CN117035168A - NSGA-II-based multi-objective integrated optimization method for forward and backward warehouse-out warehouse - Google Patents

Abstract

The invention discloses a multi-objective integrated optimization method based on a forward and backward warehouse-out warehouse, which aims to improve the storage efficiency and the operation efficiency of the forward and backward warehouse-out warehouse by optimizing the operation time, the cargo gravity center and the operation energy consumption of a stacker. According to the method, firstly, a multi-objective problem optimization model is established by adopting goods space distribution based on gravity centers, stacker operation scheduling and operation energy consumption according to the characteristics of a warehouse after advancing, then, an integrated scheduling model based on an algorithm for advancing and discharging the warehouse is provided according to the problems, a plurality of targets such as stacker operation time, goods gravity centers and operation energy consumption are comprehensively considered, and optimization solution is carried out through the algorithm, so that the purpose of multi-objective optimal solution is achieved. Experimental results show that compared with the traditional method, the method has remarkable advantages in terms of reducing the running time and the center of gravity of cargoes, and the operation energy consumption control is obviously improved. The method can effectively improve the goods storage and retrieval efficiency of the warehouse after advancing and discharging, and realize the optimal utilization of warehouse space.

Description

A multi-objective integrated optimization method for forward-back-out warehouse based on NSGA-Ⅱ

Technical field

The invention relates to the technical field of warehousing logistics, and in particular to a multi-objective integrated optimization method for forward-back-out warehouse based on NSGA-II.

Background technique

In the field of intelligent manufacturing and logistics, the development of automation, intelligence and optimization technology has become a common trend. For the warehousing and logistics industry, with the rapid growth of market demand and efficient management, more and more attention has begun to turn to the automation and intelligence level of the system. As a crucial link in warehousing logistics, three-dimensional warehouse integration optimization directly affects the storage efficiency and operating efficiency of the warehouse. Therefore, how to effectively realize the cargo space allocation and operation scheduling of forward and backward warehouses and improve the overall efficiency of warehousing logistics has become a focus of attention in the industry.

Traditional cargo location allocation and job scheduling methods often only consider a single goal, and are difficult to take into account the interaction between multiple factors, resulting in the failure of the algorithm's operating effect to be fully optimized. At the same time, traditional methods also have certain computational pressure and high computational complexity problems when processing huge amounts of data sets, which further weakens their optimization effect in large-scale warehousing and logistics systems.

Contents of the invention

The purpose of this invention is to provide a multi-objective integrated optimization method for the forward-back-out warehouse based on NSGA-II to improve the resource utilization of the forward-out warehouse and reduce the impact of manual intervention on efficiency, which has extremely high practical application value. By effectively using algorithms to optimize the interaction between multiple factors, the goal of improving the overall efficiency of warehousing logistics through cargo space allocation and job scheduling in the forward and backward warehouse is achieved.

The above technical objectives of the present invention are achieved through the following technical solutions:

A multi-objective integration optimization method for forward-back-out warehouse based on NSGA-Ⅱ, including the following steps:

Step 1. Establish a warehouse model: Based on the actual warehouse design, establish a structural model of a forward-back-out three-dimensional warehouse, abstracting it into a multi-dimensional space. The element nodes of the multi-dimensional space include stackers, shelves, outbound and inbound warehouses;

Step 2. Establish a task model: According to the actual situation, randomly define the warehousing tasks and warehousing tasks of the three-dimensional warehouse, and determine the task volume and task-related information;

Step 3. Determine the decision variables: For the problem of cargo space allocation and job scheduling in the three-dimensional warehouse, it is necessary to determine the corresponding decision variables, such as the type and quantity of items stored in each cargo space in the warehouse, as well as the execution order and time of each task, etc. ;

Step 4. Define the objective function: Based on the research purpose and practical problems, determine multiple optimization goals for the three-dimensional warehouse, such as the shortest running time, shelf stability, etc.;

Step 5. Construct the NSGA-II optimization algorithm model: Based on the above task model, decision variables and objective function, construct the NSGA-II optimization model and use the NSGA-II algorithm to solve the optimal solution;

Step 6. Carry out simulation and verification: Carry out simulation and verification based on the established model, consider the impact of different parameters on the model, obtain the optimized optimal solution, and conduct evaluation and analysis.

