Heterogeneous AGV workshop production logistics synchronous scheduling method

Abstract

A heterogeneous AGV workshop production logistics synchronous scheduling method comprises the steps that workshop production data is acquired, and the workshop production data comprises workpiece batch and process information, parallel machine information of all stages, heterogeneous AGV information and the matching relation between the heterogeneous AGV information and workpieces; constructing a mixed integer linear programming model by taking minimization of the maximum completion time and minimization of the total energy consumption of the workshop as targets; carrying out cooperative control on processing and transferring links by adopting an SAPT rule; the SAPT rule is used for dynamically deciding to adopt a Gold moment transportation mode or a full-load transportation mode according to the real-time idle state of the AGV, the batch size of workpiece sub-batches and machining; and solving the mixed integer linear programming model by adopting an improved water wave optimization algorithm, and outputting an optimal production and logistics scheduling scheme. According to the scheduling method, synchronous scheduling of production and logistics can be realized, and the maximum completion time is effectively reduced; the total energy consumption of a workshop is reduced, and the production efficiency and the energy utilization efficiency are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent manufacturing and production scheduling, and particularly relates to a heterogeneous AGV workshop production logistics synchronous scheduling method. BACKGROUND

[0002] As a typical production system, hybrid flow shop is widely distributed in discrete manufacturing industries such as chemical industry, textile industry and semiconductor industry. Such a workshop usually covers multiple processes, and each process is equipped with one or more parallel machines. In order to improve production efficiency, enterprises often use batch flow production technology, that is, a batch of workpieces is divided into multiple sub-batches, and the sub-batches are processed on different machines to shorten the production cycle and improve the equipment utilization.

[0003] In recent years, domestic and foreign scholars have conducted in-depth research on the batch flow scheduling problem. For example, some researches adopt equal batching or consistent batching strategy, and use intelligent optimization algorithms such as genetic algorithm and ant colony algorithm to solve the maximum completion time and other targets. However, these researches have a major limitation: most of them assume that the transportation resources are unlimited or only use a single type of automated guided vehicle (AGV), ignoring the key link of material transportation connecting each production unit. In actual workshops, due to the differences in workpiece size, weight and other characteristics, it is often necessary to configure multiple heterogeneous AGVs such as forklifts, carriers and tugs to meet complex logistics needs. This "special post for special use" AGV procurement strategy leads to significant differences in AGV types and carrying capacity in the workshop.

[0004] In the prior art, although a few researches have begun to focus on AGV scheduling problems, there are still obvious shortcomings, such as too simple transportation modeling, disconnection between production and logistics, lack of sub-batch transfer mechanism, etc. Therefore, the prior art cannot effectively solve the production and logistics collaborative scheduling problem in the heterogeneous AGV environment, resulting in prolonged maximum completion time, increased total energy consumption and low overall operation efficiency. This has become one of the key bottlenecks restricting enterprises to achieve intelligent production and reduce costs. SUMMARY

[0005] In order to solve the technical problems of poor scheduling compatibility, long completion time and high total energy consumption caused by the heterogeneity of AGV types, the difference in carrying capacity and the disconnection between production and logistics. The present application provides a heterogeneous AGV workshop production logistics synchronous scheduling method, which can realize the synchronous scheduling of production and logistics, effectively reduce the maximum completion time, and reduce the total energy consumption of the workshop, significantly improve the production efficiency and energy utilization efficiency.

[0006] The technical scheme adopted by the present application is as follows:

[0007] A heterogeneous AGV workshop production logistics synchronous scheduling method, comprising the following steps:

[0008] Step 1: obtaining workshop production data, the workshop production data comprising workpiece batch and process information, parallel machine information of each stage, heterogeneous AGV information and its matching relationship with workpieces;

[0009] Step 2: constructing a mixed integer linear programming model with the objectives of minimizing the maximum completion time and minimizing the total energy consumption of the workshop, the mixed integer linear programming model integrating variable sub-batch splitting, heterogeneous AGV scheduling and transportation batch constraints;

[0010] Step 3: using SAPT rules to cooperatively control the processing and transportation links; the SAPT rules are used to dynamically decide to adopt the Gold time transportation mode or the full-load transportation mode according to the real-time idle state of the AGV, the workpiece sub-batch size and the machine processing;

[0011] Step 4: using an improved water wave optimization algorithm to solve the mixed integer linear programming model, and outputting an optimal production and logistics scheduling scheme.

[0012] In the step 1, the workshop production data comprising workpiece batch and process information, parallel machine information of each stage, heterogeneous AGV information and its matching relationship with workpieces specifically refers to:

[0013] (1) workpiece batch and process information, comprising:

[0014] The workpieces are mutually independent different product types that need to be processed in the workshop, and the set of workpiece types is denoted as J, and each workpiece j (j∈J) corresponds to a total processing batch R j . Each workpiece needs to go through a fixed process flow containing p processes, and the process set is denoted as S; for any workpiece j on any process s (s∈S), the unit processing time is defined as U sj . In order to adapt to the needs of batch flow production and logistics transportation, each workpiece j is allowed to be dynamically divided into multiple workpiece sub-batches for processing, and the maximum allowed number of sub-batches on each process s is L j ;

[0015] (2) parallel machine information of each stage, comprising:

[0016] M s identical parallel machines are configured on each process s, and the machine set is denoted as I. These parallel machines collectively undertake the processing task of the process, and workpiece sub-batches can be assigned to any available machine for processing;

[0017] (3) heterogeneous AGV information and its matching relationship with workpieces:

[0018] Heterogeneous AGVs refer to the multiple types of AGVs existing in the workshop, and the set of AGV types is denoted as G. Each type contains multiple AGVs, and the total number of AGVs is K.

[0019] The heterogeneity of AGVs is reflected in their physical properties and functional expertise, which is characterized by their matching relationship with workpieces and carrying capacity. The defined parameter G kj is the maximum single carrying capacity of AGV k (k ∈ K) for workpiece j, i.e., the upper limit of carrying capacity. If G kj = 0 or is a minimum value, it means that AGV k cannot transport workpiece j, thus forming a transport capacity matrix describing the matching relationship between AGVs and workpieces.

[0020] The transport capacity matrix is a core data model that precisely defines the adaptation relationship and carrying upper limit between heterogeneous AGVs and various types of workpieces in the workshop in a structured manner. Specifically, the matrix is a two-dimensional table:

[0021] The rows usually represent each AGV or each type of AGV, numbered as k.

[0022] The columns represent each type of workpiece, numbered as j.

[0023] The elements G kj in the matrix represent the maximum batch size (i.e., the upper limit of carrying capacity) that AGV k can transport for workpiece j in a single transport.

[0024] Its core connotation and role are:

[0025] Define feasibility: if G kj > 0, it means that AGV k can transport workpiece j; if G kj = 0 or is a maximum negative value (represented as infeasible in the model), it means that the AGV cannot transport the workpiece due to physical structure, clamping tools, etc. This clearly depicts the "heterogeneous" characteristics of AGVs.

[0026] Quantify capacity: the specific value of positive G kj quantifies the transport capacity of AGV k for workpiece j. This value is directly used as a key parameter in the transport batch constraint of the step 2 mixed integer linear programming model. When the batch size R jrs of a workpiece sub-batch is greater than G kj , the model will force the sub-batch to be split into several transport sub-batches not greater than G kj according to the value of the matrix element.

[0027] In step 2, a mixed integer linear programming model is constructed that integrates variable sub-batch splitting, heterogeneous AGV scheduling, and transport batch constraints, which is mathematically expressed as follows:

[0028] (1) Optimization objective:

[0029] The optimization objective of the mixed integer linear programming model is to minimize the maximum completion time C max and the total energy consumption E all of the workshop, which constitutes a bi-objective optimization problem, whose mathematical expression is:

[0030] Min{C max , E all};

[0031] where C max is defined as the maximum value of the completion times of all workpiece sub-lots on all workstations, i.e. Here C sijr , i, j, r represent the completion time set of all workstations, all machines, all workpieces, and all sub-lots.

[0032] E all is composed of the total transportation energy consumption E T , the total processing energy consumption E W , the total standby energy consumption E F , and the total switching energy consumption E S , i.e. E all = E T + E W + E F + E S ;

[0033] The above two objectives compete with each other and need to be effectively balanced through a coordinated scheduling strategy.

[0034] (2) Core constraint conditions:

[0035] The mixed integer linear programming model accurately describes the synchronous coupling relationship between production and logistics in the heterogeneous AGV environment through the following core constraint conditions:

[0036] 2.1. Variable sub-lot splitting constraint: For each workpiece j, the sum of the batch sizes of all sub-lots of the workpiece on any workstation s must be equal to the total batch size R j of the workpiece, i.e. This constraint ensures mass conservation and allows the sub-lot batch size R jrs to change dynamically according to transportation and production conditions, rather than being fixedly divided.

[0037] 2.2. AGV load-triggered transportation batching constraint: This constraint is the key to realizing the synchronization of production and logistics in the model. When the sub-lot batch size R jrs exceeds the load upper limit G kj of the AGV k serving it,If the size of the sub-batch is larger than the AGV's carrying capacity, then the sub-batch must be split into several transport sub-batches for multiple transportation, and satisfy where z represents the index of the transport sub-batch; represents the size of the transport sub-batch, specifically, it refers to the number of workpieces contained in the zth transport sub-batch split from the rth sub-batch of workpiece j in the transportation stage a.

