A flexible job shop scheduling optimization method, system, device and medium

Abstract

The application discloses a flexible job shop scheduling optimization method, system, device and medium, and relates to the technical field of shop scheduling. The method comprises the following steps: constructing a flexible job shop scheduling mathematical model according to a flexible job processing time problem model and constraint conditions thereof; determining initial particle groups of a particle swarm algorithm for to-be-processed workpiece processes, and taking minimum processing time as a target function; taking a comprehensive prospect-regret value as an adaptability evaluation value of a particle in the particle swarm algorithm; adjusting an inertia weight by using an inertia weight power function and introducing a random number of chaotic behavior; generating a plurality of cloud droplets according to a one-dimensional normal cloud model, that is, a group of potential scheduling schemes near a current optimal solution; selecting a cloud droplet optimal value by setting a threshold value, comparing the cloud droplet optimal value with the current optimal solution, and performing more detailed search on a neighborhood of the current optimal solution to find a better solution that may exist, so that the method is more in line with complex decision-making conditions in actual production scheduling, and is helpful to find a better scheduling scheme.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of job shop scheduling, in particular to a flexible job shop scheduling optimization method, system, device and medium. BACKGROUND

[0002] Flexible job shop scheduling problem (FJSP) is one of the most important problems in production and manufacturing, and the processing time in FJSP is the key, which has been widely concerned in the fields of automobile, electronic processing and small batch production.

[0003] In recent years, although many scholars have proposed various types of meta-heuristic algorithms, particle swarm optimization (PSO) is still one of the research hotspots due to its simple structure parameters and strong global search ability, but PSO still has the disadvantages of weak local search ability and easy to fall into local optimum,

[0004] However, in the research of flexible job shop scheduling problem, the solving process of the standard PSO algorithm has the following problems: due to the complexity of FJSP problem, the solution space of FJSP increases exponentially with the number of workpieces, the number of processes and the number of optional machines. The standard PSO searches through group iteration, and when the solution space exceeds a certain scale, the particles need a large number of iterations to approach the optimal region, resulting in slow convergence of the standard PSO algorithm; the machine allocation or sequence of the bottleneck machine process on the critical path may cause a large fluctuation in the completion time, and the particle update of the standard PSO depends on the random weight and the individual historical optimum, which may cause a significant difference in the solution quality of adjacent iterations due to randomness, resulting in poor optimization stability; if there are different machine allocation combinations in the solution space of FJSP, it may lead to similar completion time, resulting in multiple local optima, which may cause the particles of the standard PSO to quickly gather in a local optimal region, resulting in loss of group diversity and falling into local optimum, thereby making it difficult to adapt to the complexity and dynamics of flexible job shop scheduling problem. SUMMARY

[0005] In view of the above problems, the present application provides a flexible job shop scheduling optimization method, system, device and medium, which greatly improves the problems existing in the prior art.

[0006] A flexible job shop scheduling optimization method, comprising the following steps:

[0007] According to the flexible job processing time problem model and constraint conditions, a flexible job shop scheduling mathematical model is constructed with the minimum processing time as an objective function;

[0008] The improved particle swarm algorithm is used to solve the flexible job shop scheduling mathematical model; the workpiece processes to be processed are taken as initial particles of the particle swarm algorithm, and the solving process specifically includes:

[0009] The initial particle position and initial particle velocity are set, wherein the initial particle position represents an initial scheduling scheme of the workpiece processing sequence and processing resource, and the particle velocity represents an adjustment scheme of the workpiece processing sequence and processing resource allocation; the comprehensive prospect-regret value is determined according to the prospect theory for measuring the deviation degree of the manufacturing efficiency index and the regret theory for reflecting the decision maker's aversion behavior to regret; the comprehensive prospect-regret value is taken as the fitness value of the particle swarm algorithm; the comprehensive prospect-regret value is determined according to the prospect theory for measuring the deviation degree of the manufacturing efficiency index and the regret theory for reflecting the decision maker's aversion behavior to regret, and specifically includes the following steps: the distance between two interval numbers is calculated for any two intervals; the value function and the decision weight are determined according to the distance; the prospect value function is calculated according to the value function and the decision weight; the prospect value function includes positive prospect value and negative prospect value; the regret value and the joy value are calculated by substituting the positive prospect value and the negative prospect value of each decision into the Hamming distance formula; the comprehensive prospect-regret theory evaluation function formula is established according to the regret value and the joy value; the comprehensive prospect-regret value is determined according to the comprehensive prospect-regret theory evaluation function formula;

[0010] The particle position and particle velocity are iteratively updated according to the inertia weight adjusted by the inertia weight power function and the random number introducing chaos behavior, the fitness value of the particle at each iteration is calculated, and the current optimal solution is selected; the current optimal solution is taken as the center to start searching in the distribution space, a plurality of cloud droplets are generated according to the one-dimensional normal cloud model, the cloud droplet optimal value is selected by setting a threshold, and the cloud droplet optimal value is compared with the current optimal solution; if the cloud droplet optimal value is greater than the current optimal solution, the iterative updating is continued, and until the cloud droplet optimal value is not greater than the current optimal solution, the optimal scheduling scheme is output;

[0011] According to the optimal scheduling scheme, the processing sequence of each workpiece, the allocated processing equipment and the start and end time of each process are generated, and the flexible job shop scheduling strategy is optimized.

[0012] Further, the flexible job processing time problem model specifically includes: the set of workpieces to be processed is J={J1, J2, …, J n}, and the set of machines that can be used in the workshop is M={M1, M2, … M m}, where the maximum number of workpieces is n, and the maximum number of available machines is m; each workpiece has different machining processes and a fixed machining order, and the process set of each workpiece is: p={p i |p1,p2,…,p n}, i=1,2,…,n; where p represents all processes of the workpiece numbered i, and p ij represents the jth process of the workpiece numbered i; the machining start time, machining end time and machining duration of the jth process of workpiece i on the kth machine are represented as S ijk , F ijk , C ijk , respectively, where k=1,2,…,m; the actual running time of the kth machine is represented as T k ; and the final end time of all processes of all workpieces is represented as F max .

[0013] Further, the constraint conditions of the flexible job machining time problem model specifically include:

[0014] Process order constraint: the processes of all workpieces must be completed in a specific order:

[0015] F ijk -F i(j-1)k ≥C ijk ;

[0016] F ijk -S ijk >0;

[0017] Machine non-repeated occupation constraint: if processes (i,j) and (a,b) are machined on the same machine k, and (i,j) is after (a,b):

[0018] S ijk ≥F abk ;

[0019] Machining time constraint:

[0020] F ijk =S ijk +C ijk .

