CN115303689A - Multi-roadway stereoscopic warehouse goods space allocation optimization method - Google Patents

Multi-roadway stereoscopic warehouse goods space allocation optimization method Download PDF

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CN115303689A
CN115303689A CN202210885399.0A CN202210885399A CN115303689A CN 115303689 A CN115303689 A CN 115303689A CN 202210885399 A CN202210885399 A CN 202210885399A CN 115303689 A CN115303689 A CN 115303689A
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goods
warehouse
stacker
roadway
shelves
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付建林
陈港生
谢家翔
丁国富
刘名远
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Southwest Jiaotong University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
    • B65G—TRANSPORT OR STORAGE DEVICES, e.g. CONVEYORS FOR LOADING OR TIPPING, SHOP CONVEYOR SYSTEMS OR PNEUMATIC TUBE CONVEYORS
    • B65G1/00—Storing articles, individually or in orderly arrangement, in warehouses or magazines
    • B65G1/02—Storage devices
    • B65G1/04—Storage devices mechanical
    • B65G1/0407—Storage devices mechanical using stacker cranes
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
    • B65G—TRANSPORT OR STORAGE DEVICES, e.g. CONVEYORS FOR LOADING OR TIPPING, SHOP CONVEYOR SYSTEMS OR PNEUMATIC TUBE CONVEYORS
    • B65G1/00—Storing articles, individually or in orderly arrangement, in warehouses or magazines
    • B65G1/02—Storage devices
    • B65G1/04—Storage devices mechanical
    • B65G1/0485—Check-in, check-out devices
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
    • B65G—TRANSPORT OR STORAGE DEVICES, e.g. CONVEYORS FOR LOADING OR TIPPING, SHOP CONVEYOR SYSTEMS OR PNEUMATIC TUBE CONVEYORS
    • B65G1/00—Storing articles, individually or in orderly arrangement, in warehouses or magazines
    • B65G1/02—Storage devices
    • B65G1/04—Storage devices mechanical
    • B65G1/137—Storage devices mechanical with arrangements or automatic control means for selecting which articles are to be removed
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
    • B65G—TRANSPORT OR STORAGE DEVICES, e.g. CONVEYORS FOR LOADING OR TIPPING, SHOP CONVEYOR SYSTEMS OR PNEUMATIC TUBE CONVEYORS
    • B65G1/00—Storing articles, individually or in orderly arrangement, in warehouses or magazines
    • B65G1/02—Storage devices
    • B65G1/14—Stack holders or separators

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  • Mechanical Engineering (AREA)
  • Warehouses Or Storage Devices (AREA)

Abstract

The invention discloses a method for optimizing the allocation of goods spaces of a multi-roadway stereoscopic warehouse, which comprises the following steps: performing warehouse-in and warehouse-out efficiency modeling with minimum product of the operation time of a stereoscopic warehouse stacker for completing a certain cargo and the warehouse-in and warehouse-out frequency of the cargo; performing shelf stability modeling by calculating the minimum equivalent gravity center of the shelf according to the product of the mass of the goods and the number of layers where the goods are positioned; taking two rows of goods shelves in each roadway as objects, calculating the quantity of goods positions distributed on the goods shelves in each row and the sum of the goods turnover rates of the goods shelves in each row, and performing stacker load balance modeling by considering balance of warehouse entry and exit frequency and balance of goods quantity in each roadway; and finally, solving the multi-objective optimization model through an improved self-adaptive multi-population genetic algorithm AMPGA. The method considers various factors to establish the multi-objective optimization model, adopts the improved self-adaptive multi-population genetic algorithm to solve, has better optimization effect and quicker convergence, and can well solve the problem of goods allocation of the multi-roadway stereoscopic warehouse.

