Double-layer and double-row layout method considering separated human-vehicle transport elevator

Abstract

The invention discloses a double-layer double-row layout method considering a separated human-vehicle transport elevator, which comprises the following steps: S1, a mixed integer linear programming model is established, the model comprises objective functions and constraint conditions, the objective functions are minimum material movement cost and minimum personnel movement cost, and the constraint conditions are constraint conditions; the constraint conditions comprise machine and line relation constraint, machine position relation constraint, machine and layer relation constraint, cargo elevator position constraint, machine and cargo elevator position constraint, safety layout constraint, personnel movement constraint and material movement constraint; s2, generating an initial population based on three-layer coding and reverse learning; and S3, solving the model based on a memetic algorithm and a solver. Based on a transportation scene in a real workshop, in order to improve the layout safety, the invention provides a new double-layer double-row layout structure considering the separated human-vehicle transportation elevator, and meanwhile, a corresponding layout method is established, and the method has a relatively good effect.

Description

Technical Field

[0001] The invention relates to the technical field of facility layout, and in particular to a double-layer double-row layout method considering a separated person-vehicle transport elevator. Background Art

[0002] With the acceleration of urbanization and the rising cost of land, industrial land is in short supply. Enterprises tend to expand space vertically, implement the policy of "industrial upstairs", and maximize land utilization by building multi-story workshops. In this environment, the multi-floor layout problem (MFLP) came into being and gradually became a research hotspot for enterprises and many scholars. The multi-floor layout problem is to arrange facilities / machines on multiple floors and determine their detailed layout on each floor to optimize the required goals. At the same time, elevators are necessary transportation equipment for vertical logistics in MFLP. They are the only way for people and vehicles on different floors to move. The correct use of elevators plays a vital role in the safety of workshop logistics interaction. Summary of the invention

[0003] To solve at least one of the above problems, the present invention proposes a double-deck double-row layout method of a separated passenger-vehicle transport elevator.

[0004] The technical solution of the present invention is: a double-deck double-row layout method considering a separated person-vehicle transport elevator, comprising the following steps:

[0005] S1. Establish a mixed integer linear programming model, the model includes an objective function and constraints, the objective function is the minimum material movement cost and the minimum personnel movement cost, the constraints include: machine-row relationship constraints, machine position relationship constraints, machine-layer relationship constraints, freight elevator position constraints, machine and freight elevator position constraints, safety layout constraints, personnel movement constraints, material movement constraints;

[0006] S2. Generate an initial population based on three-layer coding and reverse learning, wherein the three-layer coding includes the following steps:

[0007] Create a three-layer coding expression: x i ={fs i ,rb i ,ep i}, x represents an individual in the population, subscript i represents the individual number, fs represents the machine sequence, rb represents the row breakpoint sequence, and ep represents the elevator position sequence;

[0008] A non-repeating sequence with a size equal to the number of machines is randomly generated as the machine sequence fs, and then three locations are randomly selected in the facility sequence as branch breakpoints rb. Finally, the distribution row of the freight elevator is determined, and the left-right position relationship between the freight elevator and the machine is randomly determined.

[0009] A non-repeating sequence of the size of the number of machines is randomly generated as the machine sequence fs. Then three locations are randomly selected in the facility sequence as the branch breakpoints rb. Finally, the distribution row of the freight elevator is determined, and the left-right position relationship between the freight elevator and the machine is randomly determined.

[0010] S3. Solve the model based on the memetic algorithm and solver.

[0011] Beneficial effects: Based on the transportation scenario in the real workshop, this paper proposes a new double-layer double-row layout structure considering the separated passenger-vehicle transportation elevator to improve the safety of the layout. By analyzing the relevant constraints in the layout process, a mixed integer programming model for this problem is established with the minimization of employee movement cost and material handling cost as the optimization goal. Subsequently, a multi-objective adaptive memetic algorithm is developed for the combined continuous dual characteristics of the modified layout, and the effectiveness of the algorithm and the significance of the improvement effect are verified by solving examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a schematic diagram of three-layer coding;

[0013] Figure 2 Schematic diagram of crossover mutation;

[0014] Figure 3 This is a schematic diagram of the layout of test example 1. DETAILED DESCRIPTION

[0015] The specific implementation modes of the present invention will be described clearly and completely below with reference to examples and drawings. Obviously, the described examples are only some embodiments of the present invention, rather than all embodiments.

