Workshop double-target dynamic aisle arrangement planning method considering backtracking cost

Abstract

The invention discloses a workshop double-target dynamic aisle arrangement planning method considering backtracking cost, and relates to the technical field of facility layout. The method comprises the following steps: acquiring basic information of a workshop layout, wherein the basic information comprises a logistics backtracking condition, a logistics quantity, a facility condition and a distance; establishing a double-target dynamic aisle arrangement planning model: taking the minimum material carrying cost and the minimum backtracking cost as target functions, and establishing constraint conditions of double-target dynamic aisle arrangement planning, including carrying distance constraint, backtracking distance constraint and facility position constraint; the model is solved on the basis of an improved multi-target immune cloning algorithm, and the improved multi-target immune cloning algorithm is as follows: the immune cloning algorithm is taken as a framework, a variable neighborhood search strategy based on Monte Carlo judgment is combined, and better individuals are screened through a Pareto optimal mechanism. According to the method, decision support can be better provided for the workshop aisle arrangement problem.

Description

Technical Field

[0001] The present invention relates to the technical field of facility layout, and specifically to a dual-objective dynamic aisle layout planning method for a workshop considering backtracking cost. Background Art

[0002] As an important branch of the facility layout problem, the Corridor Allocation Problem (CAP) has a good layout structure and high logistics transportation efficiency, and is widely used in both manufacturing and service industries, such as production workshops, hospital sites, warehouses, office areas, etc., and is a major research hotspot in the field of facility layout.

[0003] During the processing process, some materials need to be transported from one facility to its upstream facility, and this direction is opposite to the downstream direction of the materials. This phenomenon is called logistics backtracking. The logistics backtracking phenomenon may cause cross-interference of the material transportation path and material accumulation, resulting in congestion of the passageway, thus affecting production efficiency.

[0004] At the same time, with the change of product iteration or market demand, the product variety, production batch and process often change, so the material flow between facilities will change accordingly, and the logistics backtracking phenomenon will also change. To reduce production costs, the facility layout between cycles can be adjusted to balance the Material Handling Cost (MHC) and equipment rearrangement cost in the manufacturing workshop.

[0005] However, the traditional CAP does not consider the impact of the logistics backtracking phenomenon on the production line, nor does it consider the impact of the backtracking phenomenon on the workshop layout to solve the interference and congestion problems in the production process. Summary of the Invention

[0006] To solve at least one of the above problems, the present invention proposes a dual-objective dynamic aisle layout planning method for a workshop considering backtracking cost.

[0007] The technical solution of the present invention is: a dual-objective dynamic aisle layout planning method for a workshop considering backtracking cost, including the following steps:

[0008] S1. Obtain the basic information of the workshop layout, including material flow, facility situation and distance;

[0009] S2. Establish a dual-objective dynamic aisle layout planning model: taking the minimum material handling cost and the minimum backtracking cost as the objective functions, and at the same time establish the constraint conditions for the dual-objective dynamic aisle layout planning, including handling distance constraint, backtracking distance constraint, and facility location constraint;

[0010] S3. Solve the above model based on the improved multi-objective immune cloning algorithm, where the improved multi-objective immune cloning algorithm is as follows: taking the immune cloning algorithm as the framework, combining the variable neighborhood search strategy based on Monte Carlo decision, and screening the superior individuals through the Pareto optimal mechanism.

[0011] Beneficial effects: The method of the present invention takes into account the workshop logistics backtracking, establishes a two-objective dynamic aisle layout planning model considering workshop logistics backtracking, enabling the method of the present invention to better solve the workshop layout problem; at the same time, the present invention uses an improved multi-objective immune cloning algorithm to solve the aforementioned model, which has higher solving accuracy and better stability, and can be well applied to the solution of this model. In summary, the method of the present invention can better provide decision support for the workshop aisle layout problem. Brief Description of the Drawings

[0012] Figure 1 It is a comparison diagram of the solution results of the method of the embodiment of the present invention and the existing algorithm. Detailed Embodiments

[0013] The following will clearly and completely describe the detailed embodiments of the present invention in conjunction with examples and drawings. Obviously, the described examples are only a part of the embodiments of the present invention, rather than all embodiments.

