A Low-Entropy Scheduling Method for High-Entropy Manufacturing Based on Cellular Automata

Abstract

The present invention discloses a low-entropy scheduling method for high-entropy manufacturing based on cellular automata. The technical solutions adopted include the following main contents: (1) Matching the problem: matching the prototype features and constraints of high-entropy manufacturing problems; (2) Deconstructing the manufacturing system in multi-dimensional space-time and dividing space-time layers; (3) Establishing a cellular automata network model based on plane space decomposition; (4) Designing the objective function and fitness function of the scheduling algorithm according to the low-entropy theory; (5) Establishing a system solution model and solving it. Aiming at the equipment scheduling problem in high-entropy manufacturing processes such as large equipment manufacturing, the present invention makes a mathematical model and optimization algorithm based on cellular automata and low-entropy objectives with the goal of minimizing the planned completion time, maximizing the space-time utilization rate, maximizing the equipment resource utilization rate, and minimizing the delay time, so as to solve the equipment resource scheduling problem existing in high-entropy manufacturing types, and propose an optimized scheduling method with obvious effects for the production scheduling and multiple optimization indexes of high-entropy manufacturing types.

Description

Technical Field

[0001] The present invention relates to the field of equipment scheduling in high-entropy manufacturing types such as large components and large scales, and is a scheduling method with a low-entropy target based on a cellular automata model. Background Art

[0002] Most of the parts in large equipment manufacturing are non-standard products. Some of the processing technologies are special, the process hours are long, the processing equipment is not unique and the corresponding working hours vary greatly; the in-process product structure parameters are large, and the time series and space filling are significantly restricted; the logistics equipment is the hub for flow matching and robust connection between workstations, and it is crucial to respond to flow requirements in a timely manner, and potential interferences are prominent. Therefore, reasonably scheduling limited resources in space and time can meet the differentiated requirements of different orders, effectively compress the production cycle, and improve the order delivery rate.

[0003] At present, large equipment manufacturing in China faces problems such as low production efficiency and high production costs. In order to achieve the lowest flow cost, the smallest inventory buffer, the largest space filling, the largest equipment utilization, realize the effective coupling of time, space and equipment scheduling, eliminate bottlenecks in time sequence, site, production and logistics, reduce high-entropy dissipation and disorder, and complete the manufacturing progress on time, it has become a new problem that high-entropy manufacturing enterprises urgently need to solve. Summary of the Invention

[0004] In order to solve the above problems existing in high-entropy manufacturing type enterprises, the purpose of the present invention is to provide a low-entropy scheduling method for high-entropy manufacturing based on cellular automata. The specific implementation process of the technical solution of the present invention is shown by the attached Figure 1 technical route. The technical solution adopted by a low-entropy scheduling method for high-entropy manufacturing based on cellular automata described in the present invention includes the following main contents:

[0005] 1) Matching the prototype characteristics of high-entropy manufacturing problems with dynamic constraints

[0006] Simplify the non-linear, multi-dimensional dynamic system with physical property changes into discrete events of individual self-organization, and realize the cross-level description from the microscopic structure and self-organization evolution rules of the model to the macro system.

[0007] Characterize the satisfaction problems related to the layout of the collection unit and the design of the flow path, which are associated with strengthening or weakening dynamic constraints, that is, problems such as the flux limitation of the logistics path, the game balance of network construction and material handling costs, the locally irregular layout space, and the path between units cannot cross manufacturing resources. Perform [0,1] mathematical processing on the constraint problems to adapt to the basic rules of cellular automata.

[0008] 2) Multi-dimensional space-time deconstruction and layer division of the high-entropy manufacturing system

[0009] Based on the discretization parameters of the first and second dimensions for the length and width constraints in the planar space, clarify the dynamic constraints for unit layout and logistics path design.

[0010] Taking the starting time of part processing as the division point, perform the time slicing of the third dimension for processing time constraints. Using the processing time as the time constraint, map the unit layout within each time slice of each layer, converting the three-dimensional space problem into a layout problem of a finite number of two-dimensional spaces. The time layer division is as Figure 2 shown.

[0011] Introduce the resource capacity constraints of processing equipment and logistics equipment as the fourth dimension of the multi-dimensional space-time. The equipment resource capacity affects the production scheduling process and time, realizing the multi-dimensional mutual constraint and game state.

[0012] 3) Establish a high-entropy manufacturing cellular automata network model

[0013] Set the entire production workshop as a two-dimensional network containing moving particles. Take parts and equipment as particles, and regard each layer after layer division as a cell, representing a two-dimensional site space. The equipment resources (production equipment and logistics equipment) are used as moving cells to construct an equipment resource scheduling model.

[0014] The description of the cell state attributes in a certain space-time layer is as Figure 3 shown. For the processes of describing the cell state, setting the initial conditions and boundary conditions of the production scheduling cellular automata model, and setting the evolution rules, etc., refer to Chinese Patent CN102608916A.

[0015] 4) Design a low-entropy multi-objective function and fitness function

[0016] The core of high-entropy manufacturing and low-entropy scheduling is low carbon and stability.

[0017] ① Low-entropy index inside the workshop system

[0018] The external entropy of the system can be expressed as

[0019]

[0020] In the formula: S O is the external entropy exchanged between the workshop system and the environment; n is the number of workshop subsystems; w i is the weight of the i-th type of entropy exchanged between the workshop system and the environment; S O,i is the i-th type of entropy exchanged between the workshop system and the environment.

[0021] The total entropy change equation of the workshop system should be expressed as:

[0022]

[0023] In the formula: SI is the internal entropy of the workshop system, S O is the external entropy exchanged between the workshop system and the environment.

