Consider the Finite Transportation Resources and Multi-Objective Distributed Flexible Job Shop Scheduling Method

Abstract

The present invention relates to a multi-objective distributed flexible job shop scheduling method considering limited transportation resources. The method includes the following steps: Step S1: Construct a multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon: The model includes visualized symbolic definitions, required constraint conditions, and three optimization objective definitions of the makespan, total processing energy consumption, and total processing quality; Step S2: Design a multi-objective comprehensive decision-making method based on the combination of spherical fuzzy sets and voting theory; Step S3: Determine an intelligent optimization algorithm and solve the optimal solution of the multi-objective distributed flexible job shop scheduling model considering limited transportation resources and low carbon in combination with the above decision-making method, and output the scheduling result; Applying this technical solution can quickly and effectively obtain a better scheduling plan and improve the workshop production efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling of discrete manufacturing systems, in particular to a multi-objective distributed flexible job shop scheduling method considering limited transportation resources. Background Art

[0002] Distributed Flexible Job Shop Scheduling problem (DFJSP) can be regarded as a combination problem of traditional job shops and distributed factories. The distributed factory model means that multiple factories with separate processing capabilities aggregate together to complete the production of a certain product, and the geographical locations of each factory are different. The development of globalization has made the distributed manufacturing model increasingly common. Resource sharing, reasonable division of labor and cooperation among distributed factories can make full use of resources, effectively reduce costs and management risks. The multi-objective distributed flexible job shop scheduling problem considering limited transportation resources and low carbon takes into account the production mode of distributed manufacturing and the constraint of limited transportation resources. At the same time, it also considers reducing the makespan, lowering production energy consumption, and improving processing quality. In this model, there is more than one factory that can be selected for production processing. At the same time, a process may not be limited to one machine, and processing machines can also be selected from multiple different types of machines. There is more than one transport vehicle selected for the transfer of the upper and lower processes of the workpiece. Solving such problems requires considering arranging a suitable factory for each process, then arranging a suitable machine, and also considering the processing order of the workpiece on each machine in different factories and arranging a suitable transport vehicle for adjacent processes of the workpiece. It is an NP-hard problem. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a multi-objective distributed flexible job shop scheduling method considering limited transportation resources, which can quickly and effectively obtain a better scheduling plan and improve the production efficiency of the workshop.

[0004] To achieve the above purpose, the present invention adopts the following technical solutions: A multi-objective distributed flexible job shop scheduling method considering limited transportation resources, including the following steps:

[0005] Step S1: Construct a multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon, including symbolic definition, constraint conditions, and optimization objective definitions of makespan, total processing energy consumption, and total processing quality;

[0006] Step S2: Design a multi-objective comprehensive decision-making method based on the combination of spherical fuzzy sets and voting theory;

[0007] Step S3: Determine the swarm intelligence optimization algorithm and solve the optimal solution of a multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon in combination with the above decision-making method, and output the scheduling result.

[0008] In a preferred embodiment: Step S2 specifically includes the following steps:

[0009] Step S21: The intelligent optimization algorithm generates a population containing a certain number of individuals, calculates the objective function values of all individuals in the population, and constructs the positive and negative ideal solution sets of the objective function according to the objective function values respectively;

[0010] Step S22: Introduce the spherical fuzzy set transformation formula as the objective function value mapping formula;

[0011] Step S23: Construct the upper and lower boundaries of each objective function according to the positive and negative ideal solution sets;

[0012] Step S24: Convert the upper and lower boundaries of the objective function into the upper and lower boundaries of the spherical fuzzy set;

[0013] Step S25: Substitute the objective function values of all individuals in the population into the mapping formula formed by the above steps to obtain the spherical fuzzy sets of all individuals in the population;

[0014] Step S26: Introduce voting theory, convert the spherical fuzzy set of the objective function value of the individual into a passing value, and use it as the comprehensive decision-making value.

