CN113779676B - Aisle arrangement method considering material loading and unloading points and asymmetric flow - Google Patents
Aisle arrangement method considering material loading and unloading points and asymmetric flow Download PDFInfo
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Abstract
The invention discloses a passageway arrangement method considering material loading and unloading points and asymmetric flow, which comprises the following steps: firstly, establishing a mathematical model and constraint conditions by taking the lowest total logistics cost as a target; and then solving the aisle arrangement model to realize the optimal setting of the aisle. The invention adopts a gray wolf optimization algorithm fused with reverse learning to solve, the algorithm adopts a double-layer integer coding mode to generate an initial solution, a reverse learning mechanism and a population updating mechanism are fused to expand the search solution space, and a double-threshold stopping criterion is added to reduce the redundant iterative process so as to improve the solving efficiency of the algorithm.
Description
Technical Field
The invention relates to the technical field of facility layout, in particular to a passageway arrangement method considering material loading and unloading points and asymmetric flow.
Background
The aisle arrangement problem (Corridor Allocation Problem, CAP) is a new form of facility layout problem, which adopts a layout form that facilities are continuously and gaplessly arranged at two sides of an aisle from the same starting point, and finally, the purpose of minimizing the cost of the logistics is achieved. CAP has good layout and high transportation efficiency, and can be widely used in fields such as service industry and manufacturing industry, such as classroom, administrative building, shop, hospital ward, etc., and layout design of microchip in integrated circuit board, layout design of semiconductor production line, etc. CAP has wide application prospect and huge potential value, and the proposal of CAP draws great attention to people, and becomes a new research hotspot in the field of facility layout.
The material handling points (Material Loading and Unloading Points, MLUP) are designated places where materials are manually or mechanically loaded into or unloaded from the transport equipment, and are important factors in the layout of the facility, the placement of which directly affects the cost of handling the materials. In conventional CAPs, the MLUP is located at the midpoint of the facility's immediate aisle edge, while in actual production activities, to avoid product mix-ups and transport path intersections, efficient handling is achieved, where the MLUP is placed in different locations, so it is necessary to consider the MLUP during layout. In addition, in the existing study of Facility layout problem (Facility LayoutProblem, FLP), most of the documents assume that the flow rates between facilities are symmetrical, but the flow rates between facilities are not completely symmetrical in production practice. The introduction of the asymmetric flow enables CAP to be more fit with reality, and has certain reference significance for the design of the production layout in future. In summary, the MLUP can facilitate the production activities of the pipelines in a single facility, improve the production efficiency and productivity, provide the basis for the actual layout activities by introducing asymmetric flow, and enable a decision maker to select a better layout form by combining the two factors.
In practical production practice, in order to meet the requirement of pipeline production in facilities, when the length of the facilities is large, MLUP is often placed at different positions, and the material flow rate between the facilities is also not completely symmetrical, so that the loading and unloading points need to be planned and arranged in a certain mode to form a better layout form.
Disclosure of Invention
In order to solve the above problems, the main object of the present invention is to provide a method for arranging aisles, which considers material loading and unloading points and asymmetric flow rates, and provides guidance and basis for aisle arrangement.
The technical scheme of the invention is that the aisle arrangement method considering material loading and unloading points and asymmetric flow comprises the following steps:
s1, establishing a mathematical model with the lowest total logistics cost as a target, wherein the objective function of the mathematical model is as follows:
wherein F is the total logistics cost; n is the total number of facilities; i. j is the facility number; f (f) ij A unidirectional flow from the loading point of facility i to the unloading point of facility j; d, d (·) For the distance in the x direction of the material flow interaction between a certain loading point and a certain unloading point, d ij Distance in x-direction for the logistics interaction between the loading point of facility i to the j unloading point of facility; c is the width of the aisle.
