Distributed Estimation Optimization Method for Collaborative Scheduling in the Furniture Production and Transportation Process

Abstract

The present invention discloses a distribution estimation optimization method for collaborative scheduling in the furniture production and transportation process, including: establishing a problem model for the furniture production and transportation process with the optimization goal of minimizing the sum of delay penalty costs and transportation costs; using a distribution estimation-based scheduling method to iteratively optimize the optimization goal to obtain the optimal solution to the problem of the furniture production and transportation process. The present invention defines the furniture production and transportation process as a type of production and transportation collaborative scheduling problem; uses a three-dimensional probability matrix to learn and accumulate the block structure information of high-quality population individuals, generates a new population by sampling them; then performs local search on the high-quality individuals in the population, and updates the three-dimensional probability matrix using the improved high-quality individuals, thereby improving the quality of the scheduling scheme. The method of the present invention can obtain a high-quality scheduling scheme for the furniture production and transportation process in a relatively short time, improve the production efficiency of the factory, and reduce resource waste.

Description

Technical Field

[0001] The present invention relates to a distribution estimation optimization method for collaborative scheduling in the process of furniture production and transportation, and belongs to the technical field of integrated intelligent optimization scheduling of production and transportation. Background Art

[0002] With the intensification of market competition, more and more enterprises have joined the trend of mass customization. As a kind of household configuration, furniture plays the role of storing objects. In recent years, under the influence of the trend of personalized customization services, customized furniture has become popular. Nowadays, furniture is not only a storage tool, but also plays the role of reflecting personality and decorating rooms. Customized furniture has become an important part of the current furniture industry. Due to the characteristics of complex technology, long production cycle and difficulty for customers to pick up by themselves, most furniture manufacturers adopt the service mode of advance reservation and door-to-door delivery. Therefore, how to quickly produce products and deliver them to customers in a timely manner has become an urgent problem for enterprises to solve.

[0003] In the process of furniture manufacturing, the processing and assembly of multiple components are included. The whole process can be mainly divided into four parts: mechanical processing stage, painting processing stage, assembly processing stage and product transportation stage. In the first stage, processes such as veneering, cutting, cold pressing, trimming, edge banding, and solid wood processing are included. In the second stage, the preliminarily processed parts need to be colored, and the main processes are puttying, sanding, spraying primer, polishing, etc. In the third stage, the processed components are assembled into a complete product. In the final distribution stage, the products will be loaded into vehicles and distributed to customers according to the established delivery sequence. In the traditional production mode, the production plan of products and the distribution route of vehicles are mostly planned depending on the experience of dispatchers. However, the solution of this scheduling mode is greatly affected by the ability of dispatchers, and there is a large space for optimization of the solution, which may cause excessive idleness or waste of equipment resources, resulting in an increase in operating costs. Therefore, it is necessary to design a distribution estimation optimization method for collaborative scheduling in the process of furniture production and transportation, so as to obtain a high-quality scheduling solution for the scheduling problem in the process of furniture production and transportation in a short time, thereby effectively shortening the processing time, reducing the transportation cost, and enhancing the competitiveness of enterprises. Summary of the Invention

[0004] The present invention provides a distribution estimation optimization method for collaborative scheduling in the process of furniture production and transportation, so as to establish a problem model based on the process of furniture production and transportation, and further optimize the optimization objective by using the distribution estimation scheduling method to obtain the optimal solution of the problem.

[0005] The technical solution of the present invention is as follows: A distributed estimation optimization method for collaborative scheduling in the furniture production and transportation process, including: establishing a problem model for the furniture production and transportation process with the optimization goal of minimizing the sum of delay penalty costs and transportation costs; using a distributed estimation scheduling method to iteratively optimize the optimization goal to obtain the optimal solution to the problem of the furniture production and transportation process.