[0015] In a preferred embodiment: In Step S22, specifically: Introduce the spherical fuzzy set transformation formula as the objective function mapping formula;

[0016] The spherical fuzzy set on the universe of discourse space Y is;

[0017]

[0018] where respectively represent the membership degree, neutral degree, and non-membership degree; respectively represent the membership degree, neutral degree, and non-membership degree of each element y (y ∈ Y) in ; and satisfy:

[0019]

[0020] The spherical fuzzy set transformation formula of objective o is as follows:

[0021]

[0022] In the formula represents the value after normalization of the function value of the o-th objective of the i-th individual, are respectively the membership degree, neutrality degree, and non - membership degree of the spherical fuzzy set

[0023] ; is the spherical fuzzy set of the function value of the o - th objective of the i - th individual; and are the upper and lower boundaries of the membership degree of objective o, and are the upper and lower boundaries of the neutrality degree of objective o, and are the upper and lower boundaries of the non - membership degree of objective o.

[0024] In a preferred embodiment: In step S24, specifically: convert the upper and lower boundaries of the objective function into the upper and lower boundaries of the spherical fuzzy set;

[0025] The upper and lower boundaries of the spherical fuzzy set of objective o are defined as follows:

[0026] The upper boundary of the membership degree is The lower boundary is

[0027] The upper boundary of the neutrality degree is The lower boundary is

[0028] The upper boundary of the non - membership degree is The lower boundary is

[0029]

[0030] where is the upper boundary of objective o, is the lower boundary of objective o, gpop o represents the spherical fuzzy set boundary of objective o, q o ∈(0,1) and p o ∈(0,1) are coefficients pre - assigned by the decision - maker.

[0031] In a preferred embodiment: In step S26, specifically: introduce the voting theory, convert the spherical fuzzy set of the objective function value of the individual into a passing value, and use it as the comprehensive decision - making value;

[0032] Definition of voting theory: A collective action method that selects the action with the most approvals as the result according to the choices of the voters; The implementation method is as follows:

[0033]

[0034] Where \(tu\) is the passing value, \(a\) is the affirmative vote, \(c\) is the negative vote, and \(b\) is the abstention vote;

[0035] Map the membership degree, neutral degree, and non-membership degree of the spherical fuzzy set to the affirmative vote, abstention vote, and negative vote in voting theory, and let The following formula is obtained:

[0036]

[0037] Where is the spherical fuzzy set of the function value of the \(o\)-th objective of the \(i\)-th individual of the passing value;

[0038] The fuzzy value of the population individual is obtained through this function, and this value is used as the comprehensive decision-making value of the individual:

[0039]

[0040] Furthermore, the comprehensive decision-making value matrix of the population solution is obtained:

[0041]

[0042] In a preferred embodiment: In step S3, specifically: Determine the intelligent optimization algorithm and combine the above decision-making method to solve the optimal solution of the multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon, and output the scheduling result;

[0043] Step S31: Design a four-layer coding based on processes, factories, machines, and transport vehicles;

[0044] Step S32: Determine the specific intelligent optimization algorithm;

[0045] Step S33: Solve a multi-objective distributed flexible job shop scheduling problem considering limited transportation resources and low carbon through the combined algorithm, and output the scheduling result.

[0046] In a preferred embodiment: Step S31 is specifically as follows; the encoding method adopts four-layer integer encoding, that is, the encoding of each individual is a matrix composed of the processing sequence of the processes of each workpiece, the factories and machines selected for the processes of each workpiece, and the transport vehicles selected for the adjacent processes of each workpiece. The number of encoding columns is the total number of processes of all workpieces, and the number of encoding rows is four rows, that is, 4×ns, where n is the number of all workpieces to be processed, and s is the total number of processes of the workpieces to be processed. The first layer of the encoding is the process layer, the second layer is the factory layer, the third layer is the machine layer, and the fourth layer is the transport vehicle layer; the decoding process is to define the mapping relationship between integers and processes, convert the individual vector that has been expressed in real numbers obtained by the intelligent optimization algorithm, and convert the real number vector of the individual into an integer vector through the LOV rule, and then replace it with the corresponding process, and the processing processes of each workpiece in the first layer can be obtained. According to the first layer, the factory selection for the processing processes of each workpiece in the second layer is generated, and then according to the first layer and the second layer, the machine selection for the processing processes of each workpiece in the third layer is generated. Finally, according to the first layer, the second layer and the third layer, the transport vehicle selection for the adjacent processes of each workpiece in the fourth layer is generated.