[0038] At the same time, the size of each transport sub-batch must not exceed the carrying capacity of the AGV, that is,

[0039] This mechanism directly embeds the physical transportation capacity of the AGV into the decision of production batch size, breaking through the limitation of assuming unlimited transportation capacity in traditional scheduling.

[0040] 2.3. Production and logistics timing synchronization constraints: The model ensures the continuity of processing and transportation links through a series of timing constraints. The constraints stipulate that the sub-batch must be transported after the current process is completed, and must be processed in the next process after arriving and meeting the machine availability conditions.

[0041] In particular, the mixed integer linear programming model defines a transportation method based on the "Gold time", whose constraint condition is calculated by the processing completion time of the last process, and its parameter expression is B sijr +R jrs ·U sj , R jrs , the AGV transportation time and the processing start time of the next process are parameter expressions Dynamically determine the size of the transport sub-batch and its start processing time on the next process machine to ensure that the target machine is idle when the AGV delivers the transport sub-batch, so as to realize seamless connection of production rhythm and minimize machine waiting time.

[0042] 2.4. Resource exclusivity constraints: The model ensures that at the same time, a machine can only process one workpiece sub-batch, and an AGV can only transport one workpiece (sub-batch or transport sub-batch).

[0043] Step 3 involves a heterogeneous AGV workshop production and transportation collaborative control method based on SAPT rules.

[0044] In step 3, the SAPT rule, AGV production and transportation synchronization rule, is a real-time decision-making mechanism embedded in the scheduling process. Its core purpose is to break down the information barrier between production and logistics, dynamically decide the transportation method, realize the precise connection of processing and transportation in time, and thus guarantee the continuity of the production process, and cooperatively optimize the maximum completion time and total energy consumption.

[0045] The specific implementation of the SAPT rule includes the following steps:

[0046] A1. Rule triggering and initial judgment:

[0047] When any workpiece sub-lot is about to complete processing on a machine of a certain process, the SAPT rule is triggered. First, based on the batch size R jrs of the sub-lot, the processing efficiency and the start processing time of the machine, the completion time of the sub-lot is predicted; then, the system detects whether there is an idle AGV that can transport the workpiece type at the estimated completion time. For the first process sub-lot, it is assumed that there is an available AGV; for the subsequent process sub-lot, the real-time state of the AGV needs to be dynamically queried.

[0048] A2. Dynamic selection of AGV:

[0049] If there are multiple idle and available AGVs at the completion time of the sub-lot, a secondary optimization strategy is executed to avoid subsequent transportation task conflicts. The secondary optimization strategy can be based on the rules of the closest distance, the lightest current task load, etc. If there is no idle AGV at the completion time of the sub-lot, the AGV that first completes the current transportation task and is available is located and waited for, and the AGV is pre-assigned to the sub-lot.

[0050] A3. Dynamic decision of transportation mode:

[0051] After selecting the AGV, the relationship between the batch size R jrs of the sub-lot and the upper limit of the load G kj of the AGV is used to dynamically decide the transportation mode:

[0052] Direct transportation: if R jrs ≤ G kj , i.e., the sub-lot can be loaded once by the AGV, the AGV is arranged to perform the transportation task immediately after the completion of the sub-lot.

[0053] Batch transfer decision: if R jrs > G kj , the sub-lot needs to be split into multiple transfer sub-lots. At this time, the core transportation mode decision process is entered:

[0054] ①. Calculate the Gold time:

[0055] Next process machine predicted idle time: this is the basis for calculating the Gold time, i.e., the predicted completion time C (s+1)，i′，j′，r′ of the task currently being processed on the target machine i′.

[0056] AGV transportation time: i.e., the fixed transportation time V ak of the selected AGV k in the transportation phase a.

[0057] Gold time parameter expression: Based on the above two points, the ideal time at which the AGV should leave the last machine is calculated, and its expression is:

[0058] T Gold (s+1)，i′，j′，r′ ak

[0059] The goal of this formula is: if the AGV starts at T Gold , it will arrive at machine i' just when it is idle at C (s+1)，i′，j′，r′ , so as to achieve "zero waiting".

[0060] 2. Judgment and decision:

[0061] AGV idle time: refers to the time at which the selected AGV k ends its current transportation task and restores the available state, that is, the transportation end time C ak′j′r′ of its current task.

[0062] Decision: compare the idle time C ak′j′r′ of the selected AGV with the calculated Gold time T Gold .

[0063] Gold time transportation: if C ak′j′r′ ≤ T Gold , it means that the AGV can be ready in time. In this way, the system will split the sub-batch according to a certain strategy, and arrange the AGV to start on time at T Gold .

[0064] Full-load transportation: if C ak′j′r′ > T Gold , it means that the AGV cannot catch up with the ideal connection time. Then, the conservative strategy is adopted, and the sub-batch is split into several full-load transportation sub-batches with a size of G kj .

[0065] A4. Cooperative arrangement of subsequent production:

[0066] For the split transportation sub-batches, they are regarded as independent processing units after arriving at the next process. The SAPT rule cooperates with the machine scheduling strategy, and on the basis of "first-come-first-processing", the transportation sub-batches belonging to the same atomic batch are preferentially arranged on the same machine for continuous processing, so as to reduce the switching times and switching energy consumption of the machine, and maintain the smoothness of production. In step 3, the specific process of dynamically deciding the transportation mode in the SAPT rule includes:

[0067] B1: Calculate the Gold time of the workpiece sub-batch:

[0068] The Gold time T Gold ​​is an ideal time point, aiming at making the last finished workpiece sub-lot of the previous stage be transported to the next stage machine just when the next stage machine finishes processing the previous workpiece sub-lot. The specific calculation method is as follows:

[0069] The Gold time T Gold of the workpiece j's sub-lot r on the machine i of the process s is calculated based on the predicted idle time C s′i′j′r′ of the target machine i' of the next process s' and the transportation time V ak of the AGV k, and the formula is as follows:

[0070] T Gold = C s′i′j′r′ -V ak ;

[0071] Wherein, C s′i′j′r′ is the predicted finishing time of the sub-lot j' r' currently processed on the machine i'. This formula ensures that if the AGV starts from the machine i at the time T Gold , it will arrive at the machine i' just when it is idle, i.e. at the time C s′i′j′r′ .

[0072] B2: Determine whether there is currently an idle AGV that can be used to transport the workpiece sub-lot:

[0073] This determination is based on the comparison between the task end time C akj′r′ of the AGV and the predicted finishing time C sijr of the current sub-lot. Specifically, if there is an AGV k that meets the following two conditions, it is determined to be idle and available:

[0074] a. The AGV k can transport the workpiece type j, i.e. G kj > 0;

[0075] b. The current task end time C akj′r′ of the AGV k is less than or equal to the Gold time or the finishing time of the current sub-lot, i.e. C akj′r′ ≤ max(T Gold , C sijr ), the value of max(T Gold , C sijr ) defines an "earliest feasible departure time". It means that the AGV needs to start the transportation task at least after this time point. The reason is as follows:

[0076] If T Gold > C sijr , it means that in order to perfectly connect, the material needs to wait in the buffer zone for a while until the "Gold time" before being shipped. At this time, the earliest feasible departure time is T Gold .

[0077] If C sijr > T Gold , it means that the sub-batch is already late, missing the ideal Gold time. At this time, the material should be shipped as soon as it is finished, and the earliest feasible departure time is C sijr .

[0078] If there are multiple AGVs that meet the conditions, the optimal one is selected according to the pre-defined strategy (e.g. earliest free, closest distance).

[0079] B3: Execution of transportation method:

[0080] 1) If there is an available AGV, use the Gold time transportation method:

[0081] The Gold time transportation method specifically refers to arranging the selected AGV to start at the calculated Gold time T Gold on time to execute the transfer task, ensuring the continuity of the production process.

[0082] Splitting the sub-batch into transfer sub-batches specifically refers to:

[0083] To achieve Gold time transportation, the original batch R jrs needs to be dynamically split into several transfer sub-batches The splitting strategy aims to have the first transfer sub-batch finish processing and transportation at the time when the next machine is just idle. Specifically, the batch size of the first transfer sub-batch can be determined by the following principle: its processing time in the previous process s plus the transportation time should equal the time from the current time to the next machine idle period. An example is as follows:

[0084]

[0085] Where: U sj and U s′j are the unit processing times of workpiece j at processes s and s', respectively, denotes the floor function. The remaining batch size serves as the subsequent transfer sub-batch.

[0086] The specific embodiment of achieving the next stage machine just finishing processing is that the start processing time of the first transfer sub-batch z1 on the next stage machine i' is constrained as:

[0087]

[0088] Under ideal Gold time transportation, i.e. the seamless connection of machine processing is achieved.

[0089] ​2) If there is no available AGV, adopt full-load transportation mode:

[0090] Full-load transportation mode is specifically: when the AGV is in place, the precise connection of the Gold time is not considered, but the maximum load capacity G of the AGV is taken as the upper limit, and the sub-batch R is divided into as many full-load transfer sub-batches as possible for transportation. Specifically, the batch size of the transfer sub-batch is kj , and the batch size of the last transfer sub-batch is jrs . This mode focuses on improving the efficiency of single transportation, but may increase the waiting time of the next process machine.

[0091] In step 4, the improved water wave optimization algorithm adopts a two-layer coding method:

[0092] The first layer is discrete integer coding, which is used to represent the processing sequence of the workpieces and the sub-batch division structure; its core function is to determine the processing sequence of all workpiece sub-batches in the first stage process, and implicitly define the sub-batch division number of each workpiece. The specific coding method: discrete integer coding is a sequence with a length of L total , where is the sum of the maximum allowed sub-batch numbers of all workpieces. Each element in the sequence is an integer, representing a workpiece type number j. The number j appears the kth time in the sequence, representing the kth sub-batch of workpiece j.