[0014] A two-objective dynamic aisle layout planning method for a workshop considering backtracking cost includes the following steps:

[0015] S1. Obtain the basic information of the workshop layout, including the material flow volume, facility conditions, and distances between facilities;

[0016] These can be obtained from the actual production process. The material flow volume between facilities represents the intensity of material interaction between different facilities, and the length of the facility is the dimension of the facility in the aisle direction when arranged along the aisle.

[0017] S2. Establish a two-objective dynamic aisle layout planning model: taking the minimum material handling cost and the minimum backtracking cost as the objective functions, and at the same time establishing the constraint conditions for the two-objective dynamic aisle layout planning, including the handling distance constraint, the backtracking distance constraint, and the facility location constraint;

[0018] Among them, the objective functions are as follows:

[0019]

[0020] In the formula, F 1 represents the minimum material handling cost; F 2represents the minimum backtracking cost; t represents the logistics stage number, and t = 0, 1, …, T, where T represents the total number of logistics stages; i and j both represent the facility numbers, and i, j = 0, 1, …, n, where n represents the maximum facility number, and i ≠ j; C tij represents the material flow volume between facility i and facility j in the t-th stage; C tji represents the material flow volume between facility j and facility i in the t-th stage; d tij represents the material handling distance between facility i and facility j in the t-th stage; A ti represents the displacement cost of facility i in the t-th stage compared to the previous stage; B ti represents a 0-1 variable. If facility i is rearranged in the t-th stage compared to the previous stage, then B ti = 1, otherwise it is 0; represents the backtracking distance between facility i and facility j in the t-th stage.

[0021] In this embodiment, the objective function value F 1 represents the minimum material handling cost, which is similar to the objective function of the conventional workshop layout; the difference is that in this embodiment, the objective function value F 2 is also considered, which represents the backtracking cost. This backtracking cost is mainly determined by the sum of the product of the unit distance of the facility and the backtracking distance. In the actual production process, we usually require the backtracking cost to be as low as possible.

[0022] The constraint conditions include:

[0023] The handling distance constraint, which is used to calculate the handling distance between facility i and facility j:

[0024]

[0025] In, d tij represents the material handling distance between facility i and facility j in the t-th stage; i and j both represent the facility numbers, and i, j = 0, 1, …, n, where n represents the maximum facility number, and i ≠ j; r represents the serial number of the row where the facility is located, and r = 1, 2; x tir represents the material interaction point coordinates of facility i located in the r-th row in the t-th stage; x tjr represents the material interaction point coordinates of facility j located in the r-th row in the t-th stage;

[0026] The backtracking distance constraint, which is used to calculate the backtracking distance between facility i and facility j:

[0027] In the formula, represents the backtracking distance between facility i and facility j in the t-th stage; Z tij represents a 0-1 variable. If facility i is located on the left side of facility j in the t-th stage, then Z tij= 1, otherwise 0;

[0028] Facility location constraint:

[0029]

[0030] M approaches positive infinity; Y tir represents a 0-1 variable. If facility i is located in the r-th row at the t-th stage, then Y tir = 1, otherwise 0; l i represents the length of facility i; p tijr represents a 0-1 variable. If facility i is located to the left of facility j and in the r-th row at the t-th stage, then p tijr = 1, otherwise 0; B ti represents a 0-1 variable. If facility i is rearranged at the t-th stage compared to the previous stage, then B ti = 1, otherwise 0; d ti represents the displacement distance of facility i at the t-th stage compared to the previous stage.

[0031] In this embodiment, the stage means that as the product iterates or the market demand changes, the product variety, production batches, and processes often change. As a result, the material flow between facilities will change accordingly. At this time, the production can be improved by rearranging the facilities in the workshop. For this reason, each rearrangement cycle is called a stage.