[0047] In a preferred embodiment: Step S32 is specifically as follows: Taking the optimal foraging algorithm OFA as an example of the determined intelligent optimization algorithm, the description is as follows;

[0048] The principle of the optimal foraging algorithm is as follows:

[0049] Step S321: Initialize the algorithm parameters and the population: The population size is N, the initial iteration number t = 1, and the maximum iteration number is T max ; The population P with N individuals is initialized in the following way. The i-th individual in the population P where d is the dimension of the vector in each individual, i = 1…N, j = 1…d; is the upper boundary of the vector, is the lower boundary of the vector;

[0050]

[0051] Step S322: Fitness value evaluation: Calculate the fitness value of each individual in the initial population P According to the fitness value of, and the corresponding individual are arranged in descending order; from the sorting result

[0052] the optimal fitness value and the worst fitness value and the corresponding individuals and

[0053] Step S323: Iteratively update the population: Select individuals from the sorting result as target individuals in sequence and randomly select another individual with better quality as the recruited individual The individual position update method is as follows:

[0054]

[0055] where r 1ij , r 2ij are random numbers that are uniformly distributed and independent within the interval [0, 1], and k =

[0056] t / T max is the iteration coefficient;

[0057] Step S324: Calculate the fitness values of the individuals in the new population and select individuals preferentially: Calculate the fitness values of all target individuals after update According to the following method, compare the individuals at the original position with the updated individuals and select the better individuals from them; if the following formula holds, then If it does not hold, then

[0058]

[0059] Step S325: Sort in descending order and save the optimal individual: According to the magnitude of the fitness value of, and the corresponding individuals are sorted in descending order; Select the optimal fitness value from the sorting and compare it with If

[0060] Step S326: Iteratively update. If the termination condition is satisfied, output the optimal result: When the algorithm calculates to the maximum number of iterations T max , terminate the iteration process and output the optimal individual and the optimal fitness value

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1. The present invention considers the combination of the manufacturing mode of distributed factories and flexible job shops, and at the same time considers the limited transportation resources in workshop production. With the minimum makespan, total energy consumption, and total processing quality as the optimization objectives, it can quickly and effectively obtain a better scheduling plan and improve production efficiency;

[0063] ​2. The present invention combines spherical fuzzy sets and voting theory as a method for multi-objective decision-making, and combines it with intelligent optimization algorithms, which can be used to solve the job shop scheduling problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a flowchart of a preferred embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0065] The present invention will be further described below with reference to the drawings and embodiments.

[0066] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0067] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0068] As Figure 1 shown, this embodiment provides a multi-objective distributed flexible job shop scheduling optimization method considering limited transportation resources and low carbon, which specifically includes the following steps:

[0069] Step S1: Construct a multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon, including symbolic definitions, constraint conditions, and optimization objective definitions of the makespan, total processing energy consumption, and total processing quality;

[0070] Step S2: Design a multi-objective comprehensive decision-making method based on the combination of spherical fuzzy sets and voting theory;

[0071] Step S3: Determine an intelligent optimization algorithm and combine the above decision-making method to solve the optimal solution of the multi-objective distributed flexible job shop scheduling model considering limited transportation resources and low carbon, and output the scheduling result;

[0072] In this embodiment, step S1 is specifically: constructing a multi-objective distributed flexible job shop scheduling model considering limited transportation resources and low carbon, including symbolic definitions, constraint conditions, and optimization objective definitions of the makespan, total processing energy consumption, and total processing quality;

[0073] Symbolic definitions:

[0074] Let \(f\) be the factory number, \(f\in F_c=\{1,2,\ldots,g_c\}\), where \(g_c\) is the number of factories; \(i_c\) is the workpiece number, \(i_c\in I_c = \{1,2,\ldots,n\}\), and \(n\) is the number of workpieces; \(j_c\) is the operation number, \(j_c\in J_c=\{1,2,\ldots,s\}\), and \(s\) is the number of operations of workpiece \(i_c\); \(m\ f is the number of machines in factory \(f\), \((k, l)\in\{1,2,\ldots,m\ f \}, where \(k\) and \(l\) are machine indices; \(t_{rc}\ f is the number of transport vehicles in factory \(f\), \((a_c,b_c)\in\{1,2,\ldots,t_{rc}\ f}\), where \(a_c\) and \(b_c\) are transport vehicle indices; is the \(a_c\)-th transport vehicle in factory \(f\); \(O\ ic,jc is the index of the \(j_c\)-th operation of workpiece \(i_c\); is the \(k\)-th machine in factory \(f\); is the operation \(O\ ic,jc on the machine processing time; is the operation \(O\ ic,jc-1 to \(O\ ic,jc transportation time on the transport vehicle ; \(S\ ic,jc is the start processing time of operation \(O\ ic,jc ; \(C\ ic,jc is the completion processing time of operation \(O\ ic,jc ; \(C\ ic is the completion processing time of workpiece \(i_c\); is a decision variable, which is 1 if the \(j_c\)-th operation of workpiece \(i_c\) is processed on the machine and 0 otherwise; is a decision variable, which is 1 if workpiece \(i_c\) is assigned to factory \(f\) for processing and 0 otherwise; is a decision variable, which is 1 if the process of transferring the \((j_c - 1)\)-th operation of workpiece \(i_c\) to the \(j_c\)-th operation is transported on the transport vehicle and 0 otherwise;

[0075] Constraint conditions:

[0076] Processing start time constraint: Completion time constraint: \(C\ ic =C\ ic,s ; Machine processing constraint: Workpiece processing constraint: Transportation process constraint: Factory constraint:

[0077] Optimization objective:

[0078] Makespan \(f_1\): \(f_1=\max\{C\ ic∣i_c = 1, 2, …, n};

[0079] Total processing energy consumption f2:

[0080] For the th machine of the processing process j_c; When the workpiece is transported from process j_c - 1 to process j_c, the transport vehicle transport power;

[0081] Total processing quality f3: Where is the processing quality of the workpiece i_c in the process j_c on the machine ;

[0082] In this example, step S2 is specifically: designing a multi - objective comprehensive decision - making method based on the combination of spherical fuzzy sets and voting theory;

[0083] Step S21: The intelligent optimization algorithm generates a population containing a certain number of individuals (also called solutions), calculates the objective function values of all individuals in the population, and constructs the positive and negative ideal solution sets of the objective function according to the objective function values respectively;

[0084] Step S22: Introduce the spherical fuzzy set transformation formula as the objective function value mapping formula;

[0085] Step S23: Construct the upper and lower boundaries of the objective function of each objective according to the positive and negative ideal solution sets;

[0086] Step S24: Convert the upper and lower boundaries of the objective function into the upper and lower boundaries of the spherical fuzzy set;

[0087] Step S25: Substitute the objective function values of all individuals in the population into the mapping formula formed by the above steps to obtain the spherical fuzzy sets of all individuals in the population;

[0088] Step S26: Introduce voting theory, convert the spherical fuzzy set of the objective function value of the individual into a passing value, and use it as the comprehensive decision - making value;

[0089] In this example, step S21 is specifically; find the objective function values of all individuals (also called solutions) in the population generated by the intelligent optimization algorithm, and construct the positive and negative ideal solution sets of the objective function according to the objective function values respectively:

[0090] According to the three objective functions f1, f2, and f3, that is, M = 3;

[0091] The matrix of the function values of the above - mentioned objectives generated by the population after being normalized by the minimum value:

[0092]

[0093] Where M is the number of objectives and N is the population size; i = 1...N; o = 1...M; represents the value after normalizing the function value of the o-th objective function of the i-th individual;

[0094] The positive ideal solution set is obtained by forming the maximum value of each column of the pop matrix as The negative ideal solution set is obtained by forming the minimum value of each column of the pop matrix as Where is the maximum value after normalizing the function value of the o-th objective function in the population, is the minimum value after normalizing the function value of the o-th objective function in the population;

[0095] In this example, step S22 is specifically: introducing spherical fuzzy set transformation as the objective function value mapping formula;

[0096] The spherical fuzzy set on the universe of discourse space Y is;

[0097]

[0098] Where represent membership degree, neutral degree, and non-membership degree respectively. respectively represent the membership degree, neutral degree, and non-membership degree of each element y (y ∈ Y) in And satisfy:

[0099]

[0100] The spherical fuzzy set transformation formula for objective o is as follows:

[0101]

[0102] In the formula represents the value after normalizing the function value of the o-th objective of the i-th individual, are respectively the membership degree, neutral degree, and non-membership degree of the spherical fuzzy set ; is the spherical fuzzy set of the function value of the o-th objective of the i-th individual. and are the upper and lower bounds of the membership degree of objective o, and are the upper and lower bounds of the neutral degree of objective o, and are the upper and lower bounds of the non-membership degree of objective o.