[0016] A double-deck double-row layout method considering a separated passenger-vehicle transport elevator comprises the following steps:

[0017] S1 establishes a mixed integer linear programming model, the model includes an objective function and constraints, the objective function is the minimum material movement cost and the minimum personnel movement cost, the constraints include: machine-row relationship constraints, machine position relationship constraints, machine-layer relationship constraints, freight elevator position constraints, machine and freight elevator position constraints, safety layout constraints, personnel movement constraints, material movement constraints;

[0018] In conventional layout methods, only MHC (material handling cost), which is the minimum material movement cost of this embodiment, is usually considered. This is mainly because the material movement cost is relatively high and usually requires the assistance of mechanical equipment. However, in modern production processes, due to the small number of employees, a single employee usually operates and manages multiple processes and machines, and the movement of personnel is also a more important factor in the production process: more ineffective personnel movement may lead to an increase in production costs and production time. At the same time, ineffective personnel movement will also lead to a waste of labor costs. Therefore, from the perspective of reducing costs and increasing efficiency, personnel movement is also an important optimization goal in the modern production process.

[0019] In this step, the objective function is the minimum material movement cost and the minimum personnel movement cost, wherein the personnel movement cost is a relatively complex concept, and there is currently no formula to calculate it. In this embodiment, the inventor quantifies it based on the calculation rule of MHC. The final objective function is as follows.

[0020] Minimum personnel movement cost:

[0021]

[0022] Where, Obj 1 is the minimum personnel movement cost; S represents the machine number set, S = {1, 2, ..., |S|}; o and p both represent machine numbers, o, p∈S; FH op is the flow of people between machine o and machine p; DH op is the distance a person moves from machine o to machine p.

[0023] Minimum material movement cost:

[0024]

[0025] Where, Obj 2 is the minimum material movement cost; FV op DV is the logistics volume between machine o and machine p; op is the distance the material moves from machine o to machine p.

[0026] The above-mentioned minimum personnel movement cost and minimum material movement cost can help people in this field to evaluate the layout more accurately and formulate optimization measures more targetedly.

[0027] S2. Generate an initial population based on three-layer coding and reverse learning, wherein the three-layer coding includes the following steps:

[0028] Create a three-layer coding expression: x i ={fs i ,rbi ,ep i}, x represents an individual in the population, subscript i represents the individual number, fs represents the machine sequence, rb represents the row breakpoint sequence, and ep represents the elevator position sequence;

[0029] For the initial population, its size is limited to N, and the population set X = {x i |i∈1,2,…,N}, for the expression of three-layer coding, the line breakpoint sequence indicates that, in this embodiment, since there are two-layer four-line machine settings, the line breakpoint sequence indicates that a line break setting is performed at a certain machine.

[0030] A non-repeating sequence with a size equal to the number of machines is randomly generated as the machine sequence fs, and then three locations are randomly selected in the facility sequence as branch breakpoints rb. Finally, the distribution row of the freight elevator is determined, and the left-right position relationship between the freight elevator and the machine is randomly determined.

[0031] A non-repeating sequence of the size of the number of machines is randomly generated as the machine sequence fs. Then three locations are randomly selected in the facility sequence as the branch breakpoints rb. Finally, the distribution row of the freight elevator is determined, and the left-right position relationship between the freight elevator and the machine is randomly determined;

[0032] Specifically, Figure 1 As shown in (a), the number of given machines is 5. First-level encoding: Generate a machine sequence fs = {2, 5, 1, 3, 4} in a random manner. Second-level encoding: Figure 1 As shown in the green numbers in (b), there are 4 row breakpoint positions, and then the row breakpoint sequence rb={1,3,4} is randomly generated. The third level of encoding: randomly generate a number w≤2, rw means that the freight elevator is distributed in the wth row; then select the remaining machines in the row where the freight elevator is located in the two-layer area, which are machine 2 and machine 3; Figure 3 As shown by the orange numbers in (b), there are two available freight elevator positions in the two layers, and then the freight elevator position sequence ep = {1,1,2} is randomly generated. Figure 1 As shown in (c), when the algorithm decodes, the machine distribution sequence can be determined according to rb: fs = {2} in the first row of the first floor; fs = {5,1} in the second row of the first floor; fs = {3} in the first row of the second floor; fs = {4} in the second row of the second floor. The location of the freight elevator can be determined according to ep: the first number 1 in the sequence indicates that the freight elevator is located at r1, the second number 1 indicates that the freight elevator is located at position 1 of r1 on the first floor, and the third number 2 indicates that the freight elevator is located at position 2 of r1 on the second floor. Therefore, the layout plan after decoding is as follows: Figure 1 (d) as shown.

