CN117875189B - Three-dimensional warehouse space layout method based on GA optimization GRO - Google Patents
Three-dimensional warehouse space layout method based on GA optimization GRO Download PDFInfo
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Abstract
The invention belongs to the field of logistics management, and particularly relates to a three-dimensional warehouse space layout method based on GA optimization GRO. Firstly, generating an initial layout diagram of a stereoscopic warehouse by utilizing an SLP method by combining preset design elements, and establishing a corresponding digital model; the initial layout includes initial positions of all functional areas of the layers. And then converting the spatial layout problem of the stereoscopic warehouse into a position optimization problem of each functional unit in the initial layout diagram, and constructing a corresponding single-target optimization model based on each optimization target. Finally, optimizing the single-objective optimization model by adopting a newly designed GA optimization GRO algorithm; in the iterative process, the GA algorithm is adopted to find out the better position of each functional unit, and then the global optimal scheme is obtained through the GRO algorithm. The invention solves the defects that the space layout scheme of the logistics warehouse obtained by the traditional SLP method cannot adapt to the type of goods in enterprises and is difficult to realize stereoscopic warehouse design.
Description
Technical Field
The invention belongs to the field of logistics management, and particularly relates to a three-dimensional warehouse space layout method based on GA optimization GRO.
Background
Logistics is a part of supply chain activity, which is the process of planning, implementing and controlling the consumption of goods, services and related information from place of production to place of consumption for the purpose of meeting customer needs. The logistics takes storage as a center, and the production and the market are promoted to keep synchronous. Along with the continuous expansion of the sales scale of enterprises, more and more commercial enterprises start to build local logistics storage centers to realize the distribution of goods, and the space layout of the logistics storage centers has significant influence on the inventory management efficiency of the goods.
The space layout scheme of the existing logistics storage center is designed by adopting an SLP method, and on the basis of the design of the traditional SLP method, designers are added with links such as facility arrangement type confirmation, line analysis and the like according to the characteristics of modern manufacturing enterprises, so that feedback and adjustment in each department after line analysis are emphasized. Although the SLP method pays attention to the continuity of the process and the rationality of the layout, the judgment of the quality of the layout of the equipment is too dependent on the experience of the designer, and the quantitative analysis is lacking, so that whether the layout is optimal cannot be intuitively and scientifically judged. In addition, the conventional SLP method generally considers only planar arrangement, i.e., two-dimensional space arrangement, and in a specific arrangement process, not only the interrelationship between the work units but also the decision of which floor each work unit is located on is required. Therefore, the spatial layout scheme generated by adopting the SLP method often has the characteristics of goods inventory which do not accord with logistics enterprises; lack of an overall logistic strategy plan; lack of a line analysis process; lack of dynamic flexibility; the disadvantages of multi-layer distribution are not considered.
Disclosure of Invention
The invention provides a three-dimensional warehouse space layout method based on GA optimization GRO, which aims to solve the defects that the space layout scheme of a logistics warehouse obtained by the traditional SLP method cannot adapt to the type of goods of a logistics enterprise and is difficult to realize three-dimensional warehouse design.
The invention is realized by adopting the following technical scheme:
a three-dimensional warehouse space layout method based on GA optimization GRO comprises the following steps:
s1: the functional area in the stereoscopic warehouse is divided into a warehouse-in area, a warehouse-out area, a warehouse management office, a material stacking area, a sorting area and a goods placing area, and an initial layout is generated through an SLP method.
S2: a mathematical model of the stereoscopic warehouse is created from the spatial location of each base unit in the initial layout.
S3: and constructing a single-objective optimization model for representing the spatial layout optimization problem of the stereoscopic warehouse by taking the minimized logistics cost and material handling time of the warehouse and the maximized non-logistics relationship consistency as optimization objectives.
S4: and optimizing the single-target optimization model by utilizing an algorithm of GRO optimization GA to obtain a space layout diagram of the globally optimal stereoscopic warehouse. The process is as follows:
S41: and (3) coding the positions of the functional areas to obtain the gene codes of the corresponding positions.
S42: and selecting, crossing and mutating the gene codes of each functional region by utilizing a GA algorithm, and further obtaining a better functional region position x ij and a corresponding evaluation value G i after iteration is finished.
S43: the location of the functional area is stored in a location matrix M GP, and an evaluation matrix M F is created that stores the evaluation values of the objective function for the current location.