[0103] In this example, step S23 is specifically as follows: construct the upper and lower bounds of the objective function values of each objective according to the positive and negative ideal solution sets;

[0104] The positive ideal solution set is The negative ideal solution set is

[0105]

[0106] Gg o It is indicated that the upper bound of objective o is The lower bound is Ggpop represents the boundary set of all objectives;

[0107] In this example, step S24 is specifically as follows: convert the upper and lower bounds of the objective function into the upper and lower bounds of the spherical fuzzy set;

[0108] The upper and lower bounds of the spherical fuzzy set of objective o are defined as follows:

[0109] The upper bound of the membership degree is The lower bound is

[0110] The upper bound of the neutrality degree is The lower bound is

[0111] The upper bound of the non - membership degree is The lower bound is

[0112]

[0113] Where is the upper bound of objective o, is the lower bound of objective o, gpop o represents the spherical fuzzy set boundary of objective o, q o ∈(0,1) and p o ∈(0,1) are coefficients pre - assigned by the decision - maker;

[0114] In this example, step S25 is specifically as follows: substitute the objective function values of all individuals in the population into the mapping formula formed by the above steps, and the spherical fuzzy sets of all individuals in the population can be obtained;

[0115] The specific method is: select objective o, and select the Gg of this objective from Ggpop o to obtain the upper and lower bounds and Substitute them into the spherical fuzzy set boundary formula to obtain the boundary gpop of the spherical fuzzy set of this objective o, substitute the function value of the \(o\)-th objective of individual \(i\) in the population into the spherical fuzzy set conversion formula of objective \(o\), and the spherical fuzzy set of the function value of the \(o\)-th objective of individual \(i\) can be calculated. Repeating the above process can obtain the spherical fuzzy sets of all objective functions in the population.

[0116]

[0117] where \(M\) is the number of objectives and \(N\) is the number of individuals in the population; represents the spherical fuzzy set of the function value of the \(o\)-th objective of the \(i\)-th individual.

[0118] In this example, step S26 is specifically: introducing voting theory, converting the spherical fuzzy set of the objective function of an individual into a passing value, and using it as the comprehensive decision-making value;

[0119] Since the spherical fuzzy sets obtained by the above method cannot be directly used, voting theory is introduced as a method to identify the fuzzy information of spherical fuzzy sets.

[0120] Definition of voting theory: A collective action, according to the choices of voters, uses the action with the most approvals as the selected result. The implementation method is as follows:

[0121]

[0122] where \(tu\) is the passing value, \(a\) is the number of approval votes, \(c\) is the number of opposition votes, and \(b\) is the number of abstention votes.

[0123] Map the membership degree, neutral degree, and non-membership degree of the spherical fuzzy set to the approval vote, abstention vote, and opposition vote of voting theory, and let The following formula is obtained:

[0124]

[0125] where is the spherical fuzzy set of the function value of the \(o\)-th objective of the \(i\)-th individual of the passing value.

[0126] Thus, the formula for the multi-objective decision-making method based on spherical fuzzy sets and voting theory is constructed: The specific method is to take the spherical fuzzy sets of all objective function values of individual \(i\) Convert it into a passing value The comprehensive decision-making value is obtained through the following formula.

