathematical model for material layout along the production line include: materials On the shelf level Quantity placed in the upper horizontal direction , vertical placement quantity , material placement direction ,in Taking 0 means the long side is horizontal to the shelf. Taking 1 means the short side is horizontal to the shelf; The objectives of the multi-objective optimization of material layout along the production line include minimizing material ratio deviation, minimizing worker workload, and maximizing shelf space utilization. The optimization direction of the two minimization objectives and the one maximization objective is unified, transforming the multi-objective optimization problem into a minimization optimization problem with a consistent direction. The constraints for the multi-objective optimization of material layout beside the production line include: material demand satisfaction constraint, shelf length constraint, shelf depth constraint, and shelf load-bearing constraint; Aiming at the multi-objective optimization mathematical model of material layout along the production line, the MOEA / D algorithm is improved by adopting the heuristic initialization strategy and dynamic Thompson sampling mechanism, and the heuristic initialization MOEA / D algorithm is obtained. Based on the heuristic initialization MOEA / D algorithm, a multi-objective optimization mathematical model for the material layout beside the production line is solved. Through iterative optimization, the Pareto optimal solution set is obtained, that is, the optimal layout of the materials beside the production line is obtained. The multi-objective optimization mathematical model of material layout along the production line is improved by using a heuristic initialization strategy and a dynamic Thompson sampling mechanism to obtain a specific method for the heuristic initialization of the MOEA / D algorithm: Step S1: Initialize algorithm parameters; set population size , maximum number of iterations , neighborhood size , mutation probability , crossover probability and the set of weight vectors The Chebyshev decomposition method is used to decompose the multi-objective optimization problem of material layout along the production line into multiple single-objective sub-problems with directional preferences. Each sub-problem is modeled using the maximum weighted deviation function, which effectively guides the heuristically initialized MOEA / D algorithm to find a uniformly distributed Pareto optimal solution in the solution space, as shown in the following formula: ； ； in, is the Chebyshev decomposition function; is the decision variable; is an ideal point, which represents the vector of the minimum values ​​of the components of the current objective function on the feasible solution set; For the The objective function is The weight vector under the iteration reflects the current The importance of each goal in the iteration; is the objective function value, is the number of targets; is the feasible region, which represents the set of solutions that satisfy all constraints in the decision space; For the An ideal point of the objective function; Step S2: Design a heuristic initialization strategy and design a four-stage initialization method based on the characteristics of the multi-objective optimization problem of material layout along the production line: Phase 1: Randomize material orientation For each individual, randomly set the placement direction of each material , and calculate the corresponding actual occupied size; Phase 2: Sorting the Shelf Layers The shelf layers are sorted according to the energy consumption coefficient of taking and placing materials on the shelf layers, and materials are allocated to the shelf layers with low energy consumption first, thereby obtaining the shelf layer priority ranking; Phase 3: Assigning Material Priorities Arrange the materials in descending order according to their expected ratio, give priority to materials with high ratio, and thus obtain the material ranking; Stage 4: Generate Greedy Layout Randomly allocate the quantity of materials based on material priority and shelf layer priority, subject to the following constraints: ； ； in, and For materials under current constraints On the shelf level The maximum number of horizontal and vertical positions that can be placed. and The maximum number of placements for each material in the horizontal and vertical directions is preset during the heuristic initialization phase; Step S3: Design an adaptive operator selection mechanism based on Beta distribution and Thompson sampling to dynamically adjust the selection probability of the mutation operator. In each generation, sample once from each Beta distribution and select the operator with the largest sampling value for the mutation operation. Step S4: With probability Select parent individuals in the neighborhood with probability Randomly select from the entire population to balance neighborhood search and global search; Step S5: Check and repair constraints on the new solution generated after the mutation operation: Fix 1: Depth constraint fix, if i Classification of materials k Number of shelves in the depth direction If the total depth of the rack exceeds the maximum allowable depth of the rack layer, it needs to be restricted as shown in the following formula: ； in, For the i Classification of materials k The number of shelves after repair in the depth direction, is the depth of the shelf layer, For materials Actual occupied depth; Fix 2: Fix the length constraint to ensure that the total horizontal length of all materials on each shelf does not exceed the maximum length of that shelf, as shown in the following formula: like , then scale the i The number of materials placed: ； in, is the length of the shelf layer, For materials The actual occupied length, is the number of material types; Fix 3: Requirement constraint fix like , For materials The demand for the first i If the total number of a certain material is less than the production demand, add the material to the shelf layer where there is still available space; Step S6: Population update and ideal point maintenance; use Chebyshev distance to evaluate the quality of the solution, update the solution in the neighborhood, and dynamically update the ideal point based on the newly generated individuals in each generation of evolution .