[0032] S3. Solve the above model based on the improved multi-objective immune cloning algorithm. The improved multi-objective immune cloning algorithm (MOIICA) is: taking the immune cloning algorithm as the framework, combining the variable neighborhood search strategy based on Monte Carlo decision, and screening the superior individuals through the Pareto optimal mechanism.

[0033] This step includes the following sub-steps:

[0034] S41. Initialize the model parameters; in this step, the parameters to be initialized are such as the population size N pop , cloning coefficient, maximum number of iterations, neighborhood search threshold, first threshold, etc.

[0035] S42. Generate an initial population of size N pop and perform non-dominated sorting on the initial population;

[0036] S43. Generate a memory bank population based on S42 and perform cloning operations on multiple objective individuals in the memory bank population to obtain a cloned population; when performing cloning operations, usually the first N_clone individuals in the memory bank population are selected. Here, the first N_clone individuals refer to the first N_clone individuals after non-dominated sorting.

[0037] S44, selecting an individual in the clone population, performing a neighborhood search operation, and adding the dominant solution to the memory bank population in combination with the Monte Carlo acceptance criterion;

[0038] The specific operation of this step is as follows: randomly select an individual in the clone population as the parent solution, process it through the neighborhood search operation to obtain the child solution, and compare the child solution with the parent solution: if the child solution is better than the parent solution, the child solution is added to the memory bank; if the parent solution is better than the child solution, the acceptance probability of the child solution is calculated based on the Monte Carlo criterion, and the acceptance probability is compared with the first threshold. If the acceptance probability is less than the first threshold, the child solution is accepted and added to the memory bank, otherwise the child solution is discarded. The calculation formula for the acceptance probability is as follows: o∈{1,2}, where δ o =F(S c )-F(S 0 ), F(S c ) is the objective function value of the optimal offspring at the oth optimization target, F(S 0 ) is the function value of the parent selected in each iteration on the current optimization objective; the first threshold is a number in the range of [0,1] and can be generated randomly.

[0039] S45, repeat S44 until the neighborhood search threshold is reached; the neighborhood search threshold is set to improve the convergence speed and search effect of the algorithm, so as to mine more valuable neighborhood solutions as much as possible and shorten the calculation time.

[0040] S46, repeat S43 to S45 until the number of iterations is greater than the number N_clone of target individuals in S43;

[0041] S47, performing mixed mutation operations on the individuals in the updated clone population in sequence, and adding the mutated individuals to the memory bank population and updating it;

[0042] Specifically, in this step, the mixed mutation operation includes: a two-segment mutation operation, a stage crossover mutation operation, and a two-point exchange mutation operation. The reason for selecting three mutation operations is that compared with the traditional aisle layout problem, this embodiment has a larger solution space. The combination of these three mutation operations can enhance the diversity of solutions, thereby preventing the algorithm from falling into a local optimum.

[0043] Among them, the two-fragment mutation operation refers to randomly selecting two non-interfering fragments on the chromosome at each stage and exchanging the genes on the two fragments.

[0044] The stage crossover mutation operation refers to performing the PMX operation on sequences of different stages and then recombining them into a new sequence. This is mainly considered because the final solution of the embodiments of the present invention is composed of facility sequences of multiple logistics stages. To further expand the search scope of the solution space and prevent the frontier solutions from relying too much on a single stage.

[0045] The two-point exchange mutation operation refers to introducing changes by exchanging the positions of two genes in an individual solution. First, two gene positions in the individual solution are randomly selected, and then the genes at these two positions are swapped to generate a new individual solution.

[0046] S48. Combine the updated memory pool population and the initial population, delete duplicate individuals, and perform non-dominated sorting on the combined population, and screen the top N pop non-dominated solutions and update the initial population;

[0047] S49. Repeat S43 - S48 until the maximum number of iterations is reached, and output the Pareto front solutions.

[0048] To further illustrate the effects of the method disclosed in the embodiments of the present invention, specific examples are used for illustration below.