It is further preferred that Step 4 includes the following steps:

First, set up a three-dimensional warehouse with n cargo spaces. The three-dimensional coordinates of the goods are expressed as (x _i , y _i , z _i ), and the size of the cargo spaces is l _i ×w _i ×h _i , where 1≤i≤n , based on relevant data such as the location of the entrance and exit of the three-dimensional warehouse, cargo quality, conveyor belt parameters, etc., establish a forward-back-out three-dimensional warehouse, and randomly define the warehousing tasks and outgoing tasks of the three-dimensional warehouse according to the actual situation, and determine the task volume and task-related information , at the same time, the three-dimensional warehouse also needs to meet relevant assumptions: the stacker takes out the goods from the three-dimensional warehouse in sequence according to the forward-then-out strategy, and can only take out or put one piece of goods in and out of the warehouse at a time until all the goods in the order are taken; it is not considered Start and stop time; do not consider the impact of the weight of the cargo on the stacker's driving process; secondly, construct the objective function, construct the first objective function F ₁ with the shortest running time; construct the second objective function F 2 with the lowest center of gravity; construct the second objective function F ₂ with the energy Construct the third objective function F ₃ with the lowest cost; the objective function is as follows:

Minimum running time:

Among them, t _ij represents the running time of the stacker from the current cargo location to the next cargo location. The calculation formula is: t _ij ＝d _i /v _i +d _j /v _j

Among them, d _i represents the horizontal straight-line distance from the current cargo location (x _i , y _i , z _i ) to the target cargo location (x _ij , y _ij , z _ij ), and _vi represents the horizontal traveling speed of the stacker;

d _j represents the vertical straight-line distance from the current cargo location (x _i , y _i , z _i ) to the target cargo location (x _ij , y _ij , z _ij ), and v _j represents the vertical traveling speed of the stacker;

The lowest center of gravity: F ₂ (x) = cg

Among them, cg represents the average height coordinate of the center of gravity of all cargo locations, and its calculation formula is:

Among them, m _i represents the quality of the goods on the i-th cargo position;

Lowest energy consumption:

Among them, e _i represents the energy consumption of the stacker when taking out goods i, and its calculation formula is:

e _i = w _i d _ij

Among them, w _i represents the weight of the goods on the i-th cargo space, and d _ij represents the traveling distance of the stacker from the current cargo space to the next cargo space;

At the same time, the model also needs to satisfy the following constraints:

Assume that the stacker needs to perform a "warehousing" operation, that is, place the goods on the cargo space, and at the same time perform an "outbound" operation, that is, take the goods out of the cargo space;

In order to ensure that each cargo slot has only one cargo, the following constraints must be met:

Among them, x _ij indicates whether goods are placed in the cargo location i, x _ij =1 indicates that the cargo location has goods, and x _ij =0 indicates that the cargo location is empty;

In order to ensure that only one cargo location that meets the requirements is selected when warehousing, the following constraints must be met:

y _i ∈{0,1}, indicates whether the stacker places the goods on the cargo location i, y _i =1 indicates that the cargo location is selected, y _i =0 indicates that the cargo location is not selected;

It means that only one cargo location that meets the requirements can be selected for one warehousing operation;

In order to ensure that only one cargo location that meets the requirements is selected when leaving the warehouse, the following constraints must be met:

z _i ∈ {0,1}, indicates whether the stacker takes out goods from cargo location i, z _i =1 indicates that the cargo location is selected, z _i =0 indicates that the cargo location is not selected;

It means that only one cargo location that meets the requirements can be selected for one outbound operation;

To ensure that the stacker only transports one item at a time, the following constraints need to be added:

It means that if the cargo location i is selected, the goods must be taken out and transported in the same operation.