2. The multi-objective optimization method for material layout along the production line based on evolutionary optimization according to claim 1, characterized in that: The material demand information for each type includes the material number, demand quantity in each time period, expected ratio and maximum demand quantity; The shelf structure parameters include the number of shelf layers, the length of each layer, the depth of each layer and the maximum load-bearing capacity; The material specification information includes material number, long side dimension, short side dimension and unit weight; The worker operation parameters include the energy consumption coefficients of workers picking up and placing materials corresponding to different shelf layer heights.

3. The multi-objective optimization method for material layout along the production line based on evolutionary optimization according to claim 1, characterized in that: The data preprocessing and standardization of the acquired basic information data includes cleaning, verifying and format conversion of the acquired basic information data, specifically: Analyze the historical consumption of each type of material demand data and calculate the demand volatility and correlation of each type of material; Grid the shelf space and establish a unified spatial coordinate system; Standardize material specification data and calculate the actual dimensions occupied by materials in different placement directions.

4. The multi-objective optimization method for material layout along the production line based on evolutionary optimization according to claim 3 is characterized by: The specific method of solving the multi-objective optimization mathematical model of material layout beside the production line based on the heuristic initialization MOEA / D algorithm and obtaining the Pareto optimal solution set through iterative optimization is as follows: Step C1: Use a hybrid coding method to design a coding scheme for the material position and placement, and obtain the coding vector of the material position and placement: the horizontal placement quantity and the vertical placement quantity are both coded as integer codes, and the dimensions are , is the number of material types, is the number of shelves; the placement direction is coded in binary, and the dimension ; Step C2: For each subproblem in the multi-objective optimization mathematical model for material layout along the production line, loop through steps S3-S6 until all subproblems have been processed and the number of loops reaches the set maximum number of loops. In each loop, select a subproblem to be optimized, use the dynamic Thompson sampling mechanism to select a suitable mutation operator to generate a new solution, and perform repair processing on the new solution. Then, evaluate the new solution to determine whether its quality is better than the current population and update it accordingly. At the same time, update the performance statistics of the ideal point and operator. Periodically adjust the utility value of each subproblem to dynamically optimize the overall search strategy. Step C3: When the heuristically initialized MOEA / D algorithm meets the termination condition, the final Pareto solution set is output.

5. A multi-objective optimization system for material layout along a production line based on evolutionary optimization, implemented based on the multi-objective optimization method for material layout along a production line based on evolutionary optimization according to claim 1, characterized in that: It includes data acquisition module, model building module, algorithm design module, model solving module and result output module; The data acquisition module obtains production line material demand information, shelf structure parameters, material specification information and worker operation energy consumption data, and pre-processes and standardizes these basic data; The model building module establishes a multi-objective optimization mathematical model that takes into account material ratio balance, worker workload and space utilization, and designs constraints to ensure the feasibility of the solution; The algorithm design module designs a heuristic initialization MOEA / D algorithm, adopts a heuristic initialization strategy to improve the quality of the initial solution, and realizes adaptive operator selection through dynamic Thompson sampling; The model solving module solves the multi-objective optimization mathematical model of the material layout beside the production line based on the heuristic initialization MOEA / D algorithm, and obtains the Pareto optimal solution set through iterative optimization, that is, the optimal layout of the materials beside the production line; The result output module analyzes and evaluates the model solution optimization results, generates material layout plans and provides decision support information.

6. An electronic device, configured to execute the multi-objective optimization method for material layout along a production line based on evolutionary optimization according to any one of claims 1 to 4, characterized in that: include: One or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the multi-objective optimization method for production line material layout based on evolutionary optimization.

7. A computer-readable storage medium storing executable instructions for executing the multi-objective optimization method for material layout along a production line based on evolutionary optimization according to any one of claims 1 to 4, characterized in that: When the instructions are executed, the processor executes the multi-objective optimization method for production line material layout based on evolutionary optimization.

8. A computer program product for executing the multi-objective optimization method for material layout along a production line based on evolutionary optimization according to any one of claims 1 to 4, characterized in that: The method comprises a computer program or an instruction, which, when executed by a processor, realizes the multi-objective optimization method for material layout beside a production line based on evolutionary optimization.

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