Consider the double - layer and double - row layout method of a separated human - vehicle transportation elevator

Abstract

The present invention discloses a double - layer and double - row layout method for a separated human - vehicle transportation elevator, comprising the following steps: S1, establishing a mixed - integer linear programming model, the model including an objective function and constraint conditions, the objective function being the minimum material movement cost and the minimum personnel movement cost, and the constraint conditions including: constraints on the relationship between machines and rows, constraints on the positional relationship between machines, constraints on the relationship between machines and floors, constraints on the position of freight elevators, constraints on the position of machines and freight elevators, safety layout constraints, personnel movement constraints, and material movement constraints; S2, generating an initial population based on three - layer coding and reverse learning; S3, solving the model based on the memetic algorithm and a solver. The present invention is based on the transportation scenarios in real workshops. To improve the safety of the layout, a new double - layer and double - row layout structure considering a separated human - vehicle transportation elevator is proposed, and a corresponding layout method is established, and this method has good effects.

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 scale 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 rows of the freight elevator are determined, and the left-right position relationship between the freight elevator and the machine is randomly determined.

[0009] Randomly generate a non-repeating sequence with the scale of the number of machines as the machine sequence fs. Subsequently, randomly select 3 locations in the facility sequence as the branch break points rb. Finally, determine the distribution rows of the freight elevators and randomly determine the left-right position relationship between the freight elevators and the machines

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

[0011] Beneficial effects: Based on the transportation scenarios in the actual workshop, in order to improve the safety of the layout, a new double-layer and double-row layout structure considering the separated human-vehicle transportation elevator is proposed. By analyzing the relevant constraints in the layout process and taking the minimization of the employee movement cost and the material handling cost as the optimization objectives, a mixed integer programming model for this problem is established. Subsequently, aiming at the combined continuous dual characteristics of this layout, a multi-objective adaptive memetic algorithm is developed, and the effectiveness of the algorithm and the significance of the improvement effect are verified through the solution of numerical examples Description of the Drawings

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

[0013] Figure 2 It is a schematic diagram of crossover mutation

[0014] Figure 3 It is a schematic diagram of the layout of Test Example 1 Detailed Implementation Manner

[0015] The following will clearly and completely describe the detailed implementation manner of the present invention in conjunction with the examples and the drawings. Obviously, the described examples are only a part of the embodiments of the present invention, rather than all the embodiments

[0016] A double-layer and double-row layout method considering the separated human-vehicle transportation elevator includes the following steps

[0017] S1. Establish a mixed integer linear programming model, the model includes an objective function and constraint conditions, the objective function is the minimum material movement cost and the minimum personnel movement cost, and the constraint conditions include: the constraint of the relationship between the machine and the row, the constraint of the machine position relationship, the constraint of the relationship between the machine and the layer, the constraint of the freight elevator position, the constraint of the relationship between the machine and the freight elevator, the safety layout constraint, the personnel movement constraint, and the material movement constraint

[0018] In conventional layout methods, usually only the MHC (Material Handling Cost), i.e., the minimum material movement cost in this embodiment, is 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 relatively small number of employees, a single employee usually operates and manages multiple processes and machines. Personnel movement is also a relatively important factor in the production process: excessive ineffective personnel movement may lead to an increase in production costs and production time. At the same time, ineffective personnel movement also results in a waste of labor costs. Therefore, from the perspective of cost reduction and efficiency improvement, personnel movement is also an important optimization goal in modern production processes.

[0019] In this step, the objective function is the minimum material movement cost and the minimum personnel movement cost. Among them, the personnel movement cost is a relatively complex concept, and there is currently no formula for calculating it. In this embodiment, the inventor quantifies it based on the calculation rules of MHC. The final obtained objective function is as follows.

[0020] Minimum personnel movement cost:

[0021]

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

[0023] Minimum material movement cost:

[0024]

[0025] In the formula, Obj 2 is the minimum material movement cost; FV op is the material flow between machine o and machine p; DV op is the movement distance of materials from machine o to machine p.