[0024] According to the system theory of statistical physics, for a certain production system composed of particles, if the energy of N particles in the s state is Es, then the probability of the workshop in a certain state (N, s) is:

[0025]

[0026] where N is the number of devices in the system; P N,s is the probability of the system in a certain state (N, s); let

[0027] R = ∑ N,s exp(-αN - βEs), according to the physical entropy S = KlnΩ, the internal entropy of the workshop system is:

[0028]

[0029] Substituting (3) into (4), the entropy evaluation index of the workshop system can be expressed as

[0030]

[0031] where K is the proportionality coefficient; -lnP N is the energy of the system in a certain state, that is, the production capacity. In the assumption of the equilibrium state of a closed system, there is where W is the total production state energy of the production system, and we can get

[0032]

[0033] where: N represents the spatial size; E represents the time length; V represents the number of devices.

[0034] In a closed system, the low entropy of the workshop can be expressed as a function related to the production state, spatial resources, time resources, and equipment resources. For the internal entropy S of the production system I perform differential processing:

[0035]

[0036] Also

[0037]

[0038] Let

[0039]

[0040] Then there is

[0041] dS I= αdN + βdE + χdV

[0042]

[0043] The low entropy index S within the system I is divided into three parts: the available production space in the workshop, the production time, and the equipment resources. Kα is the maximum available space in the stable workshop system; Kβ is the maximum available scheduling time in the stable workshop system; Kχ is the maximum number of available workshop equipment in the stable workshop system.

[0044] ② The low entropy index of external factors in the workshop system

[0045] The change in entropy caused by the interference of the external environment on the system is represented by S O Assume that there are k types of disturbance factors in the system, which can be represented by A1, A2, A3, …, A k represent each disturbance, and the occurrence probabilities are P1, P2, P3, …, P k , and the occurrence probabilities of all disturbances According to the influence magnitude of the disturbances, assume that the influence factors of different disturbance factors are C k . According to the theory of physical entropy and information entropy, the external entropy of the workshop system can be further described as follows:

[0046]

[0047]

[0048] Among them:

[0049] C k is the influence factor of the disturbance factor; P i is the occurrence probability of the disturbance factor; i is the disturbance factor; j is the workshop subsystem; f(i, j) is the anti-disturbance state of each system in the workshop; Q i,j is the anti-disturbance cost; X i,j is the disturbance level; S' O is the anti-interference measure, which can be described as:

[0050]

[0051]

[0052]

[0053] In the formula: T i,j is the disturbance degree of the disturbance factor i on the workshop subsystem j, and T is the total disturbance degree during production. Measured at time t 0 is the anti-interference degree at this moment, as the reference anti-interference degree:

[0054] ​

[0055] In the formula: is the reference interference level.

[0056] The influence of disturbance factors on each subsystem is uncertain. Setting the reference value of anti-interference level can keep the workshop system at a low entropy level, and there is

[0057] ③ Objective function design

[0058] The low entropy index is divided into two parts: low carbon and anti-disturbance ability, including minimizing the completion time of the assembly, minimizing the total completion time of the product, maximizing the area utilization rate, minimizing the honeycomb loss rate, and maximizing the comprehensive efficiency of logistics equipment

[0059] i: Any product among N products;

[0060] j: Any assembly among J assemblies of the product;

[0061] k: Any one of O processes in a certain assembly;

[0062] r: Any one of M machines;

[0063] m: Total assembly station node;

[0064] U: Number of total assembly stations;

[0065] h: Order number;

[0066] H: Total number of production orders;

[0067] t: Processing time;

[0068] S: Start processing time;

[0069] α: Penalty factor for early completion of the assembly;

[0070] β: Penalty factor for delay in delivering the assembly to the assembly line;

[0071] C ij : The demand arrival time of a certain assembly station node for assembly j;

[0072] E ij : Completion time of assembly j of product i;

[0073] l i : Quantity of product i; l ij represents the number of assemblies of product i;

[0074] S ijm: The start assembly time of the assembly j of product i at the assembly station node m;

[0075] T ijm : The assembly time required for the assembly j of product i at the assembly station node;

[0076] E ijm : The completion time of the assembly j of product i at the total assembly node m;

[0077] S ijkr : The start processing time of the k - process of the assembly j of product i on the equipment r;

[0078] T ijkr : The processing time of the k - process of the assembly j of product i on the equipment r;

[0079] The completion status of order h;

[0080] R ijm : A Boolean variable indicating whether the assembly j is required at the total assembly node m;

[0081] a ij : The existing processed quantity of the assembly j of product i;

[0082] z tijk : The processing preparation and conversion time of the k - th process of the assembly j of product i;

[0083] b mj : The unit - time preparation cost of different assembly units;

[0084] pc: Production efficiency cost;

[0085] w a : Channel width;

[0086] d: Stack depth;

[0087] q: The number of products processed within the operation unit.

[0088] Minimize the maximum assembly completion time F J , as follows:

[0089]

[0090] The above formula indicates the shortest completion time for batch - processing assemblies. Set the early - completion penalty factor a to ensure an appropriate inventory level and require timely delivery to the assembly line for final assembly after the assembly is completed.

[0091] Minimize the maximum assembly completion time F Z , as follows:

[0092]

[0093] The above formula indicates the shortest time for the final assembly product. By setting the distribution delay penalty factor β, the waiting or material shortage during the assembly process can be reduced, ensuring on-time delivery of the overall assembly process.

[0094] Maximize the utilization rate S1 of the unit area

[0095]

[0096] where: S bi represents the floor area occupied by component i, and S p represents the maximum available area of the site.