[0006] The problem model of the furniture production and transportation process is established as follows:

[0007] Min TC

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[0023] TC = PC + DC

[0024] In the formula, TC represents the optimization goal; i and j represent product numbers, the total number of products and the total number of customers are equal and both are N, 0 represents a virtual product, X j,i represents 1 if product i is directly processed after product j, otherwise 0; ξ represents the product processing sequence, C ξ(l) represents the completion time of the l-th product in the processing sequence, k represents the machine number, K represents the total number of machines, Pt ξ(l),kDenotes the processing time of the \(l\)th product in the processing sequence on machine \(k\), \(A_t\) ξ(l) Denotes the assembly time of the \(l\)th product in the processing sequence; \(Y\) i,c Denotes \(1\) if product \(i\) belongs to customer \(c\), otherwise \(0\); \(h\) represents the vehicle number, \(H\) represents the total number of vehicles Denotes \(1\) if product \(j\) is placed in vehicle \(h\), otherwise \(0\); Denotes the \(o\)th product in the product set transported by vehicle \(h\), \(N\) h Denotes the total number of products transported by vehicle \(h\), Denotes product weight, \(Q\) represents the maximum load of the vehicle; \(S\) h Denotes the departure time of vehicle \(h\); \(Z\) c,u Denotes \(1\) if customer \(u\) is the next delivery point of customer \(c\), otherwise \(0\); \(\psi\) h (v) represents the \(v\)th customer in the product delivery customer sequence of vehicle \(h\), Denotes the time point when vehicle \(h\) delivers the product to customer \(\psi\) h (v) Denotes the \(\psi\)th of vehicle \(h\) h (v - 1) customer point and \(\psi\) h (v) transportation time cost between customer points; \(T\) c Denotes the delay time when the vehicle delivers the product to customer \(c\), \(A\) c Denotes the time point when the vehicle delivers the product to customer \(c\), \(D\) c Denotes the delivery time of the product pre - required by customer \(c\); \(DC\) represents the penalty cost for late delivery, \(\alpha\) is the late penalty factor; \(PC\) represents the transportation cost, \(\beta\) represents the departure cost of the vehicle; \(TC\) represents the sum of the late penalty cost and the transportation cost.

[0025] The described distribution - estimation - based scheduling method includes: Step1, encoding and decoding; Step2, establishing a probability model: establishing and initializing a three - dimensional probability model; Step3, generating a new population: sampling the three - dimensional probability matrix to generate a population; Step4, local search: selecting the top \(m\%\) individuals in the population in terms of evaluation value for local search; Step5, calculating the population diversity index \(P\) ver ; Step6, judging whether the probability matrix is updated according to the population diversity index; Step7, termination condition: if the termination condition is met, output the optimal solution; otherwise, repeat Steps 3 - 6 until the termination condition is met.

[0026] The encoding and decoding include: during encoding, an encoding method based on integer sorting is adopted, and each encoded individual consists of non-repeating numbers from [1, 2,... N]; during decoding, first, the encoded individuals are sorted as the processing sequence of the products in the factory, and then the products are allocated to the transport vehicles according to the rule that the completed products are transported first. During the allocation process, if the load weight of the vehicle exceeds the maximum load allowed for the vehicle, the product is allocated to a new vehicle. Finally, the Insert operation is performed on each product at each position according to the processing sequence of the products loaded in each vehicle, and the sequence with the minimum evaluation value is used as the product delivery sequence for the vehicle.

[0027] The establishment and initialization of the three-dimensional probability model include: using a three-dimensional probability matrix of size N×N×N to record the probability information of the block structure [y, z] at the x position; where G represents the generation of the population; at the beginning stage,

[0028] The sampling of the three-dimensional probability matrix to generate a population includes: for the G-th generation population POP(G), let its size be PS, then POP(G) consists of PS π ki,G s, and π ki,G is the ki-th individual in the G-th generation population, and each encoded individual samples the block structure of the three-dimensional probability matrix by means of roulette wheel to determine the sequence of the complete individual.

[0029] The selection of the top m% individuals in the population with the best evaluation value for local search includes: selecting the top m% individuals in the population with the best evaluation value, using the variable neighborhood descent mechanism to search for the optimal individual among the top m% individuals in the population, and using the variable neighborhood search mechanism with the first jump-out principle to search for all individuals except the optimal individual among the top m% individuals in the population.

[0030] The operations of using the variable neighborhood descent mechanism for search and the variable neighborhood search mechanism with the first jump-out principle for search are the same, both being the Insert and Swap search operators.