[0093] Parameter expression description: let the coding sequence be where g l ∈J, J is the set of workpiece types. This sequence directly determines the processing sequence of the first stage: the element g l on position l represents that the lth processed unit is a sub-batch of workpiece g l . For a workpiece j, the total number of times it appears in the sequence count(j, Code1) is the actual sub-batch number L j ′ of the workpiece, L j ′≤L j .

[0094] Example: assuming there are workpiece types {1, 2, 3} and the maximum sub-batch number is 2, then L total = 6. A possible coding Code1 = [1, 3, 2, 1, 3, 2]. This coding represents:

[0095] Processing sequence: workpiece 1 sub-batch 1 → workpiece 3 sub-batch 1 → workpiece 2 sub-batch 1 → workpiece 1 sub-batch 2 → workpiece 3 sub-batch 2 → workpiece 2 sub-batch 2.

[0096] Workpieces 1, 2, and 3 are divided into 2 sub-batches.​​

[0097] The second layer is real number coding, which is used to represent the resource allocation proportion of each sub-batch to determine its batch size; its core function is to allocate a resource proportion coefficient for each potential sub-batch defined in the first layer coding, so as to dynamically and non-uniformly determine the specific batch size of each sub-batch.

[0098] Specific coding method: real number coding is a real number sequence with the same length as the first layer coding, that is, Where p l ∈[-1,1]。

[0099] Parameter expression explanation: the meaning of real number p l is associated with the workpiece sub-batch corresponding to the position g l in the first layer coding.

[0100] If p l <0, it means that the sub-batch defined at this position is an invalid sub-batch, which will be ignored in actual decoding and will not participate in scheduling. This realizes the dynamic adjustment of the number of sub-batches.

[0101] If p l ≥0, the value represents the non-normalized weight of the sub-batch in allocating the total batch size R j of its workpieces.

[0102] Sub-batch batch size calculation formula: for a valid workpiece j, let all its valid sub-batches, that is, the non-negative weight set of positions satisfying p l ≥0 and g l =j, be P j ={p l |g l =j∧p l ≥0}. Then for one of the valid sub-batches r, the corresponding weight p lr , the calculation formula of its batch size R jrs is:

[0103]

[0104] The batch size of the last sub-batch is obtained by subtracting the sum of the allocated batch sizes from R j , to ensure the conservation of material ∑ r R jrs =R j . Example: continue the above example, the total batch size of workpiece 1 R1=100, which has two positions (1st and 4th) in Code1. Assume that the corresponding Code2 values are p1=0.5 and p4=0.3.

[0105] The weight sum = 0.5 + 0.3 = 0.8.

[0106] The batch size of the first sub-batch of workpiece 1

[0107] Second sub-batch quantity R of workpiece 1 1，2，s = 100 - 62 = 38.

[0108] This coding naturally realizes variable sub-batch segmentation.

[0109] In step 4, the improved water wave optimization algorithm is a meta-heuristic algorithm based on swarm intelligence, which searches for optimization in the solution space by simulating the physical phenomena of water wave propagation, including propagation, refraction and breaking wave. For the complex production-logistics synchronous scheduling problem considering variable sub-batch and heterogeneous AGV in the application, the traditional algorithm is easy to fall into local optimum and slow in convergence speed. Therefore, the standard water wave optimization algorithm is improved in three aspects, so that it can efficiently process the mixed integer linear programming model:

[0110] C1. Adaptive segmented propagation operation:

[0111] This operation is the core of global exploration of the algorithm. Each solution (called "water wave") has an adaptive wavelength λ, which determines the search range of the solution in each iteration.

[0112] Improvements: The application designs a segmented adaptive wavelength adjustment mechanism:

[0113] In the early stage of iteration (exploration stage), all water waves use a larger initial wavelength to perform a wide range of global search to find potential good solution regions; as the iteration proceeds, the algorithm enters the transition stage, and the wavelength is exponentially attenuated according to the quality of the solution and the number of iterations. In the late stage of iteration (development stage), the wavelength is reduced, and the algorithm performs fine local search in the most promising solution region. The algorithm dynamically controls the wavelength λ through an attenuation function related to the number of iterations, so as to realize the adaptive adjustment of the search range.

[0114] Its specific implementation can be expressed by the following formula:

[0115] Wavelength update formula:

[0116]

[0117] Parameter explanation:

[0118] λ(t): wavelength value at the tth iteration.

[0119] λ initial : initial wavelength, set a larger value (such as λ max ) in the exploration stage to ensure extensive global search.

[0120] A: attenuation coefficient, a constant greater than 0, controls the severity of wavelength attenuation. The larger α, the faster the transition from exploration to exploitation.

[0121] t: current iteration number.

[0122] Although this formula itself is continuous, it clearly defines three functional phases:

[0123] Exploration phase (early iterations):

[0124] When t is small, (t / T max ) is close to 0, so is close to 1.

[0125] At this time λ(t)≈λ initial (i.e. λ max ), the wavelength keeps a large value, and the algorithm tends to conduct a large-scale random search to discover the potential good solution domain.

[0126] Transition phase (mid iterations):

[0127] As t increases, (t / T max ) gradually increases, leading to an exponential decrease in .

[0128] The wavelength λ(t) is exponentially attenuated, and the search range is smoothly and automatically reduced. The algorithm gradually transitions from extensive global exploration to local exploitation of the promising region discovered.

[0129] Exploitation phase (late iterations):

[0130] When t is close to T max , (t / T max ) is close to 1, reaches its minimum value.

[0131] At this time λ(t) is also attenuated to a minimum value (e.g. λ min ), and the algorithm conducts a very fine local search around the optimal solution to finally converge to a high-precision solution.

[0132] Technical effects: This mechanism realizes the dynamic balance of exploration and exploitation capabilities, effectively avoiding the premature fall into local optima, while ensuring rapid convergence to high-quality solutions in the later search.

[0133] C2. Elite-guided refraction operation:

[0134] When a certain water wave (solution) fails to improve after multiple iterations, its wave height h will drop to zero and trigger the refraction operation. This operation aims to significantly change the solution trapped in local optima and jump out of the current region.

[0135] Improvements: The present application proposes a cross-refractive strategy combined with elite individual information:

[0136] When the individual P2 triggers the refractive, instead of randomly generating a new solution, the optimal individual P1 in the current population is selected to perform the structural recombination of the cross operation in the genetic algorithm. Specifically, a continuous excellent gene fragment is extracted from P1 and replaced or spliced into P2, thereby generating new offspring individuals C1 and C2.

[0137] The operation is triggered when the wave height h of the individual P2 falls to zero. The core idea is to use the excellent "gene pattern" of the current elite individual in the population to restructure the individual trapped in stagnation and give it a new search direction.

[0138] The specific execution process is as follows, and we will illustrate it with an encoding example. Suppose the first layer encoding sequence is:

[0139] Elite individual P1 = [1, 3, 2, 4, 5, 1, 6]

[0140] Stagnant individual P2 = [3, 1, 5, 1, 2, 4, 6]

[0141] Step 1: Select the cross section

[0142] According to the current wavelength λ2 of the individual P2 (or a randomly determined starting point), a continuous gene fragment is selected from the elite individual P1. Suppose the selected fragment is [2, 4, 5] from the 3rd to 5th position in P1.

[0143] Step 2: Generate offspring C1 (insertion strategy)

[0144] The selected section [2, 4, 5] of P1 is directly inserted into the corresponding position (3rd to 5th) of P2, replacing the original [5, 1, 2] of P2.

[0145] At this time, the original offspring C1' = [3, 1, 2, 4, 5, 4, 6] is obtained.

[0146] Conflict processing and legality repair: Since direct insertion may cause changes in the number of workpieces (such as the increase in the number of workpieces 2, 4, 5 and the decrease in the number of workpiece 1), repair is needed. One strategy is to remove the appearance of workpieces in the replaced fragment in other positions in the sequence to ensure that the total number of sub-lots for each workpiece remains unchanged. After repair, a feasible solution C1 is obtained.

[0147] Step 3: Generate offspring C2 (splicing strategy)

[0148] Splice the selected section [2, 4, 5] of P1 to the end or beginning of P2.

[0149] C2' = [2, 4, 5, 3, 1, 5, 1, 2, 4, 6] is obtained.

[0150] Legality repair: due to splicing, the sequence is too long and the number of workpieces exceeds the limit, so pruning must be performed. One strategy is to delete enough of the earliest appearing elements that are duplicated in the selected section from the sequence until the sequence length returns to L total . The feasible solution C2 is obtained after repair.

[0151] Step 4: Evaluation and selection

[0152] Decode the two new child individuals C1 and C2 generated and evaluate their fitness (i.e. calculate their C max and E all ). Greedy selection: if the fitness of C1 or C2 is better than the original stagnation individual P2, replace P2 with the better child; otherwise, P2 remains unchanged.

[0153] Technical effect: this operation injects the good pattern of the global optimal solution into the stagnation individual, realizes a guided and directional escape from the local optimal strategy, and significantly improves the "escape" ability and search efficiency of the algorithm in a complex solution space.

[0154] C3. Multiple perturbation choppy wave operation:

[0155] This operation is a local intensive search performed on a high-quality solution (i.e. a solution better than the current historical optimal solution) to mine better potential solutions in its neighborhood.