[0033] In order to increase the diversity of the initial population, in this embodiment, a reverse learning strategy is also used and applied to the machine sequence. The calculation method is as follows:

[0034] x i,j =[x i,1 ,x i,2 ,x i,3 ,...,x i,|S| ]

[0035] lb i =min(x i,|S| ),ub i =max(x i,|S| )

[0036]

[0037] In the formula, x i,j represents the machine number at position j of individual i, |S| represents the number of machines, and x o is the inverse solution of x, o Represents x i,j The corresponding reverse machine number.

[0038] S3. Solve the model based on the memetic algorithm and solver.

[0039] In this embodiment, it is necessary not only to determine the sequence of machines but also their final positions, so it has the dual nature of combination and continuous optimization. This paper integrates linear programming LP into MA to form a two-stage solution method. In the first stage of the algorithm, the encoding and decoding method of MA is used to obtain the solution sequence and the relative position between machines, and the variable a is determined. ocw , b opc , e opcw and In the second stage of the algorithm, the above variables are substituted into the LP model to obtain the final position of the machine and the freight elevator, and the variable x is determined. o The value of .

[0040] For the meme algorithm, it mainly includes the following steps:

[0041] Crossover and mutation: Crossover and mutation operations are commonly used in intelligent optimization algorithms, which can increase population diversity and enhance the global search capabilities of the algorithm. Figure 2 (a) is a crossover operation, which acts on the machine sequence of the population individuals. Generate a random number rand∈[0,1]. If rand <p c , perform crossover operation, p c is the crossover probability. Figure 2As shown in (a), the gene fragments [1,2,3] and [5,2,4] that need to be crossed by the parent are randomly selected; after the exchange, duplicate gene numbers [5,4] and [3,1] appear on the single sequence; a one-to-one correspondence can be obtained from the exchanged fragments: numbers 5 and 1, numbers 4 and 3; finally, the conflicting numbers are eliminated to generate two new individuals. Figure 2 (b) is a mutation operation, which acts on the elevator position sequence of individuals in the population. <p m , perform mutation operation, p m is the mutation probability. Figure 2 As shown in (b), the freight elevator of the parent generation is distributed on the first row, and the formula w new =3-w, the descendant freight elevator is distributed on the second row. Then, the freight elevator position sequence is randomly generated according to the decoding method in the previous section to complete the mutation operation.

[0042] Selection operation: After completing the crossover and mutation operation, the algorithm needs to perform a selection operation based on the fitness values ​​of the individuals in the population. DFDRLP_SHVE is a dual-objective problem and cannot directly distinguish between good and bad individuals. Therefore, this embodiment uses the Pareto idea to judge the relationship between the advantages and disadvantages of individuals. If the offspring is better than the parent, it is directly replaced; if the offspring is worse than the parent, the parent is retained; if the offspring and the parent are not mutually dominant, both the parent and the offspring are retained. Based on the above situation, a new population P is generated.

[0043] Local search: Local search can greatly speed up the convergence of the algorithm, but it is easy to cause the algorithm to fall into the local optimum. To solve this defect, we introduced the adaptive learning factor ER. ER is the estimated success probability obtained by analyzing the previous accumulated experience during the algorithm iteration process, and can dynamically adjust the number of individuals executing the local search operator. This paper designs four local search operators for the solution sequence: LS 1 It is a reverse operation, LS 2 It is a two-point exchange operation, LS 3 It is a single-point insertion operation, LS 4 It is a row breakpoint mutation operation. The specific steps of this local search process are as follows:

[0044] Step 1: Input population P, population size N, current iteration number iter = 1, the upper limit of iteration number is iter_max, i∈{1,2,3,4}, ER iter,i =1 / 4, the number of individuals NL executing the local search operator iter,i , storage matrix SM iter,i = [], storage upper limit L = 5, actual success probability RR iter,i =0, reward factor r = 1 / N;

[0045] Step 2: Calculate NL iter , If sum(NL) < N, then randomly select LS in sequence i , and let NL iter,i = NL iter,i + 1, and stop when sum(NL) = N;

