Multi-objective robust optimization method for cross-region multi-agent manufacturing task allocation

Abstract

This invention provides a multi-objective robust optimization method for cross-regional multi-entity manufacturing task allocation, relating to the technical field of cross-regional multi-entity manufacturing task allocation. Based on cross-regional multi-entity manufacturing resources and tasks, and considering maritime resources, this invention constructs a cross-regional multi-entity manufacturing task allocation model. Addressing the uncertainty of maritime transport time, a 2-norm spherical uncertainty set is designed to construct a multi-objective robust squared model for cross-regional multi-entity manufacturing task allocation, simultaneously optimizing the dual objectives of total delivery time deviation and total delivery cost of manufacturing tasks. This multi-objective robust squared model considers the reality of shipping companies' advance-released schedules and the uncertainty of maritime transport time. Furthermore, this multi-objective robust squared model is transformed into an easily solvable equivalent second-order cone model, and a two-stage hybrid heuristic algorithm with initial population generation rules and chromosome constraint verification mechanisms is designed to solve it, providing a reasonable and feasible resource allocation scheme for manufacturing tasks.

Description

Technical Field

[0001] This invention relates to the field of cross-regional multi-entity manufacturing task allocation technology, and specifically to a multi-objective robust optimization method, system, storage medium, and electronic device for cross-regional multi-entity manufacturing task allocation. Background Technology

[0002] With the rapid development of global trade and emerging markets, more and more manufacturing companies are choosing to shift from traditional centralized production methods to distributed multi-factory production networks. Distributed multi-factory production, characterized by geographical dispersion, offers manufacturing companies the potential to reduce costs, improve efficiency, and achieve energy conservation and emission reduction.

[0003] Compared to the allocation of manufacturing tasks within a single factory, the geographically dispersed nature of multiple factories not only brings cost differences in raw materials, labor, and warehousing, but also poses significant challenges to long-distance logistics. When placing orders, overseas customers typically consider their own sales and inventory levels, specifying a desired delivery date and expecting efficient and timely product delivery from the manufacturer. If the delivery time of the manufacturing task is significantly earlier than the overseas customer's delivery date, it will result in expensive international port storage costs. Conversely, if the delivery time is significantly later than the overseas customer's delivery date, it will cause substantial delays and losses for the customer.

[0004] In overseas-driven manufacturing task allocation, maritime transport is often overlooked as a significant influencing factor. First, the impact of shipping schedules: anticipated shipping plans and long lead times severely limit manufacturers' processing time, affecting production allocation, scheduling, and storage. Second, the uncertainty of maritime transport is a pervasive problem, seriously impacting the reliability of the global supply chain. When actual shipping schedules deviate from published schedules, shippers, manufacturers, and their customers all face numerous losses due to delays. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the shortcomings of existing technologies, this invention provides a multi-objective robust optimization method, system, storage medium, and electronic device for cross-regional multi-entity manufacturing task allocation, solving the technical problem of ignoring the impact of uncertainties in sea freight time on cross-regional multi-entity manufacturing task allocation.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A multi-objective robust optimization method for cross-regional, multi-agent manufacturing task allocation includes:

[0010] S1. Acquire cross-regional, multi-entity manufacturing resources and manufacturing tasks;

[0011] S2. Based on the cross-regional multi-entity manufacturing resources and manufacturing tasks, and taking into account maritime resources, construct a cross-regional multi-entity manufacturing task allocation model.

[0012] S3. Based on the manufacturing task allocation model, uncertain sea transport time is represented by a 2-norm spherical uncertain set, and a multi-objective robust squared model for cross-regional multi-entity manufacturing task allocation is constructed.

[0013] S4. Transform the multi-objective robust squared model into an equivalent second-order cone model, solve the equivalent second-order cone model, and obtain the robust optimization results of cross-regional multi-subject manufacturing task allocation.

[0014] Preferably, the multi-objective robust squared model in S3 includes:

[0015] (1) The first objective function aims to minimize the L2 norm of the difference between the actual delivery date of the manufacturing task and the expected delivery date of the overseas customer under the worst-case scenario of ocean freight time deviation:

[0016]

[0017]

[0018]

[0019] (2) The second objective function aims to minimize the total delivery cost of the manufacturing task:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Where J represents the set of manufacturing tasks, J = {1, 2, ..., n}; I represents the set of factories, I = {1, 2, ..., m}; G represents the set of domestic ports, G = {1, 2, ..., p}; S represents the set of large ships, S = {1, 2, ..., q};

[0026] Assuming the uncertain parameter is the actual sea transport time δ s Inside a sphere Let ρ be the center of the sphere, ρ be the radius of the sphere, and Δs be the error value; let Matrix δ = [δ1, δ2, ..., δs [A matrix representing the actual sea travel time for each ship] This is a matrix representing the historical average sea travel time for each ship, where matrix Δ = [Δ1, Δ2, ..., Δ]. s [ ] is the deviation matrix of the actual sea travel time of each ship from its historical average sea travel time;

[0027] There are constraints on the actual sea travel time for all large ships:

[0028] ||Δ||≤ρ

[0029] Let δ be an s-dimensional real vector, and ‖·‖ be the 2-norm of the matrix; then the 2-norm spherical uncertainty set of the actual sea travel time of the large ship is expressed as:

[0030]

[0031] a s This indicates the departure date of the large ship 's' by sea;

[0032] y ijs For the decision variable y, if manufacturing task j is assigned to factory i, and the sea transport task of manufacturing task j is assigned to large ship s, the value is 1; otherwise, the value is 0. js If the sea transport task of manufacturing task j is assigned to the large ship s, take 1; otherwise, take 0; d j Indicates the customer's delivery date for manufacturing task j;

[0033] q j Indicates the number of products manufactured in task j; These represent the processing cost, warehousing cost, domestic land transportation cost, and international sea transportation cost per unit of product for manufacturing task j, respectively.

[0034] This represents the processing cost per unit of product for manufacturing task j at factory i;

[0035] x ijj′ As a decision variable, if both manufacturing tasks j and j′ are assigned to factory i, and manufacturing task j′ is completed immediately after manufacturing task j, the value is 1; otherwise, the value is 0.

[0036] This represents the daily warehousing cost per unit of product for manufacturing task j; Indicates the storage time for manufacturing task j;

[0037] This represents the domestic transportation cost per unit of product between factory i and port g;

[0038] If the large ship s departs from port g, T sg =1; otherwise T sg =0;

[0039] This represents the transportation cost per unit of product on a large ship (s).

[0040] The multi-objective robust squared model in S3 also includes:

[0041] Constraints:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] Among them, s j s j′ These represent the actual delivery dates of manufacturing tasks j and j′, respectively; M represents a very large constant.