[0031] The population diversity index P ver The expression is:

[0032]

[0033] In the formula, SPS represents the number of individuals in SPOP(G); SPOP(G) represents the top SPS individuals with the best evaluation value in POP(G), and POP(G) represents the G-th generation population; F vFor the number of different digits at the v-th position in the individuals of the high-quality population SPOP(G) of the record, where v = 1, 2,..., N, if there is only one digit at the v-th position, let F v = 0.

[0034] Judging whether the probability matrix is updated according to the population diversity index, specifically: if the population diversity index is less than or equal to the threshold, the three-dimensional probability matrix is not updated in the current iteration; otherwise, when the population diversity index is greater than the threshold, the three-dimensional probability matrix is updated according to the top SPS high-quality individuals in the evaluation value after local search.

[0035] The beneficial effects of the present invention are as follows: The present invention defines the furniture production and transportation process as a type of production and transportation collaborative scheduling problem; uses a three-dimensional probability matrix to learn and accumulate the block structure information of high-quality population individuals, generates a new population by sampling it; then performs local search on the high-quality individuals in the population, and updates the three-dimensional probability matrix using the improved high-quality individuals, so as to improve the quality of the scheduling scheme. The method of the present invention can obtain a high-quality scheduling scheme for the furniture production and transportation process in a short time, improve the production efficiency of the factory, and reduce resource waste. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is the overall algorithm flowchart of the present invention;

[0037] Figure 2 is the flowchart of the distribution estimation scheduling method of the present invention;

[0038] Figure 3 is the algorithm encoding and decoding schematic diagram of the present invention;

[0039] Figure 4 is the schematic diagram of the furniture production and transportation process of the present invention;

[0040] Figure 5 is the local search VND strategy of the present invention;

[0041] Figure 6 is the local search VNS strategy of the present invention;

[0042] Figure 7 is the schematic diagram of the local search Insert operation of the present invention;

[0043] Figure 8 is the schematic diagram of the local search Swap operation of the present invention;

[0044] Figure 9 is the schematic diagram of the local search Exchange operation of the present invention;

[0045] Figure 10 is the parameter response value change trend graph of the present invention. Detailed implementation mode

[0046] The following will further illustrate the invention in conjunction with the accompanying drawings and embodiments, but the content of the invention is not limited to the described scope.

[0047] Embodiment 1: As Figures 1-10 shown, a distributed estimation optimization method for collaborative scheduling in the furniture production and transportation process includes: establishing a problem model for the furniture production and transportation process with the optimization goal of minimizing the sum of delay penalty costs and transportation costs; and using a distributed estimation scheduling method to iteratively optimize the optimization goal to obtain the optimal solution to the problem of the furniture production and transportation process.

[0048] Optionally, the furniture production and transportation problem model is established as follows:

[0049] Min TC.

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[0065] TC = PC + DC.

[0066] In the formula, TC represents the optimization objective and is also the evaluation index in the algorithm; i and j represent the product numbers, N represents the total number of products and the total number of customers, 0 represents the virtual product, and X i,j represents 1 if product j is directly processed after product i, otherwise 0; ξ represents the product processing sequence, and C ξ(l) represents the completion time of the l-th product in the processing sequence, k represents the machine number, K represents the total number of machines, and Pt j,k represents the processing time of product j on machine k, and At j represents the assembly time of product j; Y i,c represents that product i belongs to customer c; h represents the vehicle number, H represents the total number of vehicles, represents that each product needs to be loaded into the vehicle; represents the o-th product in the product set transported by vehicle h, and N h represents the total number of products transported by vehicle h, and w j represents the weight of product j, and Q represents the maximum load of the vehicle; S h represents the departure time of vehicle h; Z c,u represents 1 if customer u is the next delivery point of customer c, otherwise 0; ψ h (v) represents the v-th customer in the product delivery customer sequence (i.e., the vehicle route) of vehicle h, represents the ψ-th h (v - 1) customer point and ψ h (v) customer point, and the transportation time cost between them, A c represents the time point when the vehicle delivers the product to customer c; T c represents the delay time when the vehicle delivers the product to customer c, α is the delay penalty factor, and D c represents the delivery time of the product required in advance by customer c, DC represents the penalty cost for late delivery, PC represents the transportation cost, β represents the departure cost of the vehicle, and TC represents the sum of the delay penalty cost and the transportation cost. The schematic diagram of the transportation process is as shown in Figure 4 shown.