[0021] Further, the random number introducing chaotic behavior is used to iteratively update the particle position and particle velocity according to the inertia weight adjusted by the inertia weight power function, specifically including the following steps:

[0022] The inertia weight w(t) adjusted by the inertia weight power function is represented as:

[0023] w(t)=(w max +w min ) / 2+exp(-λ×t / tmax) x (w max - w min ) / 2;

[0024] wherein w max is the maximum value of the inertia weight, w min is the minimum value of the inertia weight, t max is the maximum number of iterations, t is the current iteration number; λ = 5 is the convergence adjustment coefficient;

[0025] The random number introducing chaos behavior is expressed as:

[0026] r2 = z A+1 = u x (7.86 x z A - 23.3 x z A 2 + 28.75 x z A 3 - 13.3 x z A 4 ) ;

[0027] wherein r2 is a random number uniformly distributed in the range of (0, 1), u is a parameter between 0.9 and 1.08; z A is the value of the chaotic variable in the A-th iteration, and z A+1 is the value of the chaotic variable in the A+1-th iteration;

[0028] According to the inertia weight adjusted by the power function of the inertia weight and the random number introducing chaos behavior, the particle position and particle velocity updated by iteration are obtained, and are expressed as:

[0029] v qs t+1 = w (t) x v qs t + c1 x r1 x (p qs t - x qs t ) + c2 x r2 x (p gs t - x qs t ) ;

[0030] x qs t+1 = x qs t + v qs t+1 ;

[0031] Where c1 and c2 are the individual learning factor and the group learning factor, respectively; r1 is a uniformly distributed random number in the range (0,1); w(t) is the inertia weight factor; q=1,2,…,N represents the number of particles in the swarm; s is the dimension index; t is the current iteration number; x qs t and x qs t+1 Let v represent the positions of particle q in the s-th dimension at the t-th and t+1-th iterations, respectively. qs t and v qs t+1 Let p represent the velocity of particle q in the s-th dimension at the t-th and t+1-th iterations, respectively. qs t p represents the individual historical optimal position of particle q in dimension s at the t-th iteration. gs t This represents the optimal position of all particles in the s-th dimension at the t-th iteration.

[0032] Furthermore, the generation process of the multiple cloud droplets generated based on the one-dimensional normal cloud model specifically includes the following steps:

[0033] According to the normal distribution N(E) n H e 2 Generate a random number E related to entropy. n ';

[0034] According to the normal distribution N(E) x , (E n ') 2 Generate random cloud droplet positions x i ; where the expected value E x Entropy E n and hyperentropy H e These are all eigenvalues ​​of a normal cloud model;

[0035] Calculate x i Uncertainty y i ,get:

[0036] y i =exp(-(x i -E x ) 2 / (2×E n '));

[0037] According to x i and y i , will (x i ,y i As a cloud droplet within the distribution space;

[0038] The calculation is repeated multiple times until the number of cloud droplets that generate a number of particles matches the number of iterations of the particle swarm algorithm is generated.

[0039] Furthermore, the particle update of the one-dimensional normal cloud model specifically includes: assuming the particle swarm algorithm has undergone the [number]th [process]... The current optimal solution in the next iteration is g. best The worst solution at present is g worst According to the one-dimensional normal cloud model C(E) x E n H e The cloud model particle update formula is obtained as follows:

[0040] E x =g best E n =-(g best -g worst )×(t / t max ) 2 +g best H e =E n / 10.

[0041] The present invention also includes a flexible job shop scheduling optimization system, comprising:

[0042] The objective function construction module is used to construct a mathematical model for flexible operation workshop scheduling based on the flexible operation processing time problem model and its constraints, with the minimum processing time as the objective function;

[0043] The solving module is used for solving the flexible job shop scheduling mathematical model by using the improved particle swarm algorithm; the process of solving the process of each workpiece is taken as the initial particle swarm of the particle swarm algorithm, and the solving process specifically includes: setting the initial particle position and the initial particle velocity, wherein the initial particle position represents the initial scheduling scheme of the workpiece processing sequence and the processing resource, and the particle velocity represents the adjustment scheme of the workpiece processing sequence and the processing resource allocation; the comprehensive prospect-regret value is determined according to the prospect theory for measuring the deviation degree of the manufacturing efficiency index and the regret theory for reflecting the avoidance behavior of the decision maker to the regret; the comprehensive prospect-regret value is taken as the fitness value of the particle swarm algorithm for updating the particle; the comprehensive prospect-regret value is determined according to the prospect theory for measuring the deviation degree of the manufacturing efficiency index and the regret theory for reflecting the avoidance behavior of the decision maker to the regret, and specifically includes the following steps: the distance between two interval numbers is calculated for any two intervals; the value function and the decision weight are determined according to the distance; the prospect value function is calculated according to the value function and the decision weight; the prospect value function includes the positive prospect value and the negative prospect value; the regret value and the joy value are respectively calculated by substituting the positive prospect value and the negative prospect value of each decision into the Hamming distance formula; the comprehensive prospect-regret theory evaluation function formula is established according to the regret value and the joy value; the comprehensive prospect-regret value is determined according to the comprehensive prospect-regret theory evaluation function formula; the particle position and the particle velocity are iteratively updated according to the inertia weight adjusted by the inertia weight power function and the random number introducing the chaotic behavior, the fitness value of the particle at each iteration is calculated, and the current optimal solution is selected; the current optimal solution is taken as the center to start searching in the distribution space, a plurality of cloud droplets are generated according to the one-dimensional normal cloud model, the cloud droplet optimal value is selected by setting a threshold, and the cloud droplet optimal value is compared with the current optimal solution; if the cloud droplet optimal value is greater than the current optimal solution, the iterative updating is continued, and until the cloud droplet optimal value is not greater than the current optimal solution, the optimal scheduling scheme is output.

[0044] The optimization module is used for generating the processing sequence of each workpiece, the allocated processing equipment and the start and end time of each process according to the optimal scheduling scheme, and further optimizing the flexible job shop scheduling strategy.

[0045] The application also includes a flexible job shop scheduling optimization computer device, which includes a memory, a processor and a computer program stored in the memory, and the processor implements the steps of the flexible job shop scheduling optimization method when executing the computer program.

[0046] The application also includes a readable storage medium, which stores a computer program, and the computer program includes program instructions, and the program instructions are executed by the processor to implement the steps of the flexible job shop scheduling optimization method.