[0049] The operating environment of this test case is: a laptop with a processor of Intel(R) Core(TM) i7-9750H, a main frequency of 2.6 GHz, and the Windows 11 operating system. Since there is currently no research on bi-DCAP and related experimental results, to verify the accuracy of the mathematical model in this article, MATLAB R2021b is used to call the exact solver Gurobi to perform exact solutions for different objectives of the model respectively, and the solution results are used as the reference basis for the algorithm.

[0050] In this embodiment, initial data is generated based on the method in the existing literature, and the literature is as follows: "Ahonen H, de Alvarenga A G, Amaral A R S. Simulated annealing and tabu search approaches for the corridor allocation problem[J]. European Journal of Operational Research. 2014, 232(1): 221-233". During the generation process, as shown in Table 1, the number of facilities n increases by 2 in sequence from 5 to 27. The facility length l of each facility i i is generated by a random number uniformly distributed in the interval [1, 10]. The material flow volume C from facility i to facility j ij is an integer, and there is a probability of being positive, and there is The probability is 0, and its value is also randomly generated uniformly in the interval [1, 10]. The probability P is randomly selected from the set {30, 60, 90}.

[0051] Table 1 Method for generating test cases

[0052]

[0053] Since bi-DCAP has the NP-hard property, as the scale of the facilities increases, the solution time grows exponentially. Therefore, the running time of the solver is set to 18000s. To reduce random errors, each test case is solved 10 times using the algorithm, and the solution results (rounded to two decimal places) are organized in Table 1. For the convenience of comparison, the minimum value obtained for each scale is shown in bold, and “—” indicates that this objective is not calculated for this time.

[0054] Table 2 Comparison of the solution results of Gurobi solver and MOIICA

[0055]

[0056]

[0057] As can be seen from Table 1, Gurobi can obtain the optimal solution for small-scale problems. The solution results of the algorithm are consistent with those of Gurobi in test cases S5 - S11, thus verifying the correctness of the mathematical model and the algorithm. The solution results of the algorithm are better than those of Gurobi in test cases S13 - S27, and the solution time is much lower than that of Gurobi in all test cases, thus proving the high efficiency of the proposed algorithm for solving bi-DCAP.

[0058] To compare the performance of the algorithms, five test cases C27 - 1 to C27 - 5 of scale 27 are selected. The bi-DCAP is solved using the Nondominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ) and the Multi-objective Particle Swarm Optimization (MOPSO) respectively. The hypervolume (HV) index is used to comprehensively evaluate the Pareto front solutions obtained by each algorithm. Each algorithm is run 10 times. To more intuitively compare the quality of the obtained front solutions, the HV index is normalized and the average value is taken, and a box plot is drawn as Figure 1 shown.

[0059] From Figure 1It can be seen that in the calculation examples C27-1 to C27-5, the mean HV of the results obtained by MOIICA is higher than the means of NSGA-II and MOPSO, and the median of the HV value is also higher than that of NSGA-II and MOPSO, and no outliers appear. It can be obtained therefrom that the non-dominated solution set solved by MOIICA has better quality, higher stability, better diversity and coverage than the non-dominated solution sets solved by NSGA-II and MOPSO.

[0060] As described above, it is only a preferred embodiment of the present invention, and there is no limitation to the present invention in any form. Although the present invention has been disclosed above with the preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments with equivalent changes by using the disclosed technical content within the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A workshop dual-objective dynamic aisle layout planning method considering backtracking cost, characterized in that: The following steps are involved: S1. Obtain basic information on workshop layout, including logistics volume, facilities and distances; S2. Establish a dual-objective dynamic aisle layout planning model: take the minimum material handling cost and the minimum backtracking cost as the objective function, and establish the constraints of the dual-objective dynamic aisle layout planning, including the handling distance constraint, the backtracking distance constraint, and the facility location constraint; S3. Solve the above model based on an improved multi-objective immune clonal algorithm. The improved multi-objective immune clonal algorithm is: using the immune clonal algorithm as a framework, combined with a variable neighborhood search strategy based on Monte Carlo judgment, and screening better individuals through a Pareto optimal mechanism.