[0057] tr ig This represents the land transportation time from factory i to port g;

[0058] pro ij This represents the processing time of manufacturing task j in factory i.

[0059] Preferably, the equivalent second-order cone model in S4 includes:

[0060] Objective 1:

[0061]

[0062] Objective Two:

[0063]

[0064] Constraints:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079]

[0080]

[0081] Where μ represents the maximum 2-norm of the time difference between the arrival of the large ship and the time of customer delivery for all tasks; θ represents the maximum 2-norm of the decision variable y matrix.

[0082] Preferably, a two-stage hybrid heuristic algorithm with initial population generation rules and chromosome constraint verification mechanism is designed to solve the equivalent second-order cone model, including:

[0083] Phase 1:

[0084] Without considering the choice of processing plant and the start date of processing, the equivalent second-order cone model is simplified, and a genetic algorithm is designed to search for multiple maritime task schemes, and a population containing multiple chromosomes with assigned ship numbers is obtained.

[0085] Phase Two:

[0086] The last generation of the above population is used as a partial initial population containing chromosomes with multiple ship number assignments. A partial initial population containing chromosomes with multiple factory number assignments and a partial initial population containing chromosomes with multiple start processing dates are also generated. A multi-objective genetic algorithm is designed to obtain the Pareto optimal solution, and the solution is decoded as the final robust optimization result for cross-regional multi-agent manufacturing task allocation.

[0087] Preferably, the first stage specifically includes:

[0088] S411. In the equivalent second-order cone model, the objective and constraints that are only related to the decision variables for allocating the large ship are separated, and the original equivalent second-order cone model is simplified and relaxed to obtain the following sub-model:

[0089] Objective 1:

[0090]

[0091] Objective Two:

[0092]

[0093] Constraints:

[0094]

[0095]

[0096]

[0097]

[0098] S412. Solve the above sub-model, randomly generate the initial population of the first stage including multiple n columns of chromosomes, calculate the fitness of each individual in the population, and set Gen1 = 0.

[0099] Z i =aV 1 +bV 2

[0100]

[0101] Where a and b are constants, representing the weights of objectives one and two, respectively; f i s1 Nind1 represents the fitness value of the first stage corresponding to the i-th chromosome; Nind1 represents the population size of the first stage.

[0102] S413. Determine if the termination condition is met. If it is, sort the current population in non-ascending order according to fitness and output it as the last generation population Chrom1; otherwise, go to S414.

[0103] S414. Create a stallion by replicating 1 / 2 of the elite individuals using the Nind model.

[0104] S415. Select Nind1 / 2 individuals from the parent population after removing elite individuals using a roulette wheel.

[0105] S416. Merge the stallions with the selected herd;

[0106] S417, Perform a two-point crossover operation;

[0107] S418. Perform the breeder mutation operation to generate a new generation of population and calculate the fitness of each individual in the population; set Gen1 = Gen1 + 1 and return to S413.

[0108] Preferably, the second stage specifically includes:

[0109] S421. Generate the initial population for the second stage, consisting of multiple chromosome units composed of 3 n columns of chromosomes:

[0110] The first two individuals of the last generation of the first stage population Chrom1 are used as the initial population for assigning ship numbers on chromosome 3 in the second stage multi-objective genetic algorithm; where Nind2 represents the population size in the second stage, and Nind2 << Nind1.

[0111] A processing plant priority selection mechanism is introduced, using processing and transportation costs as the criterion, to generate a partial initial population of chromosome 1 with assigned plant numbers. This priority selection mechanism means that a certain selection probability is set to generate the initial population of chromosome 1 with assigned base numbers. The principle for setting the selection probability is that the lower the sum of production and domestic land transportation costs, the higher the selection probability is set for the factory.

[0112] Under the ideal assumption of zero storage time, the start date of processing can be obtained by working backward from the shipment date of the large ship assigned to the manufacturing task;

[0113]

[0114] S422. Perform constraint verification on the chromosomes in the initial population generated in S421; if it fails, correct it according to the preset constraint processing rules.

[0115] S423. Calculate the fitness of each individual in the population, and let Gen2 = 0; where the fitness function in the second stage consists of the non-dominated ordination level and the crowding degree. The higher the non-dominated ordination level, the lower the crowding degree, and the higher the fitness of the chromosome individual.

[0116] S424. Determine whether the preset termination condition is met. If it is met, output the Pareto optimal solution in the current population and decode it as the final robust optimization result of cross-regional multi-agent manufacturing task allocation; otherwise, go to S425.

[0117] S425. Preserve the parent population and perform a single-point crossover operation;

[0118] S426. Perform breeder mutation operation;

[0119] S427. Perform constraint verification on the chromosomes in the current population; if it fails, correct it according to the preset constraint processing rules and generate a progeny population containing Nind2 individuals.

[0120] S428. Merge offspring and parents, calculate the fitness of each individual in the merged population, and select the first two individuals with higher fitness (Nind2). Let Gen2 = Gen2 + 1, and proceed to S424.

[0121] Preferably, regarding constraint one: the departure time of the large ship must be later than the arrival time of the mission at the domestic port; the preset constraint processing rule specifically refers to: reducing the proportion of chromosomes that violate constraint one in the initial population through the initial population generation rule; and correcting chromosomes that violate constraint one to chromosomes that conform to constraint one by directly modifying chromosomes.

[0122] Preferably, regarding constraint two: two tasks assigned to the same processing plant cannot be processed simultaneously; the preset constraint handling rule specifically refers to:

[0123] The first step is to determine the set of tasks that need to be evaluated. If the set is not empty, proceed to the second step; otherwise, exit.

[0124] The second step is to determine whether the processing time of the last manufacturing task conflicts with that of the second-to-last manufacturing task; if so, skip to the third step; if not, skip to the fourth step.

[0125] Third, if there is no conflict, remove the last task from the task set and return to the second step; if there is a conflict, move the processing time of the last manufacturing task forward to make it non-conflicting, while keeping the domestic land transportation time unchanged. The time difference in between is used to arrange for the task to be stored in a warehouse near the processing plant, waiting for domestic transportation. Remove the last task from the task set and return to the second step.

[0126] The fourth step is to move on to the next processing plant or the next chromosome and repeat the first step.

[0127] A multi-objective robust optimization method system for cross-regional, multi-agent manufacturing task allocation includes:

[0128] The acquisition module is used to acquire manufacturing resources and tasks from multiple entities across different regions.

[0129] The construction module is used to build a manufacturing task allocation model for cross-regional multi-entity production networks based on the cross-regional multi-entity manufacturing resources and manufacturing tasks, under the premise of determining the sea transport time.

[0130] The optimization module is used to construct a multi-objective robust squared model for manufacturing task allocation based on the manufacturing task allocation model, using the 2-norm sphere uncertainty set to represent uncertain sea transport time.