[0047] This invention provides a flexible job shop scheduling optimization method, which has the following beneficial effects:

[0048] This invention uses the evaluation value of the comprehensive prospect-regret theory model as the fitness value, which can more effectively guide the algorithm evolution. This theoretical model considers the psychological factors of decision-makers when facing different decision outcomes, such as risk preference in prospect theory and regret for wrong decisions in regret theory. This allows the algorithm to not only focus on the objective function value during the search process but also comprehensively consider the influence of various factors on the decision, thus better reflecting the complex decision-making situations in actual production scheduling and helping to find better scheduling schemes. Using the minimum processing time as the objective function, it directly optimizes key indicators in flexible workshop scheduling, effectively shortening the production cycle and improving production efficiency. It employs an adaptive adjustment of the inertia weight power function, enabling the algorithm to automatically adjust the inertia weight based on the number of iterations and the particle's search state. In the early stages of the algorithm, a larger inertia weight helps the particle to perform a global search and quickly locate a better search area; in the later stages, a smaller inertia weight is beneficial for the particle to perform a fine-grained local search, improving the accuracy of the solution. This balances the algorithm's global and local search capabilities, accelerates the convergence speed, and improves the solution quality. The algorithm improves upon random numbers by employing chaotic variables. Leveraging the randomness, ergodicity, and regularity of chaotic sequences, particles can traverse the solution space more evenly during the search process, avoiding getting trapped in local optima. This enhances the algorithm's global search capability and increases the probability of finding the global optimum. Based on the fuzzy and random characteristics of the cloud model, a mutation operation is introduced to the particles. When particles get trapped in local optima or the search stalls, the cloud model can mutate them through fuzzy and random methods, enriching particle diversity, increasing the quantity and quality of particles, and further improving the algorithm's global and local search capabilities. This allows the algorithm to better adapt to the complexity and dynamism of flexible job shop scheduling problems. Attached Figure Description

[0049] Figure 1 This is a diagram showing the number of mapping iterations in an embodiment of the present invention;

[0050] Figure 2 This is a flowchart of the improved particle swarm optimization algorithm in an embodiment of the present invention;

[0051] Figure 3 The CCPSO algorithm is used to solve the Gantt chart and evolution curve of the Kacem01 example in this embodiment of the invention; Figure 3 (a) in the diagram is the Gantt chart of the Kacem01 example solved using the CCPSO algorithm. Figure 3 (b) in the figure is the evolution curve of the Kacem01 example solved by the CCPSO algorithm;

[0052] Figure 4(a) is a Gantt chart of CCPSO algorithm solving Kacem02 example, Figure 4 (a) is a Gantt chart of CCPSO algorithm solving Kacem02 example, Figure 4 (b) is an evolution curve of CCPSO algorithm solving Kacem02 example,

[0053] Figure 5 (a) is a Gantt chart of CCPSO algorithm solving Kacem05 example, Figure 5 (a) is a Gantt chart of CCPSO algorithm solving Kacem05 example, Figure 5 (b) is an evolution curve of CCPSO algorithm solving Kacem05 example,

[0054] Figure 6 (a) is a Gantt chart of CCPSO algorithm solving Kacem05 example, Figure 6 (a) is a Gantt chart of CCPSO algorithm solving Kacem05 example, Figure 6 (b) is an evolution curve of CCPSO algorithm solving Kacem05 example. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments of the present application.

[0056] The present application provides a flexible job shop scheduling optimization method, and designs an improved particle swarm algorithm (CCPSO). The algorithm takes processing time as a target function, constructs a processing satisfaction mathematical evaluation model by comprehensively using prospect-regret theory, and calculates a comprehensive prospect-regret theory value as an adaptability evaluation value to guide algorithm evolution. An inertia weight power function is adaptively adjusted, and a random number is balanced by using a chaotic variable to balance the global search ability and the local search ability of the algorithm. According to the characteristics of cloud model fuzziness and randomness, the improved particle swarm algorithm is introduced into the cloud model to perform mutation operation on particles to enrich the number and quality of particles. Experimental results verify the effectiveness of the CCPSO algorithm in reducing flexible job processing time. Specifically, the following steps are included:

[0057] S1, flexible job processing problem definition: known n pieces of workpieces to be processed, m pieces of available machine equipment, each workpiece has n processes to be processed, the processing processes and processing time of each workpiece are known, and the total processing time is the shortest under the constraint condition of flexible job processing time problem.

[0058] The flexible job processing time problem model is described as follows:

[0059] (1) The set of workpieces to be processed is J = {J1, J2, …, Jn}, and the set of machines available for processing in the workshop is M = {M1, M2, …, Mm}, where n is the maximum number of workpieces and m is the maximum number of available machines. n m

[0060] (2) Each workpiece has different processing procedures and a fixed processing order, and the set of procedures is:

[0061] p = {p1, p2, …, pi, …, pn}, i = 1, 2, …, n. i n

[0062] where P i represents all the procedures of workpiece i, and p ij represents the jth procedure of workpiece i.

[0063] (3) S ijk , F ijk , and C ijk represent the processing start time, processing end time, and processing duration of the jth procedure of workpiece i on machine k, respectively, where k = 1, 2, …, m.

[0064] (4) T k represents the actual running time of machine k, and F max represents the final end time of all procedures of all workpieces.

[0065] The optimization goal of flexible job processing time is to reasonably allocate various machines, all workpieces, and all procedures to minimize the final end time F max of all procedures, which is determined by the processing time objective function:

[0066] min F max = min{max T k} (1).

[0067] S2, Flexible Job Processing Time Problem Constraints. During the processing of all procedures, the available machines provide support for any workpiece to be processed. According to the machine processing process and the completion order of each procedure in actual processing, a specific machine can only perform a certain procedure at the same time according to the process flow and process card. After ensuring that the previous procedure is completed, the next processing time can be determined. Therefore, the processing constraints must satisfy the following conditions (2) - (4):

[0068] F ijk - F i(j-1)k ≥ C ijk ​​​​​, F ijk -S ijk >0 (2)

[0069] S ijk ≥F abk (3)

[0070] F ijk =S ijk +C ijk (4)

[0071] Formula (2) represents that all workpieces need to consume time and must be completed in a specific order; formula (3) represents the principle of machine non-repetition occupation, that is, any machine cannot complete multiple processes at the same time; and formula (4) represents the constraint of processing duration.

[0072] Table 1 Flexible job processing time problem parameters and evaluation indexes

[0073]

[0074] S3, comprehensive prospect-regret theory description

[0075] The comprehensive prospect-regret theory not only considers the risk attitude of the decision maker when facing the benefits and losses in the decision-making process, but also considers the regret aversion psychology of the decision maker when making decisions. The comprehensive prospect-regret theory comprehensively considers the decision-making attitudes of the decision maker, such as benefits, losses, and regret aversion, and can better reflect the decision-making behavior of the decision maker.

[0076] S3.1, prospect theory description: The prospect theory takes the limited rationality of the decision maker as the premise and can better describe the psychological behavior characteristics of the decision maker. The prospect theory uses the geometric distance between satisfaction degrees to measure the deviation degree of manufacturing efficiency indexes. This theory not only increases the manufacturing process constraints, making the model construction more close to the actual situation, but also improves the manufacturing speed.

[0077] For any two intervals X ij =[x ij L ,x ij U ] and E j =[E j L ,E j U ], the distance between the two interval numbers is:

[0078] d(X,E)=[(x ij L -E j L ) 2 +(xij U -E j U ) 2 ] (1 / 2) (5)。

[0079] The most important part of the prospect theory is the value function and the decision weight. The value function is:

[0080] υ ij =(d(x ij ,E j )) α ,x ij >E j or υ ij =-γ×(d(x ij ,E j )) β ,x ij <E j (6)

[0081] In formula (6), α, β (0≤α, β≤1) represent risk coefficients, which are proportional to the value of risk; γ>1 represents the risk-averse coefficient, the greater the value, the stronger the decision maker's risk-averse consciousness, and generally α=β=0.85, γ=2.25.