It is further preferred that Step 5 includes the following steps:

Step5.1. Initialize the population and generate an initial set of candidate solutions;

Randomly generate orders: Randomly generate orders to determine the quantity of each item; when generating orders, multiple constraints need to be considered for generation;

Randomly generate a cargo space allocation plan: For each group of orders, a set of cargo space allocation plans are randomly generated to determine the storage location of each cargo; when generating a cargo space allocation plan, multiple constraints need to be considered, such as the capacity of the cargo space Limitations, dimensions and weight of goods, etc. to generate initial plans;

Determine the population size: Select an appropriate population size based on the complexity and scale of the problem; the population size selected by this algorithm is Popsize;

Randomly generate Popsize logical outbound tasks from the alternative cargo locations, and generate Popsize logical inbound tasks from the alternative cargo locations. Then, check and correct the tasks, and set them as the initial population;

Step5.2. Perform non-dominated sorting on the target population, sort the individuals in the population according to their performance on multiple objective functions, and divide them into different frontiers;

The initial population is sorted, and the performance of each individual on the three objective functions is sorted and circulated until all individuals are assigned to the frontier; in each cycle, for each individual that is not assigned to the frontier Individual i, compare it with all individuals j that are not assigned to the frontier to determine whether individual j is assigned to the same frontier as individual i;

Step5.3. Calculate the crowding degree, perform Pareto sorting and crowding degree calculation on the objective function solution set in the frontier surface;

According to Pareto sorting, all individuals are sorted according to the Pareto frontier layer, and the individuals of each Pareto frontier layer are obtained in turn. For each objective function, the distance between individuals is calculated separately; the specific method is to classify the individuals according to the value of the objective function. Sort, and then calculate the distance between adjacent individuals according to the formula, in which the distance between individuals with the smallest objective function value is set to infinity, and the crowding degree of the individual in the multi-objective optimization problem is calculated; the specific method is to combine the crowding degrees of multiple objective functions Summing up, the crowding degree is the distance. After calculating the crowding degree of all individuals, all individuals are sorted according to the crowding degree and fitness value for selection and crossover operations;

Crowding calculation:

For the first objective function:

F ₁ (x ₍₁₎ ) ≤ F ₁ (x ₍₂₎ ) ≤ F ₁ (x _(N) )

For the second objective function:

F ₂ (x ₍₁₎ ) ≤ F ₂ (x ₍₂₎ ) ≤ F ₂ (x _(N) )

For the third objective function:

F ₃ (x ₍₁₎ ) ≤ F ₃ (x ₍₂₎ ) ≤ F ₃ (x _(N) )

Distance on three objective functions:

d _i,j,k =|F _l (x _(i) )-F _l (x _(j) )|, l∈{1, 2, 3}

Crowding between each individual:

Among them, x _(i) , x _(j) , x _(k) represent the i-th, j-th and k-th individuals ranked on the first, second and third objective functions, and N represents the total number of individuals. , F _l (x _(i) ), F ₂ (x _(i) ), F ₃ (x _(i) ) respectively represent the values of individual x _(i) on the three objective functions, l∈{1, 2 , 3} represents the objective function number d _i,j1 , d _i,j2 , d _i,j3 represents the distance between individuals x _(i) and x _(j) on the three objective functions;

Step5.4. Selection: Tournament selection, sort the selected rows according to Pareto level and congestion degree;

Perform Popsize selections, and randomly select Popsize/2 individuals for comparison. First compare the Pareto levels, with smaller levels given priority, and then compare the crowding degree. If there is more than one individual after the selection, random selection will be used;

Step5.5. Crossover: The crossover method adopts single-point crossover and sequential crossover. Determine the intersection point position and the first half or the second half of the crossover, and then swap row by row;

First, Popsize offspring are generated, and two different individuals are selected for crossover. After obtaining the codes of the two individuals, the crossover is performed. Single-point crossover and sequential crossover are used. The crossover probability here is P _c . First, the intersection point position is obtained, and the crossover Whether it is the first half or the second half, cross it row by row to get the crossed individual;

Step5.6. Mutation: Inversion mutation, select the mutation position through random numbers, and then exchange the genes before and after the position;

First, the mutation position is selected through random numbers, and then the genes before and after the position are exchanged; the mutation probability here is P _m . In this process, the genetic information of each individual in the population is stored, and then checked twice to ensure that there are no duplications. genes;

Step5.7. Merge the newly generated solution set with the original population, and sort the crowding degree;

Sort the obtained solutions according to Pareto, and filter out the first Popsize individuals to determine the range of Pareto optimal solutions to obtain the final Pareto optimal solution set;

Step5.8. Select the first Popsize solutions from the merged set as the new population;

Step5.9. If the termination condition is met, return the optimal solution set; otherwise, jump to Step2.