S2, based on the mathematical model, providing constraint conditions of an objective function to form an aisle arrangement model;
the constraint conditions are as follows:
d ij ≥x ip -x jd ，1≤i＜j≤n (3)
d ij ≥x jd -x ip ，1≤i＜j≤n (4)
d ji ≥x id -x jp ，1≤i＜j≤n (5)
d ji ≥x jp -x id ，1≤i＜j≤n (6)
α ij +α ik +α jk +α ji +α ki +α kj ≥1，1≤i＜j＜k≤n (9)
-α ij +α ik +α jk -α ji +α ki +α kj ≤1，i,j,k∈Q，i＜j，k≠i，k≠j (10)
-α ij +α ik -α jk +α ji -α ki +α kj ≤1，i,j,k∈Q，i＜j，k＜j，k≠i (11)
q ij ＝α ij +α ji ，1≤i，j≤n，i≠j (12)
α ij ∈{0,1}，1≤i，j≤n，i≠j (13)
q ij ∈{0,1}，1≤i，j≤n，i≠j (14)
wherein x is (·p) X is the abscissa of the loading point of the facility ip The abscissa of the loading point for facility i; x is x (·d) X is the abscissa of the unloading point of the facility id The abscissa of the unloading point for facility i; i. j and k are facility numbers; beta i For decision variables, the length of the facility i does not exceed the defined length l beta i =0, otherwise β i ＝1；α (·) Alpha is the decision variable ki Meaning that when facilities k, i are on the same row and facility k is on the left of facility i, then α ki =1, otherwise α ki ＝0；l (·) For the length of the facility in the x-direction, l i Length in x-direction for facility i; gamma ray i To the left of the discharge point, the loading point of the installation i is then gamma for the decision variables i =1, otherwise γ i =0; q is the facility set, q= {1,2, …, n };
formulas (1) - (2) are used to calculate the abscissa of the MLUP for each facilityThe method comprises the steps of carrying out a first treatment on the surface of the Equations (3) - (6) are used to constrain the handling distance of the two facilities in the x-axis direction; formulas (7) to (8) are used for restraining the same-row facilities from overlapping; equations (9) - (11) are used to constrain the decision variable α ij The method comprises the steps of carrying out a first treatment on the surface of the Equation (12) is used to constrain the decision variable q ij The method comprises the steps of carrying out a first treatment on the surface of the Equations (13) - (16) give the decision variable alpha ij 、q ij 、γ i 、β i Is defined in the definition field of (2);
s3, solving the aisle arrangement model to realize the optimal setting of the aisle; the method specifically comprises the following steps:
s31, initializing parameters, wherein the initialized parameters comprise population scale nind, maximum iteration number iter_max, local search maximum iteration number v_max, continuous non-updated maximum number of glob_max of an external file, local search threshold v1_max, convergence factor a and coefficient vector A, C;
s32, randomly generating an initial population, generating an initial solution by adopting a double-layer integer coding mode when generating the initial population, and calculating the fitness F (Y) of each individual in the population i ) Taking the first three wolves with the best adaptability as alpha wolves, beta wolves and delta wolves respectively, and the rest wolves as omega wolves;
s33, searching prey by the wolves, and updating external files and parameters a, A and C;
there are three behaviors of the gray wolf to catch up with the prey: surrounding, hunting, attacking, wherein
(1) The surrounding behavior, for each wolf, the mathematical model of surrounding the prey when the wolf catches the prey is as follows:
Y(t+1)＝Y p (t)-A·D (17)
D＝|C·Y p (t)-Y(t)| (18)
A＝2a·r 1 -a (19)
C＝2r 2 (21)
wherein Y (t) is the current position of the wolf; t is the time of the current iterationA number; y (t+1) is the updated position of the wolf; y is Y p (t) is the location of the prey; d is the distance from the wolf to the prey; A. c is a coefficient vector; a is a convergence factor linearly decreasing from 2 to 0, T is the maximum iteration number, and ζ is a regulating factor; r is (r) 1 、r 2 Is [0,1 ]]A random number in the memory;
(2) Hunting behavior, the Hunting wolf is carried out by continuously adjusting the self position according to the positions of alpha, beta and delta in the wolf group, and the mathematical model is as follows:
D α ＝|C 1 ·Y α (t)-Y(t)| (22)
D β ＝|C 2 ·Y β (t)-Y(t)| (23)
D δ ＝|C 3 ·Y δ (t)-Y(t)| (24)
Y 1 ＝Y α -A 1 ·D α (25)
Y 2 ＝Y β -A 2 ·D β (26)
Y 3 ＝Y δ -A 3 ·D δ (27)
Y(t+1)＝W 1 ×Y 1 +W 2 ×Y 2 +W 3 ×Y 3 (30)
wherein D is α 、D β 、D δ Alpha, beta and delta wolf to the respective prey; c (C) 1 、C 2 、C 3 、A 1 、A 2 、A 3 Are coefficient vectors; y is Y α (t)、Y β (t)、Y δ (t) the positions of the respective prey for α, β, δwolf, t being the number of current iterations; y (t) is the current position of the individual gray wolves; y is Y α 、Y β 、Y δ Positions of alpha, beta and delta wolf respectively; sigma (sigma) 1 、σ 2 、σ 3 Is the proportional weight of the position vector; w (W) 1 、W 2 、W 3 Respectively the learning weights of the wolves to the alpha wolves, the beta wolves and the delta wolves; y (t+1) is the updated position of the individual wolf;