[0131] The solution module is used to transform the multi-objective robust squared model into an equivalent second-order cone model, solve the equivalent second-order cone model, and obtain the robust optimization results of cross-regional multi-entity manufacturing task allocation.

[0132] A storage medium storing a computer program for a multi-objective robust optimization method for cross-regional multi-agent manufacturing task allocation, wherein the computer program causes a computer to execute the multi-objective robust optimization method for cross-regional multi-agent manufacturing task allocation as described above.

[0133] An electronic device, comprising:

[0134] One or more processors;

[0135] Memory; and

[0136] One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including a multi-objective robust optimization method for performing cross-regional multi-agent manufacturing task allocation as described above.

[0137] (III) Beneficial Effects

[0138] This invention provides a multi-objective robust optimization method, system, storage medium, and electronic device for cross-regional, multi-entity manufacturing task allocation. Compared with existing technologies, it has the following advantages:

[0139] This invention addresses the uncertainty of the 2-norm sphere for maritime transport time by constructing a multi-objective robust squared model for cross-regional, multi-agent manufacturing task allocation, optimizing the dual objectives of total delivery deviation and total delivery cost. The model considers pre-defined maritime transport plans and long, uncertain maritime transport times. Furthermore, it transforms the model into an equivalent second-order cone model and employs a two-stage hybrid heuristic algorithm with initial population generation rules and chromosome constraint verification mechanisms to solve it, providing reasonable and feasible resource allocation suggestions for manufacturing tasks. Attached Figure Description

[0140] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0141] Figure 1 This is a schematic diagram of a multi-objective robust optimization method for cross-regional, multi-entity manufacturing task allocation provided in an embodiment of the present invention;

[0142] Figure 2 A schematic diagram illustrating a manufacturing task delivery process according to an embodiment of the present invention;

[0143] Figure 3 This is a schematic diagram of important process variables provided in an embodiment of the present invention, with the delivery process of a single manufacturing task as the main line.

[0144] Figure 4 A flowchart illustrating a two-stage hybrid heuristic algorithm provided in an embodiment of the present invention;

[0145] Figure 5 A flowchart illustrating the first-stage genetic algorithm provided in an embodiment of the present invention;

[0146] Figure 6 This invention provides a schematic diagram illustrating a processing rule example for constraint two.

[0147] Figure 7 This is a schematic diagram illustrating the generation rules of the initial population in the second-stage genetic algorithm provided in this embodiment of the invention. Detailed Implementation

[0148] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0149] This application provides a multi-objective robust optimization method, system, storage medium, and electronic device for cross-regional multi-entity manufacturing task allocation, which solves the technical problem of considering the impact of uncertainties in sea freight time on cross-regional multi-entity manufacturing task allocation.

[0150] The technical solution in this application is to solve the above-mentioned technical problems, and the general idea is as follows:

[0151] like Figure 1 As shown, this embodiment of the invention designs a 2-norm sphere uncertain set for ocean shipping time and constructs a multi-objective robust squared model for cross-regional multi-agent manufacturing task allocation, optimizing the dual objectives of total delivery deviation and total delivery cost of manufacturing tasks. This model considers pre-defined ocean shipping plans and long, uncertain ocean shipping times. Furthermore, the model is transformed into an equivalent second-order cone model, and a two-stage hybrid heuristic algorithm with initial population generation rules and chromosome constraint verification mechanisms is designed to solve it, providing reasonable and feasible resource allocation suggestions for manufacturing tasks.

[0152] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0153] Example:

[0154] This invention provides a multi-objective robust optimization method for cross-regional, multi-entity manufacturing task allocation, including:

[0155] S1. Acquire cross-regional, multi-entity manufacturing resources and manufacturing tasks;

[0156] S2. Based on the cross-regional multi-entity manufacturing resources and manufacturing tasks, and taking into account maritime resources, construct a cross-regional multi-entity manufacturing task allocation model.

[0157] S3. Based on the manufacturing task allocation model, uncertain sea transport time is represented by a 2-norm spherical uncertain set, and a multi-objective robust squared model for cross-regional multi-entity manufacturing task allocation is constructed.

[0158] S4. Transform the multi-objective robust squared model into an equivalent second-order cone model, solve the equivalent second-order cone model, and obtain the robust optimization results of cross-regional multi-subject manufacturing task allocation.

[0159] In this embodiment of the invention, the multi-objective robust squared model takes into account the pre-defined shipping plan and the long and uncertain shipping time. In addition, the model is transformed into an equivalent second-order cone model, and a two-stage hybrid heuristic algorithm with initial population generation rules and chromosome constraint verification mechanism is designed to solve it, providing reasonable and feasible resource allocation suggestions for the manufacturing task.

[0160] The following will detail each step of the above technical solution:

[0161] First, it is necessary to provide supplementary explanation of the cross-regional, multi-entity manufacturing task allocation problem involved in the embodiments of the present invention, as detailed below:

[0162] Taking manufacturing tasks as the optimization target, each manufacturing task needs to go through four key links: domestic production, domestic warehousing, domestic logistics, and international logistics, before finally being delivered to overseas customers. A batch of manufacturing tasks refers to a unit consisting of tasks placed by multiple overseas users within the same or similar time period. Each manufacturing task contains only one required product model, corresponds to only one overseas user, and each customer will propose a desired delivery time to the manufacturing company. Each manufacturing task can only be assigned to one factory for processing. Each factory has an independent assembly line workshop with the capability to process any manufacturing task with the same processing quality, and each manufacturing task can be assigned to any factory. A factory can only process one manufacturing task at a time, and interruption or interruption is not allowed. Each factory is equipped with a warehouse for storing finished products. Each sea freight task is completed by a single large vessel, and each large vessel has a designated domestic port of departure, departure time, and sea freight time. The delivery time of the product arriving at the international destination port is considered the delivery time of this task. Based on the above premises, the delivery process of a batch of manufacturing tasks is illustrated by the following example. Figure 2 As shown.

[0163] A manufacturing company has n manufacturing tasks, represented by the set J = {1, 2, ..., n}, which can be assigned to m distributed factories for processing, denoted by the set of factories I = {1, 2, ..., m}. Each manufacturing task requires four core steps: processing, storage, land transportation, and sea transportation, ultimately delivering the task to an overseas customer. Focusing on the delivery process of a single manufacturing task, the key process variable relationships are as follows: Figure 3 As shown. Considering the differences in production capacity between different factories, the processing time for manufacturing tasks varies in different factories. The processing time for manufacturing task j is determined by... This indicates that it is related to the assigned factory. The start time of manufacturing task j is determined by s. j This indicates that the end time of processing is determined by c. j This indicates that the storage time in the warehouse after the manufacturing task is completed is determined by... This indicates that due to geographical differences among multiple entities across regions, the time required for land transportation missions is... This refers to the transportation time between the factory assigned to the manufacturing task and the domestic port of departure of the selected large vessel, and is directly related to the assigned factory i and the large vessel s. Shipping resources are limited, and shipping companies prepare and publish shipping schedules in advance, including the departure time of the large vessel and the sea travel time. The departure time of the large vessel selected for manufacturing task j is determined by sh. j It is stated that the sea freight time is from This indicates that each manufacturing task corresponds one-to-one with an overseas customer, and the expected delivery time for each overseas customer's manufacturing task is specified by d. j express.