S44: and defining strategies of migration, position analysis and region cooperation search of the functional region positions in the GRO algorithm.
S45: and calculating the change of the evaluation value of the objective function before and after the relocation, iteratively relocation the position of the functional area, and updating the position matrix M GP and the evaluation matrix M F.
S46: and generating an optimal space layout diagram containing the coordinates of each functional area according to the position matrix after the iteration is finished.
As a further improvement of the present invention, in step S1, the initial layout satisfies the following constraint:
(1) The shape of the area where a single large device or a plurality of functionally similar devices are located in the warehouse is approximately an envelope rectangle.
(2) The units are arranged horizontally and vertically, the central coordinates of the single large-scale equipment or independent areas in the same row are on the same horizontal line, and the boundaries of the units are parallel to the boundaries of the warehouse.
(3) The logistics transportation in the warehouse is carried along the horizontal or vertical direction of the channel.
(4) The single large-scale equipment or independent areas are sequentially distributed along the X-axis direction and are automatically line-fed.
As a further improvement of the invention, in the mathematical model of step S2, the layers of the stereoscopic warehouse are located in an XOY plane coordinate system; wherein, the space length is L; the width is H; the number of the units is n; the number of the unit lines is N; let the i-th unit be denoted m i: i=1, 2, …, n; the minimum distance requirement of adjacent units in the X-axis direction is noted as: s ij; the minimum spacing requirements of each cell and the left and right boundaries are noted as: s ia and S ib; minimum spacing requirement d ik of adjacent units in the Y direction; the distance from the center line of any row of cells to the boundary is noted as: d o;li is the length of the i-th cell; h i is the width of the ith cell; x i is the distance from the center of the ith cell to the X axis; y i is the distance from the center of the ith cell to the Y-axis; s k is the clear distance of adjacent cell boundaries in the X-axis direction; d is the row distance between the cells.
As a further improvement of the present invention, in step S3, the expression of the single-objective optimization model is as follows:
In the above-mentioned method, the step of, 、/>And/>Weights of three types of optimization targets are respectively represented; c ij represents the single stream cost from unit i to unit j; q ij represents the material transport frequency of unit i to unit j; d ij represents the transportation distance from unit i to unit j, and Manhattan distance calculation is adopted; v ij denotes the conveyance speed of the units i to j; e ij represents a non-logistic relationship value between unit i and unit j; r ij represents the proximity of unit i and unit j, also known as a relationship factor; t ik、Tjk is a flag that characterizes whether cells i and j are in the kth line, respectively, and assigns a 0 or 1 depending on whether they are in the k line.
As a further improvement of the present invention, in step S41, the gene coding of the functional region is represented by the following row vector:
Wherein x i is the functional region numbered i; n is the number of functional areas.
In the row vector, the position of each functional area is expressed by adopting (u, v, w) coordinates, and u and v represent the position coordinates of the central point of the functional area in the current layer; w represents the number of layers in which the functional region is located.
As a further improvement of the present invention, in step S42, individual iteration is performed in the genetic algorithm by adopting elite selection strategy, and cross variation is achieved by adopting roulette, and the evaluation value of each individual at the current position is recorded as G i, i=1, 2,3, …, n, and the probability of being selected is defined as p i:
。
As a further improvement of the present invention, in step S43, the position matrix M GP and the evaluation matrix M F satisfy the following expressions, respectively:
In the above formula, x ij represents the position of the ith functional region in the jth layer; d is the total layer number of the stereoscopic warehouse, and n is the number of functional areas in each layer; f (·) represents an evaluation function for evaluating the spatial layout of each layer.
As a further improvement of the present invention, in step S44, the expression of the relocation operation of the migration process of any functional area to the optimum position is as follows:
In the above-mentioned method, the step of, A displacement vector between the current position representing the functional region i and the position representing the better functional region in the t-th iteration; /(I)Representing the position of a better functional area in the t-th iteration; /(I)Representing the current position of the functional area i; /(I)A new location for functional region i; /(I)、/>Is a vector calculation coefficient; /(I)And/>Is a random vector with values in the range of [0, 1 ]; l 1 denotes the convergence component of the exploration phase customization.