Description

Multi-roadway stereoscopic warehouse goods space allocation optimization method
Technical Field
The invention belongs to the field of stereoscopic warehouse goods space allocation optimization, and particularly relates to a method for optimizing the goods space allocation of a multi-roadway stereoscopic warehouse.
Background
The optimization of the goods space allocation of the multi-lane stereoscopic warehouse is very complex and mainly embodied as follows: (1) The requirement on the warehouse-in and warehouse-out efficiency of the stereoscopic warehouse is high, and if the turnover rate is high, the stereoscopic warehouse is placed at a place close to a warehouse-in and warehouse-out opening. (2) The requirement on the stability of the goods shelf is high, and the storage of goods positions needs to meet the principle of 'heavy bottom and light top'. (3) The loading requirements of the pilers are balanced, and the workload of the pilers in each roadway needs to be balanced. The existing optimization method mostly focuses on the problem of distribution of goods spaces of two rows of goods shelves in a single roadway of a stereoscopic warehouse, the optimization target focuses on the warehouse-in and warehouse-out efficiency, the stability of goods shelves and the like, and a method capable of effectively processing the distribution optimization of the goods spaces of the complex multi-roadway stereoscopic warehouse is lacked.
Disclosure of Invention
The invention provides a method for optimizing the distribution of goods spaces of a multi-lane stereoscopic warehouse, aiming at the problem of the distribution of the goods spaces of the complex multi-lane stereoscopic warehouse.
The invention discloses a method for optimizing the distribution of goods space of a multi-lane stereoscopic warehouse, which provides a mathematical model expression method of the multi-lane stereoscopic warehouse by taking warehouse entry and exit efficiency, shelf stability and stacker load balance as optimization objective functions, and solves the mathematical model by using an improved multi-population genetic algorithm, and comprises the following specific steps of:
step 1: and modeling the in-out efficiency.
In order to meet the requirement of a stereoscopic warehouse for quickly responding to the warehouse entering and exiting frequency, goods with high warehouse entering and exiting frequency are placed at the position close to an entrance and exit, so that the working time of a stacker is shortened, the system operation efficiency is improved, namely the product of the working time of the stacker for finishing certain goods and the warehouse entering and exiting frequency of the goods is the minimum, and a design objective function is shown as a formula (1):
Figure BDA0003765652150000011
wherein, (x, y, z) represents the position information of the goods position allocated by the goods in the goods shelf, x is the number of rows of the goods shelf, y is the number of columns corresponding to the rows of the goods shelf, z is the number of layers corresponding to the rows of the goods shelf, and the final result of the goods position allocation is determined by the position information and the number of the layers; with P k The method comprises the steps of representing the warehousing-in and warehousing-out frequency of the kth goods in a warehousing order, also called turnover rate, wherein a, b and c respectively represent the total row number of shelves of the stereoscopic warehouse, the row number and the layer number of each row of shelves, and the length, the width and the height of each shelf grid in the shelves are L; v y 、V z The running speeds of the stacker in the Y-axis and Z-axis directions are represented, and N represents the total number of goods in a batch of warehousing orders; introducing a decision variable S kxyz The method is used for judging whether the kth goods are stored in the (x, y, z) goods position, if so, the kth goods are 1, and if not, the kth goods are 0.
Step 2: and modeling shelf stability.
In order to keep the stability of the goods shelf in the storage process, the storage of the goods is required to follow the principle of 'lower weight and upper light weight' in the distribution of goods positions, the goods shelf is prevented from collapsing due to unstable gravity center, and the objective function formula with the minimum integral equivalent gravity center of all the goods shelves when a plurality of stackers in the three-dimensional warehouse work simultaneously is considered as shown in the formula (2):