[0164] In step S1, cross-regional multi-entity manufacturing resources and manufacturing tasks are acquired;

[0165] The aforementioned cross-regional, multi-entity manufacturing resources and tasks specifically involve the following symbol system:

[0166] gather:

[0167] gather describe J The set of manufacturing tasks, J = {1, 2, ..., n} I Factory set, I = {1, 2, ..., m} G The set of domestic ports, G = {1, 2, ..., p} S Large ships gather, S={1,2,…,q}

[0168] Decision variables

[0169]

[0170] Relevant parameters

[0171]

[0172]

[0173] In step S2, based on the cross-regional multi-entity manufacturing resources and manufacturing tasks, and taking into account maritime resources, a cross-regional multi-entity manufacturing task allocation model is constructed.

[0174] This step focuses on the maritime transport link and proposes a dual-objective deterministic model for the allocation of manufacturing tasks in cross-regional multi-entity production networks. This model coordinates the scheduling of manufacturing tasks and optimizes both the overall on-time delivery and the total delivery cost of manufacturing tasks.

[0175] The deterministic model includes:

[0176] Objective one is to minimize the total difference between the actual delivery date of manufacturing tasks and the expected delivery date of overseas customers, that is, to maximize the overall on-time delivery of all manufacturing tasks, minimize overseas warehousing costs and delay costs, and meet customer needs.

[0177]

[0178]

[0179]

[0180]

[0181]

[0182]

[0183]

[0184] Formula (2) indicates that the actual delivery date of each manufacturing task is the start date of processing for that manufacturing task. j Processing days Warehouse storage days Land transport days With sea freight days The sum. Formula (3) Manufacturing task processing days The storage time of manufacturing task j is related to the product type and is proportional to the processing capacity and product quantity of the assigned factory i. Formula (4) indicates that the storage time of manufacturing task j in the warehouse is the shipping date of the selected large ship minus the end processing date of manufacturing task j. Ideally, the storage time of manufacturing task j in the warehouse is 0, meaning that the manufacturing task is transported to the domestic port as soon as it is completed at the base, in order to catch the large ship departing on the same day. Formula (6) indicates that the number of days of land transportation for manufacturing task j depends on the factory assigned to manufacturing task j and the shipping port of the selected large ship.

[0185] Objective 2 is to minimize the total delivery cost of manufacturing tasks. The delivery cost of each manufacturing task consists of production costs, warehousing costs, domestic land transportation costs, and international sea transportation costs.

[0186]

[0187]

[0188]

[0189]

[0190]

[0191] Formula (9) represents the unit product processing cost of manufacturing task j. It is related to the factory i to which the order is assigned and the type of product itself. Formula (10) indicates that the unit product warehousing cost of manufacturing task j is the product of the unit product warehousing cost per unit time of manufacturing task j and the warehousing time. Formula (11) indicates the unit product domestic land transportation cost of manufacturing task j. The cost of international sea freight per unit of product for manufacturing task j is related to the factory to which the manufacturing task j is assigned and the port of shipment of the selected large vessel. Formula (12) represents the cost of international sea freight per unit of product for manufacturing task j, which is related to the selected large vessel. The transportation cost of the large vessel is set to increase as the sea freight time decreases over a fixed distance.

[0192] Constraints:

[0193]

[0194]

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207] Among them, constraint (13) indicates that any manufacturing task has no sequential relationship with itself; constraint (14) indicates that each manufacturing task has a unique manufacturing task preceding it and is assigned to only one factory; constraint (15) indicates that each manufacturing task has a unique manufacturing task following it and is assigned to only one factory; constraint (16) indicates that each factory has only one first manufacturing task or is not assigned a manufacturing task; constraint (17) indicates that each factory has only one last manufacturing task or is not assigned a manufacturing task; constraint (18) indicates that for any factory, any manufacturing task cannot be both preceding and following another manufacturing task at the same time; constraint (19) indicates that for any manufacturing task... There must be the same number of pre-manufacturing tasks and post-manufacturing tasks; constraint (20) indicates the value constraint of the decision variable when the factory has not arranged any tasks; constraint (21) indicates that the start processing time of each manufacturing task is greater than 0; constraint (22) indicates that any two manufacturing tasks in the same factory cannot be processed at the same time; constraint (23) indicates that for any task, only one factory can be selected for processing, and only one large ship can be selected for overseas transportation; constraint (24) indicates the one-to-one correspondence between the two decision variables; constraint (25) indicates that the departure time of each manufacturing task must be greater than the arrival time of the manufacturing task at the domestic port; constraint (26) indicates the range of values ​​for the decision variable.

[0208] In step S3, based on the manufacturing task allocation model, an uncertain sea transport time is represented by a 2-norm spherical uncertain set, and a multi-objective robust squared model for cross-regional multi-entity manufacturing task allocation is constructed.

[0209] Typically, during the actual delivery of manufacturing tasks, overseas transportation time is affected by numerous factors such as sea weather, wind direction, and waves. There are often deviations from the pre-planned shipping schedule. Shipping schedules are extremely unpredictable and difficult to control in transportation. Variations in overseas shipping times can cause the original manufacturing task scheduling scheme to deviate from its optimal state. Therefore, robust optimization methods are used to solve the manufacturing task allocation problem under uncertain shipping times. Robust optimization considers the best solution in the worst-case scenario, representing a conservative viewpoint; the resulting optimized solution is not necessarily optimal, but it remains feasible when uncertain parameters are disturbed.

[0210] For uncertain parameters such as sea transport time, this embodiment of the invention designs a 2-norm sphere uncertainty set and establishes a multi-objective robust squared model for joint scheduling of production and logistics tasks.