[0082] According to the decision weight formula:

[0083] π + (p j )=p j δ / [p j δ +(1-p j )δ] (1 / δ) (7)

[0084] π - (p j )=p j ψ / [p j ψ +(1-p j )ψ] (1 / ψ) (8)

[0085] Among them, formula (7) represents the gain, and formula (8) represents the loss. Generally, δ=0.61, ψ=0.69.

[0086] The prospect value function is:

[0087] V i + =∑ n i=1 π + (pj )×υ ij (x ij ) (9)

[0088] V i - =∑ n i=1 π - (p j )×υ ij (x ij ) (10)

[0089] where V i + represents the positive prospect value, V i - represents the negative prospect value.

[0090] S3.2, Regret Theory Description: Regret Theory is another decision-making theory based on Prospect Theory. This theory not only focuses on the results of the current decision, but also focuses on the impact of other feasible options, emphasizing the decision maker's aversion to regret, which reduces the degree of regret for the decision maker. Therefore, the decision-making of the decision maker based on Regret Theory is directly related to the decision results and the regret-satisfaction expectation value. The regret-satisfaction expectation value formula of Regret Theory is:

[0091] Z i (x)=∑ m i=1 (G i (x)+R i (x)) (11)

[0092] where Z i (x) is the comprehensive prospect-regret theory, G i (x) is the satisfaction value, and R i (x) is the regret value.

[0093] S3.3, Construction of Comprehensive Prospect-Regret Theory Model:

[0094] Based on the Prospect Theory formula (9) and formula (10), the positive prospect value V i + and the negative prospect value V i - of each decision are calculated, and the maximum positive prospect value V i + (max) and the minimum negative prospect value V i - (min) are determined, V i + (max) and V i - (min) are calculated.The regret value G is calculated by substituting the parameters into the Hamming distance formula. i (x) and the joy value R i (x), the formula is as follows:

[0095] G i (x)=1-exp([-ψ|(V i + (x)-V i - (min)) / (V i + (max)-V i - (min))|]) (12)

[0096] R i (x) = 1 - exp([-ψ|(V) i + (x)-V i + (max)) / (V i + (max)-V i - (min))|]) (13)

[0097] The formula for calculating the overall prospect-regret theory value is:

[0098] Z i (x)=∑ m i=1 (G i (x)+R i (x))=∑ m i=1 {1-exp([-ψ|(V i + (x)-V i - (min)) / (V i + (max)-V i - (min))|])+1-exp([-ψ|(V i + (x)-V i + (max)) / (V i + (max)-V i - (min))|])} (14)。

[0099] S3.4, Application strategy of integrated prospect-regret theory in improved algorithm: according to the integrated prospect-regret theory, the integrated prospect-regret value is calculated, which not only considers the risk attitude of the decision maker when facing gains and losses G i (x), but also measures the regret aversion psychology of the decision maker when making decisions R i (x). The integrated prospect-regret theory value Z i (x) can better reflect the decision-making behavior of the decision maker. The value is used as the fitness value of the improved particle swarm optimization (CCPSO), and the quality of the CCPSO algorithm solution is evaluated according to the size of the fitness value. The quality of the solution is positively correlated with the integrated prospect-regret value, and the evolution process of the algorithm is guided by the integrated prospect-regret value.

[0100] S4, Improved particle swarm optimization algorithm.

[0101] S4.1, Standard particle swarm optimization algorithm: particle swarm optimization (PSO) is a typical swarm intelligence optimization algorithm. The algorithm is widely used in many fields because of its simple programming, few parameters, and low time complexity. The position and velocity state attributes of the standard particle swarm optimization algorithm are formula (15) and formula (16):

[0102] v qs t+1 =w(t)×v qs t +c1×r1×(p qs t -x qs t )+c2×r2×(p gs t -x qs t ) (15)

[0103] x qs t+1 =x qs t +v qs t+1 (16)

[0104] wherein c1 and c2 are respectively referred to as individual learning factor and group learning factor, and usually c1=c2=2; r1 and r2 are random numbers uniformly distributed in the range of (0, 1); w(t) is an inertia weight factor, which directly determines the convergence speed; q=1,2,…,N represents the number of particle groups; s is the dimension index, representing the problem dimension, s=1,2,…,S; t is the current iteration number; x qs trepresents the position of particle q in the s-th dimension at the t-th iteration; v qs t represents the velocity of particle q in the s-th dimension at the t-th iteration, p qs t represents the individual historical optimal position of particle q in the s-th dimension at the t-th iteration, p gs t represents the optimal position of all particles in the s-th dimension at the t-th iteration.

[0105] S4.2, Improvement of particle swarm algorithm parameters

[0106] S4.2.1, Improvement of inertia weight of particle swarm algorithm: Since inertia weight is an important factor affecting the convergence speed of particle swarm algorithm, it has an important influence on the performance and convergence speed of particle swarm algorithm. In order to solve the problems of slow convergence, low stability and easy to fall into local optimum in the solving process of standard particle swarm algorithm, a power function adaptive adjustment method of inertia weight is proposed as formula (17):

[0107] w(t)=(w max +w min ) / 2+exp (-λ×t / tmax) ×(w max -w min ) / 2 (17)

[0108] where w max is the maximum value of inertia weight, w min is the minimum value of inertia weight, w max =0.95, w min =0.4, the performance of the algorithm will be greatly improved, t max is the maximum number of iterations, t is the current number of iterations, and λ=5 is the convergence adjustment coefficient.

[0109] S4.2.2, Improvement of random number of particle swarm algorithm: In the standard particle swarm algorithm, r1 and r2 are uniformly distributed random numbers in the range of (0, 1). Integrating chaos theory into group-based algorithms is the minimum calculation cost method to balance the global detection and local exploitation ability of the algorithm. Therefore, adding chaos behavior to the random number can make the search have better dynamics and statistical properties, expand the search range, enhance the escape ability of particles from local optimal solution, and avoid the algorithm from falling into local optimum too early. Experiments show that the solution obtained by replacing the random parameter with chaotic parameter is the best, and the result of Singer mapping used in the algorithm is the best. The parameter value of Singer mapping fluctuates between (0, 1), which has great chaotic randomness. The formula of Singer mapping is as formula (18):

[0110] r2=z A+1= u x (7.86 x z A - 23.3 x z A 2 + 28.75 x z A 3 - 13.3 x z A 4 ) (18)

[0111] where u is a parameter between 0.9 and 1.08. When u = 1.04, z A = z0= 0.18, and the iteration number is Iter = 600, the graph of the initial value and the iteration number is shown in Figure 1 Fig. 1; z A is the chaotic variable value of the A-th iteration, and z A+1 is the chaotic variable value of the A+1-th iteration.