To sum up, the present invention has the following beneficial effects:

First, the present invention performs integrated optimization for forward and rear exit three-dimensional warehouses. Compared with traditional methods, it can simultaneously optimize orders and cargo locations while solving the optimization of forward and rear exit three-dimensional warehouses. It is practical, simple and effective.

Second, this algorithm can effectively handle conflicts between different optimization objectives, obtain a frontier solution set, and perform multi-objective optimization on this basis. Compared with the single-objective optimization algorithm, this algorithm can better meet the multi-objective needs of manufacturing enterprises in the actual production process, and is more in line with actual application needs.

Third, during the implementation of this algorithm, a basic heuristic method is used to generate the initial set of candidate solutions, which has high portability and scalability. The algorithm can be customized and expanded according to the specific application environment and objective function to better adapt to different needs.

Fourth, this algorithm solves the problem of warehouse cargo space allocation and job scheduling, and can improve the logistics and warehousing efficiency of production enterprises. In practical applications, it can bring significant benefits and economic benefits to production enterprises.

Description of the drawings

Figure 1 is a schematic diagram of the forward and rear exit three-dimensional warehouse proposed by the present invention;

Figure 2 is a flow chart of the NSGA-II algorithm proposed by the present invention;

Figure 3 shows the coding of the single-point crossover operation in the warehousing part;

Figure 4 shows the coding of the sequential crossover operation part of the outbound part;

Figure 5 shows the partial coding of the inversion mutation operation;

Figure 6 is an overall flow chart of the present invention;

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings.

Embodiment, a multi-objective integrated optimization method for forward-back-out warehouse based on NSGA-Ⅱ, as shown in Figures 1 to 6, including the following steps:

Step 1. Establish a warehouse model: Based on the actual warehouse design, establish a structural model of a forward-back-out three-dimensional warehouse, abstracting it into a multi-dimensional space. The element nodes of the multi-dimensional space include stackers, shelves, outbound and inbound warehouses;

Step 2. Establish a task model: According to the actual situation, randomly define the warehousing tasks and warehousing tasks of the three-dimensional warehouse, and determine the task volume and task-related information;

Step 3. Determine the decision variables: For the problem of cargo space allocation and job scheduling in the three-dimensional warehouse, it is necessary to determine the corresponding decision variables, such as the type and quantity of items stored in each cargo space in the warehouse, as well as the execution order and time of each task, etc. ;

Step 4. Define the objective function: Based on the research purpose and practical problems, determine multiple optimization goals for the three-dimensional warehouse, such as the shortest running time, shelf stability, etc.;

Step 5. Construct the NSGA-II optimization algorithm model: Based on the above task model, decision variables and objective function, construct the NSGA-II optimization model and use the NSGA-II algorithm to solve the optimal solution;

Step 6. Carry out simulation and verification: Carry out simulation and verification based on the established model, consider the impact of different parameters on the model, obtain the optimized optimal solution, and conduct evaluation and analysis.

Step4 includes the following steps:

First, set up a three-dimensional warehouse with n cargo spaces. The three-dimensional coordinates of the goods are expressed as (x _i , y _i , z _i ). The size of the cargo spaces is l _i ×w _i ×h _i , where 1≤i≤n , based on relevant data such as the location of the entrance and exit of the three-dimensional warehouse, cargo quality, conveyor belt parameters, etc., establish a forward-back-out three-dimensional warehouse, and randomly define the warehousing tasks and outgoing tasks of the three-dimensional warehouse according to the actual situation, and determine the task volume and task-related information , at the same time, the three-dimensional warehouse also needs to meet relevant assumptions: the stacker takes out the goods from the three-dimensional warehouse in sequence according to the forward-then-out strategy, and can only take out or put one piece of goods in and out of the warehouse at a time until all the goods in the order are taken; it is not considered Start and stop time; do not consider the impact of the weight of the cargo on the stacker's driving process; secondly, construct the objective function, construct the first objective function F ₁ with the shortest running time; construct the second objective function F 2 with the lowest center of gravity; construct the second objective function F ₂ with the energy Construct the third objective function F ₃ with the lowest cost; the objective function is as follows:

Minimum running time:

Among them, t _ij represents the running time of the stacker from the current cargo location to the next cargo location. The calculation formula is: t _ij ＝d _i /v _i +d _j /v _j

Among them, d _i represents the horizontal straight-line distance from the current cargo location (x _i , y _i , z _i ) to the target cargo location (x _ij , y _ij , z _ij ), and V _i represents the horizontal traveling speed of the stacker;

d _j represents the vertical straight-line distance from the current cargo location (x _i , y _i , z _i ) to the target cargo location (x _ij , y _ij , z _ij ), and v _j represents the vertical traveling speed of the stacker;

The lowest center of gravity: F ₂ (x) = cg

Among them, cg represents the average height coordinate of the center of gravity of all cargo locations, and its calculation formula is:

Among them, m _i represents the quality of the goods on the i-th cargo position;

Lowest energy consumption:

Among them, e _i represents the energy consumption of the stacker when taking out goods i, and its calculation formula is:

e _i = w _i d _ij

Among them, w _i represents the weight of the goods on the i-th cargo space, and d _ij represents the traveling distance of the stacker from the current cargo space to the next cargo space;

At the same time, the model also needs to satisfy the following constraints:

Assume that the stacker needs to perform a "warehousing" operation, that is, place the goods on the cargo space, and at the same time perform an "outbound" operation, that is, take the goods out of the cargo space;

In order to ensure that each cargo slot has only one cargo, the following constraints must be met:

Among them, x _ij indicates whether goods are placed in the cargo location i, x _ij =1 indicates that the cargo location has goods, and x _ij =0 indicates that the cargo location is empty;

In order to ensure that only one cargo location that meets the requirements is selected when warehousing, the following constraints must be met:

y _i ∈ {0, 1}, indicates whether the stacker places the goods on the cargo location i, y _i =1 indicates that the cargo location is selected, y _i =0 indicates that the cargo location is not selected;

It means that only one cargo location that meets the requirements can be selected for one warehousing operation;

In order to ensure that only one cargo location that meets the requirements is selected when leaving the warehouse, the following constraints must be met:

z _i ∈ {0, 1}, indicates whether the stacker takes out the goods from the cargo location i, z _i =1 indicates that the cargo location is selected, z _i =0 indicates that the cargo location is not selected;

It means that only one cargo location that meets the requirements can be selected for one outbound operation;

To ensure that the stacker only transports one item at a time, the following constraints need to be added:

It means that if the cargo location i is selected, the goods must be taken out and transported in the same operation.

Step5 includes the following steps:

Step5.1. Initialize the population and generate an initial set of candidate solutions;

Randomly generate orders: Randomly generate orders to determine the quantity of each item; when generating orders, multiple constraints need to be considered for generation;

Randomly generate a cargo space allocation plan: For each group of orders, a set of cargo space allocation plans are randomly generated to determine the storage location of each cargo; when generating a cargo space allocation plan, multiple constraints need to be considered, such as the capacity of the cargo space Limitations, dimensions and weight of goods, etc. to generate initial plans;

Determine the population size: Select an appropriate population size based on the complexity and scale of the problem; the population size selected by this algorithm is Popsize;

Randomly generate Popsize logical outbound tasks from the alternative cargo locations, and generate Popsize logical inbound tasks from the alternative cargo locations. Then, check and correct the tasks, and set them as the initial population;

Step5.2. Perform non-dominated sorting on the target population, sort the individuals in the population according to their performance on multiple objective functions, and divide them into different frontiers;

The initial population is sorted, and the performance of each individual on the three objective functions is sorted and circulated until all individuals are assigned to the frontier; in each cycle, for each individual that is not assigned to the frontier Individual i, compare it with all individuals j that are not assigned to the frontier to determine whether individual j is assigned to the same frontier as individual i;