Figure BDA0003765652150000021
wherein, M k Indicating the quality of the kth good in the warehousing order.
And step 3: and (4) modeling the stacker load in a balanced manner.
In order to reduce the load of the stacker and improve the operation efficiency of the warehouse, the balance of the number of goods in and out of the warehouse in each roadway is required, namely, the goods in a batch of warehousing orders are scattered and stored on the goods shelves in different roadways, so that the phenomena that the service life of the stacker is influenced due to the congestion of the roadways and the overload work of the stacker caused by the accumulation of the goods in one roadway are avoided, the operation efficiency of the stacker is reduced, and the warehouse operation is not facilitated; taking each tunnel for operation of the stacker crane as an object, considering the balance of warehouse entry and exit frequency in each tunnel and the balance of the number of goods in the tunnel, and designing an objective function expression as shown in formulas (3) to (6):
Figure BDA0003765652150000022
Figure BDA0003765652150000023
Q i ＝O 2i-1 +O 2i i＝1,2,...,a/2 (5)
Figure BDA0003765652150000024
wherein, O x Represents the sum of the turnover rates, Q, of the goods stored on the x-th row of racks i The sum of the turnover rates of the goods stored in the ith roadway is shown,
Figure BDA0003765652150000025
representing the average of the turnover rates of all the goods in a batch of orders, n i Indicating the number of allocated cargo space within each lane.
And 4, step 4: the improved self-adaptive multi-population genetic algorithm AMPGA is used for solving.
Self-adaptive selection crossover operator selection: a cosine improved adaptive genetic operator is adopted, and the constructed operator is as follows:
Figure BDA0003765652150000026
Figure BDA0003765652150000027
wherein: f. of max The maximum fitness value in the population;f avg the average fitness value of the population is obtained; p is cmax And P cmin Respectively as the maximum value and the minimum value of the crossing rate; f' is the greater fitness value of the two individuals to be crossed; p mmax And P mmin The maximum value and the minimum value of the variation rate are respectively; f is the fitness value of the individual to be mutated.
Selection of a cross mode: in order to reflect the diversity of each population, single-point crossing, two-point crossing and sequential crossing are simultaneously used for multiple populations, and each population randomly selects a crossing mode for crossing.
Evolution and reversion: in order to improve the local search capability of the genetic algorithm, evolution reversion operation is introduced after selection, crossing and mutation, namely, two points are randomly selected on each individual chromosome, and the sequence in the interval of the two points is inverted; unlike the mutation, the mutation is random, and the evolution reversion is unidirectional, and is accepted only when the individual fitness value is improved after reversion, otherwise, the reversion is invalid.
The beneficial technical effects of the invention are as follows:
aiming at the optimization problem of the distribution of the goods space of the multi-lane stereoscopic warehouse, the invention comprehensively considers the warehousing and ex-warehouse efficiency, the shelf stability and the stacker load balancing principle, establishes a multi-objective function model for optimizing the distribution of the goods space of the multi-lane stereoscopic warehouse, and designs a self-adaptive multi-population genetic algorithm (AMPGA) to optimize the distribution of the goods space in the stereoscopic warehouse. The effectiveness of the established model is verified through experimental simulation, the goods allocation results of the 3 algorithms under different order scales are compared, the result shows that the AMPGA algorithm has better optimization effect and faster convergence under large-scale orders, and the problem of goods allocation of the multi-lane stereoscopic warehouse can be well solved.
Drawings
FIG. 1 is a flow chart of the AMPGA algorithm.
FIG. 2 is a graph of the variation of an objective function with iteration number according to an embodiment.
Fig. 3 is a distribution diagram of the optimized goods of 50 orders.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