[0211] The 2-norm spherical uncertainty set: assuming the uncertainty parameter is the actual sea transport time δ s Inside a sphere Let ρ be the center of the sphere, ρ be the radius of the sphere (the maximum standard deviation of all shipping time deviations), and Δ be the radius of the sphere. s Let be the error value (the deviation between the ship's length *s* and the historical average sea transport time); Matrix δ = [δ1, δ2, ..., δ s [A matrix representing the actual sea travel time for each ship] This is a matrix representing the historical average sea travel time for each ship, where matrix Δ = [Δ1, Δ2, ..., Δ]. s [ ] is the deviation matrix of the actual sea travel time of each ship from its historical average sea travel time;

[0212] There are constraints on the actual sea travel time for all large ships:

[0213] ||Δ||≤ρ (27)

[0214] δ is an s-dimensional real vector, and ||·|| is the 2-norm of the matrix, i.e., the largest singular value. The value of parameter ρ is given in advance, reflecting that the standard deviation of all shipping time deviations does not exceed ρ. When ρ = 0, this is a deterministic problem, indicating that the shipping time of all large ships takes the standard value; when ρ > 0, it indicates that the shipping time of all large ships deviates from the standard value to some extent. The value of ρ is adjusted according to the decision-maker's risk preference. Therefore, the 2-norm spherical uncertainty set of the actual shipping time of large ships is expressed as:

[0215]

[0216] The multi-objective robust squared model includes:

[0217] Objective one is to minimize the sum of squares of the differences between the actual delivery date of the manufacturing task and the expected delivery date of the overseas customer, considering the worst-case scenario of ocean freight time deviation. In the original deterministic model, the original parameter, ocean freight time, is considered. In case of uncertainty, the parameters Adjusted to δ s Furthermore, the uncertain parameter of sea transport time exists only in formula (7) of the objective function 1 of the original deterministic model.

[0218] The degree of on-time delivery of all products for objective 1 is described by the matrix 2-norm. Specifically, the first objective function is to minimize the 2-norm of the difference between the actual delivery date of the manufacturing task and the expected delivery date of the overseas customer under the worst-case scenario of ocean freight time deviation.

[0219]

[0220]

[0221]

[0222] Objective two is to minimize the total delivery cost of each manufacturing task. The delivery cost of each manufacturing task consists of production costs, warehousing costs, domestic land transportation costs, and international sea transportation costs; that is, the second objective function aims to minimize the total delivery cost of each manufacturing task.

[0223]

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[0225]

[0226]

[0227]

[0228] Constraints:

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[0231]

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[0235]

[0236]

[0237]

[0238]

[0239]

[0240]

[0241]

[0242]

[0243] In step S4, the multi-objective robust square model is transformed into an equivalent second-order cone model, and the equivalent second-order cone model is solved to obtain the robust optimization results of cross-regional multi-subject manufacturing task allocation.

[0244] The multi-objective robust squared model is transformed into an equivalent second-order cone model:

[0245] Target 1 is

[0246]

[0247] Objective 2 is

[0248]

[0249] Constraints:

[0250]

[0251]

[0252]

[0253]

[0254]

[0255]

[0256]

[0257]

[0258]

[0259]

[0260]

[0261]

[0262]

[0263]

[0264]

[0265]

[0266]

[0267] Where μ represents the maximum 2-norm of the time difference between the arrival of the large ship and the time of customer delivery for all tasks; This represents the maximum value of the 2-norm of the decision variable y matrix.

[0268] The proof is as follows:

[0269] The objective of this robust squared model is expressed using a matrix.

[0270]

[0271] Since y≠0, by the triangle inequality we get:

[0272]

[0273] From the compatibility of norms, we get:

[0274] ‖yΔ‖≤‖y‖‖Δ‖≤ρ‖y‖

[0275] The proof is as follows:

[0276] ‖yΔ‖ 2 =(yΔ) T yΔ=Δ T y T yΔ

[0277] Let λ max (y T y) is y T The largest eigenvalue of y, therefore

[0278] Δ T y T yΔ≤Δ T (λ max (y T y)I)Δ=λ max (y T y)‖Δ‖ 2 =|y| 2 ||Δ|| 2

[0279] Therefore, we have ||Δy||≤|Δ||y||.

[0280] Therefore, the objective function of this robust least squares problem has an upper bound:

[0281]

[0282] And when

[0283]

[0284] When, then ||Δ|| = ρ, and

[0285]

[0286] That is, the upper bound of the objective function is attainable.

[0287] The above analysis proves that the transformed equivalent second-order cone model is solvable. Accordingly, the embodiments of this invention employ the following... Figure 4The two-stage hybrid heuristic algorithm shown solves the equivalent second-order cone model, including:

[0288] Phase 1:

[0289] Without considering the choice of processing plant and the start date of processing, the equivalent second-order cone model is simplified, and a genetic algorithm is designed to search for multiple maritime transport mission schemes, and a population containing chromosomes with multiple assigned ship numbers is obtained.

[0290] Phase Two:

[0291] The last generation of the above population is used as a partial initial population containing chromosomes with multiple ship number assignments. A partial initial population containing chromosomes with multiple factory number assignments and a partial initial population containing chromosomes with multiple start processing dates are also generated. A multi-objective genetic algorithm is designed to obtain the Pareto optimal solution, and the solution is decoded as the final robust optimization result for cross-regional multi-agent manufacturing task allocation.

[0292] The goal of the first stage is to solve for and allocate the decision variable y of the large ship. ijs Related solutions are sought by searching for a group of multi-task maritime mission schemes with high on-time delivery rates and good maritime economic benefits; such as Figure 5 As shown, it specifically includes:

[0293] S411. In the equivalent second-order cone model, the ship decision variable y of the original model is... ijs Remove information containing base details and adjust the decision variable to y. js And it is known Then we can separate the decision variable y that is only related to the allocation of the large ship. js Based on the relevant objectives and constraints, the following sub-models are simplified:

[0294] Objective 1:

[0295]

[0296] Objective Two:

[0297]

[0298] Constraints:

[0299]

[0300]

[0301]

[0302]

[0303] S412. Solve the above sub-model, randomly generate the initial population of the first stage including multiple n columns of chromosomes, calculate the fitness of each individual in the population, and set Gen1 = 0.

[0304] Z i =aV 1 +bV 2 (81)

[0305]

[0306] Where a and b are constants, representing the weights of objectives one and two, respectively; f i s1 Nind1 represents the fitness value of the first stage corresponding to the i-th chromosome; Nind1 represents the population size of the first stage.

[0307] S413. Determine if the termination condition is met. If it is, sort the current population in non-ascending order according to fitness and output it as the last generation population Chrom1; otherwise, go to S414.

[0308] S414. Create a stallion by replicating 1 / 2 of the elite individuals using the Nind model.

[0309] S415. Select Nind1 / 2 individuals from the parent population after removing elite individuals using a roulette wheel.

[0310] S416. Merge the stallions with the selected herd;

[0311] S417, Perform a two-point crossover operation;

[0312] This step employs a two-point crossover strategy, randomly setting two crossover points in an individual's chromosomes, and then performing partial gene exchange between the two crossover points.

[0313] S418. Perform the breeder mutation operation to generate a new generation of population and calculate the fitness of each individual in the population; set Gen1 = Gen1 + 1 and return to S413.