[0112] The particle swarm algorithm formula improved according to the inertia weight (17) and the random number formula (18) is as follows:

[0113] v qs t+1 = w(t) x v qs t + c1 x r1 x (p qs t - x qs t ) + c2 x r2 x (p gs t - x qs t ) (19)

[0114] x qs t+1 = x qs t + v qs t+1 (20)

[0115] where c1 and c2 are respectively an individual learning factor and a group learning factor, and usually c1 = c2 = 2; r1 is a random number uniformly distributed in the range of (0, 1); w(t) is an inertia weight factor, which directly determines the convergence speed; q = 1, 2, …, N represents the number of the particle swarm; s is a dimension index, representing the problem dimension, s = 1, 2, …, S; t is the current iteration number; x qs t and x qs t+1 respectively represent the s-dimensional position of the particle q at the t-th and t+1-th iteration; v qs t and v qs t+1Let p represent the velocity of particle q in the s-th dimension at the t-th and t+1-th iterations, respectively. qs t p represents the individual historical optimal position of particle q in dimension s at the t-th iteration. gs t This represents the optimal position of all particles in the s-th dimension at the t-th iteration.

[0116] S4.3, Particle Swarm Optimization (PSO) algorithm introduces the normal cloud model: Normal cloud model C(E x E n H e The normal cloud model is a transformation model between qualitative and quantitative computation, characterized by both stability and stochastic uncertainty. It has been widely applied in decision processing and information analysis. The normal cloud model has three eigenvalues: the expected value E... x Entropy E n and hyperentropy H e The expected value E x Entropy E represents the spatial distribution characteristics of cloud droplets. n It is a measure of randomness and fuzziness, entropy E n The value is directly proportional to the distribution range and distribution characteristics of cloud droplets within the distribution space, and the hyperentropy H e This reflects the discreteness of cloud droplets.

[0117] The algorithm process for the one-dimensional normal cloud model is as follows:

[0118] Step 1: Based on the normal distribution N(E) n H e 2 Generate a random number E related to entropy. n '.

[0119] Step 2: Based on the normal distribution N(E) x , (E n ') 2 Generate random cloud droplet positions x i .

[0120] Step 3: Calculate x i Uncertainty y i The calculation formula is:

[0121] y i =exp(-(x i -E x ) 2 / (2×E n ')) (twenty one).

[0122] Step 4: Calculate the value x based on Step 1 i and the calculated value y in Step 3i ,Bundle As a cloud droplet within the distribution space.

[0123] Step 5: Repeat Step 1 to Step 4 until the number of cloud droplets generated matches the computational requirements is calculated. This improves the particle swarm optimization algorithm and determines the number of particles that match the requirements in the t-th iteration.

[0124] Let g be the current optimal solution of the improved particle swarm optimization algorithm after the t-th iteration. best The worst solution at present is g. worst According to the one-dimensional normal cloud model C(E) x E n H e To improve the solution accuracy, E n A non-linear decreasing strategy should be adopted, and the particle update formula for the cloud model is:

[0125] E x =g best E n =-(g best -g worst )×(t / t max ) 2 +g best H e =E n / 10 (22)

[0126] Where E x E represents the center of cloud droplet distribution in space, indicating the most likely location where it will occur. x =g best Ensure the search revolves around the current optimal solution and avoids deviation; E n It measures randomness and fuzziness; a larger value indicates a more dispersed distribution, and the dynamic E... n This ensures that the algorithm can adaptively adjust the search range, balancing global and local searches; H e Entropy represents entropy, describes the uncertainty of entropy, and controls the degree of dispersion of cloud droplets. H e =E n / 10 can maintain appropriate solution diversity and prevent premature convergence of the algorithm.

[0127] Particle swarm optimization (PSO) suffers from drawbacks such as slow convergence, poor optimization stability, and a tendency to get trapped in local optima prematurely. Cloud models, however, possess fuzziness and stability, making them a suitable model for improving PSO. Mutation operations on the particles enrich their quantity and quality, enhancing the algorithm's local search capabilities. As the number of iterations comparing particles increases, the cloud droplets approach the optimal solution more closely, improving both overall search speed and quality.

[0128] Improved Particle Swarm Optimization Algorithm Process:

[0129] Step 1: According to the flexible job processing time problem model and constraint condition formula (1) to formula (4), a mathematical model is constructed.

[0130] Step 2: The initial improved particle swarm algorithm iteration number t = 1, set algorithm parameters, position boundary value, speed boundary value, including particle number N, maximum iteration number t max , initial particle position x q , initial particle speed v q , position boundary value x max , x min , speed boundary value v max , v min , dimension D. In practical application, the particle number N is generally determined according to the scale of the workshop and the complexity of the problem, which directly determines the search efficiency and accuracy of the algorithm. The initial particle position x q represents an initial scheme of workpiece processing sequence and scheduling; the speed v q determines the direction and speed of particle movement in the solution space. The setting of position and speed boundary value can ensure that the particle searches within a reasonable range and avoid unreasonable scheduling scheme.

[0131] Step 3: According to formula (5) - formula (14), the comprehensive prospect-regret value is calculated, and this value is used as the fitness evaluation value of the CCPSO algorithm to guide the evolution of the algorithm. In flexible job shop scheduling, the comprehensive prospect-regret value considers the deviation degree of manufacturing efficiency index and the decision maker's aversion to regret. By taking this value as the fitness evaluation value, the algorithm can more comprehensively evaluate the pros and cons of each scheduling scheme and guide the particle to search in a better direction.

[0132] Step 4: According to the inertia weight power function adjustment formula (17) and random number formula (18), the parameters w(t) and r2 are adaptively changed, and the iteration is carried out according to the speed formula (19) and position formula (20), the fitness value of the particle is calculated and the current optimal solution is selected. In the iteration process, the adaptive adjustment of inertia weight w(t) can balance the global search and local search ability of the algorithm. In the early stage of the algorithm, larger w(t) can make the particle search widely in the solution space and find possible better areas; with the iteration, smaller w(t) can make the particle search in the local area, improve the accuracy of the solution. The chaotic random number r2 can increase the randomness of the search and avoid the algorithm falling into local optimum.

[0133] Step 5: Calculate the global optimal value g bestThe fitness value is calculated and the cloud model is calculated, starting to search the distribution space with the current optimal solution as the center. According to the one-dimensional normal cloud model algorithm formula (21) and formula (22) steps, s cloud droplets are generated, and the optimal value is selected from the s cloud droplets by comparison. The optimal value is compared with the current optimal value g calculated by the CCPSO algorithm best If the cloud droplet optimal value is larger, the current global optimal value g is updated best Otherwise, the current global optimal value does not change.

[0134] Step 6: Set the algorithm evolution threshold = 5. If the individual optimal value does not change within a certain number of iterations, it is determined that the algorithm is premature, and the update is continued according to Step 5. In the flexible job processing time problem, due to the complexity of the workshop production situation, the algorithm may converge to a local optimal solution too early. By judging whether the algorithm is premature and searching again using the cloud model, the algorithm can be prevented from falling into a local optimum, ensuring that the algorithm can continue to find a better scheduling scheme.