The invention discloses a method for optimizing the allocation of goods space of a multi-lane stereoscopic warehouse, which provides a mathematical model expression method of the multi-lane stereoscopic warehouse by taking warehouse entry and exit efficiency, shelf stability and stacker load balance as optimization objective functions, and solves the mathematical model by using an improved multi-population genetic algorithm, and comprises the following specific steps:
step 1: and modeling the in-out efficiency.
In order to meet the requirement of a stereoscopic warehouse for quickly responding to the warehouse entering and exiting frequency, goods with high warehouse entering and exiting frequency are placed at the position close to an entrance and exit, so that the working time of a stacker is shortened, the system operation efficiency is improved, namely the product of the working time of the stacker for finishing certain goods and the warehouse entering and exiting frequency of the goods is the minimum, and a design objective function is shown as a formula (1):
Figure BDA0003765652150000031
wherein, (x, y, z) represents the position information of the goods position distributed by the goods in the goods shelf, x is the number of rows of goods shelves, y is the number of columns corresponding to the rows of goods shelves, z is the number of layers corresponding to the rows of goods shelves, and the final result of the goods position distribution is determined by the position information; with P k The method comprises the steps of (1) representing the warehousing-in and warehousing-out frequency (also called turnover rate) of the kth goods in a warehousing order, wherein a, b and c respectively represent the total row number of stereoscopic warehouse shelves, the row number and the layer number of each row of shelves, and the length, the width and the height of each goods grid in each shelf are L; v y 、V z Representing the running speeds of the stacker in the Y-axis and Z-axis directions, and N representing the total number of goods in a batch of warehousing orders; introducing a decision variable S kxyz The method is used for judging whether the kth goods are stored in the (x, y, z) goods position, if so, the kth goods are 1, and if not, the kth goods are 0.
And 2, step: and modeling shelf stability.
In order to maintain the stability of the goods shelf in the storage process, the storage of the goods is required to follow the principle of 'heavy bottom and light top' in the distribution of the goods space, and the goods shelf is prevented from collapsing due to unstable gravity center. The existing research method is to take the sum of products of the quality of goods and the number of layers where the goods are located and the minimum as an objective function, but aims at the stability of two rows of goods shelves which are responsible for the pilers in a certain roadway of a warehouse, and does not consider the integral stability of all goods shelves in the warehouse when a plurality of pilers work simultaneously in the stereoscopic warehouse. Therefore, the objective function formula with the minimum equivalent gravity center of all the entire goods shelves when the plurality of stackers in the three-dimensional warehouse work simultaneously is considered as shown in formula (2):
Figure BDA0003765652150000041
wherein M is k Indicating the quality of the kth good in the warehousing order.
And step 3: and (4) modeling the stacker load in a balanced manner.
In order to reduce the load of the stacker and improve the operation efficiency of the warehouse, the balance of the number of goods in and out of the warehouse in each roadway is required, namely, the goods in a batch of warehousing orders are scattered and stored on the goods shelves in different roadways, so that the phenomena that the goods are stacked in one roadway, the roadway is blocked, the stacker works in an overload mode to influence the service life of the stacker is avoided, the operation efficiency of the stacker is reduced, and the warehouse operation is not facilitated. Each roadway for operation of the stacker is taken as an object, the balance of warehouse entry and exit frequency in each roadway and the balance of the number of cargos in the roadway are considered, and the load condition of the stacker in each roadway can be better reflected. The designed target function expression is shown in formulas (3) to (6):