s34, generating a reverse solution Y' by utilizing a reverse learning mechanism, and if the random number Rand<Custom value p c Then carrying out information interaction on the reverse solution, otherwise, not carrying out information interaction, then mixing the initial solution and the reverse solution, carrying out fitness calculation and arranging from high to low, taking the first nind individuals as a new population, and taking the first three individuals as alpha wolves, beta wolves and delta wolves;
the specific way of generating the reverse solution Y' by using the reverse learning mechanism is as follows:
is provided with
Is a feasible solution generated at the t-th iteration,>
is the number of the ith row and jth column of the solution sequence, the inverse solution formula is as follows:
s35, carrying out local search on alpha wolves, beta wolves and delta wolves; if the external file is updated, then glob=0, otherwise glob=glob+
1, a step of; outputting a current optimal solution if the glob > glob_max, otherwise executing the step 6;
the local search includes the steps of:
s351, initializing parameters: inputting the alpha wolf, the beta wolf and the delta wolf obtained in the step S34 as initial solutions Y_alpha, Y_beta and Y_delta and respectively as respective current optimal solutions;
s352, respectively performing double-layer mutation and local mutation operations on Y_alpha, Y_beta and Y_delta to generate a new solution Y_alpha new 、Y_β new 、Y_δ new ；
S353, comparing the new solution with the initial solution, and updating y_α, y_β, y_δ and search depth: if F (Y_alpha) new )>min (F (Y_alpha), F (Y_beta), F (Y_delta)) or F (Y_beta) new )>min (F (Y_alpha), F (Y_beta), F (Y_delta)) or (Y_delta) new )>min (F (y_α), F (y_β), F (y_δ)), then the search depth v1 is reset, otherwise the neighborhood search depth is noted further.
S354, comparing the search depth with a local search threshold value, and executing a step S355 if the search depth does not exceed the threshold value; otherwise, outputting the current local optimal solutions Y_alpha, Y_beta, Y_delta and the objective function values F (Y_alpha), F (Y_beta) and F (Y_delta);
s355, (1) if F (Y-alpha) new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_α new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_alpha) new )>F (y_β), let y_δ=y_β, y_β=y_α new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_alpha) new )>F (y_δ), let y_δ=y_α new ；
(2) If F (Y_beta) new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_β new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_beta) new )>F (y_β), let y_δ=y_β, y_β=y_β new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_beta) new )>F (y_δ), let y_δ=y_β new ；
(3) If F (Y_delta) new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_δ new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_delta) new )>F (y_β), let y_δ=y_β, y_β=y_δ new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_delta) new )>F (y_δ), let y_δ=y_δ new ；
The iteration number is reset if Y_alpha is updated, the iteration number is unchanged if Y_beta or Y_delta is updated, otherwise the iteration number is added with 1.
And S356, outputting the current local optimal solutions Y_alpha, Y_beta, Y_delta and the objective function values F (Y_alpha), F (Y_beta) and F (Y_delta) thereof if the iteration times reach v_max, otherwise, looping steps S352 to 356 until the termination condition of the local search is met.
S36, enabling the iter to be=iter+1, if the iter is > iter_max, stopping outputting the current optimal solution by the algorithm, otherwise, repeating the steps S33-S36.
The invention has the technical effects that:
(1) The invention provides an extended aisle arrangement method considering material loading and unloading points and asymmetric flow, which can form a better layout form and reduce the overall carrying distance.
(2) According to the invention, a gray wolf optimization algorithm (Grey Wolf Optimizer with Opposition-based Learning, OGWO) fused with reverse Learning is adopted for solving, the algorithm adopts a double-layer integer coding mode to generate an initial solution, a reverse Learning mechanism and a population updating mechanism are fused to expand a search solution space, a double-threshold stopping criterion is added, and a redundant iteration process is reduced to improve the solving efficiency of the algorithm.
Drawings
In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described.