[0314] This step employs the breeder GA mutation strategy, using compression ratio (MutShrink) and gradient partitioning (Gradient) to control the mutation distance. The greater the compression ratio and the fewer the gradient partitions, the greater the mutation magnitude and the stronger the global search capability.

[0315] The second stage involves designing a multi-objective genetic algorithm to solve the equivalent second-order cone model of the robust optimization model for cross-regional multi-entity manufacturing task allocation under uncertain maritime transport times; specifically including:

[0316] S421. Generate the initial population for the second stage, consisting of multiple chromosome units composed of 3 n columns of chromosomes:

[0317] The first step is to use the first two individuals of the last generation of the first stage population Chrom1 as the initial population for the second stage multi-objective genetic algorithm to assign ship numbers on chromosome 3; where Nind2 represents the population size in the second stage, and it should be noted that Nind1 is much larger than Nind2.

[0318] The second step is to introduce a processing plant priority selection mechanism based on processing and transportation costs as the judgment indicators, and generate a partial initial population of chromosome 1 with factory numbers assigned. This priority selection mechanism means that a certain selection probability is set to generate the initial population of chromosome 1 with base number assigned. The principle for setting the selection probability is that the lower the sum of production and domestic land transportation costs, the higher the selection probability is set for the factory.

[0319] To elaborate, firstly, for each export task, based on the sum of production and domestic land transportation costs, C... pro+str Sort the processing plants from smallest to largest and calculate the processing plant priority matrix. Nind2 rows and n columns. For example, for task j, its processing plant priority order matrix. In column j, the first row lists the processing plants with the lowest production and domestic land transportation costs, the second row lists the processing plants with the second lowest costs, and so on. Therefore, for all export tasks, C pro+str The lowest-ranking processing plant in the processing plant priority matrix The position numbers in the text are all in the first row.

[0320] The first two individuals of the initial population of chromosome 1, assigned to the base number, are all set as priority order matrices for each processing plant. The first line in the table. In the subsequent Nind2 / 2 individuals, each exit task has a certain probability P. The processing plant is selected from the pool. P is set to [0.5, 0.33, 0.25, 0.2, 0.167, 0.14, 0.125, 0.11, 0.1, 0.09, ...], representing a probability of 0.5 for selecting the processing plant. The processing factory in the first row corresponding to this task is selected with a probability of 0.33 from the second row, and so on. This is set... The smaller the location number of the processing plant, the lower the probability of it being selected.

[0321] The third step is to calculate the start date of processing by working backward from the manufacturing task's deadline delivery date, under the ideal assumption of zero storage time.

[0322]

[0323] The above three steps will generate the initial populations of the three decision variables. The three initial populations are interconnected by chromosome individual numbers, that is, chromosomes in the three populations with the same individual number form a chromosome unit.

[0324] S422. Perform constraint verification on the chromosomes in the initial population generated in S421; if it fails, correct it according to the preset constraint processing rules.

[0325] (1) Regarding constraint one: the departure time of the large ship must be later than the arrival time of the mission at the domestic port; the preset constraint processing rule specifically refers to: reducing the proportion of chromosomes that violate constraint one in the initial population through the initial population generation rule (corresponding to step S422); and correcting chromosomes that violate constraint one to chromosomes that conform to constraint one by directly modifying chromosomes (corresponding to subsequent step S427).

[0326] (2) Regarding constraint two: two tasks assigned to the same processing plant cannot be processed simultaneously; the preset constraint handling rules specifically refer to:

[0327] The first step is to determine the set of tasks that need to be evaluated. If the set is not empty, proceed to the second step; otherwise, exit.

[0328] The second step is to determine whether the processing time of the last manufacturing task conflicts with that of the second-to-last manufacturing task; if so, skip to the third step; if not, skip to the fourth step.

[0329] Third, if there is no conflict, remove the last manufacturing task from the manufacturing task set and return to the second step; if there is a conflict, move the processing time of the last manufacturing task forward to make it non-conflicting, while keeping the domestic land transportation time unchanged. The time difference is used to arrange for the manufacturing task to be stored in a warehouse near the processing plant, waiting for domestic transportation. Then, remove the last manufacturing task from the manufacturing task set and return to the second step.

[0330] The fourth step is to move on to the next processing plant or the next chromosome and repeat the first step.

[0331] Specifically, such as Figure 6 As shown:

[0332] The first step was to determine that there was a time conflict between the second manufacturing task (manufacturing task 2) and the third manufacturing task (manufacturing task 3).

[0333] The second step is to move the processing time of the third manufacturing task forward while keeping the domestic land transportation time unchanged. The time difference is used to store the manufacturing task in a warehouse near the processing plant, waiting for domestic transportation. Upon reassessment, it was found that the processing time of the third manufacturing task conflicts with that of the first manufacturing task (manufacturing task 1).

[0334] The third step is to adjust the first manufacturing task in a manner similar to the third manufacturing task.

[0335] Step 4: Stop judging once the final determination is that there is no conflict in the manufacturing task; then move on to the next processing plant or the next chromosome.

[0336] Specific examples Figure 7 As shown, in this embodiment of the invention, a CV matrix is ​​set to determine whether a population violates constraint one. The CV matrix is ​​a matrix that stores the degree to which individuals in the population violate each constraint, including the number of rows corresponding to the number of chromosomes and the number of columns corresponding to the number of constraint conditions.

[0337] S423. Calculate the fitness of each individual in the population, and let Gen2 = 0; where the fitness function in the second stage consists of the non-dominated ordination level and the crowding degree. The higher the non-dominated ordination level, the lower the crowding degree, and the higher the fitness of the chromosome individual.

[0338] S424. Determine whether the preset termination condition is met. If it is met, output the Pareto optimal solution in the current population and decode it as the final robust optimization result of cross-regional multi-agent manufacturing task allocation; otherwise, proceed to S425.

[0339] S425. Preserve the parent population and perform a single-point crossover operation;

[0340] In this step, only chromosome 1 (assigned to the base numbered chromosome) and chromosome 3 (assigned to the large ship numbered chromosome) in the chromosome unit are subjected to single-point crossover operation. In the two chromosome individuals that have undergone crossover operation, one crossover point is randomly set in each individual for splitting, and the genes on the right side of the crossover point are exchanged, thus obtaining two different chromosomes.

[0341] S426. Perform breeder mutation operation;

[0342] This step only performs breeder GA mutation operations on chromosome 1 (assigned to base number chromosome) and chromosome 3 (assigned to large ship number chromosome) within the chromosome unit. The mutation distance is controlled by the compression ratio (MutShrink) and gradient partitioning (Gradient). The larger the compression ratio and the fewer the gradient partitions, the greater the mutation amplitude and the stronger the global search capability.