[0097] Average overall equipment efficiency of the beam

[0098] When the production capacity remains unchanged, to reduce the number of equipment, it is necessary to improve the OEE of the equipment. The utilization of the equipment is measured by the average overall equipment efficiency, that is, the average value of the OEE of the equipment production:

[0099]

[0100] Establish the following model for the low-entropy scheduling of the workshop:

[0101] EI1 = (1 - S1) × a#(21

[0102] EI2 = (F J + F Z ) × b#(22

[0103]

[0104] minEI = EI1 + EI2 + EI3#(24)

[0105] In the formula: a, b, c are weighting factors, EI1 is the spatial resource utilization rate index, EI2 is the time resource utilization rate index, and EI3 is the equipment utilization rate index.

[0106] ④ Robust design of low-entropy scheduling

[0107] According to the physical entropy formula, construct the workshop entropy evaluation index formula:

[0108]

[0109] where: K is the Boltzmann coefficient; p i is the probability of the corresponding functional unit crashing; m is the crashing situation of the corresponding functional unit. Inside the unit, the equipment is used as the unit, usually with the same equipment function and type, p iRepresents the probability of the i-th device in the equipment crashing. Assuming there are x devices in the unit, then:

[0110]

[0111] The robustness h inside the unit is:

[0112]

[0113] The overall robustness of the complex workshop is:

[0114]

[0115] Where: m i Represents the crashing situation of unit a i , n i Represents the frequency of the workshop failure caused by the overall or partial crashing of unit a i , and N represents the total frequency of the workshop failures.

[0116] The objective function most relevant to robustness is the equipment layout cost Q. Let the maximum crashing probability distribution of each unit be The minimum is The maximum equipment layout cost is Q max , the minimum is Q max , then:

[0117]

[0118] Where Is the initial physical entropy value, Q is the equipment layout cost of the initial layout, and Q0 is the optimized layout cost.

[0119] 5) Establish a high-entropy manufacturing low-entropy navigation model

[0120] ① Two-dimensional layout model construction

[0121] Each parameter involved in the construction process of the layer layout model:

[0122] B: The set of all parts to be processed;

[0123] b i : The i-th part involved in the scheduling, b i ∈B;

[0124] F: The set of all layers;

[0125] f j : The j-th layer, f j ∈F;

[0126] F|b i : The set of layers that part i may pass through;

[0127] B|b i : The set of components associated with component i in terms of time;

[0128] B|f j : The set of all components in the j-th layer;

[0129] b k |f j : Represents the k-th component in the j-th layer;

[0130] x i ,y i ,t i : Respectively represent the two-dimensional coordinates and start time of component i;

[0131] SS i : The set of feasible layout solutions for component i, SS i ={(x i1 ,y i1 ),(x i2 ,y i2 ),…,(x in ,y in )};

[0132] SS i |f j : The set of feasible layout solutions for component i in the j-th layer;

[0133] SS ik |f j : The k-th solution of component i in the j-th layer, SS ik |f j ∈SS i |f j ;

[0134] F(b i |f j ): The set of solutions for the two-dimensional spatial layout of component i in the j-th layer;

[0135] SB: The set of components that have been laid out;

[0136] SB|f j : The set of components that have been laid out in the j-th layer;

[0137] F(b i |SS i |SB|f j ): The set of sites in the j-th layer of the set of components SB|f where component i is laid out according to the two-dimensional layout rules j .

[0138] On the f j layer, place B|f jThe components in it are randomly sorted to obtain a scheduling sequence. Let the number of the k-th component to be arranged be k, then its solution set can be denoted as: SS k |f j = F(b k |f j ), where SB = {b1, b2, …, b k-1}.

[0139] For component k, the solution set on each layer can be expressed as: {SS k |f1, SS k |f2, …, SS k |f m}, where Therefore, the final deployable solution set of component k is: SS k = (SS k |f1) ∩ (SS k |f2) ∩ … ∩ (SS k |f m ). Similarly, the solution sets of other components can be obtained. SS i is the deployable solution set of multiple independent components.

[0140] The solution process is as follows:

[0141] For the deployable solution set SS i of the i-th component, judge whether b1, b2, …, b i-1 belong to B|b i . If there are b1, b2, …, b i-1 ∈ B|b i , then remove the solution set within the influence range of the deployment solutions of b1, b2, …, b i from SS i-1 , update SS i , and randomly select a solution from the updated SS i as the initial two-dimensional deployment point (x i , y i , y i ) of b

[0142] Repeat the above steps until the scheduling sequence is empty, that is, all components are deployed, as Figure 4 shown.

[0143] In the objective function, the layer layout model has a direct relationship with the space resource utilization rate EI1.

[0144] According to the scheduling result of the layer layout model, the state of the f j layer layout cells can be obtained, and ∑S bi / S p can be calculated.

[0145] ② Construction of 3D Production Scheduling Model

[0146] Let:

[0147] The set of workstations S = {s1, s2, …, s m};

[0148] The set of buffers P = {p1, p2, …, p m};

[0149] The set of workpiece particles B = {b1, b2, …, b n};

[0150] The operation O ij is the j-th operation of the i-th workpiece particle;

[0151] The processing time matrix of the workstation group x is T, where T i represents a row matrix, and A i represents a column matrix. In the matrix, T ijxy represents the processing time required for the j-th operation of workpiece i on the y-th workstation in the workstation group x. The scheduling objective function is:

[0152]

[0153] The constraint conditions are as follows:

[0154] Resource constraint:

[0155] At most one workpiece can be processed on the same device at the same time;

[0156]

[0157] A workpiece can only be processed on one device for one operation;

[0158]

[0159] Once the processing of each workpiece starts, it cannot be paused.

[0160] Process constraint:

[0161] There is a precedence constraint relationship between the operations of the same workpiece;

[0162] There is no precedence constraint relationship between the operations of different workpieces.