FIG. 1 is a schematic view of an aisle layout with material handling points and asymmetric flow rates considered in an embodiment of the invention;
FIG. 2 is a schematic diagram of decoding sequence of the algorithm according to the embodiment of the present invention;
FIG. 3 is a diagram showing the position update of the wolves according to the embodiment of the present invention;
FIG. 4 is a flow chart of a wolf optimization algorithm incorporating reverse learning in accordance with an embodiment of the present invention;
FIG. 5 is a partial search flow chart according to an embodiment of the present invention;
FIG. 6 is a graph of bias bins for solving different scale CAPs for OGWO and GWO in accordance with an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples and drawings.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention.
Examples
The invention relates to a method for arranging a passageway by considering material loading and unloading points and asymmetric flow, which is shown in fig. 1, and comprises the following steps:
s1, establishing a mathematical model with the lowest total logistics cost as a target, wherein the objective function of the mathematical model is as follows:
wherein F is the total logistics cost; n is the total number of facilities; i. j is the facility number; f (f) ij A unidirectional flow from the loading point of facility i to the unloading point of facility j; d, d (·) For the distance in the x direction of the material flow interaction between a certain loading point and a certain unloading point, d ij Distance in x-direction for the logistics interaction between the loading point of facility i to the j unloading point of facility; c is the width of the aisle.
S2, based on the mathematical model, providing constraint conditions of an objective function to form an aisle arrangement model;
the constraint conditions are as follows:
d ij ≥x ip -x jd ，1≤i＜j≤n (3)
d ij ≥x jd -x ip ，1≤i＜j≤n (4)
d ji ≥x id -x jp ，1≤i＜j≤n (5)
d ji ≥x jp -x id ，1≤i＜j≤n (6)
α ij +α ik +α jk +α ji +α ki +α kj ≥1，1≤i＜j＜k≤n (9)
-α ij +α ik +α jk -α ji +α ki +α kj ≤1，i,j,k∈Q，i＜j，k≠i，k≠j (10)
-α ij +α ik -α jk +α ji -α ki +α kj ≤1，i,j,k∈Q，i＜j，k＜j，k≠i (11)
q ij ＝α ij +α ji ，1≤i，j≤n，i≠j (12)
α ij ∈{0,1}，1≤i，j≤n，i≠j (13)
q ij ∈{0,1}，1≤i，j≤n，i≠j (14)
wherein x is (·p) X is the abscissa of the loading point of the facility ip The abscissa of the loading point for facility i; x is x (·d) X is the abscissa of the unloading point of the facility id The abscissa of the unloading point for facility i; i. j and k are facility numbers; beta i For decision variables, the length of the facility i does not exceed the defined length l=4 then β i =0, otherwise β i ＝1；α (·) Alpha is the decision variable ki Meaning that when facilities k, i are on the same row and facility k is on the left of facility i, then α ki =1, otherwise α ki ＝0；l (·) For the length of the facility in the x-direction, l i Length in x-direction for facility i; gamma ray i To the left of the discharge point, the loading point of the installation i is then gamma for the decision variables i =1, otherwise γ i =0; q is the facility set, q= {1,2, …, n };
formulas (1) to (2) are used to calculate the abscissa of the MLUP of each facility; equations (3) - (6) are used to constrain the handling distance of the two facilities in the x-axis direction; formulas (7) to (8) are used for restraining the same-row facilities from overlapping; equations (9) - (11) are used to constrain the decision variable α ij The method comprises the steps of carrying out a first treatment on the surface of the Equation (12) is used to constrain the decision variable q ij The method comprises the steps of carrying out a first treatment on the surface of the Equations (13) - (16) give the decision variable alpha ij 、q ij 、γ i 、β i Is defined in the definition field of (2);
s3, solving the aisle arrangement model to realize the optimal setting of the aisle; the method specifically comprises the following steps:
s31, initializing parameters, wherein the initialized parameters comprise population scale nind, maximum iteration number iter_max, local search maximum iteration number v_max, continuous non-updated maximum number of glob_max of an external file, local search threshold v1_max, convergence factor a and coefficient vector A, C;