[0343] The start date of processing of chromosome 2 in the chromosome unit is calculated using the formula in step S421, without crossover and mutation operations, taking chromosome 1 and chromosome 3 after crossover and mutation as known conditions.

[0344] S427. Perform constraint verification on the chromosomes in the current population; if it fails, correct it according to the preset constraint processing rules and generate a progeny population containing Nind2 individuals.

[0345] S428. Merge offspring and parents, calculate the fitness of each individual in the merged population, and select the first two individuals with higher fitness (Nind2). Let Gen2 = Gen2 + 1, and proceed to S424.

[0346] This invention provides a multi-objective robust optimization method system for cross-regional, multi-entity manufacturing task allocation, comprising:

[0347] The acquisition module is used to acquire manufacturing resources and tasks from multiple entities across different regions.

[0348] The construction module is used to build a manufacturing task allocation model for cross-regional multi-entity production networks based on the cross-regional multi-entity manufacturing resources and manufacturing tasks, under the premise of determining the sea transport time.

[0349] The optimization module is used to construct a multi-objective robust squared model for manufacturing task allocation based on the manufacturing task allocation model, using the 2-norm sphere uncertainty set to represent uncertain sea transport time.

[0350] The solution module is used to transform the multi-objective robust squared model into an equivalent second-order cone model, solve the equivalent second-order cone model, and obtain the robust optimization results of cross-regional multi-subject manufacturing task allocation.

[0351] This invention provides a storage medium storing a computer program for a multi-objective robust optimization method for cross-regional multi-entity manufacturing task allocation, wherein the computer program causes a computer to execute the multi-objective robust optimization method for cross-regional multi-entity manufacturing task allocation as described above.

[0352] This invention provides an electronic device, comprising:

[0353] One or more processors;

[0354] Memory; and

[0355] One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including a multi-objective robust optimization method for performing cross-regional multi-agent manufacturing task allocation as described above.

[0356] It is understood that the multi-objective robust optimization method system, storage medium and electronic device for cross-regional multi-entity manufacturing task allocation provided in the embodiments of the present invention correspond to the multi-objective robust optimization method for cross-regional multi-entity manufacturing task allocation provided in the embodiments of the present invention. The explanation, examples and beneficial effects of the relevant contents can be referred to the corresponding parts of the multi-objective robust optimization method for cross-regional multi-entity manufacturing task allocation, and will not be repeated here.

[0357] In summary, compared with existing technologies, it has the following beneficial effects:

[0358] This invention addresses the uncertainty of the 2-norm sphere for maritime transport time by constructing a multi-objective robust squared model for cross-regional, multi-agent manufacturing task allocation. This model optimizes the dual objectives of total delivery deviation and total delivery cost for manufacturing tasks. The model considers pre-defined maritime transport plans and long, uncertain maritime transport times. Furthermore, it transforms the model into an equivalent second-order cone model and employs a two-stage hybrid heuristic algorithm with initial population generation rules and chromosome constraint verification mechanisms to solve it, providing reasonable and feasible resource allocation suggestions for manufacturing tasks.

[0359] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0360] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective robust optimization method for cross-regional, multi-entity manufacturing task allocation, characterized in that, include: S1. Acquire manufacturing resources and tasks across multiple regions and entities; S2. Based on the cross-regional multi-entity manufacturing resources and manufacturing tasks, and taking into account maritime resources, construct a cross-regional multi-entity manufacturing task allocation model. S3. Based on the manufacturing task allocation model, uncertain sea transport time is represented by a 2-norm spherical uncertain set, and a multi-objective robust squared model for cross-regional multi-entity manufacturing task allocation is constructed. S4. Transform the multi-objective robust square model into an equivalent second-order cone model, solve the equivalent second-order cone model, and obtain the robust optimization results of cross-regional multi-subject manufacturing task allocation. The multi-objective robust squared model in S3 includes: (1) The first objective function aims to minimize the 2-norm of the difference between the actual delivery date of the manufacturing task and the expected delivery date of the overseas customer under the worst-case scenario of ocean freight time deviation: (2) The second objective function aims to minimize the total delivery cost of the manufacturing task: Where J represents the set of manufacturing tasks, J={1,2,…,n}; I represents the set of factories, I={1,2,…,m}; G represents the set of domestic ports, G={1,2,…,p}; S represents the set of large ships, S={1,2,…,q}; Assuming the uncertain parameter is the actual sea transport time δ s Inside a sphere Let ρ be the center of the sphere and ρ be the radius of the sphere. Let be the error value; ;matrix This is a matrix representing the actual sea travel time for each ship. This is a matrix representing the historical average sea travel time for each ship. This is a matrix showing the deviation between the actual sea travel time of each ship and its historical average sea travel time. There are constraints on the actual sea travel time for all large ships: Let s be an s-dimensional real vector. If the matrix is ​​a 2-norm, then the 2-norm spherical uncertainty set of the actual sea travel time of the large ship is represented as: a s This indicates the departure date of the large ship 's' by sea; y ijs For the decision variable y, if manufacturing task j is assigned to factory i, and the sea transport task of manufacturing task j is assigned to large ship s, the value is 1; otherwise, the value is 0. js If the sea transport task of manufacturing task j is assigned to the large ship s, take 1; otherwise, take 0; d j Indicates the customer's delivery date for manufacturing task j; q j Indicates the number of products manufactured in task j; These represent the processing cost, warehousing cost, domestic land transportation cost, and international sea transportation cost per unit of product for manufacturing task j, respectively. This represents the processing cost per unit of product for manufacturing task j at factory i; As a decision variable, if both manufacturing tasks j and j' are assigned to factory i, and manufacturing task j' is completed immediately after manufacturing task j', the value is 1; otherwise, the value is 0. This represents the daily warehousing cost per unit of product for manufacturing task j; Indicates the storage time for manufacturing task j; This represents the domestic transportation cost per unit of product between factory i and port g; If the large ship s departs from port g, T sg =1; otherwise T sg =0; This represents the transportation cost per unit of product on a large ship (s). The multi-objective robust squared model in S3 also includes: Constraints: in, These represent the actual delivery dates of manufacturing tasks j and j', respectively; M represents a very large constant. tr ig This represents the land transportation time from factory i to port g; pro ij This represents the processing time of manufacturing task j in factory i.

2. The multi-objective robust optimization method for cross-regional, multi-entity manufacturing task allocation as described in claim 1, characterized in that, The equivalent second-order cone model in S4 includes: Objective 1: Objective Two: Constraints: Where μ represents the maximum value of the 2-norm of the time difference between the arrival of the large ship and the time of customer delivery for all tasks; This represents the maximum value of the 2-norm of the decision variable y matrix.