[0163] ③ Construction of the Fourth-Dimension Logistics Equipment Scheduling Model

[0164] The logistics equipment scheduling objective is to minimize the total time used to complete all operation handling tasks. Assuming a constant speed, that is, to minimize the total distance of equipment k handling task w.

[0165]

[0166] s.t.

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173] The meanings of the parameters are as follows:

[0174] N: The total number of all processes to be processed;

[0175] S: Represents the set of available devices s, s ∈ S;

[0176] i s : The available time for scheduling device s,

[0177] L i,j,k : The sum of the travel times among the starting node j, the target node g, and the origin i of the device;

[0178] Whether to call device k to execute process w;

[0179] Whether the called device k passes through the starting node j when executing process w;

[0180] Whether the called device k passes through the target node g when executing process w;

[0181] The q-th process processed by device k;

[0182] The start, running, and end times of;

[0183] x kk' : The distance between device k and device k';

[0184] The priority of device k when executing process w at time t;

[0185] where

[0186] When there is congestion in the logistics path at the same time, the lower priority gives way to the higher priority.

[0187] 6) Solving the problem of high-entropy manufacturing and low-entropy navigation

[0188] A two-layer genetic algorithm is used to find the optimal scheduling scheme of equipment resources under constraints such as unique occupancy and task processing priority. The outer-layer genetic algorithm determines the integrated processing equipment scheduling scheme, corresponding to an optimal logistics equipment scheduling integrated scheme obtained by an inner-layer genetic algorithm. The inner and outer-layer genetic algorithms interact, iterate, and reach a balance through gaming. In order to evaluate the solution effect of logistics scheduling, the inner-layer genetic algorithm uses SPEA2 to seek Pareto solutions. As Figure 5 shown, the part inside the dashed box represents the inner layer, and the part outside the dashed box represents the outer layer. The algorithm process is as follows:

[0189] ① Obtain the two-dimensional component layout result and the set of component processes of f i ; i

[0190] ② Encode the outer-layer production scheduling, initialize the population P(a), and set the number of iterations;

[0191] ③ Decode the individuals of P(a) to obtain the matching relationship between tasks and logistics equipment and the task time constraints;

[0192] ④ Encode the inner-layer logistics equipment scheduling, initialize the inner-layer population, and set the same number of iterations as the outer layer;

[0193] ⑤ Use the inner-layer genetic algorithm to solve the optimal inner-layer scheduling solution corresponding to each individual in the outer-layer population P(a);

[0194] ⑥ For the returned inner-layer optimal solutions, the outer layer obtains the corresponding production scheduling chromosomes, assigns a fitness function to each individual, and retains the excellent individuals to enter the next-generation population set;

[0195] ⑦ Check if the termination condition is met. If so, the algorithm terminates; otherwise, continue to execute step ②.

[0196] Combined with the characteristics of production scheduling, the following design is adopted for the outer-layer algorithm.

[0197] In the static scheduling unit, each workpiece contains only one process. The number of workpieces is equal to the number of processes n in the unit scheduling, and the length of the station chromosome is equal to the length of the process chromosome n. The subsets of available processing stations and logistics handling stations for each process are {g1, g2,..., g m}, {c1, c2,..., c i}, {p1, p2,..., p j}; the gene subset of the process chromosome is {g1', g2',..., g n '}, where g' n∈ {1, 2, …, n}.

[0198] The objective function is set as the fitness function.

[0199]

[0200] Using the roulette wheel selection method, if the fitness of an individual i is f i , then the probability of its being selected is

[0201]

[0202] The SPEA2 is adopted for the inner - layer algorithm to seek Pareto solutions.

[0203] The logistics equipment scheduling adopts an integer coding mechanism. Every four digits form a group, representing the allocation of a forklift starting from a certain origin, going to a certain starting node to execute a handling task and then going to a certain target node. The reciprocal of the sum of two objectives, the total handling time and the distance, is selected as the fitness function:

[0204]

[0205] After each generation of individuals is generated, it is necessary to inspect and eliminate the individuals. The constraint conditions are as follows:

[0206]

[0207] If this value is 0, it means that this chromosome does not conform to the actual constraints, and this individual should be eliminated and re - selected.

[0208] Based on the SWARM platform, develop a high - entropy manufacturing low - entropy navigation optimization prototype system and complete system testing. Conduct laboratory simulations and carry out empirical analysis of core enterprises.

[0209] The technical concept of the present invention is: aiming at the equipment scheduling problem in high - entropy manufacturing processes such as large - scale equipment manufacturing, with the low - entropy idea of the shortest planned completion time, the maximum spatio - temporal utilization rate, the maximum equipment resource utilization rate, and the least delay time, design a mathematical model and an optimization algorithm based on the cellular automaton structure and with low entropy as the optimization goal to solve the equipment resource scheduling problem in high - entropy manufacturing modes.

[0210] The beneficial effects of the present invention are mainly manifested in: proposing an obvious optimization scheduling method for the production scheduling of high - entropy manufacturing types and its multiple optimization indexes. Brief Description of the Drawings

[0211] Figure 1 is the technical roadmap of this application;

[0212] Figure 2 is the schematic diagram of the three - dimensional spatio - temporal layer division of the site;

[0213] Figure 3 It is a schematic diagram for describing the cell state of a certain time slice layer;

[0214] Figure 4 It is a flow chart for establishing a high-entropy manufacturing and low-entropy navigation model;

[0215] Figure 5 It is a structure diagram of a double-layer genetic algorithm;

[0216] Figure 6 It is an abstract model of a cellular automaton for workshop production scheduling;

[0217] Figure 7 It is a workshop layout diagram;

[0218] Figure 8 It is a Gantt chart for workshop production scheduling. Specific implementation manners

[0219] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0220] Enterprise H in the embodiment has characteristics such as large product volume, large demand variation, many types, and long production cycle, which conform to the basic characteristics of high-entropy manufacturing, and is used as the research object of the example. Analyze its product process, production workshop, and logistics equipment capabilities and scheduling requirements. Analyze and solve based on the developed high-entropy manufacturing and low-entropy navigation optimization prototype system on the SWARM platform.