[0026] Through the above minimum personnel movement cost and minimum material movement cost, it helps personnel in this field to more accurately evaluate the layout and simultaneously formulate more targeted optimization measures.

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

[0028] Establish a three - layer coding expression: x i = {fs i , rbi , ep i}, where \(x\) represents an individual in the population, the subscript \(i\) represents the individual number, \(fs\) represents the machine sequence, \(rb\) represents the row break point 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 three - layer encoding expression, the row break point sequence indicates that in this embodiment, due to the presence of two - layer and four - row machine settings, the row break point sequence represents the line - break setting at a certain machine.

[0030] Randomly generate a non - repeating sequence with the size of the number of machines as the machine sequence \(fs\). Then randomly select 3 positions in the facility sequence as the branch row break points \(rb\). Finally, determine the distribution row of the elevator and randomly determine the left - right position relationship between the elevator and the machines.

[0031] Randomly generate a non - repeating sequence with the size of the number of machines as the machine sequence \(fs\). Then randomly select 3 positions in the facility sequence as the branch row break points \(rb\). Finally, determine the distribution row of the elevator and randomly determine the left - right position relationship between the elevator and the machines;

[0032] Specifically, as Figure 1 (a) shows, given that the number of machines is 5. First - layer encoding: Randomly generate a machine sequence \(fs=\{2,5,1,3,4\}\). Second - layer encoding: As shown by the green numbers in Figure 1 (b), there are 4 row break point positions. Then randomly generate the row break point sequence \(rb = \{1,3,4\}\). Third - layer encoding: Randomly generate a number \(w\leq2\), \(rw\) represents that the elevator is distributed in the \(w\) - th row; then select the remaining machines in the row where the elevator is located in the two - layer area, which are machine 2 and machine 3 respectively; as Figure 3 (b) shows the orange numbers, there are 2 available elevator positions in each of the two - layer areas. Then randomly generate the elevator position sequence \(ep=\{1,1,2\}\). As Figure 1 (c) shows, during algorithm decoding, according to \(rb\), the machine distribution sequence can be determined: \(fs = \{2\}\) in the first row of the first layer; \(fs=\{5,1\}\) in the second row of the first layer; \(fs = \{3\}\) in the first row of the second layer; \(fs=\{4\}\) in the second row of the second layer. According to \(ep\), the position of the elevator can be determined: the first number 1 in the sequence represents that the elevator is located in \(r1\), the second number 1 represents that the elevator is located at position 1 in \(r1\) of the first layer, and the third number 2 represents that the elevator is located at position 2 in \(r1\) of the second layer. Therefore, the decoded layout scheme is as Figure 1 (d) shows.

[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. Its 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] Wherein, x i,j represents the machine number at position j of individual i, |S| represents the number of machines, x o is the reverse solution of x, x o represents the reverse machine number corresponding to x i,j .

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

[0039] In this embodiment, not only the sequence of machines needs to be determined, but also their final positions, so it has the dual nature of both combinatorial and continuous optimization. In this paper, linear programming LP is incorporated into MA to form a two-stage solution method. In the first stage of the algorithm, the solution sequence and the relative positions between machines are obtained by using the encoding and decoding methods of MA, and the variables a ocw , b opc , e opcw and are determined. In the second stage of the algorithm, the above variables are substituted into the LP model to solve for the final positions of the machines and the freight elevator, and the value of the variable x o is determined.