3. The multi-objective robust optimization method for cross-regional, multi-entity manufacturing task allocation as described in claim 2, characterized in that, Design a two-stage hybrid heuristic algorithm with initial population generation rules and chromosome constraint verification mechanism to solve the equivalent second-order cone model, including: Phase 1: Without considering the choice of processing plant and the start date of processing, the equivalent second-order cone model is simplified, and a genetic algorithm is designed to search for multiple maritime task schemes, and a population containing multiple chromosomes with assigned ship numbers is obtained. Phase Two: The last generation of the above population is used as a partial initial population containing chromosomes with multiple ship number assignments. A partial initial population containing chromosomes with multiple factory number assignments and a partial initial population containing chromosomes with multiple start processing dates are also generated. A multi-objective genetic algorithm is designed to obtain the Pareto optimal solution, and the solution is decoded as the final robust optimization result for cross-regional multi-agent manufacturing task allocation.

4. The multi-objective robust optimization method for cross-regional, multi-entity manufacturing task allocation as described in claim 3, characterized in that, The first stage specifically includes: S411. In the equivalent second-order cone model, separate the variable y that is only related to the allocation of the large ship variable. js Based on the relevant objectives and constraints, the original equivalent second-order cone model is simplified and relaxed to obtain the following sub-model: Objective 1: Objective Two: Constraints: S412. Solve the above sub-model, randomly generate the initial population of the first stage including multiple n columns of chromosomes, calculate the fitness of each individual in the population, and set Gen1=0. Where a and b are constants, representing the weights of objectives one and two, respectively; Nind1 represents the fitness value of the first stage corresponding to the i-th chromosome; Nind1 represents the population size of the first stage. S413. Determine if the termination condition is met. If it is, sort the current population in non-ascending order according to fitness and output it as the last generation population Chrom1; otherwise, go to S414. S414. Create a stallion by replicating 1 / 2 of the elite individuals using the Nind model. S415. Select Nind1 / 2 individuals from the parent population after removing elite individuals using a roulette wheel. S416. Merge the stallions with the selected herd; S417, Perform a two-point crossover operation; S418. Perform the breeder mutation operation to generate a new generation of population and calculate the fitness of each individual in the population; set Gen1 = Gen1 + 1 and return to S413.

5. The multi-objective robust optimization method for cross-regional, multi-entity manufacturing task allocation as described in claim 3 or 4, characterized in that, The second stage specifically includes: S421. Generate the initial population for the second stage, consisting of multiple chromosome units composed of 3 n columns of chromosomes: The first two individuals of the last generation of the first-stage population Chrom1 are used as the initial population for chromosome 3 allocation of ship numbers in the second-stage multi-objective genetic algorithm; where Nind2 represents the population size in the second stage, and Nind2... Nind1; A processing plant priority selection mechanism is introduced, using processing and transportation costs as the criterion, to generate a partial initial population of chromosome 1 with assigned plant numbers. This priority selection mechanism means that a certain selection probability is set to generate the initial population of chromosome 1 with assigned base numbers. The principle for setting the selection probability is that the lower the sum of production and domestic land transportation costs, the higher the selection probability is set for the plant. Under the ideal assumption of zero storage time, the start date of processing can be obtained by working backward from the ship's shipment date assigned to the manufacturing task. S422. Perform constraint verification on the chromosomes in the initial population generated in S421; if it fails, correct it according to the preset constraint processing rules. S423. Calculate the fitness of each individual in the population, and set Gen2=0; where the fitness function in the second stage consists of the non-dominated ordination level and the crowding degree. The higher the non-dominated ordination level, the lower the crowding degree, and the higher the fitness of the chromosome individual. S424. Determine whether the preset termination condition is met. If it is met, output the Pareto optimal solution in the current population and decode it as the final robust optimization result of cross-regional multi-agent manufacturing task allocation; otherwise, go to S425. S425. Preserve the parent population and perform a single-point crossover operation; S426. Perform breeder mutation operation; S427. Perform constraint verification on the chromosomes in the current population; if it fails, correct it according to the preset constraint processing rules and generate a progeny population containing Nind2 individuals. S428. Merge offspring and parents, calculate the fitness of each individual in the merged population, and select the top 2 individuals with higher fitness; set Gen2 = Gen2 + 1, and proceed to S424.

6. The multi-objective robust optimization method for cross-regional, multi-entity manufacturing task allocation as described in claim 5, characterized in that, (1) Regarding constraint one: the departure time of the large ship must be later than the arrival time of the mission at the domestic port; the preset constraint processing rule specifically refers to: reducing the proportion of chromosomes that violate constraint one in the initial population through the generation rule of the initial population; and correcting chromosomes that violate constraint one to chromosomes that conform to constraint one by directly modifying chromosomes. And / or (2) Regarding constraint two: two tasks assigned to the same processing plant cannot be processed simultaneously; the preset constraint handling rules specifically refer to: The first step is to determine the set of tasks that need to be evaluated. If the set is not empty, proceed to the second step; otherwise, exit. The second step is to determine whether there is a conflict in the processing time between the last manufacturing task and the second-to-last manufacturing task. If yes, skip to step three; if no, skip to step four. Third, if there is no conflict, remove the last task from the task set and return to the second step; if there is a conflict, move the processing time of the last manufacturing task forward to make it non-conflicting, while keeping the domestic land transportation time unchanged. The time difference is used to arrange for the manufacturing task to be stored in a warehouse near the processing plant, waiting for domestic transportation. Remove the last task from the task set and return to the second step. The fourth step is to move on to the next processing plant or the next chromosome and repeat the first step.

7. A multi-objective robust optimization method system for cross-regional, multi-entity manufacturing task allocation, characterized in that, For performing the multi-objective robust optimization method as described in claim 1, including: The acquisition module is used to acquire manufacturing resources and tasks from multiple entities across different regions. The construction module is used to build a manufacturing task allocation model for cross-regional multi-entity production networks based on the cross-regional multi-entity manufacturing resources and manufacturing tasks, under the premise of determining the sea transport time. The optimization module is used to construct a multi-objective robust squared model for manufacturing task allocation based on the manufacturing task allocation model, using the 2-norm sphere uncertainty set to represent uncertain sea transport time; The solution module is used to transform the multi-objective robust squared model into an equivalent second-order cone model, solve the equivalent second-order cone model, and obtain the robust optimization results of cross-regional multi-entity manufacturing task allocation.

8. A storage medium, characterized in that, It stores a computer program for a multi-objective robust optimization method for cross-regional multi-entity manufacturing task allocation, wherein the computer program causes a computer to execute the multi-objective robust optimization method for cross-regional multi-entity manufacturing task allocation as described in any one of claims 1 to 6.

9. An electronic device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including a multi-objective robust optimization method for cross-regional multi-agent manufacturing task allocation as described in any one of claims 1 to 6.

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