[0156] Improvements: the present application designs a Gaussian perturbation strategy for encoding characteristics:

[0157] When performing a choppy wave operation on an elite individual, the algorithm performs multiple iterations (e.g. 2-3 times). In each iteration, a Gaussian perturbation N(0, σ 2 ) is applied to the second layer of real number coding (i.e. the batch resource allocation proportion p l ) of the individual, where the standard deviation σ is dynamically controlled by the current wavelength λ. The core of this strategy is to perform a controlled and subtle random perturbation on the second layer coding (batch allocation proportion) of the elite solution in order to find better solutions in its neighborhood. The "multiple perturbation" and "dynamic control" characteristics are achieved through the following specific steps and formulas:

[0158] 1. Specific process of perturbation execution:

[0159] For an elite individual X i , whose second layer coding is A single choppy wave operation is as follows: generate a perturbation: for each element p l, a Gaussian perturbation (i.e. normally distributed random noise) is applied. A new solution is generated: the element p of the second layer encoding Code2' of the new solution l is generated by the following formula:

[0160] p l ′= p l +N(0, σ 2 )

[0161] where N(0, σ 2 ) denotes a normally distributed random number with mean 0 and standard deviation σ.

[0162] 2. Dynamic control mechanism of the standard deviation σ

[0163] This is the essence of the improvement. The standard deviation σ is not fixed, but is dynamically determined by the current wavelength λ of the individual, and its calculation formula is:

[0164] σ = α·λa: perturbation intensity coefficient, a pre-set constant, usually taking values in the interval [0.1, 0.3]. It determines the size of the perturbation range relative to the wavelength.

[0165] λ: the current adaptive wavelength of the individual.

[0166] The technical effect of this mechanism is:

[0167] Early iteration / exploration phase: the wavelength λ is large, so σ is also large. This means that the perturbation amplitude of the elite solution is larger, which helps to explore in a wider neighborhood and avoid falling into local extrema too early.

[0168] Late iteration / development phase: the wavelength λ becomes very small after attenuation, so σ also becomes small. This means that the perturbation is limited to a very subtle range, so that the elite solution can be finely adjusted to approach the true local optimal solution.

[0169] 3. Cycle and selection of "multiple perturbations" The above process will be performed K times (e.g. K = 2 or 3). After each perturbation:

[0170] The new solution X i ′ is immediately decoded and evaluated.

[0171] Greedy selection strategy: if the new solution X i ′ is better than the current solution X i , then immediately replace X i with X i .

[0172] AdjustWavelength(λ) (usually slightly reduced) to adaptively shrink the search range in the subsequent perturbation.

[0173] The key innovation is that the perturbation only acts on the second layer encoding, while strictly maintaining the processing order and sub-lot structure defined by the first layer encoding.

[0174] Technical effect: This targeted perturbation fine-tunes the lot size allocation of each sub-lot while maintaining a good job sequence, thereby further optimizing the objective function value without compromising the structural goodness of the solution. It enables deep exploration of different lot size allocation strategies under the same sequencing scheme, improving the local search accuracy of the algorithm.

[0175] C4. Deep integration with scheduling model: heuristic decoding:

[0176] Instead of directly processing the objective function, the improved water wave optimization algorithm converts the encoding (i.e., water wave) into a complete scheduling scheme through a heuristic decoder and evaluates it.

[0177] Specific process: The algorithm uses the first layer encoding to determine the processing sequence of jobs at the first process. Then, combined with the sub-lot size calculated by the second layer encoding, it calls the SAPT rule proposed in step 3 of the invention to dynamically allocate machines and AGVs for each sub-lot and determine its transportation method (Gold time transportation or full-load transportation), and finally calculates the maximum completion time C max and total energy consumption E all of the scheduling scheme.

[0178] Technical effect: This decoding mechanism ensures that every solution produced by the algorithm during the search process is a feasible solution that meets all production and logistics constraints. It delegates complex constraint handling to the decoding rules, allowing the algorithm to focus on optimization search at a high level, greatly improving search efficiency and solution quality.

[0179] In step 4, the improved water wave optimization algorithm is used to solve the mixed integer linear programming model, with the following steps:

[0180] First, the algorithm initializes. Set the population size PS, the initial wavelength λ of each individual (value range [λ min , λ max ]) and the initial wave height h. Then, generate the initial population. To improve the quality of the initial solution, the invention uses a population initialization method based on multiple rules:

[0181] Random initialization: about 70% of the individuals in the population are generated completely randomly to ensure the diversity of the population.

[0182] Heuristic initialization: The remaining 30% of individuals were generated using two different heuristic rules:

[0183] a. Shortest processing time priority rule: This rule aims to minimize the maximum completion time by prioritizing sub-batches with shorter processing times.

[0184] b. Reduce transport frequency rule: This aims to minimize total energy consumption by reducing transport frequency by making sub-batch sizes close to integer multiples of AGV capacity.

[0185] Phase Two: Iterative Optimization and Dynamic Evaluation

[0186] This stage is the main loop of the algorithm, which continues until the termination condition is met (such as reaching the maximum number of iterations or the quality of the solution is stable).

[0187] 1. Propagation Operation (Global Exploration): For every individual X in the population i According to its current wavelength λ i The defined range is used to generate a new solution X by randomly changing its first-level encoding (processing order) and second-level encoding (batch ratio). i The wavelength of the new solution will be adaptively adjusted according to its fitness value: the better the solution quality, the shorter the wavelength, so as to allow for more refined subsequent searches in its vicinity.

[0188] 2. Decoding and Evaluation: Decoding the newly generated solution X i Heuristic decoding is then performed. The decoder first determines the processing sequence of the first operation based on the first layer of encoding, and then calculates the specific batch size of each sub-batch based on the second layer of encoding. Subsequently, the SAPT rule defined in step 3 is invoked to dynamically allocate machines, select AGVs, and decide on the transportation method for each sub-batch, ultimately simulating the entire production-logistics process and calculating the two objective function values ​​of the solution: maximum completion time C. max Total energy consumption E all .

[0189] 3. Selection and Update:

[0190] If the new solution X i Dominant solution X i (i.e., both target values ​​are better), then use X. i Replace X i and reset X i ′ wave height.

[0191] If the new solution X i If not accepted, then the original solution X i The wave height h i Subtract 1.

[0192] 4. Refraction operation (escaping local optima): Check the wave height h of each individual.i If h i decreases to 0, it means that the individual is trapped in a local optimum. At this point, the elite-guided reflection operation is triggered. The individual will be crossed with the historical best solution in the current population to generate one or two new offspring solutions by exchanging partial code segments to inject new search information and help the population jump out of the local optimum region.

[0193] 5. Chopping operation (local exploitation): Check if the new solution X i dominates any of the historical best solutions set (Pareto front) found in the current population. If yes, perform multiple perturbation chopping operations on the new solution. This operation will produce slightly mutated solutions within the neighborhood of the good solution by applying 2-3 times small range Gaussian perturbation (mainly for the second layer batch code) and evaluate them. Once a better solution is found, update the historical best solution set. This step is a deep exploitation of the good solution aiming to improve the convergence and distribution of the Pareto front.

[0194] Phase three: result output:

[0195] When the algorithm meets the termination condition, the iteration ends. Finally, the algorithm outputs the Pareto optimal solution set maintained in the iteration process. The solution set contains multiple non-dominated scheduling schemes, each of which corresponds to a complete production sequence, sub-batch segmentation, machine allocation, AGV scheduling and transportation mode decision. The decision maker can select a final scheme from the solution set according to the actual production demand.

[0196] In step 4, the "optimal production and logistics scheduling scheme" refers to one or more executable scheduling instruction sets selected from the Pareto optimal solution set after solving by the improved water wave optimization algorithm. The scheme clearly specifies when and where each workpiece sub-batch is processed and transported by what resources, and its specific content is completely defined by the following elements: 4.1. Sub-batch segmentation and batch scheme:

[0197] The scheme first clearly defines how each workpiece is divided into sub-batches and the specific batch size of each sub-batch. This is finally determined by decoding the two-layer encoding algorithm.

[0198] Specific content: for each workpiece j, the scheme outputs its final sub-batch set and the processing batch size R jrs of each sub-batch r in each process s.

[0199] Parameter expression: this result directly corresponds to the sub-batch batch size variable R jrs defined in the model and satisfies the constraints:

[0200]

[0201] where L' is the actual number of sub-lots of workpiece j (determined by the non-negative weights active in the encoding). j is the actual number of sub-lots of workpiece j (determined by the non-negative weights active in the encoding).

[0202] 4.2. Production scheduling scheme (machine assignment & processing timing)

[0203] This scheme defines the processing timing diagram of all sub-lots on all machines, i.e. "who processes which sub-lot on which machine at which time". In detail: for each sub-lot jrof each workpiece j, the scheme specifies:

[0204] the assigned machine i: i.e. the decision variable Y sijr = 1.

[0205] the start processing time B sijr ;

[0206] the end processing time C sijr ;

[0207] the parameter expressions: these time parameters satisfy the model's processing constraints, e.g. the due time constraint:

[0208] C sijr = B sijr + R jrs · U sj

[0209] and the machine exclusivity constraint, which ensures that for any two different sub-lots, their processing times on the same machine do not overlap.