[0135] Step 7: Determine whether the maximum number of iterations t is reached max If it is reached, the current optimal value is output. If it is not reached, the iteration number t+1 is returned to Step 3 to continue iteration. The optimal value is the optimal scheduling scheme found after considering various constraint conditions, comprehensive prospect-regret value and multiple iterations and optimization. The scheme specifically defines the processing order of each workpiece, the assigned processing equipment and the start and end time of each process.

[0136] The application provides a flexible job shop scheduling optimization method, constructs a flexible job shop scheduling mathematical model according to a flexible job processing time problem model and constraint conditions thereof, determines an initial particle swarm of a particle swarm algorithm for a workpiece process to be processed, takes minimum processing time as a target function, and takes a particle position as an encoding representation of workpiece processing sequence and processing resource allocation, and takes a dimension as a variable quantity that needs to be decided in the flexible job shop scheduling problem; a comprehensive prospect-regret value is taken as an adaptive evaluation value of a particle updated by the particle swarm algorithm, wherein the prospect theory is used for measuring a deviation degree of a manufacturing efficiency index, the regret theory reflects an avoidance behavior of a decision maker to regret, and the particle adjusts a position and a speed in a solution space in a direction of making the comprehensive prospect-regret value more optimal. This makes the algorithm not only pursue a simple minimum processing time and the like traditional target, but also seek an optimal scheduling scheme that can better meet a preference of a decision maker and actual production requirements on the basis of considering risk and regret factors. The risk preference and the decision attitude are integrated into the algorithm to guide the particle swarm to search in a more optimal direction; according to an inertia weight adjusted by using an inertia weight power function and a random number introduced by a chaotic behavior, in a scheduling initial stage, the larger inertia weight enables the particle to quickly explore in a wide solution space, and attempts different workpiece processing sequence and resource allocation combinations to cope with variability of a production environment. With the iteration advancing, the inertia weight gradually decreases, the particle starts to focus on a currently discovered optimal region, and selects a current optimal solution; a plurality of cloud droplets generated according to a one-dimensional normal cloud model, i.e., a group of potential scheduling schemes near the current optimal solution, select a cloud droplet optimal value by setting a threshold, compare the cloud droplet optimal value with the current optimal solution, search a neighborhood of the optimal scheduling scheme found on the basis of the optimal scheduling scheme in a more detailed manner to find a possibly existing more optimal solution, and then optimize the flexible job shop scheduling strategy.

[0137] Experimental analysis:

[0138] To verify the performance of the improved particle swarm algorithm (CCPSO), the Kacem example is selected, and the simulation results of the CCPSO, a standard particle swarm algorithm (PSO), an inertia weight improved particle swarm algorithm (SPSO) and an improved algorithm (PSOGA) fusing a particle swarm and a genetic algorithm are compared, and the algorithm parameters are as follows: the particle number of the particle swarm is N=50, the maximum iteration number t max =400; the maximum time difference is the difference between the longest processing time algorithm and the shortest processing time algorithm in each example, and the maximum deviation rate is the ratio of the maximum time difference to the longest processing time in each example. The maximum time difference and the maximum deviation rate reflect the effect of the improved algorithm.

[0139] Kacem example analysis: from table 2, it can be seen that in Kacem example, the processing time increases rapidly with the increase of the number of machines and workpieces. For PSO algorithm, since the parameters are not improved, the processing time is the longest in the five examples. In Kacem01 example, the maximum time difference is 2.1s, the maximum deviation rate is 12.50%, the evolution curve and gantt chart of Kacem01 example are shown in Figure 3 ; in Kacem02 example, the maximum time difference is 5.2s, the maximum deviation rate is 18.64%, the evolution curve and gantt chart of Kacem02 example are shown in Figure 4 ; in Kacem03 example, the maximum time difference is 7.6s, the maximum deviation rate is 21.23%; in Kacem04 example, the maximum time difference is 10.5s, the maximum deviation rate is 21.92%; in Kacem05 example, the maximum time difference is 20.3s, the maximum deviation rate is 24.73%; in Kacem01 and Kacem02 examples, the processing time of PSOGA algorithm is more than that of SPSO algorithm, while in Kacem03, Kacem04 and Kacem05 examples, with the increase of the number of machines and workpieces, compared with SPSO algorithm, PSOGA shows obvious advantages; while in Kacem01 and Kacem02 examples, the advantage of CCPSO algorithm is not obvious; in Kacem01 example, the processing time of CCPSO algorithm is 0.20s longer than that of SPSO algorithm, and close to that of PSOGA algorithm; in Kacem02 example, the processing time of CCPSO algorithm is 0.1s less than that of SPSO algorithm, and 0.3s less than that of PSOGA algorithm; in Kacem03 example, the processing time of CCPSO algorithm is 1.1s less than that of SPSO algorithm, and 0.2s less than that of PSOGA algorithm; in Kacen04 example, the processing time of CCPSO algorithm is 3.2s less than that of SPSO algorithm, and 0.7s less than that of PSOGA algorithm; in Kacem05 example, the processing time of CCPSO algorithm is 5.5s less than that of SPSO algorithm, and 1.3s less than that of PSOGA algorithm, the evolution curve and gantt chart of Kacem05 example are shown in Figure 5 . With the increase of the number of machines and workpieces, the advantage of CCPSO algorithm in processing time gradually emerges compared with other three algorithms, the processing time gradually shortens, and the maximum time difference and the maximum deviation rate also gradually increase.

[0140] Table 2 comparison of processing time of Kacem example

[0141]

[0142] Processing case verification: a mechanical processing workshop receives a batch of orders, processing tasks, processing machines, processes and process routes are shown in table 4 and table 5, in order to verify the effect of CCPSO algorithm, compared with PSO, SPSO, PSOGA three algorithms, the processing workpiece has 5 processes such as turning outer circle, milling groove, milling inner cavity, drilling and milling end face.

[0143] Table 3 processing machine table

[0144]

[0145] As shown in table 5, the shortest processing time is CCPSO algorithm, the time is 2621min, compared with the longest processing time of PSO algorithm, reduces 408min, reduces 13.47%, compared with the processing time of PSOGA algorithm, reduces 88min, reduces 3.27%, compared with SPSO algorithm, reduces 184min, reduces 6.61%.

[0146] Table 4 processing task workpiece process table

[0147]

[0148] Table 5 processing time of each algorithm

[0149]

[0150] CCPSO algorithm, iteration number t=224 times to find the optimal solution, while PSOGA in iteration number t=241 times, SPSO in iteration number t=306 times, PSO in iteration number t=347 times to find the optimal solution, CCPSO algorithm has better optimization performance compared with the other three algorithms. Figure 6 As shown in gantt chart and evolution curve.