[0127]

[0128] where \(t = 1,\cdots,T\) max , \(o = 1,\cdots,M\);

[0129] Furthermore, the comprehensive decision-making value matrix of all solutions in the population is obtained:

[0130]

[0131] In this example, step S3 is specifically as follows: Determine the intelligent optimization algorithm and solve the optimal solution of the multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon in combination with the above method, and output the scheduling result;

[0132] Step S31: Four-layer coding based on processes, factories, machines, and transport vehicles;

[0133] Step S32: Determine the specific intelligent optimization algorithm;

[0134] Step S33: Solve the multi-objective distributed flexible job shop scheduling problem considering limited transportation resources and low carbon in combination with the intelligent optimization algorithm;

[0135] In this example, step S31 is specifically as follows: Four-layer coding based on processes, factories, machines, and transport vehicles;

[0136] The coding method adopts four-layer integer coding, that is, the coding of each individual is a matrix composed of the processing sequence of the processes of each workpiece, the factories and machines selected by the processes of each workpiece, and the transport vehicles selected by the adjacent processes of each workpiece. The number of coding columns is the total number of processes of all workpieces, and the number of coding rows is four rows, that is, 4×ns, where n is the number of all workpieces to be processed, and s is the total number of processes of the workpieces to be processed. The first layer of the coding is the process layer, the second layer is the factory layer, the third layer is the machine layer, and the fourth layer is the transport vehicle layer; The decoding process is to define the mapping relationship between integers and processes, convert the individual vector expressed in real numbers obtained by the intelligent optimization algorithm, and convert the real vector of the individual into an integer vector through the LOV rule, and then replace it with the corresponding process, so as to obtain the processing processes of each workpiece in the first layer. Generate the factory selection of the processing processes of each workpiece in the second layer according to the first layer, then generate the machine selection of the processing processes of each workpiece in the third layer according to the first layer and the second layer, and finally generate the transport vehicle selection of the adjacent processes of each workpiece in the fourth layer according to the first layer, the second layer, and the third layer;

[0137] The mapping relationship between integers and processes is specifically as follows:

[0138] The integers start from the number 1 and go in ascending order to the total number of processes, and the corresponding processes start from the first process of the first workpiece and traverse in numerical order to the last process of the last workpiece;

[0139] Suppose there are two workpieces, each workpiece has three processes, and the total number of processes is 6. Define the process relationship corresponding to the numbers 1 to 6:

[0140]

[0141] Among them, 101 represents the first process of the first workpiece, 102 represents the second process of the first workpiece, and so on.

[0142] The real number vector generated by the intelligent optimization algorithm is: 0.1 0.2 0.5 0.6 0.3 0.4

[0144] The LOV rule is specifically as follows: Sort the real number vector from smallest to largest to obtain the mapping relationship between the real number and its sorting position. For example, the position of 0.1 in the entire real number vector is 1, and the position of 0.6 in the entire real number vector is 6;

[0145]

[0146] Through the LOV rule, the above real number vector can be converted into an integer vector: 1 2 5 6 3 4

[0148] Replace the integer vector with the process sequence: 101 101 202 203 103 201

[0150] In this example, step S32 has: determining a specific intelligent optimization algorithm;

[0151] Taking the Optimal Foraging Algorithm (OFA) as the determined intelligent optimization algorithm as an example for illustration. OFA is a population-based optimization technique. During the process of the optimal individual in the current population guiding the evolution of other individuals, it randomly explores the entire search space to achieve overall evolution.

[0152] The principle of the best foraging algorithm is as follows:

[0153] Step S321: Initialize the algorithm parameters and the population: The population size is N, the initial iteration number t = 1, and the maximum iteration number is T max . Use the following method: Initialize the population P with N individuals. The i-th individual in the population P where d is the dimension of the vector in each individual, i = 1, 2,... N, j = 1, 2,... d; is the upper boundary of the vector, is the lower boundary of the vector;

[0154]

[0155] Step S322: Fitness value evaluation: Calculate the fitness value of each individual in the initial population P According to the fitness value According to the size of and the corresponding individuals sort them in descending order. From the sorting result select the optimal fitness value and the worst fitness value as well as the corresponding individuals and

[0156] Step S323: Iteratively update the population: Select individuals from the sorting result as target individuals in sequence and randomly select another individual with better quality as the recruited individual The individual position update method is as follows:

[0157]

[0158] where r 1ij , r 2ij are random numbers that follow a uniform distribution and are independent within the interval [0, 1], and k = t / T max is the iteration coefficient;

[0159] Step S324: Calculate the fitness values of the individuals in the new population and select the individuals with better performance: Calculate the fitness values of all the updated target individuals According to the following method, compare the individuals at the original positions with the updated individuals and select the individuals with better performance from them. If the following formula holds, then If it does not hold, then