[0067] Optionally, the specific steps of the distribution estimation optimization scheduling method are as follows:

[0068] Step 1. Encoding and decoding method: During encoding, an encoding method based on integer sorting is adopted. Each encoded individual consists of non-repeating numbers from [1, 2,... N]. During decoding, first, the encoded individual is sorted as the processing sequence of the products in the factory. Then, according to the rule that the completed products are transported first, the products are assigned to the transport vehicles. During the assignment process, if the load weight of the vehicle exceeds the maximum allowable load of the vehicle, the product is assigned to a new vehicle. Finally, the Insert operation is sequentially performed on the products at each position according to the processing sequence of the products loaded in each vehicle, and the sequence with the minimum evaluation value is used as the product delivery sequence of the vehicle. For example, when N = 8, the encoded individual is π = [2, 3, 5, 4, 1, 6, 7, 8], and the processing sequence ξ = [2, 3, 5, 4, 1, 6, 7, 8]; the product sets loaded in each vehicle The product delivery sequence ψ of each vehicle 1 = [5, 4, 2, 3], ψ 2 = [7, 6, 1, 8]. The schematic diagram is as Figure 3 shown.

[0069] Step 2. Establishment and initialization of the probability model: A three-dimensional matrix with a scale of N×N×N is adopted to record the information of high-quality individual block structures (product numbers at two adjacent positions of the encoded individual), where represents the probability that the block structure [y, z] is selected at the x position, and the larger its value, the higher the probability that the block structure [y, z] is selected at the x position; at the beginning stage, For example, if the encoded individual of the G-th generation is [2, 3, 4, 1, 5], then the information of the block structures [2, 3], [3, 4], [4, 1], [1, 5] is respectively stored in the probability matrix positions.

[0070] Step 3. Population generation: For the G-th generation population POP(G), let its size be PS, then POP(G) consists of PS π ki,G s, π ki,G is the ki-th individual in the G-th generation population, represents the product number at the N-th position in the π ki,G individual; each encoded individual samples the block structure through the roulette wheel method to determine the complete individual sequence; represents the product number at the N-th position in the π ki,G individual.

[0071] The roulette wheel mentioned above includes:

[0072] Step 1: Let the position number si = 1, the population individual number ki = 1, and the workpiece to be selected J sis empty;

[0073] Step 2: If si = 1, continue to Step 3; otherwise, jump to Step 4;

[0074] Step 3: Calculate S G-1 (x), where S G-1 (x) is the total probability at position x, generate a random number If the condition p s ∈[S G-1 (t), S G-1 (t + 1)], where t = 1,..., N - 1, then J s = t + 1; if p s ∈[0, S G-1 (1)], then J s = 1;

[0075] Step 4: Generate a random number If it satisfies If J s = 1;

[0076] Step 5: Let si = si + 1. If si <= N, jump to Step 2;

[0077] Step 6: Let ki = ki + 1. If ki <= PS, jump to Step 2;

[0078] Step 7: Output the population and update the elite population SPOP(G).

[0079] Step 4, Local Search: Select the top 30% - 50% of the individuals in the population with the best evaluation values and perform local search operations designed based on the Insert and Swap search operators. Specifically, first, for the optimal individual among the selected individuals, use the VND (Variable Neighborhood Descent mechanism) to perform search operations of Insert first and then Swap. This mechanism has good search performance, but its complexity is relatively high. In the present invention, this mechanism is only used for the optimal individual, thereby reducing the complexity while increasing the search depth of the algorithm. In addition, if the optimal individual has not changed for 5 consecutive times, perform the Exchange operation on it; then, for the remaining individuals except the optimal individual among the selected individuals, use the VNS (Variable Neighborhood Search mechanism with the first jump principle) to perform search operations of Insert first and then Swap on the individuals, so as to achieve rapid optimization of the solution and improve the search width of the algorithm to a certain extent. Applying the above technical solutions, through using corresponding search methods for different individuals in the population, a detailed and in-depth search of the solution space is realized, specifically as Figure 5 and 6As shown. The specific operation of Insert is as follows: Take out π in the order from left to right ki,G of the product numbers, and insert them into all the remaining positions in sequence, and retain the solution with the optimal evaluation value. For example Figure 7 As shown. The specific operation of Swap is as follows: Take out π in the order from left to right ki,G of the product numbers, and exchange them with the product numbers in all the remaining positions in sequence, and retain the solution with the optimal evaluation value. For example Figure 8 As shown; The specific operation of Exchange: Randomly select two individual product numbers and reverse the sequence within the numbers. For example Figure 9 As shown.