[0210] 4.3. Logistics scheduling scheme (AGV assignment, transportation mode & transportation timing)

[0211] This scheme defines the transportation plan of all sub-lots between processes, i.e. "who is transported by which AGV in which way at which time". In detail: for each sub-lot jrof each workpiece jthat needs to be transported from process s to process s+1 (or its transport sub-lot), the scheme specifies:

[0212] the assigned AGV k: i.e. the decision variable Z akj = 1.

[0213] the transportation mode: it is explicitly "direct transportation", "Gold moment transportation" or "full load transportation".

[0214] the transport sub-lot batch size (if split): it satisfies

[0215] the transportation start and end times C akjr .

[0216] Parameter expression: this part of the result is a direct embodiment of the application of SAPT rules. For example, if the Gold moment transportation is adopted, the first transfer batch is at the start time of the next process It is ensured that it is perfectly connected with the machine idle time by the following formula:

[0217]

[0218] This achieves the synchronization goal of "zero waiting".

[0219] 4.4. Global performance indicators:

[0220] The scheme finally outputs two key optimization target values to quantify its performance:

[0221] Maximum completion time: C max = max s，i，j，r {C sijr};

[0222] Total energy consumption of workshop: E all = E T +E W +E F +E S .

[0223] A mixed flow shop production logistics synchronization scheduling system, the system comprises:

[0224] A data acquisition module for acquiring workshop production data;

[0225] A model construction module for constructing a mixed integer linear programming model;

[0226] A rule base module for storing and executing SAPT rules;

[0227] An optimization solving module for running an improved water wave optimization algorithm and outputting a production and logistics scheduling scheme;

[0228] A scheduling execution module for issuing the scheduling scheme to the workshop production equipment and AGV control system.

[0229] The technical effects of the heterogeneous AGV workshop production logistics synchronization scheduling method are as follows:

[0230] 1) The mixed integer linear programming model constructed in step 2 of the present application is the theoretical basis and innovation core of the present application. Its advantages mainly lie in the following four aspects:

[0231] 2.1. Integrity and systematicness: for the first time, the unified modeling of the three core elements is realized:

[0232] Limitations of traditional research: Existing research mostly treats production scheduling or logistics transportation in isolation, either ignoring the transportation link or assuming homogeneous and unlimited transportation resources.

[0233] Advantages of the model: The model integrates the three interrelated core elements of "variable sub-batch splitting", "heterogeneous AGV scheduling", and "transportation batching" into a unified mathematical framework for the first time. It is no longer a single production scheduling model or a simple transportation addition model, but a real "production-logistics" synchronous optimization system. This systematic modeling can capture the complex coupling relationship between the links in reality, laying a solid foundation for generating a globally optimal collaborative scheduling scheme.

[0234] 2.2. Precision and dynamics: Precise quantification of logistics constraints on production through mathematical constraints:

[0235] Limitations of traditional research: Even if transportation is considered, fixed transportation time or simple assumptions are often used, which cannot reflect the direct impact of AGV carrying capacity on production batch size.

[0236] Advantages of the model: The model precisely quantifies the feedback mechanism of the physical limitations of heterogeneous AGVs on production scheduling decisions through a series of rigorous mathematical constraints. This mechanism means that the division of sub-batches is no longer simply to balance machine load, but must dynamically adapt to the carrying capacity of AGVs. When the sub-batch is too large, the model will force it to be split into smaller transportation sub-batches, which directly affects the processing start time of the subsequent process. This dynamic adaptability greatly enhances the model's ability to describe the complexity of real workshops.

[0237] 2.3. Collaboration and foresight: Embed synchronous optimization logic through "Gold time" mechanism:

[0238] Limitations of traditional research: The collaboration between production and logistics usually stays in post-adjustment or simple rules, lacking a forward-looking synchronous mechanism.

[0239] Advantages of the model: The most creative advantage of the model is the introduction of the "Gold time" transportation timing synchronization constraint.

[0240] 2.4. Industrial applicability and scalability: Provide accurate evaluation benchmarks for advanced optimization algorithms:

[0241] Limitations of traditional research: Simplified models cannot effectively guide actual production, and the generated schemes may be difficult to implement in reality.

[0242] Advantages of the model: Since the model highly fits the actual production scene, it provides a comprehensive and accurate mathematical evaluation of the overall performance of a scheduling scheme. This precise model serves as a "scale" for the improved intelligent optimization algorithm in step 4 to search and evaluate in this highly realistic environment, ensuring that the final output scheduling scheme is not only mathematically optimal, but also executable, efficient, and low-consumption in the workshop. In addition, the framework of the model has good scalability, which can easily introduce more practical factors such as AGV path planning, dynamic failure, etc., laying a foundation for further research. 2) The AGV production and transportation synchronization rule proposed in step 3 of the invention is the control logic and execution intelligence of the invention. The specific advantages are as follows:

[0243] 3.1. Achieved a breakthrough from "static planning" to "dynamic real-time control":

[0244] Limitations of traditional research and models: The mixed integer linear programming model in step 2 is a "static" optimization model that assumes all information is known and unchanging. However, in actual workshops, there are various random disturbances (such as minor processing delays, temporary AGV stalls), and a pre-prepared, fine-to-second static plan is likely to fail in execution.

[0245] Advantages of SAPT rule: SAPT rule, as a real-time decision maker embedded in the scheduling generation process, does not rely on a fixed and unchanging perfect plan. Instead, it dynamically makes transportation decisions based on the real-time state of AGV (idle, busy, task end time) at this critical decision point before each sub-batch is processed. This "event-triggered" control mechanism gives the scheduling system strong anti-interference ability and robustness, allowing the plan to adapt to the dynamic changes in the workshop and ensuring the executability of the optimized scheme in practice.

[0246] 3.2. Provides an online balancing mechanism for "production efficiency" and "logistics energy consumption":

[0247] Limitations of traditional research: Most researches balance these two goals at the model level, but lack specific means to fine-tune at the execution level.

[0248] Advantages of SAPT rule: The core decision of SAPT rule - choosing "Gold time transportation" or "full load transportation" - essentially weighs "time" and "energy consumption" online at each transportation task.

[0249] Choosing Gold time transportation is to compress machine idle time and prioritize production cycle. It realizes the "seamless connection" of production rhythm through precise timing control.

[0250] The selection of full-load transportation is to prioritize the efficiency of single transportation and avoid AGV waiting to reduce the energy consumption per unit of transportation (corresponding to the optimization of ETET) when perfect connection cannot be achieved.

[0251] This dynamic decision-making mechanism enables the system to flexibly adjust the optimization focus under the guidance of global goals based on real-time local conditions, achieving the unity of macro goals and micro execution.

[0252] 3.3. Full play and use of the flexibility advantage of "variable sub-batch":

[0253] Limitations of traditional research: Even if the model allows variable sub-batch, its advantages cannot be realized without appropriate execution rules. Advantages of SAPT rules: SAPT rules are the key to the successful implementation of variable sub-batch strategy. It is not only a decision maker for transportation mode, but also the final executor of sub-batch segmentation. When the rule decision adopts "Gold time transportation", it will segment the sub-batch into unequal transfer sub-batches according to the specific strategy to adapt to the time window. This proves that variable sub-batch is not segmented for segmentation, but an active and intelligent adaptive behavior to meet higher synchronization goals.

[0254] 3) The improved water wave optimization algorithm used in step 4 of the present invention is the efficient solving engine and performance guarantee of the present invention. Its advantage lies in that it is not a ready-made general algorithm, but a deeply customized and multiple improved special solver, which is embodied in the following four aspects:

[0255] 4.1. Dual improvement of solving efficiency and quality: overcoming the difficulties of traditional algorithms:

[0256] Limitations of traditional algorithms: In the face of the complex solution space of high dimension, dispersion and multiple objectives in the present invention, traditional algorithms such as genetic algorithm (NSGA-II) or particle swarm algorithm (MOPSO) are prone to premature convergence and fall into local optimum, making it difficult to find high-quality solution set.

[0257] Advantages of the algorithm: Through the synergistic effect of the three improved operators of adaptive propagation, elite guided refraction and multiple disturbance ripples, the algorithm realizes the search closed loop of "exploration - jump out - potential tapping".

[0258] Adaptive propagation automatically balances between global exploration and local development through dynamic wavelength.

[0259] Elite guided refraction uses the information of optimal solution to help stagnant individuals jump out of local optimum.

[0260] Multiple disturbance ripples perform fine neighborhood search on elite solutions.

[0261] As shown in the experimental results of Table 3, the algorithm is comprehensive in the GD, IGD and HV indicators, proving its significant advantages in convergence speed, solution set diversity and approximation of the true Pareto front.

[0262] 4.2. Deeply fit with problem characteristics: innovative encoding and decoding design:

[0263] Limitations of general algorithms: General algorithms usually use a single encoding, making it difficult to represent mixed decision variables such as sequencing, batching, and batch allocation simultaneously.

[0264] Advantages of the algorithm: The two-layer joint encoding scheme designed in the present application is the key to solving the problem.

[0265] The first layer of discrete encoding directly and efficiently represents the processing order of the workpieces and the sub-batch structure.

[0266] The second layer of real number encoding flexibly realizes the dynamic allocation of variable sub-batch quantities and the dynamic adjustment of sub-batch quantities through non-normalized proportion and negative value invalidation mechanisms.

[0267] This encoding method perfectly matches the mixed variable characteristics of the problem, ensuring that the algorithm search process is always within a meaningful solution space. More importantly, the heuristic decoder seamlessly connects the encoding with the SAPT rules, ensuring that each evaluated solution is a feasible solution that meets all complex constraints, avoiding the huge computational overhead of handling constraints in traditional optimization.