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

[0041] Crossover and mutation: Crossover and mutation operations are commonly used means in intelligent optimization algorithms, which can increase population diversity and improve the global search ability of the algorithm. Figure 2 (a) is the crossover operation, which acts on the machine sequence of the population individuals. Generate a random number rand ∈ [0, 1], if rand < p c , perform the crossover operation, p c is the crossover probability. For example Figure 2 ​(As shown in (a), randomly select the gene segments [1, 2, 3] and [5, 2, 4] of the parent generation to be crossed; after the exchange, duplicate gene numbers [5, 4] and [3, 1] appear on a single sequence; from the exchanged segments, a one-to-one correspondence can be obtained: number 5 and 1, number 4 and 3; finally, eliminate the conflicting numbers to generate two new individuals.) Figure 2 ((b) is the mutation operation, which acts on the elevator position sequence of the population individuals. If rand < p m , perform the mutation operation, where p m is the mutation probability. As Figure 2 (shown in (b), the elevators of the parent generation are distributed on the first row. After calculation by the formula w new = 3 - w, the elevators of the offspring are distributed on the second row. Subsequently, randomly generate the elevator position sequence according to the decoding method in the previous section to complete the mutation operation.)

[0042] Selection operation: After completing the crossover and mutation operations, the algorithm needs to perform a selection operation according to the fitness values of the population individuals. DFDRLP_SHVE is a two-objective problem, and it is impossible to directly distinguish the quality of individuals. Therefore, in this embodiment, the Pareto idea is used to judge the superiority and inferiority relationship between individuals. If the offspring is superior to the parent, directly replace it; if the offspring is inferior to the parent, retain the parent; if the offspring and the parent show a non-dominant relationship, retain both the parent and the offspring. According to the above situation, a new population P is generated.)

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

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

[0045] Step 2: Calculate NL iter , If sum(NL) < N, then randomly select LS one by one 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: Denote the number of offspring that are better than the parent or non-dominant to each other as the successful times a iter,i , and denote 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] To further illustrate the effects of the embodiments of the present invention, specific examples are used for illustration below.

[0054] Test Example 1: In this test example, the scale of the calculation example is 9, and the passenger elevator is set on the left side of the corridor. The data included in this calculation example is 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 model solution Gap values corresponding to the four objectives are all 0, indicating that the optimal solutions are all obtained. It can be seen from Table 1 that the goal programming method can obtain the optimal values of individual objectives and can provide a selection scheme that better meets the needs of enterprises. We draw the scheme obtained by the goal programming method as Figure 3 shown, verifying the accuracy of the model established in this paper. Figure 3 In which E represents the freight elevator, Figure 3 (a) represents the layout schematic diagram of Layout 3, Figure 3 (b) represents the layout schematic diagram of Layout 4. It can be Figure 3 seen that since the passenger elevator is located at the far left of the corridor, when the minimization of the employee movement cost is the primary goal, the position of the freight elevator has little influence, and all machines tend to be distributed on the left side. When the minimization of the vehicle handling cost is the primary goal, the position of the freight elevator has a greater influence, and the machines are distributed on both sides around the freight elevator.

[0061] Test Example 2: Based on the original data of Test Example 1, for the problem characteristics, we assumed that the pedestrian flow was half of the material flow as supplementary data to improve the example. These three are all benchmark examples in this field, including the material flow matrix and the facility length matrix (S9 has been given above, and S5 and S10 can be obtained by referring to 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 Dan Ji, etc.). After a large number of preliminary experiments, the solution parameters of the algorithm were determined: the population size N = 50, the crossover probability Pc = 0.9, and the mutation probability Pm = 0.2. The termination condition of the embodiment of the present invention is the running time Runtime. For the convenience of comparison, the calculation results of Gurobi were directly used as the comparative example.

[0062] Table 2 Directly adopt the results of Gurobi

[0063] 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 adopting the method of the embodiment of the present invention

[0065]

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

[0067] At the same time, Gurobi usually only gives a relatively optimal layout plan, while this embodiment will give multiple non-inferior solutions, which can give decision-makers more choice space.

[0068] The above is only a preferred embodiment of the present invention, and does not impose any form of limitation on the present invention. Although the present invention has been disclosed above with a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the equivalent embodiments by using the above-disclosed technical content without departing from 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 still fall 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 the same size as 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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