Figure BDA0003765652150000042
Figure BDA0003765652150000043
Q i ＝O 2i-1 +O 2i i＝1,2,...,a/2 (5)
Figure BDA0003765652150000051
wherein, O x Representing the sum of the turnover rates, Q, of the goods stored on the x-th row of racks i The sum of the turnover rates of the goods stored in the ith roadway is shown,
Figure BDA0003765652150000052
representing the average of the turnover of all goods in a batch of orders, n i Indicating the number of allocated cargo space within each lane.
And 4, step 4: the improved Adaptive Multi-population Genetic Algorithm AMPGA (Adaptive Multi-population Genetic Algorithm) is used for solving, and the specific flow is shown in FIG. 1.
Self-adaptive selection crossover operator selection: aiming at the defects and shortcomings of the existing linear adaptive selection and crossover operators, the invention adopts a cosine improved type adaptive genetic operator, and the constructed operator is as follows:
Figure BDA0003765652150000053
Figure BDA0003765652150000054
wherein: f. of max The maximum fitness value in the population; f. of avg The average fitness value of the population is obtained; p cmax And P cmin Respectively as the maximum value and the minimum value of the crossing rate; f' is the greater fitness value of the two individuals to be crossed; p is mmax And P mmin The maximum value and the minimum value of the variation rate are respectively; f is the fitness value of the individual to be mutated.
Selection of a cross mode: in order to embody the diversity of each population, single-point crossing, two-point crossing and sequential crossing are simultaneously used for multiple populations, and each population randomly selects a crossing mode for crossing.
Evolution and reversion: in order to improve the local search capability of the genetic algorithm, evolution reversion operation is introduced after selection, crossing and mutation, namely two points are randomly selected on each individual chromosome, and the sequence in the two point intervals is inverted; unlike the mutation, the mutation is random, and the evolution reversion is unidirectional, and is accepted only when the individual fitness value is improved after reversion, otherwise, the reversion is invalid.
Example (b):
according to 50 sample data of goods to be warehoused in a certain enterprise warehousing order, a standard genetic algorithm, a general multi-population genetic algorithm and the self-adaptive multi-population genetic algorithm designed by the invention are respectively adopted for simulation experiments, the table 1 shows warehousing goods order information and optimized goods position information, and the table 2 shows experiment results of 3 algorithms. Fig. 2 is a graph of the objective function values of the 3 algorithms as a function of the number of iterations, and fig. 3 is a distribution diagram of the cargo after optimization.
Table 1 warehouse goods order information and goods location information before and after optimization
Figure BDA0003765652150000061
Table 2 comparison of experimental results of the algorithms
Algorithm SGA MPGA AMPGA
Value of the objective function F 6.1123 5.7435 5.5604
Time consuming convergence 67.57 65.53 57.23
As can be seen from the results of table 1 and fig. 3, the goods with high turnover rate are allocated on the goods position close to the warehouse entry and exit port, and the goods with low turnover rate are allocated on the corresponding slightly distant position, so that the warehouse entry and exit efficiency requirement is met; from the stability of the whole shelf, goods with large mass are distributed at the lower layer of the shelf, and goods with small mass are distributed at the upper layer; from the load condition of the stacker, the distribution of goods on the goods shelves in each roadway is basically balanced, and the load balance of the stacker is met; the above results demonstrate the effectiveness of the optimization model established by the present invention from the side. From the optimization result, the optimization result of the general multi-population genetic algorithm is improved by 6.03% compared with that of the SGA, but the optimization result of the cosine adaptive multi-population genetic algorithm is improved by 9.03%, and the convergence speed is higher due to the introduction of adaptive crossover and mutation operators, so that the solving speed and the solving precision are effectively improved.