[0268] 4.3. Organic unification of optimization objectives and scheduling logic: embedded SAPT rules:

[0269] Limitations of traditional solutions: Production scheduling and logistics transportation are usually optimized separately or simply concatenated, failing to achieve true synchronization.

[0270] Advantages of the algorithm: Instead of directly optimizing an abstract mathematical model, the algorithm embeds the SAPT rules of Step 3 during the decoding process. This means that when evaluating the merits of a "gene encoding", the algorithm is essentially evaluating the performance of a complete set of coordinated scheduling solutions generated by the encoding and intelligently adjusted through the SAPT rules. This ensures that the algorithm's search direction always follows the trajectory of "synchronous optimization of production and logistics", fundamentally guaranteeing that the final output is a truly coordinated solution, rather than a simple combination of production and transportation plans.

[0271] 4.4. Strong engineering practicality and interpretability:

[0272] Limitation of theoretical model: the mixed integer programming model of step 2 is accurate, but cannot be directly used to solve large-scale practical problems. Advantage of the algorithm: the improved water wave optimization algorithm as a meta-heuristic algorithm has the ability to handle large-scale practical cases. At the same time, the improved operator of the algorithm has a clear physical background (water wave motion), and the encoding and decoding process corresponds to the actual workshop decision logic (first arrange what, then determine how big each batch is, and finally allocate vehicles), so that the whole optimization process has good interpretability and is easy for engineering and technical personnel to understand and accept.

[0273] 4) The method overcomes the limitations of the existing scheduling research, such as the disconnection between production and logistics, insufficient consideration of heterogeneous AGV constraints, poor flexibility of traditional equal batching strategy, and the inability of single AGV scheduling model to reflect actual transportation bottlenecks, realizes deep coupling of production rhythm and logistics rhythm, significantly improves the overall production efficiency of the workshop and reduces the total energy consumption. Experimental verification shows that the method can effectively reduce the maximum completion time by 3.14% to 13.08%, and reduce the total energy consumption of the workshop by 0.17% to 1.27%. BRIEF DESCRIPTION OF DRAWINGS

[0274] The application will be further described below in combination with the drawings and examples:

[0275] Figure 1 is the architecture schematic diagram of the mixed flow shop production and logistics synchronous scheduling system provided by the embodiment of the application.

[0276] Figure 2 is the schematic diagram of the transportation situation when the number of carriers is limited.

[0277] wherein: (a) is the equal batching carrier limit, (b) is the unequal batching carrier limit, and (c) is the unequal batching of transportation decision;

[0278] Figure 3 is the Gantt chart of the traditional non-batching processing strategy provided by the embodiment of the application.

[0279] Figure 4 is the Gantt chart of the equal batching processing strategy provided by the embodiment of the application.

[0280] Figure 5 is the comparison diagram of different transportation situations when the number of carriers is limited provided by the embodiment of the application.

[0281] wherein: (a) is the traditional transportation ignoring capacity constraints, (b) is the waiting transportation, (c) is the full-load transportation, and (d) is the Gold moment transportation proposed by the application;

[0282] Figure 6 is the judgment flowchart of the AGV production and transportation synchronous rule provided by the embodiment of the application.

[0283] Figure 7 is an encoding schematic diagram of the improved water wave optimization algorithm provided by the embodiment of the application.

[0284] Figure 8 is an operation schematic diagram of the refraction operation in the improved water wave optimization algorithm provided by the embodiment of the application.

[0285] Figure 9 is an overall algorithm framework diagram of the improved water wave optimization algorithm provided by the embodiment of the application.

[0286] Figure 10 is a production and transportation collaborative scheduling Gantt chart obtained by solving a certain example by using the SAPT rule provided by the embodiment of the application.

[0287] Figure 11 is a production and transportation scheduling Gantt chart obtained by solving the same example by using the NAFT rule provided by the embodiment of the application.

[0288] Figure 12 is a box plot of performance comparison of different algorithms provided by the embodiment of the application.

[0289] Figure 13 is a comparison diagram of Pareto frontiers obtained by three algorithms for an actual case provided by the embodiment of the application.

[0290] Figure 14 is a production and transportation scheduling Gantt chart of an optimal scheduling scheme of an actual case provided by the embodiment of the application. DETAILED DESCRIPTION

[0291] The application will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0292] Embodiment 1: mixed flow shop production logistics synchronous scheduling based on the improved water wave optimization algorithm

[0293] This embodiment takes the ball neck arm production line of a certain mechanical processing enterprise as an application scenario, and implements the scheduling method described in the application. The workshop includes 3 processes: rough / precision milling of the plane (stage 1), turning the ball head (stage 2), and drilling the pin hole (stage 3). Stage 1 is configured with 3 parallel machines, stage 2 is configured with 2 parallel machines, and stage 3 is configured with 2 parallel machines. The workshop is equipped with 6 AGVs of 4 types (a certain number of latent AGVs, traction AGVs, backpack AGVs, and forklift AGVs), and the matching relationship and load capacity of the workpiece types are shown in Table 1. The current order contains 6 types of workpieces, and the batch information is shown in Table 2. The unit time transportation energy consumption is 1.2, the unit time processing energy consumption is 5.5, the unit time switching energy consumption is 2.5, and the unit time standby energy consumption is 1.5.

[0294] Table 1 AGV and workpiece relationship information

[0295]

[0296] Table 2 Processing information

[0297]

[0298] S1. Data acquisition and parameter setting:

[0299] Acquire workshop basic data, including:

[0300] Workpiece information: 6 types of workpieces, batch size, unit processing time of each process, as shown in Table 2;

[0301] Equipment information: number of parallel machines at each stage;

[0302] AGV information: type, number, matching relationship with workpieces, maximum carrying capacity, as shown in Table 1;

[0303] Energy consumption parameters: energy consumption per unit time of transportation 1.2, energy consumption per unit time of processing 5.5, energy consumption per unit time of switching 2.5, standby energy consumption per unit time 1.5.

[0304] Set the parameters of the improved water wave optimization algorithm: population size PS = 100, minimum wavelength λ_min = 2, maximum wavelength λ_max = 4, maximum wave height h_max = 8, and iteration number 500.

[0305] S2. Model construction and algorithm initialization:

[0306] Construct a mixed integer linear programming model with the objectives of minimizing the maximum completion time and minimizing the total energy consumption of the workshop. Use a population initialization method based on multiple rules to generate the initial population, where 70% of the individuals are generated completely randomly, and 30% of the individuals are generated using rules aimed at reducing completion time and rules aimed at reducing transportation frequency, respectively.

[0307] S3. Algorithm solution and SAPT rule application:

[0308] Run the improved water wave optimization algorithm, which uses two-layer coding, and fuse AGV production and transportation synchronization rules during decoding:

[0309] For each completed processing sub-batch, determine the current available AGV state;

[0310] If the sub-batch size is not greater than the available AGV capacity, directly assign transportation;

[0311] If the sub-batch size is larger than the AGV capacity, the Gold time is calculated: according to the machine processing speed, transportation time and sub-batch size, the optimal segmentation point and transportation start time are calculated to make the next process machine just end the previous task and seamlessly connect the current transfer sub-batch;

[0312] According to the comparison of AGV idle time and Gold time, dynamic decision is made to use Gold time transportation or full load transportation; the processing start and end time of each sub-batch, AGV allocation, transportation start and end time are recorded, and the objective function value is calculated. The essence is performance evaluation simulation after the generation of scheduling scheme. It quantifies the pros and cons of the scheme by simulating the dynamic operation of the workshop, and its specific connotation is as follows:

[0313] 1. Dynamic scheduling simulation and event recording

[0314] This is not a simple static record, but a time-based simulation. The system will maintain a global clock and state queues of two types of resources (machines and AGVs).

[0315] For processing events: when a sub-batch is assigned to machine i, the system will determine its start time B sijr according to the earliest available time of the machine and the ready time of the sub-batch (i.e. the time it arrives at the machine buffer), and calculate its end time C sijr . This end time updates the state of the machine and may trigger new scheduling decisions (such as the machine starting to look for the next processing task).

[0316] For transportation events: when AGV k is assigned a task, the system will check its release time (the time it completes the previous task) and the transportable time of the sub-batch (the processing completion time), take the later of the two as the transportation start time, and calculate the transportation end time C akjr .

[0317] 2. Integrated calculation of objective function

[0318] The calculation of the target value depends deeply on the full time data recorded in the above simulation:

[0319] Maximum completion time C max : At the end of the simulation, the system scans the end time of the last sub-batch on the last machine of all processes, and the maximum value is C max . This reflects the total throughput time of the entire production order.

[0320] Total energy consumption E all of the workshop: the essence of its calculation is to segmentally integrate the energy consumption of all device states (processing, transportation, idle, switching) in the simulation process.

[0321] EW (Process energy consumption) = Σ [total processing time of each machine × processing power]

[0322] E T (Transportation energy consumption) = Σ [total transportation time of each AGV × transportation power]

[0323] E5 (standby energy consumption) = Σ [total simulation time - total busy time of each device (machine + AGV) × standby power]

[0324] E S (Switching energy consumption) = Σ [number of switching times of each machine × single switching energy consumption]

[0325] During the running of the algorithm, the adaptive propagation, cross refraction, multiple disturbance and other improved operations are sequentially performed, and the population is continuously evolved.