s32, randomly generating an initial population, generating an initial solution by adopting a double-layer integer coding mode when generating the initial population, adopting a coding release mode of a decoding sequence of the algorithm in the embodiment as shown in figure 2, and then calculating the fitness F (Y i ) Taking the first three wolves with the best adaptability as alpha wolves, beta wolves and delta wolves respectively, and the rest wolves as omega wolves;
s33, searching prey by the wolves, and updating external files and parameters a, A and C;
there are three behaviors of the gray wolf to catch up with the prey: surrounding, hunting, attacking, wherein
(1) The surrounding behavior, for each wolf, the mathematical model of surrounding the prey when the wolf catches the prey is as follows:
Y(t+1)＝Y p (t)-A·D (17)
D＝|C·Y p (t)-Y(t)| (18)
A＝2a·r 1 -a (19)
C＝2r 2 (21)
wherein Y (t) is the current position of the wolf; t is the number of current iterations; y (t+1) is the updated position of the wolf; y is Y p (t) is the location of the prey; d is the distance from the wolf to the prey; A. c is a coefficient vector; a is a convergence factor linearly decreasing from 2 to 0, T is the maximum iteration number, and ζ is a regulating factor; r is (r) 1 、r 2 Is [0,1 ]]A random number in the memory;
(2) Hunting behavior, the Hunting wolf is carried out by continuously adjusting the self position according to the positions of alpha, beta and delta in the wolf group, and the mathematical model is as follows:
D α ＝|C 1 ·Y α (t)-Y(t)| (22)
D β ＝|C 2 ·Y β (t)-Y(t)| (23)
D δ ＝|C 3 ·Y δ (t)-Y(t)| (24)
Y 1 ＝Y α -A 1 ·D α (25)
Y 2 ＝Y β -A 2 ·D β (26)
Y 3 ＝Y δ -A 3 ·D δ (27)
Y(t+1)＝W 1 ×Y 1 +W 2 ×Y 2 +W 3 ×Y 3 (30)
wherein D is α 、D β 、D δ Alpha, beta and delta wolf to the respective prey; c (C) 1 、C 2 、C 3 、A 1 、A 2 、A 3 Are coefficient vectors; y is Y α (t)、Y β (t)、Y δ (t) the positions of the respective prey for α, β, δwolf, t being the number of current iterations; y (t) is the current position of the individual gray wolves; y is Y α 、Y β 、Y δ Positions of alpha, beta and delta wolf respectively; sigma (sigma) 1 、σ 2 、σ 3 Is the proportional weight of the position vector; w (W) 1 、W 2 、W 3 Respectively the learning weights of the wolves to the alpha wolves, the beta wolves and the delta wolves; y (t+1) is the updated position of the individual wolf;
s34, generating a reverse solution Y' by utilizing a reverse learning mechanism, if the random number Rand is less than 0.8, carrying out information interaction on the reverse solution, otherwise, not carrying out information interaction, then mixing the initial solution and the reverse solution, carrying out fitness calculation, arranging from high to low, taking the previous nind individuals as a new population, and taking the previous three individuals as alpha wolves, beta wolves and delta wolves;
the specific way of generating the reverse solution Y' by using the reverse learning mechanism is as follows:
is provided with
Is one generated at the t-th iterationFeasible solution (Tex)>
Is the number of the ith row and jth column of the solution sequence, the inverse solution formula is as follows:
s35, carrying out local search on alpha wolves, beta wolves and delta wolves; if the external file is updated, then glob=0, otherwise glob=glob+
1, a step of; outputting a current optimal solution if the glob > glob_max, otherwise executing the step 6;
the local search includes the steps of:
s351, initializing parameters: inputting the alpha wolf, the beta wolf and the delta wolf obtained in the step S34 as initial solutions Y_alpha, Y_beta and Y_delta and respectively as respective current optimal solutions;
s352, respectively performing double-layer mutation and local mutation operations on Y_alpha, Y_beta and Y_delta to generate a new solution Y_alpha new 、Y_β new 、Y_δ new ；
S353, comparing the new solution with the initial solution, and updating y_α, y_β, y_δ and search depth: if F (Y_alpha) new )>min (F (Y_alpha), F (Y_beta), F (Y_delta)) or F (Y_beta) new )>min (F (Y_alpha), F (Y_beta), F (Y_delta)) or (Y_delta) new )>min (F (y_α), F (y_β), F (y_δ)), then the search depth v1 is reset, otherwise the neighborhood search depth is noted further.