[0160]

[0161] Step S325: Sort in descending order and save the optimal individual: According to the size of the fitness value sort and the corresponding individuals in descending order. Select the optimal fitness value from the sorting and compare it with . If

[0162] Step S326: Iteratively update. If the termination condition is met, output the optimal result: When the algorithm calculates to the maximum number of iterations T max , terminate the iterative process and output the optimal individual and the optimal fitness value

[0163] In this example, step S33 specifically includes: solving the multi-objective distributed flexible job shop scheduling problem considering limited transportation resources and low carbon by combining intelligent optimization algorithms, and outputting a scheduling plan;

[0164] Introduce the comprehensive decision value of the individual obtained by the above method into the best foraging algorithm, and use this comprehensive decision value as the fitness value of the best foraging algorithm:

[0165]

[0166] The optimal one is obtained by the algorithm Decode the encoding of this individual to obtain the optimal scheduling plan, and present it in the form of a Gantt chart for users to use.

Claims

1. A method for scheduling a finite transportation resource and multi-objective distributed flexible job shop, characterized in that It includes the following steps: Step S1: Construct a multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon, including symbolic definitions, constraint conditions, and the definition of optimization objectives such as makespan, total processing energy consumption, and total processing quality; Step S2: Design a multi-objective comprehensive decision-making method based on the combination of spherical fuzzy sets and voting theory; Step S3: Determine the swarm intelligence optimization algorithm and solve the optimal solution of a multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon by combining the above decision-making method, and output the scheduling result; Step S2 specifically includes the following steps: Step S21: The intelligent optimization algorithm generates a population containing a certain number of individuals, calculates the objective function values of all individuals in the population, and constructs the positive and negative ideal solution sets of the objective function according to the objective function values respectively; Step S22: Introduce the spherical fuzzy set transformation formula as the objective function value mapping formula; Step S23: Construct the upper and lower bounds of each objective function according to the positive and negative ideal solution sets; Step S24: Convert the upper and lower bounds of the objective function into the upper and lower bounds of the spherical fuzzy set; Step S25: Substitute the objective function values of all individuals in the population into the mapping formula formed by the above steps to obtain the spherical fuzzy sets of all individuals in the population; Step S26: Introduce voting theory, convert the spherical fuzzy set of the objective function value of an individual into a passing value, and use it as the comprehensive decision-making value; In Step S22, specifically: Introduce the spherical fuzzy set transformation formula as the objective function mapping formula; Spherical fuzzy sets on the universe of discourse space Y is; wherein respectively represent the membership degree, the neutrality degree, and the non-membership degree; respectively represented as for each element y, y ∈ Y, on the membership degree, the neutrality degree, and the non-membership degree; and satisfy: The spherical fuzzy set transformation formula of objective o is as follows: where represents the value after normalization of the function value of the $o$-th objective of the $i$-th individual, are respectively spherical fuzzy sets Membership degree, neutral degree, non - membership degree; The spherical fuzzy set of the function value of the o - th objective of the i - th individual; and are the upper and lower bounds of the membership degree of objective o, and are the upper and lower bounds of the neutral degree of objective o, and are the upper and lower bounds of the non - membership degree of objective o; In Step S24, specifically: Convert the upper and lower bounds of the objective function into the upper and lower bounds of the spherical fuzzy set; The definition of the upper and lower bounds of the spherical fuzzy set of objective o is as follows: The upper boundary of the membership degree is The lower boundary is The upper boundary of the neutrality degree is The lower boundary is The upper boundary of the non-membership degree is The lower boundary is Among them is the upper boundary of target o, is the lower boundary of target o, gpop o represents the spherical fuzzy set boundary of target o, q o ∈(0,1) and p o ∈(0,1) are coefficients pre-assigned by the decision maker; Step S26, specifically: Introduce voting theory, convert the spherical fuzzy set of the objective function value of an individual into a passing value, and use it as the comprehensive decision-making value; Definition of voting theory: A collective action method that selects the action with the most approvals as the result according to the choices of voters; The implementation method is as follows: Where tu is the passing value, a is the number of approval votes, c is the number of opposition votes, and b is the number of abstention votes; Map the membership degree, neutral degree, and non-membership degree of the spherical fuzzy set to the affirmative votes, abstention votes, and negative votes in voting theory, and let The following formula is obtained: wherein is the spherical fuzzy set of the function value of the o-th target of the i-th individual pass value; Obtain the fuzzy value of the population individual through this function, and use this value as the comprehensive decision-making value of the individual: Furthermore, obtain the comprehensive decision-making value matrix of the population solution:

2. The method for considering limited transportation resources and multi-objective distributed flexible job shop scheduling according to claim 1, characterized in that: In Step S3, specifically: Determine the intelligent optimization algorithm and solve the optimal solution of a multi-objective distributed flexible job shop scheduling problem model considering limited transportation resources and low carbon by combining the above decision-making method, and output the scheduling result; Step S31: Design a four-layer coding based on processes, factories, machines, and transport vehicles; Step S32: Determine the specific intelligent optimization algorithm; Step S33: Solve a multi-objective distributed flexible job shop scheduling problem considering limited transportation resources and low carbon through the combined algorithm, and output the scheduling result.

3. The method for considering limited transportation resources and multi-objective distributed flexible job shop scheduling according to claim 2, characterized in that: Step S31 is specifically as follows: The encoding method adopts four-layer integer encoding, that is, the encoding of each individual is a matrix composed of the processing sequence of the processes of each workpiece, the factories and machines selected for the processes of each workpiece, and the transport vehicles selected for the adjacent processes of each workpiece. The number of encoding columns is the total number of processes of all workpieces, and the number of encoding rows is four rows, that is, 4×ns, where n is the number of all workpieces to be processed, and s is the total number of processes of the workpieces to be processed. The first layer of the encoding is the process layer, the second layer is the factory layer, the third layer is the machine layer, and the fourth layer is the transport vehicle layer; The decoding process is as follows: Define the mapping relationship between integers and processes, convert the individual vector expressed in real numbers obtained by the intelligent optimization algorithm, and convert the real vector of the individual into an integer vector through the LOV rule, and then replace it with the corresponding process, so as to obtain the processing processes of each workpiece in the first layer. Generate the factory selection of the processing processes of each workpiece in the second layer according to the first layer, then generate the machine selection of the processing processes of each workpiece in the third layer according to the first layer and the second layer, and finally generate the selection of the transport vehicle for the adjacent processes of each workpiece in the fourth layer according to the first layer, the second layer and the third layer.

4. The method for considering limited transportation resources and multi-objective distributed flexible job shop scheduling according to claim 2, wherein: Step S32 is specifically as follows: Taking the optimal foraging algorithm OFA as an example of the determined intelligent optimization algorithm, the description is as follows; The principle of the optimal foraging algorithm is as follows: Step S321: Initialize the algorithm parameters and the population: The population size is N, the initial iteration number t = 1, and the maximum iteration number is T max ; Initialize the population P with N individuals in the following way. The i-th individual in the population P where d is the dimension of the vector in each individual, i = 1...N, j = 1...d; is the upper boundary of the vector, is the lower boundary of the vector; Step S322: Fitness value evaluation: Calculate the fitness value of each individual in the initial population P ; According to the size of the fitness value , sort and the corresponding individuals in descending order; Select the optimal fitness value and the worst fitness value as well as the corresponding individuals and and Step S323: Iteratively update the population: Select individuals from the sorting result as target individuals in sequence And randomly select another individual with better quality as the recruited individual The individual position update method is as follows: where r 1ij , r 2ij are independent random numbers uniformly distributed in the interval [0, 1], and k = t / T max is the iteration coefficient; Step S324: Calculate the fitness values of the individuals in the new population and select the superior individuals: Calculate the fitness values of all the target individuals after update of the fitness values According to the following method, compare the individuals at the original positions with the updated individuals and select the superior individuals therefrom; if the following formula holds, then if it does not hold, then Step S325: Save the optimal individual in descending order: According to the fitness value , sort and the corresponding individual in descending order; Select the optimal fitness value from the sorting and compare it with . If Step S326: Iterative update. If the termination condition is met, output the optimal result: When the algorithm calculates to the maximum number of iterations T max the iterative process is terminated, and the optimal individual is output and the optimal fitness value

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