[0046] Step 3: NL iter,i individuals in the population respectively execute the LS i operation;

[0047] Step 4: Record the number of offspring that are better than the parent or non-dominant to each other as the successful times a iter,i , and record the number of offspring that are inferior to the parent as the failure times b iter,i , and fill them into the matrix SM iter,i = [SM iter,i ,[a iter,i ; b iter,i ; If size(SM i ,2) > L, then delete them sequentially from the front to the back;

[0048] Step 5: Calculate RR iter,i , if a iter,i = 0, RR iter,i = 1 / N, otherwise RR iter,i = sum(SM iter,i (1,:)) / sum(SM iter,i ));

[0049] Step 6: Normalize RR iter,i , if RR iter,i / ER iter,i > 1, then RR iter,i = RR iter,i + r;

[0050] Step 7: Normalize RR again iter,i , and update the population P';

[0051] Step 8: Let iter = iter + 1, if iter ≤ iter_max, let ER iter,i = RR iter-1,i , and return to Step 2; otherwise output P'.

[0052] After calculating the values of variables a ocw , b opc , e opcw and by the memetic algorithm, substitute these variables into the model, and use the GUROBI solver to solve it, and finally obtain the fitness value of the sequence.

[0053] In order to further illustrate the effects of the embodiments of the present invention, a specific example is used below to illustrate the effects of the embodiments of the present invention.

[0054] Test case 1: In this test case, the case size is 9, and the passenger elevator is set on the left side of the corridor. The data included in this case are as follows:

[0055] l=[2,8,9,7,3,4,6,8,9,2];wi 1 =2;wi 2 =2;

[0056]

[0057] The final results are shown in Table 1:

[0058] Table 1 Results of Test Example 1

[0059]

[0060] As shown in Table 1, the Gap values ​​of the models corresponding to the four goals are all 0, indicating that the optimal solution is obtained. As can be seen from Table 1, the goal programming method can obtain the optimal value of a single goal and provide a selection plan that is more in line with the needs of the enterprise. We plot the solution obtained by the goal programming method as follows Figure 3 As shown, the accuracy of the model established in this paper is verified. Figure 3 The E in the middle represents a freight elevator. Figure 3 (a) is a schematic diagram showing the layout of layout 3, Figure 3 (b) is a schematic diagram showing the layout of layout 4. Figure 3 It can be seen that since the passenger elevator is located on the far left side of the corridor, when minimizing employee movement costs is the primary goal, the location of the freight elevator has little impact, and all machines are distributed to the left. When minimizing vehicle handling costs is the primary goal, the location of the freight elevator has a greater impact, and the machines are distributed to both sides around the freight elevator.

[0061] Test Example 2: Based on the original data of Test Example 1, we assume that the passenger flow is half of the logistics flow as supplementary data to improve the example according to the characteristics of the problem. These three are benchmark examples in this field, including the logistics flow matrix and the facility length matrix (S9 has been given above, S5 and S10 can be obtained from the literature, for details, see the literature "Mathematical formulation and a novel two-stage algorithm for double-row layout problem with fixed loading and unloading points" by Ji Dan et al.). After a large number of preliminary experiments, the algorithm solution parameters are determined: population size N = 50, crossover probability Pc = 0.9, mutation probability Pm = 0.2. The termination condition of the embodiment of the present invention is the runtime Runtime. For ease of comparison, the calculation results of Gurobi are directly used as a comparative example.

[0062] Table 2 Results of using Gurobi directly

[0063] Calculation example Time / s <![CDATA[Obj 1 ]]> <![CDATA[Obj 2 ]]> Machine sequence S5 0.72 95 154 2|1|53|4 S9 231.98 1252.5 2026 954|7618|2|3 S10 3798.24 1308 2198 11026|7548|3|9

[0064] Table 3 Results of using the method of the embodiment of the present invention

[0065]

[0066] It can be seen from Table 2 and Table 3 that when the example scale is small (for example, the number of examples is 5), the speed of obtaining the result by directly using Gurobi is faster than that of the method of this embodiment; however, when the example scale increases, the time required by the method of this embodiment is much less than that of directly using Gurobi. This shows that compared with Gurobi, this embodiment has more advantages in large-scale examples.

[0067] Meanwhile, Gurobi usually only gives a relatively optimal layout solution, while this embodiment gives multiple non-inferior solutions, which can give decision makers more room for choice.