[0221] A high-entropy manufacturing and low-entropy scheduling method based on cellular automata includes the following steps:

[0222] 1) Match the problem characteristics and constraints of the high-entropy manufacturing system, and perform multi-dimensional space-time deconstruction and layer division;

[0223] Based on the discretization parameter division of the first and second dimensions of the length and width constraints in the plane space, clarify the dynamic constraints of unit layout and logistics path design.

[0224] Taking the start time of part processing as the division point, perform the third-dimensional time slicing of the processing time constraint. Using the processing time as the time constraint, map the unit layout within each time slice of each layer, converting the three-dimensional space problem into a layout problem of a finite number of two-dimensional spaces.

[0225] Introduce the resource capacity constraints of processing equipment and logistics equipment as the fourth dimension of multi-dimensional space-time. The equipment resource capacity affects the production scheduling process and time, and establish the basic structure of multi-dimensional manufacturing.

[0226] 2) Analyze the logistics demand and equipment capacity, and establish a cellular automaton network model

[0227] Set the entire production workshop as a two-dimensional network containing mobile particles. Use parts and equipment as particles, and each layer after layer division is regarded as a cell, representing a two-dimensional site space. The equipment resources (production equipment and logistics equipment) are used as mobile cells to construct an equipment resource scheduling model.

[0228] According to the description and setting of the cell state, the state attributes of the cells in a certain space-time layer, the initial conditions and boundary conditions, and the evolution rules, unify the workstations of the same type into the same workstation group, and establish the Figure 6 abstract model of the cellular automaton for workshop production scheduling as shown.

[0229] Set of state attributes of the buffer cell at time t:

[0230]

[0231] Where:

[0232] is the state of the buffer cell C (2n+1)j at time t;

[0233] w ct is the total capacity of the work-in-process in the buffer cell area, with the unit of unit;

[0234] w co is the occupied space in the buffer cell, a dynamic attribute, 0 ≤ w co ≤ w ct ;

[0235] w cl is the unoccupied space in the buffer cell, a dynamic attribute, w cl = w ct - w co ;

[0236] lq is the number of parts waiting to be processed in the buffer cell, that is, the queue length, a dynamic attribute, lq ∈ N;

[0237] w q is the waiting time of the workpiece in the buffer cell queue, a dynamic attribute, with the unit of day.

[0238] The initial state attributes of the buffer cell are shown in Table 1:

[0239] Table 1

[0240]

[0241]

[0242] Set of state attributes of the workstation cell at time t:

[0243]

[0244] Among them:

[0245] is the state of the station cell C (2n)j at time t;

[0246] st is the station group where the station cell is located, a static attribute, st ∈ {C 2n}, n ∈ N *

[0247] pe is the processing efficiency or handling efficiency of the station cell, a static attribute;

[0248] T is the processing time or handling time of the station cell within the scheduling period, a static attribute, unit: day;

[0249] s s is the busy / idle state of the station cell, a dynamic attribute, s s ∈ {0, 1, 2} 0: idle, 1: busy, 2: faulty;

[0250] s ct is the total processing capacity of the station cell within the period, a static attribute, s ct = pe × T, unit: unit;

[0251] s co is the occupied capacity of the station cell, equal to the sum of the processing capacities of the processed, being processed, and corresponding buffer waiting for processing parts, a dynamic attribute, 0 ≤ s co ≤ s ct ;

[0252] s cl is the remaining capacity of the station, a dynamic attribute, s cl = s ct - s co .

[0253] The initial state attributes of the station cell are shown in Table 2:

[0254] Table 2

[0255]

[0256]

[0257] ② Initial condition and boundary condition setting

[0258] The moving particles, i.e., parts, are classified into 4 categories according to the processing degree: processed, being processed, unprocessed, and to-be-processed. The state attribute expression of the part particle at time t

[0259]

[0260] Wherein:

[0261] k is the part number, k ∈ N * ;

[0262] b t is the number of processing operations required for the particle, a static attribute;

[0263] b f is the number of operations completed by the particle at time t, a dynamic attribute;

[0264] nb is the number of the next operation that the particle enters, a dynamic attribute;

[0265] fst pair is the work station group that the particle will enter next, a dynamic attribute;

[0266] wl is the processing capacity required for the next operation of the particle, with the unit of unit, a dynamic attribute.

[0267] s n is the space capacity required to be occupied by the particle, a static attribute;

[0268] dp is the priority of particle processing, a static attribute, dp ∈ N * ;

[0269] qn is the serial number of the particle in the queue, a dynamic attribute, qn ∈ N * ;

[0270] t a is the time when the particle enters the cell, which is divided into two categories: the time to reach the buffer cell and the time to reach the work station cell, that is, the start queuing time and the start processing time, a dynamic attribute.

[0271] The initial state attributes of the part particle are shown in Table 3:

[0272] Table 3

[0273]

[0274]

[0275] 3) Establish a navigation model under the low-entropy multi-objective function and fitness function

[0276] ① Low-entropy index inside the scheduling system

[0277] For a production system composed of particles, the probability of the workshop being in a certain state (N, s) is:

[0278]

[0279] The entropy evaluation index of the workshop system is expressed as:

[0280]

[0281] In the assumption of the equilibrium state of a closed system, where W is the total production state energy of the production system, the following can be obtained:

[0282]

[0283] In a closed system, the low entropy of the workshop can be expressed as a function related to the production state, spatial resources, time resources, and equipment resources.