2. The method according to claim 1, characterized in that The objective function is as follows: Where F1 represents the minimum material handling cost; F2 represents the minimum backtracking cost; t represents the logistics stage number, and t=0,1,…,T, T represents the total number of logistics stages; i and j both represent the facility number, and i,j=0,1,…,n, n represents the maximum facility number, and i≠j; C tij represents the logistics volume of facility i and facility j at stage t; C tji represents the logistics volume of facility j and facility i at stage t; d tij A represents the material handling distance between facility i and facility j at stage t; ti represents the displacement cost of facility i in stage t compared with the previous stage; B ti represents a 0-1 variable. If facility i is rearranged in stage t compared to the previous stage, then B ti =1, otherwise 0; represents the backtracking distance between facility i and facility j at stage t.

3. The method according to claim 1, characterized in that The constraints are as follows: Transport distance constraints: Where, d tij represents the material handling distance between facility i and facility j at stage t; i and j both represent facility numbers, and i, j = 0, 1, ..., n, n represents the maximum facility number, and i ≠ j; r represents the serial number of the row where the facility is located, and r = 1, 2; x tir represents the coordinates of the material interaction point of facility i located in row r at stage t; x tjr represents the coordinates of the material interaction point of facility j located in row r at stage t; Backtracking distance constraint: In the formula, represents the backtracking distance between facility i and facility j at stage t; Z tij represents a 0-1 variable. If facility i is to the left of facility j in stage t, then Z tij =1, otherwise 0; Facility location constraints: p tijr +p tjir ≤Y tir 、 p tijr +p tjir ≤Y tjr ,、p tijr +p tjir +1≥Y tir +Y tjr ,、 Y tir -Y (t-1)ir ≤B ti ,,Y (t-1)ir -Y tir ≤B ti ,、 Md ti ≥B ti ,、 In the formula, M tends to positive infinity; Y tir represents a 0-1 variable. If facility i is located in the rth row in stage t, then Y tir =1, otherwise 0; l i represents the length of facility i; p tijr represents a 0-1 variable. If facility i is to the left of facility j and is located in the rth row at stage t, then p tijr =1, otherwise 0; B ti represents a 0-1 variable. If facility i is rearranged in stage t compared to the previous stage, then B ti =1, otherwise 0; d ti Represents the displacement distance of facility i in stage t compared with the previous stage.

4. The method according to claim 1, characterized in that: S4 includes the following sub-steps: S41, initializing model parameters; S42, generating a scale of N pop , and perform non-dominated sorting on the initial population; S43, create a memory bank population (currently empty), and based on the initial population generated by S42, select the first N_clone individuals to perform cloning operations to obtain a clone population; S44, select an individual in the clone population, perform a neighborhood search operation, and add the dominated solution to the memory bank population in combination with the Monte Carlo acceptance criterion; S45, repeat S44 until the neighborhood search threshold is reached; S46, repeat S43 to S45 until the number of iterations is greater than the number of target individuals in S43; S47, perform mixed mutation operations on the individuals in the clone population in turn, and add the mutated individuals to the memory bank population and update them; S48, merge the updated memory bank population and the initial population, delete duplicate individuals, and perform non-dominated sorting on the merged population to screen the first N pop non-dominated solutions and update the initial population; S49, repeat S43 to S48 until the maximum number of iterations is reached, and output the Pareto front solution.

5. The method according to claim 4, characterized in that S44 includes the following operations: randomly selecting an individual in the clone population as the parent solution, processing it through a neighborhood search operation to obtain a child solution, and comparing the child solution with the parent solution: if the child solution is better than the parent solution, the child solution is added to the memory bank; if the parent solution is better than the child solution, the acceptance probability of the child solution is calculated based on the Monte Carlo criterion, and the acceptance probability is compared with a first threshold value. If the acceptance probability is less than the first threshold value, the child solution is accepted and added to the memory bank, otherwise the child solution is discarded.

6. The method according to claim 4, characterized in that In S47, the mixed mutation operation includes: a two-segment mutation operation, a stage crossover mutation operation and a two-point exchange mutation operation.

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