[0068] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from 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 falls within the scope of the technical solution of the present invention.

Claims

1. A double-deck double-row layout method for a separated passenger-vehicle transport elevator, characterized in that: The following steps are involved: S1. Establish a mixed integer linear programming model, the model includes an objective function and constraints, the objective function is the minimum material movement cost and the minimum personnel movement cost, the constraints include: machine-row relationship constraints, machine position relationship constraints, machine-layer relationship constraints, freight elevator position constraints, machine and freight elevator position constraints, safety layout constraints, personnel movement constraints, material movement constraints; S2. Generate an initial population based on three-layer coding and reverse learning, wherein the three-layer coding includes the following steps: Create a three-layer coding expression: x i ={fs i ,rb i ,ep i }, x represents an individual in the population, subscript i represents the individual number, fs represents the machine sequence, rb represents the row breakpoint sequence, and ep represents the elevator position sequence; A non-repeating sequence with a size equal to the number of machines is randomly generated as the machine sequence fs, and then three locations are randomly selected in the facility sequence as branch breakpoints rb. Finally, the distribution row of the freight elevator is determined, and the left-right position relationship between the freight elevator and the machine is randomly determined. A non-repeating sequence of the size of the number of machines is randomly generated as the machine sequence fs. Then three locations are randomly selected in the facility sequence as the branch breakpoints rb. Finally, the distribution row of the freight elevator is determined, and the left-right position relationship between the freight elevator and the machine is randomly determined. S3. Solve the model based on the memetic algorithm and solver.

2. The method according to claim 1, characterized in that: The minimum personnel movement cost is as follows: Where Obj1 is the minimum personnel movement cost; S represents the machine number set, S = {1, 2, ..., |S|}; o and p both represent machine numbers, o, p∈S; FH op is the flow of people between machine o and machine p; DH op is the distance a person moves from machine o to machine p; The minimum material movement cost is as follows: Where Obj2 is the minimum material movement cost; FV op DV is the logistics volume between machine o and machine p; op is the distance the material moves from machine o to machine p.

3. The method according to claim 1, characterized in that The constraints specifically include: Relationship constraints between machines and rows: Where C is the set of floor numbers, C = {1, 2}, c∈C; W is the set of distribution row numbers, W = {1, 2}, w∈W; Machine position relationship constraints: In the formula, e opcw means that if machine o and machine p are both distributed in the wth row of layer c, and p is to the right of o, it is 1, otherwise it is 0, o, p ∈ {S, m}, c ∈ C, w ∈ W, S represents the machine number set, S = {1, 2, ..., |S|}; e pocw means that if machine o and machine p are both distributed in the wth row of layer c, and o is to the right of p, then it is 1, otherwise it is 0; a ocw Indicates that if machine o is distributed in the wth row of layer c, it is 1, otherwise it is 0; a pcw It means that if machine p is distributed in the wth row of layer c, it is 1, otherwise it is 0; Relationship constraints between machines and layers: Where b opc It means that if machine o and machine p are both distributed in layer c, its value is 1, otherwise it is 0; Cargo elevator location constraints: In the formula, Indicates that if the freight elevator is located in the wth row, its value is 1, otherwise it is 0; Machine and cargo elevator position constraints: In the formula, x o represents the horizontal coordinate of machine o, l o represents the length of machine o, xm represents the horizontal coordinate of the freight elevator; wi2 represents the length of the passenger elevator and the freight elevator; Safe layout constraints: In the formula, Z = sum(l o ); Personnel movement constraints: In the formula, DH op represents the distance a person moves from machine o to machine p; x p represents the horizontal coordinate of machine p; wi1 represents the width of the passenger elevator and freight elevator; Material movement constraints Where DV op is the distance the material moves from machine o to machine p; Indicates the distance from machine o to the horizontal coordinate of the center of the freight elevator; It represents the distance from machine p to the horizontal coordinate of the center of the freight elevator; h represents the height of the floor.

4. The method according to claim 1, characterized in that: In S3, the solution sequence and the relative positions between machines are obtained based on the meme algorithm and substituted into the model, and then the model is solved using GUROBI.

5. The method according to claim 1 or 4, characterized in that: An adaptive learning factor is inserted into the local search process of the meme algorithm. The adaptive learning factor is used to dynamically adjust the number of individuals executing the local search operator according to the estimated success probability obtained through analysis based on previous accumulated experience during the algorithm iteration process.

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