[0151] The application introduces the evaluation value of the comprehensive prospect-regret theory model as the fitness value to guide the evolution of the algorithm, expands the application range of the comprehensive prospect-regret theory in the improved particle swarm, takes the minimum processing time as the objective function, proposes an improved particle swarm algorithm, adopts an inertia weight power function for adaptive adjustment, improves random numbers by using chaotic variables, introduces a cloud model for mutation operation of particles in the improved particle swarm algorithm according to the characteristics of fuzziness and randomness of the cloud model, enriches the number and quality of particles, and improves the global and local search ability of the algorithm.

[0152] Based on the same inventive concept, the present application also provides a flexible job shop scheduling optimization system, comprising:

[0153] A target function construction module is configured to construct a flexible job shop scheduling mathematical model with a minimum processing time as a target function according to a flexible job processing time problem model and constraint conditions thereof.

[0154] A solution module is configured to solve the flexible job shop scheduling mathematical model by using an improved particle swarm algorithm, and to take the processing procedures of the workpieces to be processed as initial particles of the particle swarm algorithm, and the solving process specifically includes: setting initial particle positions and initial particle velocities, wherein the initial particle positions represent initial scheduling schemes of the processing sequences of the workpieces and processing resources, and the particle velocities represent adjustment schemes of the processing sequences of the workpieces and the allocation of the processing resources; determining a comprehensive prospect-regret value according to a prospect theory for measuring the deviation degree of a manufacturing efficiency index and a regret theory for reflecting the avoidance behavior of a decision maker to regret; and taking the comprehensive prospect-regret value as an adaptability value of the particles updated by the particle swarm algorithm; the determination of the comprehensive prospect-regret value according to the prospect theory for measuring the deviation degree of the manufacturing efficiency index and the regret theory for reflecting the avoidance behavior of the decision maker to regret specifically includes the following steps: calculating the distance between two interval numbers for any two intervals; determining a value function and a decision weight according to the distance; calculating a prospect value function according to the value function and the decision weight; the prospect value function includes a positive prospect value and a negative prospect value; calculating a regret value and a joy value by substituting the positive prospect value and the negative prospect value of each decision into a Hamming distance formula; establishing a comprehensive prospect-regret theory evaluation function formula according to the regret value and the joy value; determining the comprehensive prospect-regret value according to the comprehensive prospect-regret theory evaluation function formula; iteratively updating the particle positions and the particle velocities according to an inertia weight adjusted by using an inertia weight power function and a random number introduced by a chaotic behavior, calculating the adaptability value of the particles at each iteration, and selecting a current optimal solution; starting to search from a distribution space with the current optimal solution as the center, generating a plurality of cloud droplets according to a one-dimensional normal cloud model, selecting a cloud droplet optimal value by setting a threshold, comparing the cloud droplet optimal value with the current optimal solution, and if the cloud droplet optimal value is greater than the current optimal solution, continuing the iterative updating until the cloud droplet optimal value is not greater than the current optimal solution, and outputting an optimal scheduling scheme.

[0155] An optimization module is configured to generate the processing sequences of each workpiece, the allocated processing devices, and the start and end times of each procedure according to the optimal scheduling scheme, and to optimize the flexible job shop scheduling strategy.

[0156] The present application also provides a flexible job shop scheduling optimization computer device, which comprises a memory, a processor, and a computer program stored in the memory, and the processor implements the steps of the flexible job shop scheduling optimization method when executing the computer program.

[0157] The application further provides a readable storage medium, which stores a computer program, and the computer program comprises program instructions, which are executed by a processor to execute the steps of the flexible job shop scheduling optimization method.

[0158] The above merely provides the preferred embodiments of the application, but the protection scope of the application is not limited thereto, and any person skilled in the art, according to the technical scheme and the inventive concept of the application, makes equivalent replacement or change within the technical range disclosed by the application, which should be covered within the protection scope of the application.

Claims

1. A method for optimizing the scheduling of flexible workshops, characterized in that, Includes the following steps: Based on the flexible operation processing time problem model and its constraints, a mathematical model for flexible operation workshop scheduling is constructed with the minimum processing time as the objective function. An improved particle swarm optimization algorithm is used to solve the mathematical model of flexible workshop scheduling; The process of the workpiece to be processed is used as the initial particle swarm for the particle swarm algorithm. The solution process specifically includes: The process involves setting initial particle positions and initial particle velocities, where the initial particle positions represent the initial scheduling scheme for workpiece processing sequence and processing resources, and the particle velocities represent the adjustment scheme for workpiece processing sequence and processing resource allocation. A comprehensive prospect-regret value is determined based on prospect theory (used to measure deviations from manufacturing efficiency indicators) and regret theory (used to reflect decision-makers' avoidance of regret). This comprehensive prospect-regret value is then used to update the fitness values ​​of particles in a particle swarm optimization algorithm. Specifically, determining the comprehensive prospect-regret value based on prospect theory (used to measure deviations from manufacturing efficiency indicators) and regret theory (used to reflect decision-makers' avoidance of regret) includes the following steps: For any two intervals, calculate the distance between the numbers of the two intervals; determine the value function and decision weights based on the distance; calculate the prospect value function based on the value function and decision weights; the prospect value function includes positive and negative prospect values; substitute the positive and negative prospect values ​​of each decision into the Hamming distance formula to calculate the regret value and gratification value respectively; establish a comprehensive prospect-regret theory evaluation function based on the regret value and gratification value; and determine the comprehensive prospect-regret value based on the comprehensive prospect-regret theory evaluation function. Based on the inertial weight adjusted by the power function of inertial weight and the random number introduced by chaotic behavior, the particle position and particle velocity are iteratively updated, the fitness value of the particle is calculated at each iteration, and the current optimal solution is selected. With the current optimal solution as the center, the search begins to move outward to the distribution space. Multiple cloud droplets are generated according to the one-dimensional normal cloud model. The optimal value of the cloud droplet is selected by setting a threshold. The optimal value of the cloud droplet is compared with the current optimal solution. If the optimal value of the cloud droplet is greater than the current optimal solution, the iterative update continues until the optimal value of the cloud droplet is no greater than the current optimal solution. The optimal scheduling scheme is then output. The optimal scheduling scheme generates the processing sequence of each workpiece, the allocated processing equipment, and the start and end times of each process, thereby optimizing the flexible workshop scheduling strategy.

2. The flexible workshop scheduling optimization method according to claim 1, characterized in that, The flexible operation processing time problem model specifically includes: the set of workpieces to be processed is J={J1,J2,…,J…} n The set of machines that can be used in the workshop is M = {M1, M2, ..., M}. m }, where the maximum number of workpieces is n, and the maximum number of usable machines is m; each workpiece has different processing steps but a fixed processing sequence, and its set of steps is: p = {p i |p1,p2,…,p n }, i=1,2,…,n; where p represents all the processes of the workpiece numbered i, p ij This represents the j-th operation of workpiece number i; the start time, end time, and duration of the j-th operation of workpiece i on machine k are denoted as S. ijk F ijk C ijk Where k = 1, 2, ..., m; the actual running time of machine k is represented by T. k The final completion time for all processes of all workpieces is represented by F. max .