As a further improvement of the present invention, in mathematical modeling, the position of each functional region is regarded as an approximate position of the better functional region, and the expression of the corresponding position analysis is as follows:
In the above-mentioned method, the step of, Representing a displacement vector between the position of the randomly selected functional region r and the functional region i; /(I)Representing the location of the randomly selected functional region r; /(I)Is the calculated vector coefficient: l 2 denotes the convergence component of the development phase customization.
As a further improvement of the present invention, defining g 1 and g 2 as two randomly selected functional regions, the expression of the region collaborative search strategy is as follows:
In the above-mentioned method, the step of, Representing the collaboration vector; /(I)And/>The current positions of the functional areas g 1 and g 2 are indicated, respectively.
The technical scheme provided by the invention has the following beneficial effects:
The method comprises the steps of firstly adopting an SLP method to generate an initial layout diagram of spatial layout of the stereoscopic warehouse, then combining a mathematical model of the stereoscopic warehouse to convert the spatial layout optimization problem into the position optimization problem of each functional unit contained in the spatial layout optimization problem, and establishing a corresponding single-target optimization model. And finally, carrying out iterative optimization on the single-target optimization model by utilizing the improved GA optimization GRO algorithm, and finding out a global optimal scheme of the spatial position of each functional unit in the stereoscopic warehouse, thereby obtaining an optimal spatial layout.
The technical scheme provided by the invention provides a new solution to the problems of warehouse space layout design and the like. The optimization targets in the optimization model constructed by the invention comprise minimization of logistics cost and material handling time of the warehouse and maximization of non-logistics relation consistency, so that the obtained layout scheme can be adapted to the type of goods of a logistics enterprise; generating a space layout diagram which accords with the logistics strategic plan, and considering the line problem of enterprise logistics management; the warehouse can be designed into a multi-layer stereoscopic warehouse according to the requirement, so that the defects of the traditional SLP method are overcome.
According to the invention, aiming at the problem of solving the single-objective optimization model of space layout optimization, a new algorithm model based on GA optimization GRO is adopted, and the new iterative optimization algorithm pre-adjusts the initial value and the parameters of GRO calculation by utilizing the GA algorithm, so that the problem that the time consumption is long in processing large-scale complex problems can be overcome on the basis of keeping the advantages of the GRO algorithm in searching efficiency.
Drawings
Fig. 1 is a step flowchart of a stereoscopic warehouse space layout method based on GA optimization GRO provided in embodiment 1 of the present invention.
Fig. 2 is a flowchart of the initial layout diagram generation process in embodiment 1 of the present invention.
Fig. 3 is a mathematical model of each layer of the stereoscopic warehouse in example 1 of the present invention.
FIG. 4 is a flow chart of iterative optimization of a single-objective optimization model using an algorithm for GA optimization GRO.
Fig. 5 is a schematic plan view of a functional unit location migration operation using a GRO algorithm in embodiment 1 of the present invention.
Fig. 6 is a schematic diagram of a region collaborative search strategy implemented by using a GRO algorithm in embodiment 1 of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Example 1
The embodiment provides a three-dimensional warehouse space layout method based on GA optimization GRO, and the general idea of the scheme is as follows: firstly, generating an initial layout diagram of a stereoscopic warehouse by utilizing an SLP method in combination with preset design elements, and establishing a corresponding digital model; the initial layout includes initial positions of all functional areas of the layers. And then converting the spatial layout problem of the stereoscopic warehouse into a position optimization problem of each functional unit in the initial layout diagram, and constructing a corresponding single-target optimization model based on each optimization target. Finally, optimizing the single-objective optimization model by adopting a newly designed GA optimization GRO algorithm; in the algorithm of GA optimization GRO, the GA algorithm is adopted to find out the optimal position of each functional unit, and then the space layout diagram of the global optimal stereoscopic warehouse is obtained through the GRO algorithm.
Specifically, as shown in fig. 1, the spatial layout method of the stereoscopic warehouse based on GA optimization GRO provided in this embodiment includes the following steps:
s1: the functional area in the stereoscopic warehouse is divided into a warehouse-in area, a warehouse-out area, a warehouse management office, a material stacking area, a sorting area and a goods placing area, and an initial layout is generated through an SLP method.
In the layout application of equipment and space, the SLP method performs systematic analysis on the logistics state of the warehouse-in and warehouse-out through qualitative analysis of space logistics and non-logistics factors, so that a reasonable preliminary layout scheme is obtained. Specifically, when the present embodiment performs space design with SLP, the initial layout should satisfy the following constraint:
(1) The shape of the area where a single large device or a plurality of functionally similar devices are located in the warehouse is approximately an envelope rectangle.