[0080] Step5. The population diversity index P ver is calculated as follows:

[0081] Record the number F of different digits at the v-th position of each individual in the high-quality group SPOP(G), v , v = 1, 2,..., N. If there is only one digit at the v-th position, let F v = 0; P can be obtained from the following formula ver :

[0082]

[0083] In the formula, SPS represents the number of individuals in SPOP(G); SPOP(G) represents the first SPS individuals in POP(G) with the best evaluation values, and POP(G) represents the G-th generation population. For example, π 1,1 = [3, 4, 1, 2, 5], π 2,1 = [3, 1, 2, 4, 5], π 3,1 = [1, 3, 4, 2, 5] are three individuals in SPOP(G), then F1 = 2, F2 = 3, F3 = 3, F4 = 2, F5 = 0, P ver = (2 / 3 + 3 / 3 + 3 / 3 + 2 / 3 + 0) / 5 = 2 / 3.

[0084] Step6. Update the probability matrix: Select the first SPS individuals in POP(G) with the best evaluation values as the high-quality group SPOP(G), and use a three-dimensional matrix with a scale of N×N×N Record the occurrence times of block structures at each position of SPOP(G); since the core of the three-dimensional distribution estimation algorithm lies in the probability matrix, the information accumulated in the probability matrix will directly affect the algorithm performance. In the conventional three-dimensional distribution estimation algorithm, as the number of iterations increases, the three-dimensional probability matrix will accumulate a large amount of information about the same block structure. On the one hand, it will waste a large amount of time and space resources on repetitive work. On the other hand, a large amount of information about the same block structure will cause premature convergence of the global search and the algorithm will fall into a local optimum. To effectively reduce the occurrence of such problems, this application proposes a diversity index P ver , which is used to measure the diversity of individuals in the high-quality population. When the value of P ver is less than or equal to the threshold B, it means that the similarity of individuals in the high-quality population is too high and the block structure has no statistical value, and the probability matrix is not updated in this iteration; on the contrary, when the value of P ver is greater than the threshold B, the block structure has statistical value and the update operation of the probability matrix is performed.

[0085] The update formula is as follows:

[0086]

[0087] where r represents the learning efficiency, is the matrix for recording the occurrence times of block structures and information at each position of SPOP(G), and SM G (x) is the cumulative sum of the occurrence times of the block structure (y, z) at position x in

[0088] Step7. Termination condition: If the termination condition is satisfied, the solution to the problem can be obtained; otherwise, repeat Step3 - Step6 until the termination condition is satisfied.

[0089] The main parameters of the three-dimensional distribution estimation algorithm are the population size PS, the high-quality population size SPS, the learning efficiency γ, and the threshold B. To determine the values of the relevant parameters for the best performance of the algorithm, the following parameter experiments are designed:

[0090] Four level values are selected for each parameter, and the specific situations are shown in Table 1 below:

[0091] Table 1

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[0093] Perform 20 experiments for each of the 16 groups of parameters with different levels, and take the average value of the experimental results as the response value of the parameter combination. The following parameter orthogonal table can be obtained, as shown in Table 2:

[0094] Table 2

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[0096] Take the mean value of the same parameter in the orthogonal parameter table at the same level as the response value of the parameter combination. Thus, the following response value table of parameter combinations can be obtained, as shown in Table 3. It can be seen from the following table the range and influence level of each parameter combination, where the greater the range, the greater the influence level. From the change of the response values of each parameter in the following table, the corresponding response value change trend graph can be obtained, specifically as Figure 10 shown.

[0097] Table 3

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[0099] Through the analysis of the experimental results, it can be concluded that the algorithm performance is optimal when PS = 40, SPS = 8, γ = 0.3, and B = 0.2.