3. The flexible workshop scheduling optimization method according to claim 2, characterized in that, The constraints of the flexible operation processing time problem model specifically include: Process sequence constraint: All processes for all workpieces must be completed in a specific order. F ijk -F i(j-1)k ≥C ijk ; F ijk -S ijk >0; Machine non-duplication constraint: If operations (i,j) and (a,b) are processed on the same machine k, and (i,j) follows (a,b): S ijk ≥F abk ; Processing time constraints: F ijk =S ijk +C ijk 。 4. The flexible workshop scheduling optimization method according to claim 1, characterized in that, The step of iteratively updating the particle position and particle velocity based on the inertial weight adjusted by the power function of the inertial weight and the random number introduced with chaotic behavior specifically includes the following steps: The inertial weight w(t) adjusted using the power function of the inertial weight is expressed as: w(t)=(w max +w min ) / 2+exp (-λ×t / tmax) ×(w max -w min ) / 2; Among them, w max It is the maximum value of the inertia weight, w min The minimum value of the inertia weight, t max λ is the maximum number of iterations, t is the current number of iterations; λ=5 is the convergence adjustment coefficient; Introducing random numbers with chaotic behavior, denoted as: r2=z A+1 =u×(7.86×z A -23.3×z A 2 +28.75×z A 3 -13.3×z A 4 ); Where r2 is a uniformly distributed random number in the range (0,1), and u is a parameter between 0.9 and 1.08; z A The chaotic variable value z is the value of the A-th iteration. A+1 It is the value of the chaotic variable in the (A+1)th iteration; Based on the inertial weight adjusted using the power function of the inertial weight and the random numbers introduced with chaotic behavior, the iteratively updated particle position and particle velocity are obtained, expressed as: v qs t+1 =w(t)×v qs t +c1×r1×(p qs t -x qs t )+c2×r2×(p gs t -x qs t ); x qs t+1 =x qs t +v qs t+1 ; Where c1 and c2 are the individual learning factor and the group learning factor, respectively; r1 is a uniformly distributed random number in the range (0,1); w(t) is the inertia weight factor; q=1,2,…,N represents the number of particles in the swarm; s is the dimension index; t is the current iteration number; x qs t and x qs t+1 Let v represent the positions of particle q in the s-th dimension at the t-th and t+1-th iterations, respectively. qs t and v qs t+1 Let p represent the velocity of particle q in the s-th dimension at the t-th and t+1-th iterations, respectively. qs t p represents the individual historical optimal position of particle q in dimension s at the t-th iteration. gs t This represents the optimal position of all particles in the s-th dimension at the t-th iteration.

5. The flexible workshop scheduling optimization method according to claim 4, characterized in that, The generation process of the multiple cloud droplets generated based on the one-dimensional normal cloud model specifically includes the following steps: According to the normal distribution N(E) n H e 2 Generate a random number E related to entropy. n '; According to the normal distribution N(E) x ,(E n ') 2 Generate random cloud droplet positions x i ; where the expected value E x Entropy E n and hyperentropy H e These are all eigenvalues ​​of the normal cloud model; Calculate x i Uncertainty y i ,get: y i =exp(-(x i -E x ) 2 / (2×E n ')); According to x i and y i , will (x i ,y i As a cloud droplet within the distribution space; The calculation is repeated multiple times until the number of cloud droplets that generate a number of particles matches the number of iterations of the particle swarm algorithm is generated.

6. The flexible workshop scheduling optimization method according to claim 5, characterized in that, The particle update of the one-dimensional normal cloud model specifically includes: Let g be the current optimal solution of the particle swarm optimization algorithm after the t-th iteration. best The worst solution at present is g worst According to the one-dimensional normal cloud model C(E) x E n H e The cloud model particle update formula is obtained as follows: E x =g best ,E n =-(g best -g worst )×(t / t max ) 2 +g best ,H e =E n / 10。 7. A flexible workshop scheduling optimization system, characterized in that, include: The objective function construction module is used to construct a mathematical model for flexible operation workshop scheduling based on the flexible operation processing time problem model and its constraints, with the minimum processing time as the objective function. The solver module is used to solve the mathematical model of flexible job shop scheduling using an improved particle swarm optimization algorithm; The process of processing the workpiece is used as the initial particle swarm in the particle swarm optimization algorithm. The solution process specifically includes: setting the initial particle positions and initial particle velocities, where the initial particle positions represent the initial scheduling scheme of the workpiece processing sequence and processing resources, and the particle velocities represent the adjustment scheme of the workpiece processing sequence and processing resource allocation; determining the comprehensive prospect-regret value based on prospect theory (used to measure the degree of deviation from manufacturing efficiency indicators) and regret theory (used to reflect decision-makers' avoidance of regret); and using the comprehensive prospect-regret value as the fitness value for updating particles in the particle swarm optimization algorithm. The determination of the comprehensive prospect-regret value based on prospect theory (used to measure the degree of deviation from manufacturing efficiency indicators) and regret theory (used to reflect decision-makers' avoidance of regret) specifically includes the following steps: for any two intervals, calculating the distance between the numbers of the two intervals; determining the value function and decision weights based on the distance; and calculating the prospect value function based on the value function and decision weights. The prospect value function includes positive and negative prospect values. The positive and negative prospect values ​​of each decision are substituted into the Hamming distance formula to calculate the regret and euphoria values ​​respectively. Based on the regret and euphoria values, a comprehensive prospect-regret theory evaluation function is established. The comprehensive prospect-regret value is determined according to this function. The particle position and velocity are iteratively updated using the inertial weight adjusted by the power function and random numbers incorporating chaotic behavior. The fitness value of the particle is calculated for each iteration, and the current optimal solution is selected. A search is initiated in the distribution space centered on the current optimal solution. Multiple cloud droplets are generated based on a one-dimensional normal cloud model. The optimal value of each cloud droplet is selected by setting a threshold. The optimal value of the cloud droplet is compared with the current optimal solution. If the optimal value of the cloud droplet is greater than the current optimal solution, iterative updates continue until the optimal value of the cloud droplet is no greater than the current optimal solution, at which point the optimal scheduling scheme is output. The optimization module is used to generate the processing sequence of each workpiece, the allocated processing equipment, and the start and end times of each process according to the optimal scheduling scheme, thereby optimizing the flexible job shop scheduling strategy.

8. A computer device for optimizing flexible workshop scheduling, characterized in that, include: The memory, the processor, and the computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the flexible job shop scheduling optimization method according to any one of claims 1-6.

9. A readable storage medium, characterized in that, The readable storage medium stores a computer program, which includes program instructions that, when executed by a processor, perform the steps of the flexible job shop scheduling optimization method according to any one of claims 1-6.

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