(2) The units are arranged horizontally and vertically, the central coordinates of the single large-scale equipment or independent areas in the same row are on the same horizontal line, and the boundaries of the units are parallel to the boundaries of the warehouse.
(3) The logistics transportation in the warehouse is carried along the horizontal or vertical direction of the channel.
(4) The single large-scale equipment or independent areas are sequentially distributed along the X-axis direction and are automatically line-fed.
In addition, in the goods placement area in the stereoscopic warehouse, each shelf also needs to be classified according to the ex-warehouse quantity index. Specifically, the technicians sequence the designed shelves for storing different types of goods according to the ex-warehouse frequency in order from more to less, and calculate the accumulated ex-warehouse sales and the percentage of the accumulated ex-warehouse sales to the total ex-warehouse. The different types of shelves are then classified into a according to the duty cycle: important; b: second important; c: three general categories are important. Finally, dividing according to the specific characteristics of ABC classification; and the weighting calculation yields the total ABC classification.
In the scheme of the embodiment, the multi-layer warehouse needs to be designed layer by layer, and the SLP method can enable the layout of the multi-layer factory building to be more reasonable and scientific. As shown in fig. 2, the technician can also obtain the comprehensive relationship of each operation unit through PQ analysis of the logistic relationship and the non-logistic relationship, and then the floor division is performed according to the following steps:
the first step: according to the product logistics path and the aim of improving the carrying efficiency for reducing the use times and the running time of the elevator, firstly, arranging the operation units directly connected with the outside on a low floor, selecting corresponding units and calculating the area. Judging whether the first floor can be accommodated or not, wherein the number of the operation units is J.
And a second step of: judging whether a new operation unit can be added to the first floor, if so, operating according to the third step, and if not, switching to the next floor of the fourth step layout, wherein the number of the operation units of the first floor is J;
And a third step of: selecting an operation unit with high comprehensive correlation with the I layer as J+1 operation units of the I layer, confirming whether the layout is proper according to the available residual area, if so, returning to the second step, wherein the number of the operation units of the I layer building is J=J+1; if not, the unit of operation is removed and the process returns to the second step.
Fourth step: selecting a job unit with a high comprehensive correlation with the job units laid out in the I layer as a1 st job unit of the I+1 layer, and then turning to the second step to find all the job units of the I+1 layer, wherein I=I+1;
To ensure that the resulting layout scheme is viable, it is assumed that some job units are at the top level if they appear to be undeployed during the layout process. If the area required by the layout in the I layer is larger than or equal to the total area of the layer, the operation unit of the last layout is removed, and then the operation unit is continuously searched until the layout area of the I layer is close. If the operation unit grades are the same, selecting the material flow relationship with the highest relationship, and then performing the second step.
When an elevator at each floor is used as a working unit and a certain working unit has an integrated relationship with the rest floors, the elevator is converted into an integrated relationship between the working unit and the elevator. And finally, obtaining the required initial layout.
S2: a mathematical model of the stereoscopic warehouse is created from the spatial location of each base unit in the initial layout.
In this embodiment, the mathematical model of the stereoscopic warehouse is shown in fig. 3. In the figure, each layer of the stereoscopic warehouse is positioned in an XOY plane coordinate system; wherein, the space length is L; the width is H; the number of the units is n; the number of the unit lines is N; let the i-th unit be denoted m i: i=1, 2, …, n; the minimum distance requirement of adjacent units in the X-axis direction is noted as: s ij; the minimum spacing requirements of each cell and the left and right boundaries are noted as: s ia and S ib; minimum spacing requirement d ik of adjacent units in the Y direction; the distance from the center line of any row of cells to the boundary is noted as: d o;li is the length of the i-th cell; h i is the width of the ith cell; x i is the distance from the center of the ith cell to the X axis; y i is the distance from the center of the ith cell to the Y-axis; s k is the clear distance of adjacent cell boundaries in the X-axis direction; d is the row distance between the cells.