Step5.3. Calculate the crowding degree, perform Pareto sorting and crowding degree calculation on the objective function solution set in the frontier surface;

According to Pareto sorting, all individuals are sorted according to the Pareto frontier layer, and the individuals of each Pareto frontier layer are obtained in turn. For each objective function, the distance between individuals is calculated separately; the specific method is to classify the individuals according to the value of the objective function. Sort, and then calculate the distance between adjacent individuals according to the formula, in which the distance between individuals with the smallest objective function value is set to infinity, and the crowding degree of the individual in the multi-objective optimization problem is calculated; the specific method is to combine the crowding degrees of multiple objective functions Summing up, the crowding degree is the distance. After calculating the crowding degree of all individuals, all individuals are sorted according to the crowding degree and fitness value for selection and crossover operations;

Crowding calculation:

For the first objective function:

F ₁ (x ₍₁₎ ) ≤ F ₁ (x ₍₂₎ ) ≤ F ₁ (x _(N) )

For the second objective function:

F ₂ (x ₍₁₎ ) ≤ F ₂ (x ₍₂₎ ) ≤ F ₂ (x _(N) )

For the third objective function:

F ₃ (x ₍₁₎ ) ≤ F ₃ (x ₍₂₎ ) ≤ F ₃ (x _(N) )

Distance on three objective functions:

d _i,j,k =|F _l (x _(i) )-F _l (x _(j) )|, l∈{1, 2, 3}

Crowding between each individual:

Among them, x _(i) , x _(j) , x _(k) represent the i-th, j-th and k-th individuals ranked on the first, second and third objective functions, and N represents the total number of individuals. , F _l (x _(i) ), F ₂ (x _(i) ), F ₃ (x _(i) ) respectively represent the values of individual x _(i) on the three objective functions, l∈{1, 2 , 3} represents the objective function number d _i,j1 , di _,j2 , d _i,j3 represents the distance between individuals x _(i) and x _(i) on the three objective functions;

Step5.4. Selection: Tournament selection, sort the selected rows according to Pareto level and congestion degree;

Perform Popsize selections, and randomly select Popsize/2 individuals for comparison. First compare the Pareto levels, with smaller levels given priority, and then compare the crowding degree. If there is more than one individual after the selection, random selection will be used;

Step5.5. Crossover: The crossover method adopts single-point crossover and sequential crossover. Determine the intersection point position and the first half or the second half of the crossover, and then swap row by row;

First, Popsize offspring are generated, and two different individuals are selected for crossover. After obtaining the codes of the two individuals, the crossover is performed. Single-point crossover and sequential crossover are used. The crossover probability here is P _c . First, the intersection point position is obtained, and the crossover Whether it is the first half or the second half, cross it row by row to get the crossed individual;

Step5.6. Mutation: Inversion mutation, select the mutation position through random numbers, and then exchange the genes before and after the position;

First, the mutation position is selected through random numbers, and then the genes before and after the position are exchanged; the mutation probability here is P _m . In this process, the genetic information of each individual in the population is stored, and then checked twice to ensure that there are no duplications. genes;

Step5.7. Merge the newly generated solution set with the original population, and sort the crowding degree;

Sort the obtained solutions according to Pareto, and filter out the first Popsize individuals to determine the range of Pareto optimal solutions to obtain the final Pareto optimal solution set;

Step5.8. Select the first Popsize solutions from the merged set as the new population;

Step5.9. If the termination condition is met, return the optimal solution set; otherwise, jump to Step2.

Case implementation:

Taking a single lane forward and backward three-dimensional warehouse as an example, there is a row of 10 layers and 10 rows of shelves on both sides of the lane. The speeds of the stacker in the x, y, and z directions are 1m/s, 0.5m/s, and 0.5m/s respectively. , the length, width and height of the cargo space are all 1m, the conveyor belt speed is 1.5m/s, and 40 goods are randomly generated on the shelves on both sides. The surface cargo space is occupied, and the number of warehousing orders is 20. The goods are divided into four types , there is no difference except weight, the masses are 100kg, 200kg, 300kg, 400kg respectively, and the quantities are 10, 5, 5, 5 respectively. Outbound tasks are randomly generated. Algorithm parameters: crossover probability P _c =0.8, mutation probability P _m =0.1, maximum number of iterations MaxIterations =500.