[0100] To determine the proportion m of the number of population individuals executed in the local search, different values of m are taken and experiments are carried out. Among them, V1, V2, V3, V4, V5, and V6 are respectively the three-dimensional distribution estimation algorithms with m taking 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7. The specific experimental results are shown in Table 4 below. It can be seen from the following table that when the value of m is in the range of 0.3 - 0.5, the algorithm performance is the best.

[0101] Table 4

[0102] Problem scale V1 V2 V3 V4 V5 V6 50×20×2 5321 5106 5099 5088 5132 5142

[0103] To verify the effectiveness of the algorithm improvement in this application, the running results of the improved three-dimensional distribution estimation algorithm and the conventional three-dimensional distribution estimation algorithm for the furniture production and transportation process scheduling problem under different scale data are compared. It can be seen from the experimental results in Table 5 below that on all test cases, the solution effect of the method in this application is better than that of the traditional distribution estimation algorithm. Thus, the effectiveness of the improvement strategy of the present invention can be seen.

[0104] Table 5

[0105] Problem scale Conventional estimation of distribution algorithm Improved estimation of distribution algorithm (the present invention) 20×10×2 3122 3003 20×20×2 3954 3862 50×20×2 7362 5088 100×20×2 12181 11989

[0106] To verify the effectiveness of the distribution estimation optimization scheduling method in this application for solving the furniture production and transportation process scheduling problem, the running results of the distribution estimation optimization scheduling method and the traditional genetic algorithm for solving the furniture production and transportation process scheduling problem under different scales are compared. It can be seen from the experimental results in Table 6 below that on all test cases, the solution effect of the method in this application is better than that of the genetic algorithm. Thus, the effectiveness of the method in this application can be verified.

[0107] Table 6

[0108] Problem scale Traditional genetic algorithm Method of the present invention 20×10×2 3423 3003 20×20×2 4021 3862 50×20×2 7532 5088 100×20×2 14191 11989

[0109] Embodiment 2: A distribution estimation optimization system for collaborative scheduling in the furniture production and transportation process, comprising: a building module, configured to establish a problem model of the furniture production and transportation process with the objective of minimizing the sum of the delay penalty cost and the transportation cost; an obtaining module, configured to iteratively optimize the objective by using a distribution estimation scheduling method to obtain an optimal solution to the problem of the furniture production and transportation process.

[0110] Embodiment 3: A processor for running a program, wherein, when the program runs, it executes the distribution estimation scheduling method for collaborative scheduling of the furniture production and transportation process described in any one of the above. Wherein, when the program runs, it executes the distribution estimation optimization method for collaborative scheduling of the furniture production and transportation process described in any one of the above.

[0111] The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those of ordinary skill in the art.

Claims

1. A distributed estimation optimization method for collaborative scheduling in the furniture production and transportation process, characterized in that Including: Taking the minimization of the sum of the delay penalty cost and the transportation cost as the optimization objective, a problem model for the furniture production and transportation process is established; Using the estimation of distribution scheduling method to iteratively optimize the optimization objective to obtain the optimal solution of the furniture production and transportation process problem; The estimation of distribution scheduling method includes: Step1. Encoding and decoding; Step2. Establishing a probability model: establishing and initializing a three-dimensional probability model; Step3. Generating a new population: sampling the three-dimensional probability matrix to generate a population; Step4. Local search: selecting the top m% of the individuals in the population with the best evaluation values for local search; Step 5. Calculate the population diversity index P ver ; Step6. Judging whether the probability matrix is updated according to the population diversity index; Step7. Termination condition: if the termination condition is satisfied, the optimal solution is output; otherwise, repeat steps Step3 - Step6 until the termination condition is satisfied; The establishment and initialization of the three-dimensional probability model include: using a three-dimensional probability matrix of size N×N×N to record the probability information of the block structure [y,z] at the x position; where G represents the generation of the population; at the beginning stage, The sampling of the three-dimensional probability matrix to generate a population includes: for the G-th generation population POP(G), let its size be PS, then POP(G) consists of PS π ki,G s. π ki,G is the ki-th individual in the G-th generation population, where ki ∈ [1, 2,..., PS]; each encoded individual samples the block structure of the three-dimensional probability matrix by means of roulette wheel to determine the sequence of the complete individual.