[0284] There is

[0285]

[0286] Kα is the maximum available space in the stable workshop system; Kβ is the maximum available scheduling time in the stable workshop system; Kχ is the maximum number of available workshop equipment in the stable workshop system.

[0287] ② Low entropy index of external factors of the scheduling system

[0288] The interference of the external environment of the system causes a change in the entropy of the workshop S O , and let the influence factor of different disturbance factors be C k , the external entropy of the workshop system:

[0289]

[0290]

[0291] S O The anti-interference metric can be described as:

[0292]

[0293]

[0294]

[0295] At time t 0 Measure as the anti-interference degree at this moment, as the reference anti-interference degree:

[0296]

[0297] ③ Objective function design

[0298] Minimize the maximum assembly completion time F J , as follows:

[0299]

[0300] Minimize the maximum total assembly completion time FZ , as follows:

[0301]

[0302] Maximize the unit area utilization rate S1

[0303]

[0304] Average comprehensive efficiency of beam current equipment

[0305]

[0306] Establish the following model for low-entropy scheduling in the workshop:

[0307] EI1 = (1 - S1) × a#(18)

[0308] EI2 = (F J + F Z ) × b#(19)

[0309]

[0310] minEI = EI1 + EI2 + EI3#(21)

[0311] Where: a, b, c are weighting factors, EI1 is the spatial resource utilization rate index, EI2 is the time resource utilization rate index, and EI3 is the equipment utilization rate index.

[0312] ④ Robust design of low-entropy scheduling:

[0313] Inside the unit, taking the equipment as the unit, usually the functions and types of equipment are the same, p i represents the probability that the i-th equipment in the equipment breaks down. Assuming there are x pieces of equipment in the unit, then:

[0314]

[0315] The robustness h inside the unit is:

[0316]

[0317] The overall robustness of the complex workshop is:

[0318]

[0319] The objective function most relevant to robustness is the equipment layout cost Q, and there is:

[0320]

[0321] 4) Establishment of the high-entropy manufacturing low-entropy navigation model

[0322] ① Two-dimensional layout model construction

[0323] Arrange component i according to the two-dimensional layout rules into the set of the j-th layer sites of the existing component set SB|f j of the set of sites on the j-th layer.

[0324] On layer f j randomly sort the components in B|f j to obtain a scheduling sequence. Let the number of the first component to be arranged be 1, then its solution set can be denoted as: SS1|f j = F(b1|f j ); Let the number of the second component to be arranged be 2, then its solution set can be denoted as: SS2|f j = F(b2|f j ); Let the number of the k-th component to be arranged be k, then its solution set can be denoted as: SS k |f j = F(b k |f j ), where SB = {b1, b2, …, b k-1}.

[0325] For component k, the solution sets on each layer can be expressed as: {SS k |f1, SS k |f2, …, SS k |f m}, where Therefore, the final available layout solution set of component k is: SS k = (SS k |f1) ∩ (SS k |f2) ∩ … ∩ (SS k |f m ), and the solution sets of other components can be obtained in the same way. SS i is the available layout solution set of multiple independent components.

[0326] The solution process is as follows:

[0327] Schedule according to the coding order of the components. For the first component b1, the available layout solution set is denoted as SS1, and randomly select a solution from SS1 as the initial two-dimensional layout point (x1, y1) of b1;

[0328] Schedule the second component b2, the available layout solution set is SS2, judge whether b2 belongs to B|b2, that is, whether there is a time association between b1 and b2. If b1 ∈ B|b2, then remove the solution set within the influence range of the layout solution of b1 from SS2 and update SS2. Randomly select a solution from the updated SS2 as the initial two-dimensional layout point (x2, y2) of b2;

[0329] Similarly, for the set of deployable solutions SS of the i-th component i , determine whether b1, b2, …, b i-1 belongs to B|b i . If there are b1, b2, …, b i ∈B|b i , then remove from SS i the set of solutions within the influence range of the deployment solutions of b1, b2, …, b i-1 , update SS i , and randomly select a solution from the updated SS i as the initial two-dimensional deployment point (x i , y i ) of b i ;

[0330] Repeat the above steps until the scheduling sequence is empty, that is, all components are deployed.

[0331] According to the scheduling result of the layer layout model, obtain the state of the layer layout cells of f j , and calculate ∑S bi / S p .

[0332] ② Construction of three-dimensional production scheduling model

[0333] Suppose:

[0334] The set of workstations S = {s1, s2, …, s m};

[0335] The set of buffers P = {p1, p2, …, p m};

[0336] The set of workpiece particles B = {b1, b2, …, b n};

[0337] The process O ij represents the j-th process of the i-th workpiece particle;

[0338] The production scheduling objective function:

[0339]

[0340] s.t.

[0341] Resource constraint:

[0342] At most one workpiece can be processed on the same device at the same time;

[0343]

[0344] A workpiece can only be processed on one piece of equipment in one process;

[0345]

[0346] Once the processing of each workpiece starts, it cannot be paused.

[0347] Process constraints:

[0348] There is a sequential constraint relationship between the processes of the same workpiece;

[0349] There is no sequential constraint relationship between the processes of different workpieces.

[0350] ③ Construction of the fourth-dimensional logistics equipment scheduling model

[0351] The logistics equipment scheduling goal is to minimize the total distance of the handling tasks w of equipment k.

[0352]

[0353] s.t.