The following table shows the Pareto solution set that has not been optimized by this method.

The following table shows the Pareto solution set obtained by this method.

It can be seen from the above table that the effectiveness of this method is proved. This method can effectively perform multi-objective integrated optimization of the forward and rear exit three-dimensional warehouse.

This specific embodiment is only an explanation of the present invention, and it is not a limitation of the present invention. Those skilled in the art can make modifications to this embodiment without creative contribution as needed after reading this specification. However, as long as the rights of the present invention are All requirements are protected by patent law.

Claims (3)

1. A multi-objective integrated optimization method for a forward and backward warehouse-out warehouse based on NSGA-II is characterized in that:

the method comprises the following steps:

step1, establishing a warehouse model: according to the actual warehouse design, a structural model of the stereoscopic warehouse is established, and is abstracted into a multidimensional space, wherein element nodes of the multidimensional space comprise a stacker, a goods shelf, a warehouse-out and a warehouse-in;

step2, establishing a task model: according to actual conditions, a warehouse-in task and a warehouse-out task of the stereoscopic warehouse are defined randomly, and task quantity and task related information are determined;

step3, determining decision variables: aiming at the goods space distribution and job scheduling problems of the stereoscopic warehouse, corresponding decision variables need to be determined;

step4, defining an objective function: determining a plurality of optimization targets of the stereoscopic warehouse according to the research purpose and the actual problem;

step5, constructing an NSGA-II optimization algorithm model: based on the task model, the decision variables and the objective function, an NSGA-II optimization model is constructed, and an NSGA-II algorithm is utilized to solve an optimal solution;

step6, simulation and verification are carried out: and according to the established model, performing simulation and verification, taking the influence of different parameters on the model into consideration, obtaining an optimized optimal solution, and performing evaluation and analysis.

2. The multi-objective NSGA-ii based forward and backward warehouse-out optimization method according to claim 1, wherein:

step4 comprises the following steps:

first, there are n cargo spaces in the set-up body warehouse, and the three-dimensional coordinates of the cargo are respectively expressed as (x _i ,y _i ,z _i ) The size of the cargo space is l _i ×w _i ×h _i Wherein i is more than or equal to 1 and less than or equal to n, the stereoscopic warehouse is established according to the related data such as the stereoscopic warehouse entrance and exit position, the cargo quality, the conveyor belt parameters and the like, the warehouse-in task and the warehouse-out task of the stereoscopic warehouse are defined randomly according to actual conditions, the task quantity and the task related information are determined, and meanwhile, the stereoscopic warehouse also needs to meet related assumptions: the stacker sequentially takes out the goods from the stereoscopic warehouse according to the forward and backward strategy, and only can take out or put in one goods at a time to go into and out of the warehouse until the goods in all orders are taken out; irrespective of the start-stop time; the influence of the weight of the goods in the running process of the stacker is not considered; second, constructing an objective function, constructing a first objective function F with the shortest run time ₁ The method comprises the steps of carrying out a first treatment on the surface of the Constructing the second objective function F with lowest center of gravity ₂ The method comprises the steps of carrying out a first treatment on the surface of the Constructing a third objective function F with minimum energy consumption ₃ The method comprises the steps of carrying out a first treatment on the surface of the The objective function is as follows:

shortest run time:

wherein t is _ij The running time of the stacker from the current cargo position to the next cargo position is represented by the following calculation formula: t is t _ij ＝d _i /v _i +d _j /v _j