[0326] Figure 2 The schematic diagram of the transport situation when the number of carriers is limited is provided by the embodiment of the application. Figure 2 It can be seen that the traditional equal batch strategy exposes obvious defects when the number of AGVs is limited: when multiple sub-batches are completed at the same time, due to insufficient transportation resources, the phenomenon of queuing and waiting for transportation of workpieces will inevitably occur, which leads to a large amount of idle time of the machine in the subsequent process, forming a passive situation of “production waiting for logistics”. This blocking phenomenon directly reveals how the logistics link becomes the key bottleneck restricting the overall efficiency.

[0327] In contrast, the variable batch strategy proposed in the application avoids the concentrated competition of transportation resources by dynamically adjusting the sub-batch size, so that the workpiece completion time is naturally staggered. More importantly, the Gold moment transportation mechanism shown in the figure realizes the precise matching of material delivery and machine idle period, and changes the traditional “processing-waiting-transportation” mode into a seamless connection process of “processing-transportation-processing”. This comparison fully proves the necessity of taking the logistics constraint into the core of production scheduling decision-making, and the significant advantage of the SAPT rule of the application in realizing the maximum utilization of resources through dynamic coordination.

[0328] Figure 3 The Gantt chart of the traditional non-batch processing strategy provided by the embodiment of the application is shown in Figure 1. Figure 3It can be seen that the traditional non-batch processing strategy processes the entire workpiece as a single batch, causing the machine of the previous process to be occupied for a long time, while the machine of the subsequent process is idle for a long time. This "tight in front and loose in back" production rhythm causes serious resource idling and process imbalance. Specifically, when a large batch of workpieces are processed on the front machine, the subsequent multiple machines are still idle, and due to the blocked material transfer, they cannot start work in advance. This interruption of the production rhythm directly leads to the extension of the production cycle and the reduction of the machine utilization, fully exposing the inherent disadvantages of the traditional method in coordinating the continuity of production logistics, and thus highlighting the necessity and superiority of the present application in realizing production-logistics synchronous scheduling through dynamic batching.

[0329] Figure 4 is the Gantt chart of the equal batch processing strategy provided by the embodiment of the present application. From Figure 3 It can be seen from the equal batch Gantt chart that although the workpiece is divided into multiple sub-batches, which shortens the production cycle to some extent, the machines of the subsequent processes still have obvious idle time. This exposes the limitations of the equal batch strategy: although partial overlap between processes is achieved through batching, the fixed batch division method cannot fully adapt to the dynamic rhythm of the production line, resulting in a waiting gap between material flow and machine processing, which restricts the further improvement of the overall efficiency.

[0330] Figure 5 is a comparison chart of different transportation situations considering the limited number of carriers provided by the embodiment of the present application. Among them, (a) is the traditional transportation ignoring the capacity constraint, (b) is the waiting transportation, (c) is the full-load transportation, and (d) is the Gold time transportation proposed by the present application; Figure 5 The key differences between different transportation strategies under the constraint of carrier capacity are revealed: the traditional transportation ignoring the capacity constraint (a) cannot be implemented due to its deviation from reality; the waiting transportation strategy (b) guarantees the feasibility of transportation, but at the cost of the efficiency of the machines of the subsequent processes, forming "car waiting for material" idling; the full-load transportation strategy (c) pursues the efficiency of single transportation, but the fixed transportation rhythm is difficult to match the dynamic production rhythm.

[0331] In contrast, the Gold time transportation (d) proposed by the present application shows a fundamental advantage: by intelligently dividing the sub-batches and accurately calculating the shipping time, the material arrival time is perfectly matched with the idle window of the downstream machine, realizing the ideal state of "material to machine idle". This strategy not only eliminates the non-value-added waiting time, but also deeply couples production and logistics, making the entire system work like a precision mesh, thus fundamentally improving the overall efficiency

[0332] Figure 10 is the production and transportation collaborative scheduling Gantt chart obtained by solving a certain example by using the SAPT rule provided by the embodiment of the present application. FromFigure 10 As can be seen from the Gantt chart, after adopting the SAPT rule, the production and logistics links exhibit a highly coordinated operating state: after the materials are processed in the upstream process, the AGV can always pick up and transfer them at just the right time, so that the workpiece arrives at the downstream process just in time to meet the machine's idle window.

[0333] This continuous flow model of "processing-transfer-processing" completely eliminates the material waiting or machine idleness common in traditional scheduling. More importantly, different transfer batches of the same workpiece are all arranged for continuous processing on the same machine, a design that significantly reduces equipment changeover frequency. The entire scheduling scheme is like a meticulously choreographed symphony, with each production resource operating at a distinct yet closely coordinated rhythm, vividly illustrating the efficiency innovation brought about by the deep integration of production rhythm and logistics rhythm.

[0334] Figure 11 This is a production and transportation scheduling Gantt chart obtained by solving the same computational example using NAFT rules, as provided in this embodiment of the invention. Figure 11 As can be seen in the Gantt chart, the adoption of the NAFT rule resulted in significant discontinuities in the production process: materials often need to wait for AGVs to complete their preceding transport tasks before they can be transferred, while the workpieces are still en route even when the downstream machines are ready. This discontinuous pattern of "processing-waiting-transporting-waiting-processing" creates numerous non-value-adding waiting gaps between production stages, significantly reducing machine utilization and making the entire production process loose and inefficient. This fully exposes the rigidity and shortcomings of traditional fixed rules in dealing with complex logistics constraints.

[0335] Figure 12 This is a box plot comparing the performance of different algorithms provided in embodiments of the present invention. Figure 12 As can be seen from the box plot, the improved water wave optimization algorithm proposed in this invention significantly outperforms the comparative algorithms in both solution stability and accuracy. Its shortest box length and lowest position indicate that the algorithm can converge closely to the optimal solution in multiple runs, with a fluctuation range much smaller than NSGA-II and MOPSO. This compact distribution characteristic verifies the effective combination of the adaptive wavelength mechanism and the elite-guided strategy, enabling the algorithm to maintain stable search while accurately locating the high-quality solution domain, fully demonstrating the reliability and superiority of the algorithm in solving this complex scheduling problem.

[0336] S4. Results Output and Analysis:

[0337] After the algorithm finishes running, it outputs the Pareto front solution set. Figure 13 This example demonstrates a comparison of the Pareto fronts obtained by the IMWWO algorithm with those obtained by the NSGA-II and MOPSO algorithms. It is evident that the solution set obtained by IMWWO is superior to the compared algorithms in both convergence and distribution.Figure 13 The production transportation coordination Gantt chart of the point A scheme is drawn as shown in FIG. 3. Figure 14 The scheme finally realizes the maximum completion time C_max=1950 minutes and the total energy consumption E_all=66623 units of the workshop. Compared with the scheme using the traditional non-advance full-load transportation strategy (C_max=2213, E_all=66500), the maximum completion time is reduced by 11.88%, and the total energy consumption is reduced by 0.17%, effectively verifying the superiority of the method in shortening the production cycle and reducing the energy consumption.

[0338] Example 2: Parameter sensitivity analysis

[0339] In order to verify the robustness of the parameter setting of the algorithm, the key parameters of the IMWWO algorithm are analyzed for sensitivity in this embodiment, as shown in Table 3. Three parameters, population size (PS), maximum wavelength (λ_max), and maximum wave height (h_max), are selected, each with three different levels (PS: 50, 100, 200; λ_max: 3, 4, 5; h_max: 5, 8, 10). Under the condition that other parameters are fixed, 30 independent simulation experiments are conducted on the problem of Example 1, and the average value of the Hypervolume index of the obtained non-dominated solution set is recorded.

[0340] Table 3 Parameter sensitivity analysis results

[0341]

[0342] The results show that when the parameters are set as PS=100, λ_max=4, and h_max=8, the algorithm performs best (with the highest HV value). When the parameters change within a certain range, the algorithm performance remains relatively stable, proving that the algorithm has good robustness.

Claims

1. A heterogeneous AGV shop floor production logistics synchronization scheduling method, characterized in that The method comprises the following steps: Step 1: obtaining workshop production data, wherein the workshop production data comprises workpiece batch and process information, parallel machine information at each stage, heterogeneous AGV information and matching relationship thereof with workpieces; Step 2: constructing a mixed integer linear programming model for minimizing maximum completion time and minimizing total energy consumption of the workshop, wherein the mixed integer linear programming model integrates variable sub-batch segmentation, heterogeneous AGV scheduling and transportation batch constraint; Step 3: adopting SAPT rules to cooperatively control processing and transportation links; the SAPT rules are used for dynamically deciding to adopt Gold time transportation mode or full-load transportation mode according to real-time idle state of AGVs, workpiece sub-batch size and machine processing; Step 4: adopting an improved water wave optimization algorithm to solve the mixed integer linear programming model, and outputting an optimal production and logistics scheduling scheme.

2. The heterogeneous AGV shop floor production logistics synchronized scheduling method according to claim 1, characterized in that: In the step 1, (1) the workpiece batch and process information comprises: The workpieces are mutually independent different product types that need to be processed in the workshop, and the set of workpiece types is denoted as J. Each workpiece j (j∈J) corresponds to a total processing batch R j ; Each workpiece needs to go through a fixed process flow including p process routes, and the set of process routes is denoted as S. For any workpiece j and any process route s (s∈S), the unit processing time is defined as U sj ; In order to adapt to the needs of batch flow production and logistics transportation, each workpiece j is allowed to be dynamically divided into multiple workpiece sub-batches for processing, and the maximum allowed number of sub-batches at each process route is L j ; (2) the parallel machine information at each stage comprises: M machines are configured on each process s s Parallel machines with the same function, the set of machines is denoted as I; these parallel machines are responsible for the processing task of the process together, and the workpiece sub-lot can be assigned to any available machine for processing; (3) the heterogeneous AGV information and the matching relationship thereof with workpieces: The heterogeneous AGV refers to multiple types of automatic guided vehicles existing in the workshop, AGV type set is denoted as G, and multiple AGVs are included in each type, and the total number of AGVs is K.