S3: and constructing a single-objective optimization model for representing the spatial layout optimization problem of the stereoscopic warehouse by taking the minimized logistics cost and material handling time of the warehouse and the maximized non-logistics relationship consistency as optimization objectives. The expression of the single-objective optimization model is as follows:
In the above-mentioned method, the step of, 、/>And/>Weights of three types of optimization targets are respectively represented; c ij represents the single stream cost from unit i to unit j; q ij represents the material transport frequency of unit i to unit j; d ij represents the transportation distance from unit i to unit j, and Manhattan distance calculation is adopted; v ij denotes the conveyance speed of the units i to j; e ij represents a non-logistic relationship value between unit i and unit j; r ij represents the proximity of unit i and unit j, also known as a relationship factor; t ik、Tjk is a flag that characterizes whether cells i and j are in the kth line, respectively, and assigns a 0 or 1 depending on whether they are in the k line.
Objective function (one)
Analysis of the single-objective optimization model established in this embodiment shows that the spatial layout optimization problem of the stereoscopic warehouse is essentially a multi-objective optimization problem. The corresponding optimization objectives include: (1) The stream cost G 1 of the warehouse is minimized:
(2) Non-logistic relationship affinity G 2 for warehouse maximization:
(3) The transit time G 3 of the cargo is minimized:
and combining the optimization targets, giving weights to the optimization targets, and constructing the following objective function so as to convert the multi-target optimization problem into a single-target optimization problem.
Wherein,、/>And/>The weight of the logistics cost, the non-logistics relation consistency and the carrying time are respectively represented, and the weight value satisfies the following conditions: /(I)+/>+/>=1。
In the objective function, the index E ij for evaluating the non-logistic relationship closeness G 2 needs to be quantified according to the level of closeness, and the quantization table used in this example is as follows:
table 1: quantization table of degree of closeness between functional units
The relationship factor R ij is converted from D ij, and the corresponding conversion relationship is shown as follows:
table 2: conversion relation table of relation factor value
(II) constraint function
The constraint function part of the single-objective optimization model created in the present embodiment is a first part as follows for indicating that the respective functional units do not collide in the horizontal and vertical directions:
；
the following second section is used to indicate that the dimensions of the individual functional units do not exceed the length and width of the warehouse:
；
The last part of the following is used to limit the non-repeated arrangement of the individual functional units:
。
S4: and optimizing the single-target optimization model by utilizing an algorithm of GA optimization GRO to obtain a space layout diagram of the globally optimal stereoscopic warehouse.
The single-objective optimization problem established in the step S3 is difficult to directly solve, so that the implementation selects iterative optimization of the solution of the model through a machine learning algorithm. In order to obtain the global optimal solution of the single-target optimization model more efficiently, the implementation designs an algorithm for GA optimization GRO. The GRO algorithm is a heuristic algorithm which mimics the major events of panning, and in the GRO element heuristic algorithm, the seeker plays the same role as the population of particles in the PSO algorithm. In the embodiment, a Genetic Algorithm (GA) and a panning optimization algorithm (GRO) are combined, the optimal functional layout of each functional area in the multi-layer space of the stereoscopic warehouse is found on the basis of an initial layout scheme generated by an SLP method through selection, crossing and variation strategies in the GA algorithm, and then the detailed positions of the functional areas of each layer are migrated by utilizing the GRO algorithm to determine a final global optimal layout scheme.
Specifically, as shown in fig. 4, the iterative optimization procedure of the algorithm for GA optimization GRO is as follows:
1. part of a genetic algorithm
S41: and (3) coding the positions of the functional areas to obtain the gene codes of the corresponding positions.
The gene coding of the functional region is represented by the following row vector:
Wherein x i is the functional region numbered i; n is the number of functional areas.
In the row vector, the position of each functional area is expressed by adopting (u, v, w) coordinates, and u and v represent the position coordinates of the central point of the functional area in the current layer; w represents the number of layers in which the functional region is located. In the coding process, the maximum value of uvw is firstly determined, binary value transformation is carried out, and the length of a gene chain in the subsequent cross mutation can be determined. The length of the chromosome to be encoded is L, the required accuracy is m bits after a decimal point, and then the following relationship exists between the length of the chromosome encoding and the accuracy:
S42: and selecting, crossing and mutating the gene codes of each functional region by utilizing a GA algorithm, and further obtaining a better functional region position x ij and a corresponding evaluation value G i after iteration is finished.