S354, comparing the search depth with a local search threshold value, and executing a step S355 if the search depth does not exceed the threshold value; otherwise, outputting the current local optimal solutions Y_alpha, Y_beta, Y_delta and the objective function values F (Y_alpha), F (Y_beta) and F (Y_delta);
s355, (1) if F (Y-alpha) new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_α new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_alpha) new )>F (y_β), let y_δ=y_β, y_β=y_α new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_alpha) new )>F (y_δ), let y_δ=y_α new ；
(2) If it isF(Y_β new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_β new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_beta) new )>F (y_β), let y_δ=y_β, y_β=y_β new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_beta) new )>F (y_δ), let y_δ=y_β new ；
(3) If F (Y_delta) new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_δ new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_delta) new )>F (y_β), let y_δ=y_β, y_β=y_δ new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_delta) new )>F (y_δ), let y_δ=y_δ new ；
The iteration number is reset if Y_alpha is updated, the iteration number is unchanged if Y_beta or Y_delta is updated, otherwise the iteration number is added with 1.
And S356, outputting the current local optimal solutions Y_alpha, Y_beta, Y_delta and the objective function values F (Y_alpha), F (Y_beta) and F (Y_delta) thereof if the iteration times reach v_max, otherwise, looping steps S352 to 356 until the termination condition of the local search is met.
S36, enabling the iter to be=iter+1, if the iter is > iter_max, stopping outputting the current optimal solution by the algorithm, otherwise, repeating the steps S33-S36.
That is, a set of random decimal sequences z=which are equal in length to the facility sequences and monotonically increase is generated when the iteration number t=1
[Z 1 ,Z 2 ,…,Z n ]The method comprises the steps of carrying out a first treatment on the surface of the The sequence is calculated and reordered according to equation (30), and the updated sequence is then mapped to a discrete facility sequence according to specified criteria. For better illustration, we take the problem of n=9 as an example, the original facility sequence y= [8,5,4,2,3,7,9,1,6 ]]And randomly generating an increment array Z, wherein the facility number 8 corresponds to the minimum value 0.1 in Z, and the facility number 1 corresponds to the value 4.5 with the sequence index of 8 in Z. After formula calculation, the newly generated Z is incrementally ordered, the minimum value is 0.2, the minimum value corresponds to the number 8 in the facility sequence, the value 6.5 with the sequence index of 8 corresponds to the number 1 in the facility sequence, and according to the strategy, the new facility sequence Y is finally obtained new ＝[3,8,5,6,2,7,1,4,9]. The specific operation is shown in fig. 3.
The computer hardware used for the example test herein was configured as the Pentium (R) Dual-CoreCPUE6700, main frequency 3.20GHz, memory 4GB, window 7 operating system. In view of the fact that no operation result of the test cases exists at present in the epCAP, a LINGO optimizer is adopted to write a program according to the provided mixed integer linear programming model and solve small-scale cases, so that the accuracy of the epCAP model is proved, and a certain basis is provided for an algorithm. To further test the solution performance of OGWO, the algorithm was run using MATLAB R2016, solving for 38 cases in the 5-49 scale of epCAP. The calculation of a large number of calculation examples shows that the algorithm has good superiority.
The current literature has not been studied on the epCAP, so that the OGWO algorithm is used for solving the 9-80-scale CAP examples in order to more effectively verify that the OGWO has certain advantages in terms of solving quality and efficiency and has certain universality. Since there is a difference between epCAP and CAP coding (the epCAP coding mode is double-layer integer coding, the CAP coding mode is single-layer integer coding), the OGWO algorithm will not have the crossover and variation of the second-layer coding and the parameter setting will also have a difference when solving CAP. For small-scale CAP (9-18 scale), the solving quality of OGWO is obviously improved relative to GWO; in the middle-scale CAP (20-49), the solving quality of OGWO is better than that of CAP-Heuristic, GA, GWO except for Ste36-04 and Ste36-05, which shows that the OGWO has certain advantages in the aspect of treating the middle-scale problem; for large-scale problems (60-80), the OGWO is superior to the GWO algorithm in solving results and solving time, so that the improved algorithm has obvious advantages, and the solving quality and the solving efficiency are obviously improved. In summary, the OGWO algorithm is also efficient and stable in solving for conventional CAPs.
In addition, 8 examples of S9H, am a, H20, N30-01, ste36-01, sko42-01, sko49-01, akv70-01, etc. were selected, and the algorithm OGWO and GWO were applied to run 10 times, respectively, and a box diagram for solving the deviation gap was made, as shown in FIG. 6.