Claims (1)

1. A method for optimizing the distribution of goods space in a multi-lane stereoscopic warehouse is characterized by providing a mathematical model expression method of the multi-lane stereoscopic warehouse by taking the warehouse entry and exit efficiency, the shelf stability and the stacker load balance as optimization objective functions, solving the mathematical model by using an improved multi-population genetic algorithm, and specifically comprising the following steps of:
step 1: modeling the warehouse-in and warehouse-out efficiency;
in order to meet the requirement of a stereoscopic warehouse for quickly responding to the warehouse entering and exiting frequency, goods with high warehouse entering and exiting frequency are placed at the position close to an entrance and exit, so that the working time of a stacker is shortened, the system operation efficiency is improved, namely the product of the working time of the stacker for finishing certain goods and the warehouse entering and exiting frequency of the goods is the minimum, and a design objective function is shown as a formula (1):
Figure FDA0003765652140000011
wherein, (x, y, z) represents the position information of the goods position distributed by the goods in the goods shelf, x is the number of rows of goods shelves, y is the number of columns corresponding to the rows of goods shelves, z is the number of layers corresponding to the rows of goods shelves, and the final result of the goods position distribution is determined by the position information; with P k The method comprises the steps of representing the warehousing-in and warehousing-out frequency of the kth goods in a warehousing order, also called turnover rate, wherein a, b and c respectively represent the total row number of shelves of the stereoscopic warehouse, the row number and the layer number of each row of shelves, and the length, the width and the height of each shelf grid in the shelves are L; v y 、V z The running speeds of the stacker in the Y-axis and Z-axis directions are represented, and N represents the total number of goods in a batch of warehousing orders; introducing a decision variable S kxyz Used for judging whether the kth goods are stored in the (x, y, z) goods position, if so, the kth goods is 1, and if not, the kth goods is 0;
step 2: modeling the shelf stability;
in order to keep the stability of the goods shelf in the storage process, the storage of the goods is required to follow the principle of 'lower weight and upper light weight' in the distribution of goods positions, the goods shelf is prevented from collapsing due to unstable gravity center, and the objective function formula with the minimum integral equivalent gravity center of all the goods shelves when a plurality of stackers in the three-dimensional warehouse work simultaneously is considered as shown in the formula (2):
Figure FDA0003765652140000012
wherein, M k Indicating the quality of the kth goods in the warehousing order;
and step 3: modeling the stacker in a load balancing manner;
in order to reduce the load of the stacker and improve the operation efficiency of the warehouse, the balance of the number of goods in and out of the warehouse in each roadway is required, namely, the goods in a batch of warehousing orders are scattered and stored on the goods shelves in different roadways, so that the phenomena that the service life of the stacker is influenced due to the congestion of the roadways and the overload work of the stacker caused by the accumulation of the goods in one roadway are avoided, the operation efficiency of the stacker is reduced, and the warehouse operation is not facilitated; taking each tunnel for operation of the stacker crane as an object, considering the balance of warehouse entry and exit frequency in each tunnel and the balance of the number of goods in the tunnel, and designing an objective function expression as shown in formulas (3) to (6):
Figure FDA0003765652140000021
Figure FDA0003765652140000022
Q i ＝O 2i-1 +O 2i i＝1,2,...,a/2 (5)
Figure FDA0003765652140000023
wherein, O x Representing the sum of the turnover rates, Q, of the goods stored on the x-th row of racks i The sum of the turnover rates of the goods stored in the ith roadway is shown,
Figure FDA0003765652140000024
representing the average of the turnover of all goods in a batch of orders, n i Indicating the number of goods positions distributed in each roadway;
and 4, step 4: solving by using an improved self-adaptive multi-population genetic algorithm AMPGA;
self-adaptive selection crossover operator selection: a cosine improved type adaptive genetic operator is adopted, and the constructed operator is as follows:
Figure FDA0003765652140000025
Figure FDA0003765652140000026
wherein: f. of max The maximum fitness value in the population; f. of avg The average fitness value of the population is obtained; p cmax And P cmin Respectively the maximum value and the minimum value of the crossing rate; f' is the greater fitness value of the two individuals to be crossed; p is mmax And P mmin The maximum value and the minimum value of the variation rate are respectively; f is the fitness value of the individual to be mutated;
selection of a cross mode: in order to embody the diversity of each population, single-point crossing, two-point crossing and sequential crossing are simultaneously used for multiple populations, and each population randomly selects a crossing mode for crossing;
evolution and reversion: in order to improve the local search capability of the genetic algorithm, evolution reversion operation is introduced after selection, crossing and mutation, namely, two points are randomly selected on each individual chromosome, and the sequence in the interval of the two points is inverted; unlike the mutation, the mutation is random, and the 'evolution reversion' is unidirectional, and is accepted only when the individual fitness value is improved after reversion, otherwise, the reversion is invalid.
CN202210885399.0A 2022-07-26 2022-07-26 Multi-roadway stereoscopic warehouse goods space allocation optimization method Pending CN115303689A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116090961A (en) * 2023-04-07 2023-05-09 天津万事达物流装备有限公司 Automatic storage system of stacker
CN116579721A (en) * 2023-07-14 2023-08-11 中油管道物资装备有限公司 Warehouse goods position optimization method and device, electronic equipment and storage medium

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116090961A (en) * 2023-04-07 2023-05-09 天津万事达物流装备有限公司 Automatic storage system of stacker
CN116090961B (en) * 2023-04-07 2023-06-20 天津万事达物流装备有限公司 Automatic storage system of stacker
CN116579721A (en) * 2023-07-14 2023-08-11 中油管道物资装备有限公司 Warehouse goods position optimization method and device, electronic equipment and storage medium
CN116579721B (en) * 2023-07-14 2023-09-19 中油管道物资装备有限公司 Warehouse goods position optimization method and device, electronic equipment and storage medium

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