In the genetic algorithm of this embodiment, an elite selection strategy is adopted to iterate individuals, roulette is adopted to realize cross variation, the evaluation value of each individual at the current position is marked as G i, i=1, 2,3, …, n, and the probability of being selected is defined as p i:
。
in elite selection strategies, the greater the current location rating of an individual, the greater the probability that it is selected. In the selection process of each generation, an individual with the highest evaluation value can be generated, so that in the selection process of each generation, the optimal individual of the generation can be reserved and transmitted to the next generation, and further, the result can be converged more quickly in the iteration process, and the optimal solution can be found.
In the iterative process of the genetic algorithm of this embodiment, since the position information of any functional unit is determined by three values together, three gene chains are selected to cross-mutate together. The detailed steps are as follows:
(1) Determining a first functional region gene chain as a father body by adopting a roulette method; then, in each round of the tournament selection method, a plurality of individuals are randomly selected from the population, wherein two of which scoring values are highest win and are selected as parent 1 and parent 2.
(2) Using the random number method, 0,1 is used to determine whether to cross points or segments.
(3) Again using the random number method, two positions of the intersection are determined. And according to the second step, if the two positions are crossed by points, carrying out numerical exchange to finish the crossing operation. If the two positions are crossed, a segment of numerical exchange between the two positions completes the crossing operation. The general crossover probability is between [0.4,0.99 ].
(4) The father and mother obtained in the first step are respectively crossed and transformed to obtain three gene chains according to the method of the third step.
(5) And (3) sequentially adopting a random number method for the three gene chains obtained in the fourth step, and determining whether mutation occurs or not by using 0 and 1.
(6) If the variation is generated, determining the position of the variation by adopting a random number method; and finally obtaining the offspring gene chain data.
(7) Binary decoding operation is carried out on the gene chain data of the offspring and the gene chain data of the parent, so that space position data is obtained.
(8) Comparing the evaluation values of the parent and the offspring, and keeping good and eliminating bad.
And circularly executing the steps until the preset iteration times are reached, and obtaining the preliminary better functional area position x ij and the corresponding evaluation value G i after multiple operations.
2. Part of panning optimization algorithm
S43: the location of the functional area is stored in a location matrix M GP, and an evaluation matrix M F is created that stores the evaluation values of the objective function for the current location.
In this embodiment, the constructed position matrix M GP and the evaluation matrix M F satisfy the following expressions, respectively:
in the above formula, x ij represents the position of the ith functional region in the jth layer; d is the total layer number of the stereoscopic warehouse, and n is the number of functional areas in each layer; f (-) represents the evaluation function (i.e., the objective function in the single-objective optimization model) for evaluating each layer of spatial layout.
S44: and defining strategies of migration, position analysis and region cooperation search of the functional region positions in the GRO algorithm.
(44.1) Migration operation:
In panning optimization algorithms, as shown in fig. 5, when the model finds a better location than the home location, the system will migrate the functional area to the layout there. Where the best working position is the best point of the search space during algorithm execution. Because its exact location is unknown, the better functional area location is taken as an estimate of the best location. The expression of the relocation operation of the migration process of any functional area to the optimal position is as follows:
In the above-mentioned method, the step of, A displacement vector between the current position representing the functional region i and the position representing the better functional region in the t-th iteration; /(I)Representing the position of a better functional area in the t-th iteration; /(I)Representing the current position of the functional area i; a new location for functional region i; /(I) 、/>Is a vector calculation coefficient; vector/>Mathematical modeling for migration. When (when)When=1, migration to the assumed position is indicated. When taking other lower and higher values then means migrating to a place between the search location and the better location or after the better location, respectively. Vector/>Mathematical modeling of this problem has been proposed. When/>=1 Indicates the exact position to migrate to the better position, and when other values are taken, it indicates that migration to other positions with similar coordinates is considered. /(I)And/>Is a random vector with values in the range of [0, 1 ]; l 1 denotes the convergence component of the exploration phase customization.
In this embodiment, the convergence component is defined as follows:
in the above equation, if e is equal to 1, the convergence component linearly decreases from 2 to For values greater than 1, it decreases non-linearly.
(44.2) Position analysis:
In mathematical modeling of panning optimization algorithms, the location of each functional region is considered as an approximate location of the better functional region, and the corresponding location analysis is expressed as follows:
In the above-mentioned method, the step of, Representing a displacement vector between the position of the randomly selected functional region r and the functional region i; /(I)Representing the location of the randomly selected functional region r; /(I)Is the calculated vector coefficient: l 2 denotes the convergence component of the development phase customization. Parameters l 1 and l 2 cause the algorithm to change from the exploration phase to the development phase. L 2 is used to make the algorithm more focused on the determination of a specific location than l 1.