As can be seen from fig. 6, for different scale examples, the OGWO algorithm has smaller box length and concentrated values, which proves that the OGWO algorithm has lower data dispersion and stronger algorithm convergence.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the technical scope of the present invention disclosed in the embodiments of the present invention should be covered by the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (4)
1. The aisle arrangement method considering the material loading and unloading points and the asymmetric flow is characterized by comprising the following steps of:
s1, establishing a mathematical model with the lowest total logistics cost as a target, wherein the objective function of the mathematical model is as follows:
wherein F is the total logistics cost; n is the total number of facilities; i. j is the facility number; f (f) ij A unidirectional flow from the loading point of facility i to the unloading point of facility j; d, d (·) For the distance in the x direction of the material flow interaction between a certain loading point and a certain unloading point, d ij Distance in x-direction for the logistics interaction between the loading point of facility i to the j unloading point of facility; c is the width of the aisle;
s2, based on the mathematical model, providing constraint conditions of an objective function to form an aisle arrangement model;
the constraint conditions are as follows:
d ij ≥x ip -x jd ，1≤i＜j≤n
d ij ≥x jd -x ip ，1≤i＜j≤n
d ji ≥x id -x jp ，1≤i＜j≤n
d ji ≥x jp -x id ，1≤i＜j≤n
α ij +α ik +α jk +α ji +α ki +α kj ≥1，1≤i＜j＜k≤n
-α ij +α ik +α jk -α ji +α ki +α kj ≤1，i,j,k∈Q，i＜j，k≠i，k≠j
-α ij +α ik -α jk +α ji -α ki +α kj ≤1，i,j,k∈Q，i＜j，k＜j，k≠i
q ij ＝α ij +α ji ，1≤i，j≤n，i≠j
α ij ∈{0,1}，1≤i，j≤n，i≠j
q ij ∈{0,1}，1≤i，j≤n，i≠j
wherein x is (·p) X is the abscissa of the loading point of the facility ip The abscissa of the loading point for facility i; x is x (·d) X is the abscissa of the unloading point of the facility id The abscissa of the unloading point for facility i; i. j and k are facility numbers; beta i For decision variables, the length of the facility i does not exceed the defined length l beta i =0, otherwise β i ＝1；α (·) Alpha is the decision variable ki Meaning that when facilities k, i are on the same row and facility k is on the left of facility i, then α ki =1, otherwise α ki ＝0；l (·) For the length of the facility in the x-direction, l i Length in x-direction for facility i; gamma ray i To the left of the discharge point, the loading point of the installation i is then gamma for the decision variables i =1, otherwise γ i =0; q is the facility set, q= {1,2, …, n };
s3, solving the aisle arrangement model to realize the optimal setting of the aisle; the method specifically comprises the following steps:
s31, initializing parameters, wherein the initialized parameters comprise population scale nind, maximum iteration number iter_max, local search maximum iteration number v_max, continuous non-updated maximum number of glob_max of an external file, local search threshold v1_max, convergence factor a and coefficient vector A, C;
s32, randomly generating an initial population, generating an initial solution by adopting a double-layer integer coding mode when generating the initial population, and calculating the fitness F (Y) of each individual in the population i ) Taking the first three wolves with the best adaptability as alpha wolves, beta wolves and delta wolves respectively, and the rest wolves as omega wolves;
s33, searching prey by the wolves, and updating external files and parameters a, A and C;
s34, generating a reverse solution Y' by utilizing a reverse learning mechanism, and if the random number Rand<Custom value p c Then carrying out information interaction on the reverse solution, otherwise, not carrying out information interaction, then mixing the initial solution and the reverse solution, carrying out fitness calculation and arranging from high to low, taking the first nind individuals as a new population, and taking the first three individuals as alpha wolves, beta wolves and delta wolves;
s35, carrying out local search on alpha wolves, beta wolves and delta wolves; if the external file is updated, the glob=0, otherwise, the glob=glob+1; if the glob > glob_max, outputting the current optimal solution, otherwise executing the S36 step;
s36, enabling the iter to be=iter+1, if the iter is > iter_max, stopping outputting the current optimal solution by the algorithm, otherwise, repeating the steps S33-S36.