[0354]

[0355]

[0356]

[0357]

[0358]

[0359]

[0360] 5) Solving the problem of high-entropy manufacturing and low-entropy navigation

[0361] Use an improved double-layer genetic algorithm to solve the scheduling problem of the system. Take the production scheduling layer as the outer layer and the logistics equipment scheduling layer as the inner layer.

[0362] Combined with the characteristics of production scheduling, the following parameters are adopted for the outer-layer algorithm. The population size N' is generally between 10 and 160. For the example model of this study, N' should be selected as a smaller value within the interval and set to 20. Double-point crossover is adopted, and the crossover probability P c ' is generally between 0.25 and 100. In the example of this study, 0.6 is selected. The mutation probability P m ' is generally around 0.001, and 0.001 is selected. The tournament selection scale k has the best effect when it is around 60% to 80% of the population size, and 60 is selected. The number of iterations is 80.

[0363] The SPEA2 algorithm is used to find the Pareto solution for the inner-layer algorithm. According to the characteristics of the model, the population size is set to 50. After experiments, the crossover probability P c is set to 0.6, and the mutation probability P m is set to 0.001. The size of the external affiliated population is 30, the tournament selection size is 30, and the termination condition is that the number of evolutionary generations Gen = 80.

[0364] According to the enterprise situation, the weighting factors a = 7, b = 7, and c = 5 are set.

[0365] The high-entropy manufacturing scheduling cellular automaton model based on heuristic scheduling rules usually can only obtain a sub-optimal solution. Therefore, it is necessary to conduct multiple experiments and select the result with the optimal objective value as the scheduling plan. Ten experiments are carried out on the workshop, and the experimental objective function values are obtained as shown in the table.

[0366] Table 4

[0367]

[0368] The sum of various indicators EI in the third experiment is the lowest, that is, the result of the third scheduling plan is the best. The two-dimensional layout solution and equipment scheduling data of the third experiment are exported, and one of the workshop layouts is drawn as Figure 7 shown, and the production scheduling Gantt chart is drawn as Figure 8 shown.

Claims

1. A low-entropy scheduling method for high-entropy manufacturing based on a cellular automaton, characterized in that It includes the following steps: 1) Matching the problem prototype features and dynamic constraints of the high-entropy manufacturing system Characterize typical local details according to the characteristics of high-entropy manufacturing, simplify the multi-dimensional dynamic system with non-linearity and accompanying physical property changes into discrete events of individual self-organization, and achieve cross-level description from the microscopic structure and self-organization evolution rules of the model to the macroscopic system; Conduct [0,1] mathematical processing on the constrained problem to adapt to the basic rules of the cellular automaton; 2) Multi-dimensional spatio-temporal deconstruction and layer division of the high-entropy manufacturing system Based on the discretization parameters of the first and second dimensions of the length and width constraints in the plane space, clarify the dynamic constraints of the unit layout and the logistics path design; take the starting time of part processing as the division point, conduct the third-dimensional time slicing of the processing time constraint, use the processing time as the time constraint, map the unit layout within the time slice of each layer, and convert the three-dimensional space problem into the layout problem of a finite number of two-dimensional spaces; introduce the resource capacity constraints of processing equipment and logistics equipment as the fourth dimension of multi-dimensional spatio-temporal, and the equipment resource capacity affects the production scheduling process and time, with multi-dimensional mutual constraints and games; among them, the equipment resources include production equipment and logistics equipment; 3) Establishing a high-entropy manufacturing cellular automaton network model Set the entire production workshop as a two-dimensional network containing moving particles, use parts and equipment as particles, regard each layer after layer division as a cell, representing a two-dimensional site space, and use equipment resources as moving cells to construct an equipment resource scheduling model; Describe the state attributes of the cells in a certain spatio-temporal layer, including cell state description, setting the initial conditions and boundary conditions of the production scheduling cellular automaton model, and setting the evolution rules; 4) Designing a low-entropy multi-objective function and a fitness function Systematically define and describe the entropy indicators of the internal and external environment impacts of the workshop scheduling system, define the anti-interference degree and the reference anti-interference degree, design the objective function and its constraint conditions of low-entropy optimization including low-carbon and anti-disturbance, and establish a low-entropy scheduling basic model and robustness evaluation.

2. The high-entropy manufacturing low-entropy scheduling method based on a cellular automaton according to claim 1, wherein In step 4), the analysis, derivation and description of the internal and external entropy change indicators of the system mainly include the following process: The total entropy change equation of the workshop system is expressed as: Among them, S O is the external entropy of the system, and S I is the internal entropy of the system; The probability of the workshop in a certain state (N, s) is: Among them, N is the number of equipment in the system; Es is the energy, that is, the production capacity, possessed by the particles with the number N of particles in the s state; The internal entropy of the workshop production system is expressed as: The internal entropy evaluation index of the workshop system is expressed as: S I = -K∑ N,s P N,s lnP N,s Among them: N represents the space size; E represents the time length; V represents the number of equipment; Differentiate the physical entropy S of the production system I to obtain: dS I = αdN + βdE + χdV S I It is divided into three parts: the production space available in the workshop, production time, and equipment resources; The external entropy of the workshop system can be expressed as: It is further described as: S ' O The anti-interference degree is described as: For reference immunity: The low-entropy indicators included in the objective function design are divided into two parts: low carbon and anti-disturbance ability, including minimizing the assembly completion time, minimizing the total product completion time, maximizing the area utilization rate, minimizing the honeycomb loss rate, and maximizing the comprehensive efficiency of logistics equipment Minimize the maximum assembly completion time F J : Minimize the maximum assembly completion time F Z : Maximize the unit area utilization rate S1: Average Overall Equipment Effectiveness Establish the following model for the low-entropy scheduling of the workshop: EI1 = (1 - S1) × a EI2 = (F J + F Z ) × b minEI = EI1 + EI2 + EI3 In the formula: a, b, c are weighting factors, EI1 is the space resource utilization rate index, EI2 is the time resource utilization rate index, and EI3 is the equipment utilization rate index; Construct the workshop entropy evaluation index formula in the robust design of low-entropy scheduling: The robustness h inside the unit is: The overall robustness of the complex workshop is: p i represents the probability that the i-th device in the equipment crashes. Assume there are x devices in the unit:

3. A low-entropy scheduling method for high-entropy manufacturing based on a cellular machine as claimed in claim 1, characterized in that Step 4) includes the process of establishing a high-entropy manufacturing low-entropy navigation model, which is specifically as follows: ① Construction of the two-dimensional layout model: On layer f j Randomly sort the components in B|f j to obtain a scheduling sequence; the number of the k-th component to be arranged is k, and the solution set is denoted as: SS k |f j = F(b k |f j ), where SB = {b1, b2,..., b k-1}; The solution set of component k on each layer is represented as: {SS k |f1, SS k |f2, …, SS k |f m}, where The final deployable solution set of component k: SS k =(SS k |f1) ∩ (SS k |f2) ∩ … ∩ (SS k |f m ), and the solution sets of other components can be obtained in the same way; SS i is the deployable solution set of multiple independent components; The solution process is as follows: For the set of feasible layout solutions SS of the i-th component i , judge whether b1, b2, …, b i-1 belong to B|b i . If there are b1, b2, …, b i ∈B|b i , then remove from SS i the set of solutions within the influence range of the layout solutions of b1, b2, …, b i-1 , update SS i . Randomly select a solution from the updated SS i as the initial two-dimensional layout point (x i , y i , y i ) of b ; Repeat the above steps until the scheduling sequence is empty, that is, all components are laid out; ② Construction of Three-dimensional Production Scheduling Model The processing time matrix of station group x is T, T i represents a row matrix, A i represents a column matrix, and in the matrix T ijxy represents the processing time required for operation j of workpiece i on station y of station group x. The scheduling objective function: s.t. Resource Constraints: At most one workpiece can be processed on the same device at the same time; A workpiece can only be processed on one device in one process; Once the processing of each workpiece starts, it cannot be paused; Process Constraints: There is a sequence constraint relationship between the processes of the same workpiece; There is no sequence constraint relationship between the processes of different workpieces; ③ Construction of Logistics Equipment Scheduling Model in the Fourth Dimension The goal of logistics equipment scheduling is to minimize the time used to complete the handling tasks of all processes. Assuming a constant speed, that is, to minimize the total distance of equipment k to handle task w. The scheduling objective function: When there is a congestion on the logistics path at the same time, the lower priority gives way to the higher priority.

4. The high-entropy manufacturing low-entropy scheduling method based on a cellular automaton according to claim 1, wherein Step 4) also includes a problem-solving method, which is specifically as follows: A two-layer genetic algorithm is used to find the optimal scheduling scheme of equipment resources under the constraints of unique occupancy and task processing priority; the outer genetic algorithm determines the integrated processing equipment scheduling scheme, corresponding to an optimal integrated logistics equipment scheduling scheme obtained by the inner genetic algorithm. The inner and outer genetic algorithms interact, iterate, and reach a balance; in order to evaluate the solution effect of logistics scheduling, the inner genetic algorithm uses SPEA2 to seek Pareto solutions; The algorithm process is as follows: ① Obtain layer f i Two-dimensional component layout result and f i ; component process set of ② Encode the outer production scheduling, initialize the population P(a), and set the number of iterations; ③ Decode the individuals of P(a) to obtain the matching relationship between tasks and logistics equipment and the task time constraints; ④ Encode the inner logistics equipment scheduling, initialize the inner population, and set the same number of iterations as the outer layer; ⑤ Use the inner genetic algorithm to solve the optimal inner scheduling solution corresponding to each individual in the outer population P(a); ⑥ For the returned inner optimal solution, the outer layer obtains the corresponding production scheduling chromosome, assigns a fitness function to each individual, and retains the excellent individuals to enter the next generation population set; ⑦ Check if the termination condition is met. If so, the algorithm terminates; otherwise, continue to execute step ②.

5. The high-entropy manufacturing low-entropy scheduling method based on a cellular machine according to claim 4, characterized in that Combined with the characteristics of production scheduling, the following design is adopted for the outer layer algorithm: In the static scheduling unit, each workpiece contains only one operation. The number of workpieces is equal to the number of operations \(n\) in the unit scheduling, and the length of the station chromosome is equal to the length of the operation chromosome \(n\). The subsets of available processing stations and material handling stations for each operation are \(\{g_1, g_2, \ldots, g m \}\), \(\{c_1, c_2, \ldots, c i \}\), \(\{p_1, p_2, \ldots, p j \}\); the subset of genes of the operation chromosome is \(\{g_1', g_2', \ldots, g n '\}, where \(g ' n \in \{1, 2, \ldots, n\}\); Set the objective function as the fitness function Using the roulette wheel selection method, if the fitness of an individual i is f i , then the probability of its being selected is Use SPEA2 to seek Pareto solutions for the inner layer algorithm; The logistics equipment scheduling adopts an integer coding mechanism. Each group of four digits represents the allocation of a forklift to start from a certain origin, go to a certain starting node to perform a handling task, and then go to a certain target node; select the reciprocal of the sum of the two objectives of the total handling time and the distance as the fitness function: After each generation of individuals is generated, it is necessary to check and eliminate the individuals. The constraint conditions are as follows: If this value is 0, it means that this chromosome does not conform to the actual constraints, and this individual should be eliminated and reselected.

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