(44.3) Region collaborative search:
Since the determination of the functional areas is sometimes performed by team cooperation, the present embodiment describes cooperation between the functional areas by the following mathematical model, and defines that g 1 and g 2 are two randomly selected functional areas, the expression of the area cooperation search strategy is as follows:
In the above-mentioned method, the step of, Representing the collaboration vector; /(I)And/>The current positions of the functional areas g 1 and g 2 are indicated, respectively.
Under the area collaborative search strategy, as shown in FIG. 6, the desired area to find a specific location is specified by g 1 and g 2, but the exact location to find the area is randomly determined by seeker i. Thus, three persons cooperate in this way.
S45: and calculating the change of the evaluation value of the objective function before and after the relocation, iteratively relocation the position of the functional area, and updating the position matrix M GP and the evaluation matrix M F.
In panning optimization algorithms, the functional region is moving continuously, and one key parameter in the migration decision is to obtain a better objective function value. Thus, in order to determine whether the functional area is left in the original position or is moved to a new position, the two positions are compared by the evaluation function. In this process, if the value of the objective function is increased, the functional area updates its position; otherwise, it remains in the previous position. Namely:
s46: and generating an optimal space layout diagram containing the coordinates of each functional area according to the position matrix after the iteration is finished.
When the implementation solves the single-objective optimization problem of the spatial layout design of the stereoscopic warehouse, the adopted algorithm of GA optimization GRO firstly utilizes the algorithm of GA to iterate and generate a preferable scheme of the spatial layout, and then utilizes the algorithm of GRO to finely adjust the position information of each functional unit in the spatial layout diagram, so as to generate a final global optimal scheme. The new iterative optimization algorithm pre-presets the initial value and the parameters of the GRO algorithm by utilizing the GA algorithm, so that the problem that the time consumption is long in processing large-scale complex problems can be overcome on the basis of keeping the advantages of the GRO algorithm in the aspect of searching efficiency; provides a new solution for the space layout design problem of the stereoscopic warehouse.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (8)
1. A three-dimensional warehouse space layout method based on GA optimization GRO is characterized by comprising the following steps:
S1: dividing a functional area in the stereoscopic warehouse into a warehouse-in area, a warehouse-out area, a warehouse management office, a material stacking area, a sorting area and a goods placing area, and generating an initial layout by an SLP method;
S2: establishing a mathematical model of the stereoscopic warehouse according to the space position of each basic unit in the initial layout;
In the mathematical model, each layer of the stereoscopic warehouse is positioned in an XOY plane coordinate system; wherein, the space length is L; the width is H; the number of the units is n; the number of the unit lines is N; let the i-th unit be denoted m i: i=1, 2, …, n; the minimum distance requirement of adjacent units in the X-axis direction is noted as: s ij; the minimum spacing requirements of each cell and the left and right boundaries are noted as: s ia and S ib; minimum spacing requirement d ik of adjacent units in the Y direction; the distance from the center line of any row of cells to the boundary is noted as: d o;li is the length of the i-th cell; h i is the width of the ith cell; x i is the distance from the center of the ith cell to the X axis; y i is the distance from the center of the ith cell to the Y-axis; s k is the clear distance of adjacent cell boundaries in the X-axis direction; d is the row distance between the cells;
s3: constructing a single-objective optimization model for representing the spatial layout optimization problem of the stereoscopic warehouse by taking the minimized logistics cost and material handling time of the warehouse and the maximized non-logistics relationship consistency as optimization targets;
the expression of the single-objective optimization model is as follows:
；
In the above-mentioned method, the step of, 、/>And/>Weights of three types of optimization targets are respectively represented; c ij represents the single stream cost from unit i to unit j; q ij represents the material transport frequency of unit i to unit j; d ij represents the transportation distance from unit i to unit j, and Manhattan distance calculation is adopted; v ij denotes the conveyance speed of the units i to j; e ij represents a non-logistic relationship value between unit i and unit j; r ij represents the proximity of unit i and unit j, also known as a relationship factor; t ik、Tjk is a mark for representing whether the units i and j are in the kth row, and the value is 0 or 1;
s4: optimizing the single-target optimization model by utilizing an algorithm of GA optimization GRO to obtain a space layout diagram of the globally optimal stereoscopic warehouse; the process is as follows:
s41: coding the positions of all the functional areas to obtain gene codes of the corresponding positions;
S42: selecting, crossing and mutating the gene codes of each functional area by utilizing a GA algorithm, and further obtaining a better functional area position x ij and a corresponding evaluation value G i after iteration is finished;
s43: storing the position of the functional area in a position matrix M GP, and creating an evaluation matrix M F for storing the evaluation value of the objective function on the current position;
S44: defining strategies of migration, position analysis and region cooperation search of the position of a functional region in a GRO algorithm;
S45: calculating the change of the evaluation value of the objective function before and after the relocation, iteratively relocation the position of the functional area, and updating the position matrix M GP and the evaluation matrix M F;
s46: and generating an optimal space layout diagram containing the coordinates of each functional area according to the position matrix after the iteration is finished.