2. The aisle arrangement method considering material loading points and asymmetric flow rates as claimed in claim 1, wherein the step S33 includes surrounding behavior and hunting behavior when the wolf catches up with the hunting object;
the mathematical model of the surrounding behavior is as follows:
Y(t+1)＝Y p (t)-A·D
D＝|C·Y p (t)-Y(t)|
A＝2a·r 1 -a
C＝2r 2
wherein Y (t) is the current position of the wolf; t is the number of current iterations; y (t+1) is the updated position of the wolf; y is Y p (t) is the location of the prey; d is the distance from the wolf to the prey; A. c is a coefficient vector; a is a convergence factor linearly decreasing from 2 to 0, T is the maximum iteration number, and ζ is a regulating factor; r is (r) 1 、r 2 Is [0,1 ]]A random number in the memory;
the mathematical model of hunting behavior is as follows:
D α ＝|C 1 ·Y α (t)-Y(t)|
D β ＝|C 2 ·Y β (t)-Y(t)|
D δ ＝|C 3 ·Y δ (t)-Y(t)|
Y 1 ＝Y α -A 1 ·D α
Y 2 ＝Y β -A 2 ·D β
Y 3 ＝Y δ -A 3 ·D δ
Y(t+1)＝W 1 ×Y 1 +W 2 ×Y 2 +W 3 ×Y 3
wherein D is α 、D β 、D δ Alpha, beta and delta wolf to the respective prey; c (C) 1 、C 2 、C 3 、A 1 、A 2 、A 3 Are coefficient vectors; y is Y α (t)、Y β (t)、Y δ (t) the positions of the respective prey for α, β, δwolf, t being the number of current iterations; y (t) is the current position of the individual gray wolves; y is Y α 、Y β 、Y δ Positions of alpha, beta and delta wolf respectively; sigma (sigma) 1 、σ 2 、σ 3 Is the proportional weight of the position vector; w (W) 1 、W 2 、W 3 Respectively the learning weights of the wolves to the alpha wolves, the beta wolves and the delta wolves; y (t+1) is the updated position of the individual wolf.
3. The aisle arrangement method considering the material loading and unloading points and the asymmetric flow according to claim 1, wherein the specific way of generating the inverse solution Y' by the inverse learning mechanism in the step S34 is as follows:
is provided with
Is a feasible solution generated at the t-th iteration,>
is the number of the ith row and jth column of the solution sequence, the inverse solution formula is as follows:
4. the aisle placement method considering material handling points and asymmetric traffic as set forth in claim 1, wherein the local search includes the steps of:
s351, initializing parameters: inputting the alpha wolf, the beta wolf and the delta wolf obtained in the step S34 as initial solutions Y_alpha, Y_beta and Y_delta and respectively as respective current optimal solutions;
s352, respectively performing double-layer mutation and local mutation operations on Y_alpha, Y_beta and Y_delta to generate a new solution Y_alpha new 、Y_β new 、Y_δ new ；
S353, comparing the new solution with the initial solution, and updating y_α, y_β, y_δ and search depth: if F (Y_alpha) new )>min (F (Y_alpha), F (Y_beta), F (Y_delta)) or F (Y_beta) new )>min (F (Y_alpha), F (Y_beta), F (Y_delta)) or (Y_delta) new )>min (F (y_α), F (y_β), F (y_δ)), then resetting the search depth v1, otherwise noting the neighborhood search depth further;
s354, comparing the search depth with a local search threshold value, and executing a step S355 if the search depth does not exceed the threshold value; otherwise, outputting the current local optimal solutions Y_alpha, Y_beta, Y_delta and the objective function values F (Y_alpha), F (Y_beta) and F (Y_delta);
s355, (1) if F (Y-alpha) new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_α new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_alpha) new )>F(Y_
Beta), let y_delta=y_beta, y_beta=y_alpha new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_alpha) new )>F (y_δ), let y_δ=y_α new The method comprises the steps of carrying out a first treatment on the surface of the (2) If F (Y_beta) new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_β new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_beta) new )>F (y_β), let y_δ=y_β, y_β=y_β new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_beta) new )>F (y_δ), let y_δ=y_β new The method comprises the steps of carrying out a first treatment on the surface of the (3) If F (Y_delta) new )>F (y_α), let y_δ=y_β, y_β=y_α, y_α=y_δ new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_delta) new )>F (y_β), let y_δ=y_β, y_β=y_δ new The method comprises the steps of carrying out a first treatment on the surface of the If F (Y_delta) new )>F (y_δ), let y_δ=y_δ new The method comprises the steps of carrying out a first treatment on the surface of the Resetting the iteration number if Y_alpha is updated, keeping the iteration number unchanged if Y_beta or Y_delta is updated, otherwise, recording the iteration number to be added with 1;
and S356, outputting the current local optimal solutions Y_alpha, Y_beta, Y_delta and the objective function values F (Y_alpha), F (Y_beta) and F (Y_delta) thereof if the iteration times reach v_max, otherwise, looping steps S352 to 356 until the termination condition of the local search is met.
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