3. The heterogeneous AGV shop floor production logistics synchronized scheduling method according to claim 2, characterized in that: The heterogeneity of AGVs is characterized by its matching relationship with workpieces and carrying capacity: define parameter G kj Gk j is the maximum single carrying capacity of AGV k (k∈K) for workpiece j, i.e. the upper limit of carrying capacity; if G kj =0 or is a minimum value, it means that AGV k cannot transport workpiece j, thus forming a transport capacity matrix describing the matching relationship between AGVs and workpieces.

4. The heterogeneous AGV shop floor production logistics synchronized scheduling method according to claim 3, characterized in that: The transportation capacity matrix defines the adaptation relationship and upper limit of carrying capacity between the heterogeneous AGVs in the workshop and various types of workpieces, and the matrix is a two-dimensional table: The row represents each AGV or each type of AGV, and is numbered as k; The column represents each type of workpiece, and is numbered as i; The element G in the matrix kj denotes the maximum batch quantity that the AGV k can carry when transporting the workpiece j for a single time, i.e. the upper limit of the load quantity. Definition of feasibility: if G kj >0, it means AGV k can transport workpiece j; if G kj =0 or a maximum negative value, it means that the AGV cannot transport the workpiece due to physical structure, clamping tool reasons; this depicts the heterogeneous characteristics of AGV; Quantification of capacity: the specific value of positive G kj quantifies the transportation capacity of AGV k for workpiece j, which is directly used as a key parameter in the transportation batch constraint of step 2 mixed integer linear programming model; when the batch size R jrs > G kj , the model will split the sub-batch into several transportation sub-batches not greater than G kj according to the value of the matrix element.

5. The heterogeneous AGV shop floor production logistics synchronized scheduling method according to claim 4, characterized in that: In step 2, an integrated mixed integer linear programming model of variable sub-batch partition, heterogeneous AGV scheduling and transportation batch constraint is constructed, and the optimization objective of the mixed integer linear programming model is to minimize the maximum completion time C max and minimize the total energy consumption E all of the workshop, which constitutes a double-objective optimization problem, and the mathematical expression is as follows: Min{C max , E all}; where C max is defined as the maximum of the completion times of all workpiece sub-lots on all workstations, i.e. Here denotes the set of completion times of all workstations, all machines, all workpieces, all sub-lots. E all From the total energy consumption of the workshop, from the total energy consumption of transportation E T , the total energy consumption of processing E W , the total energy consumption of standby E F and the total energy consumption of switching E S , that is, E all = E T + E W + E F + E S .

6. The heterogeneous AGV shop floor production logistics synchronized scheduling method according to claim 5, characterized in that: The mixed integer linear programming model describes the synchronous coupling relationship between production and logistics in the heterogeneous AGV environment through the following core constraint conditions: 2.

1. Variable sublot splitting constraint: for each job j, the sum of the lot sizes of all sublots of this job on any process s must equal the total lot size R of this job j i.e. This constraint ensures the material balance and allows sublot lot sizes R jrs to dynamically change according to the transportation and production situation; 2.

2. AGV load-triggered transportation batching constraint: When the sub-batch size R jrs Exceeding the load limit G of the AGV k it serves kj If this occurs, the sub-batch is divided into several transshipment sub-batches for multiple shipments, and the following conditions are met: Where z represents the index of the transfer sub-batch; This indicates the batch size of the transfer sub-batch, specifically the number of workpieces contained in the z-th transfer sub-batch, which is split off from the r-th sub-batch of workpiece j during the transportation stage a. At the same time, the batch quantity of each transport batch shall not exceed the load capacity of the AGV, that is 2.

3. Production and logistics time sequence synchronization constraint: the constraint stipulates that the sub-batch must be transported after the current process is completed, and must be processed in the next process after the transportation arrives and meets the machine availability condition; 2.

4. Resource exclusivity constraint: the model ensures that one workpiece sub-batch is processed by one machine and one workpiece is transported by one AGV at the same time.

7. The heterogeneous AGV shop floor production logistics synchronized scheduling method according to claim 6, characterized in that: The mixed integer linear programming model defines the transport mode based on the "Gold Moment", whose constraint condition is calculated by the processing completion time of the last process, and the parameter expression is B sijr + R jrs · U sj , R jrs , and the parameter expression of the AGV transport time and the processing start time of the next process is Dynamically determine the batch size of the transfer sub-batch and the start processing time on the next process machine to ensure that the target machine is just idle when the AGV delivers the transfer sub-batch, so as to realize seamless connection of the production rhythm and minimize the machine waiting time.

8. The heterogeneous AGV shop floor production logistics synchronized scheduling method according to claim 7, characterized in that: In the step 3, the SAPT rules realize the connection of processing and transportation links in time by dynamically deciding the transportation mode, and cooperatively optimize the maximum completion time and total energy consumption.

9. The heterogeneous AGV shop floor production logistics synchronized scheduling method of claim 1, wherein: In the step 4, the improved water wave optimization algorithm adopts a two-layer coding mode: The first layer is discrete integer coding, which is used to represent the processing order of workpieces and the sub-batch segmentation structure; Specific encoding: Discrete integer encoding is a sequence of length L total where, is the sum of the maximum allowed sub-lots for all workpieces; each element in the sequence is an integer representing a workpiece type number j; the number j appears the kth time in the sequence, representing the kth sub-lot of workpiece j; Parameter expression explanation: Let the encoding sequence be where g l ∈ J, J is the set of workpiece types; The sequence directly determines the first stage processing sequence: element g in position l l represents the lth processed unit is a workpiece g l The total number of times a workpiece j appears in the sequence count(j, Code1) is the actual number of sub-lots L to which the workpiece is divided j ′, L j ′≤L j ; The second layer is real number coding, which is used to represent the resource allocation proportion of each sub-batch to determine the batch size; Specific encoding method: real number encoding is a real number sequence with the same length as the first layer encoding, that is where p l ∈[-1, 1]; Parameter expression description: the meaning of the real number p1 is associated with the workpiece sub-batch at the corresponding position g1 in the first layer coding; If p l <0, it means that the sub-batch defined by this position is an invalid sub-batch, which will be ignored in actual decoding and will not participate in scheduling; this realizes dynamic adjustment of the number of sub-batches. If p l ≥ 0, this value represents the non-normalized weight of this sub-lot in the allocation of the total lot quantity R j of its workpieces. The sub-lot quantity calculation formula: for an effective workpiece j, let all its effective sub-lots, i.e. the non-negative weight set of the position satisfying p1≥0 and g1=j, be P j ={p1|g1=j∧p l ≥0};then for one of the effective sub-lots r, the corresponding weight p 1r , the calculation formula of the quantity R jrs of the batch corresponding to the weight is: The last sub-lot is batched through R j Subtract the sum of the allocated batches to get the balance, to ensure material conservation r R jrs = R j .

10. The heterogeneous AGV shop floor production logistics synchronized scheduling method of claim 9, wherein: In the step 4, the optimal production and logistics scheduling scheme refers to one or more executable scheduling instruction sets selected from a Pareto optimal solution set by the improved water wave optimization algorithm; specifically as follows: 4.

1. Sub-batch segmentation and batch size scheme: The scheme first determines how each workpiece is divided into sub-batches and the specific batch size of each sub-batch; this is finally determined by decoding the two-layer coding of the algorithm; Details: For each job j, the scheme outputs its final set of sublots and the lot size R for each sublot r at each operation s jrs ; Parameter expression: This result directly corresponds to the sublot size variable R defined in the model jrs and satisfies the constraint: Where L′ j This is the actual number of sub-batches of workpiece j; 4.

2. Production scheduling scheme: machine allocation and processing time sequence; The schedule defines the processing timing diagram of all sub-lots on all machines; Specifically, for each sub-lot j r on each operation s, the schedule specifies: Machine i assigned: i.e. decision variable Y sijr = 1 for the machine; Start of processing time B sijr ; Completion processing time C sijr ; Parameter expressions: these time parameters satisfy the model's processing constraints, such as the makespan constraint: C sijr = B sijr + R jrs · U sj and the machine exclusivity constraint, which ensures that for any two different sub-lots, their processing times on the same machine do not overlap; 4.

3. Logistics scheduling scheme: AGV assignment, transportation mode, and transportation timing; The schedule defines the transportation plan of all sub-lots between operations; Specifically, for each sub-lot j r or its transportation sub-lot that needs to be transported from operation s to operation s+1, the schedule specifies: AGV k assigned: i.e. decision variable Z akj AGV with Z = 1; Transportation mode: explicitly whether it is "direct transportation", "Gold time transportation", or "full-load transportation"; Transporter batch size If split: meets Transport start and end time C akjr ; Parameter expression: If using Gold time transportation, the start time of the first transport batch at the next process This is ensured to perfectly fit into the machine idle time by the following equation: 4.

4. Global performance indicators: The schedule will eventually output two key optimization objective values to quantify its performance: Maximum completion time: C max = max s,i,j,r {C siir}; Total energy consumption of the workshop: E all = E T + E W + E F + E S .

Images