2. The GA-optimized GRO-based stereoscopic warehouse spatial layout method of claim 1, wherein: in step S1, the initial layout satisfies the following constraint:
(1) The shape of the area where a single large-scale device or a plurality of devices with similar functions are positioned in the warehouse is approximate to an envelope rectangle;
(2) The units are arranged horizontally and vertically, the central coordinates of the single large-scale equipment or independent areas in the same row are on the same horizontal line, and the boundaries of the units are parallel to the boundaries of the warehouse;
(3) The logistics transportation in the warehouse is transported along the horizontal or vertical direction of the channel;
(4) The single large-scale equipment or independent areas are sequentially distributed along the X-axis direction and are automatically line-fed.
3. The GA-optimized GRO-based stereoscopic warehouse spatial layout method of claim 1, wherein: in step S41, the gene encoding of the functional region is represented by the following row vectors:
；
wherein x i is the functional region numbered i; n is the number of functional areas;
In the row vector, the position of each functional area is expressed by adopting (u, v, w) coordinates, and u and v represent the position coordinates of the central point of the functional area in the current layer; w represents the number of layers in which the functional region is located.
4. The GA-optimized GRO-based stereoscopic warehouse spatial layout method of claim 2, wherein: in step S42, individual iteration is performed in the genetic algorithm by adopting elite selection strategy, roulette is adopted to realize cross variation, the evaluation value of each individual at the current position is marked as G i, i=1, 2,3, …, n, and the selected probability is defined as p i:
。
5. The GA-optimized GRO-based stereoscopic warehouse spatial layout method of claim 4, wherein: in step S43, the position matrix M GP and the evaluation matrix M F satisfy the following expressions:
；
In the above formula, x ij represents the position of the ith functional region in the jth layer; d is the total layer number of the stereoscopic warehouse, and n is the number of functional areas in each layer; f (·) represents an evaluation function for evaluating the spatial layout of each layer.
6. The GA-optimized GRO-based stereoscopic warehouse spatial layout method of claim 5, wherein in step S44, the expression of the relocation operation of the migration process of the functional area to the optimal location is as follows:
；
In the above-mentioned method, the step of, A displacement vector between the current position representing the functional region i and the position representing the better functional region in the t-th iteration; /(I)Representing the position of a better functional area in the t-th iteration; /(I)Representing the current position of the functional area i; a new location for functional region i; /(I) 、/>Is a vector calculation coefficient; /(I)And/>Is a random vector with values in the range of [0, 1 ]; l 1 denotes the convergence component of the exploration phase customization.
7. A GA optimized GRO-based stereoscopic warehouse spatial layout method as claimed in claim 6, wherein in mathematical modeling, the location of each functional region is regarded as an approximate location of the better functional region, and the corresponding location analysis is expressed as follows:
；
In the above-mentioned method, the step of, Representing a displacement vector between the position of the randomly selected functional region r and the functional region i; /(I)Representing the location of the randomly selected functional region r; /(I)Is the calculated vector coefficient: l 2 denotes the convergence component of the development phase customization.
8. The GA-optimized GRO-based stereoscopic warehouse spatial layout method of claim 7, wherein: defining g 1 and g 2 as two randomly selected functional regions, the expression of the region collaborative search strategy is as follows:
；
In the above-mentioned method, the step of, Representing the collaboration vector; /(I)And/>The current positions of the functional areas g 1 and g 2 are indicated, respectively.
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