2. The distributed estimation optimization method for collaborative scheduling in the furniture production and transportation process according to claim 1, characterized in that, The problem model of the furniture production and transportation process is established as follows: Min TC ξ = {ξ(1), ξ(2),... ξ(l),..., ξ(N)}, ξ(l) ∈ {1, 2,..., N} TC = PC + DC In the formula, TC represents the optimization objective; i and j represent product numbers, and the total number of products and the total number of customers are equal, both being N. 0 represents a virtual product, and X j,i represents 1 if product i is directly processed after product j, and 0 otherwise; ξ represents the product processing sequence, and C ξ(l) represents the completion time of the l-th product in the processing sequence, k represents the machine number, K represents the total number of machines, and Pt ξ(l),k represents the processing time of the l-th product on machine k in the processing sequence, and At ξ(l) represents the assembly time of the l-th product in the processing sequence; Y i,c represents 1 if product i belongs to customer c, and 0 otherwise; h represents the vehicle number, H represents the total number of vehicles, represents 1 if product j is placed in vehicle h, and 0 otherwise; represents the o-th product in the product set transported by vehicle h, and N h represents the total number of products transported by vehicle h, represents the product 's weight, Q represents the maximum load of the vehicle; S h represents the departure time of vehicle h; Z c,u represents 1 if customer u is the next delivery point of customer c, and 0 otherwise; ψ h (v) represents the v-th customer in the product delivery customer sequence of vehicle h, represents the time point when vehicle h delivers the product to customer ψ h (v); represents the ψ h (v - 1)-th customer point and ψ h (v)-th customer point of vehicle h, and the transportation time cost between them; T c represents the delay time when the vehicle delivers the product to customer c, and A c represents the time point when the vehicle delivers the product to customer c, and D c represents the delivery time of the product required in advance by customer c; DC represents the penalty cost for late delivery, α is the late penalty factor; PC represents the transportation cost, β represents the departure cost of the vehicle; TC represents the sum of the late penalty cost and the transportation cost.

3. The distribution estimation optimization method for collaborative scheduling in the furniture production and transportation process according to claim 1, wherein The encoding and decoding includes: during encoding, an encoding method based on integer sorting is adopted, and each encoded individual consists of non-repeating numbers from [1, 2,... N]; during decoding, first, the encoded individual is sorted as the processing sequence of the products in the factory, and then the products are assigned to the transportation vehicles according to the rule that the completed products are transported first. During the assignment process, if the load weight of the vehicle exceeds the maximum allowable load of the vehicle, the product is assigned to a new vehicle. Finally, the Insert operation is performed on each product at each position according to the processing sequence of the products loaded in each vehicle, and the sequence with the minimum evaluation value is used as the product delivery sequence of the vehicle.

4. The distributed estimation optimization method for collaborative scheduling in the furniture production and transportation process according to claim 1, characterized in that The selection of the top m% of the individuals in the population with the best evaluation values for local search includes: selecting the top m% of the individuals in the population, using the variable neighborhood descent mechanism to search for the best individual among the top m% of the individuals in the population, and using the variable neighborhood search mechanism with the first jump-out principle to search for all individuals except the best individual among the top m% of the individuals in the population.

5. The distributed estimation optimization method for collaborative scheduling in the furniture production and transportation process according to claim 4, characterized in that The operations of using the variable neighborhood descent mechanism to search and the variable neighborhood search mechanism with the first jump-out principle to search are the same, both being the Insert and Swap search operators.

6. The distribution estimation optimization method for collaborative scheduling in the furniture production and transportation process according to claim 1, characterized in that The population diversity index P ver The expression is: Wherein, SPS represents the number of individuals in SPOP(G); SPOP(G) represents the top SPS individuals in terms of evaluation values in POP(G), and POP(G) represents the G-th generation population; F v is the number of different digits at the v-th position among the individuals in the recorded high-quality population SPOP(G), where v = 1, 2,..., N. If there is only one digit at the v-th position, let F v = 0.

7. The distributed estimation optimization method for collaborative scheduling in the furniture production and transportation process according to claim 1, wherein Judging whether the probability matrix is updated according to the population diversity index is specifically: if the population diversity index is less than or equal to the threshold, the three-dimensional probability matrix is not updated in the current iteration; otherwise, when the population diversity index is greater than the threshold, the three-dimensional probability matrix is updated according to the top SPS high-quality individuals with the best evaluation values after local search.

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