Wherein d _i Representing the current cargo space (x _i ,y _i ,z _i ) To the target cargo space (x _ij ,y _ij ,z _ij ) Straight distance in horizontal direction v _i Indicating the horizontal running speed of the stacker;

d _j representing the current cargo space (x _i ,y _i ,z _i ) To the target cargo space (x _ij ,y _ij ,z _ij ) V is the straight distance in the vertical direction _j Representing the vertical running speed of the stacker;

the center of gravity is the lowest: f (F) ₂ (x)＝cg

Wherein cg represents the average value of the height coordinates of the centers of gravity of all cargo positions, and the calculation formula is as follows:

wherein m is _i Representing the mass of the cargo on the ith cargo space;

the energy consumption is the lowest:

wherein e _i The energy consumption of the stacker when the goods i are taken out is represented, and the calculation formula is as follows:

e _i ＝w _i d _ij

wherein w is _i Representing the weight of the cargo at the ith cargo space, d _ij Representing the travel distance of the stacker from the current cargo space to the next cargo space;

at the same time, the model also needs to satisfy the following constraint conditions:

the stacker is supposed to perform 'warehouse entry' operation, namely, goods are placed on a goods space, and meanwhile, the stacker is supposed to perform 'warehouse exit' operation, namely, the goods are taken out from the goods space;

wherein x is _ij Indicating whether the cargo is placed in the cargo space i, x _ij =1 indicates that the cargo space has cargo, x _ij =0 indicates that the cargo space is empty;

y _i e {0,1}, indicating whether the stacker is to place cargo on cargo space i, y _i =1 indicates that the cargo space is selected, y _i =0 indicates that the cargo space was not selected;

indicating that one warehouse-in operation can only be performedSelecting a cargo space meeting the requirements;

z _i e {0,1}, indicates whether the stacker is to remove a good from the good i, z _i Let 1 denote the selected cargo space, z _i =0 indicates that the cargo space was not selected;

indicating that only one cargo space meeting the requirements can be selected in one ex-warehouse operation;

indicating that the cargo must be removed and transported in the same operation if cargo space i is selected.

3. The multi-objective integrated optimization method for the forward and backward warehouse-out based on NSGA-II according to claim 2, wherein the method comprises the following steps:

step5 comprises the following steps:

step5.1, initializing a population, and generating an initial candidate solution set;

randomly generating an order: randomly generating orders to determine the quantity of each item; in generating an order, a plurality of constraint conditions need to be considered for generation;

randomly generating a cargo allocation scheme: for each set of orders, randomly generating a set of cargo space allocation schemes to determine a storage location for each cargo; in generating the cargo space allocation scheme, a plurality of constraint conditions such as capacity limitation of cargo space, size and weight of cargo and the like need to be considered to generate an initial scheme;

determining the population quantity: selecting proper population quantity according to the complexity and the scale of the problem; the population size selected by the algorithm is Popsize;

randomly generating Popsize out-of-stock tasks conforming to logic from the candidate goods places, generating Popsize in-stock tasks conforming to logic from the candidate goods places, and then checking and correcting the tasks to be set as an initial population;

step5.2, performing non-dominant ranking on the target population, ranking the individuals in the population according to the performances of the individuals on a plurality of target functions, and dividing the individuals into different front faces;

ranking the initial population, ranking the performance of each individual on three objective functions and cycling until all individuals are sorted into the leading faces; in each cycle, for each individual i that is not classified into the leading face, it is compared with all individuals j that are not classified into the leading face to determine whether to classify the individual j into the same leading face as the individual i;

step5.3, calculating the crowding degree, and performing pareto sorting and crowding degree calculation on the objective function solution set in the front surface;

according to Pareto sequencing, sequencing all individuals according to Pareto front layers, sequentially obtaining individuals of each Pareto front layer, and respectively calculating the distance between the individuals for each objective function; sequencing individuals according to the value of the objective function, and then calculating the distance between adjacent individuals according to a formula, wherein the interval between individuals with the minimum objective function value is set to be infinity, and the crowding degree of the individuals in the multi-objective optimization problem is calculated; the specific method is that the crowding degree of a plurality of objective functions is summed, the crowding degree is the distance, after the crowding degree of all individuals is calculated, all the individuals are ordered according to the crowding degree and the fitness value so as to carry out the selection and crossing operation;

and (3) calculating the crowding degree:

for the first objective function:

F ₁ (x ₍₁₎ )≤F ₁ (x ₍₂₎ )≤F ₁ (x _(N) )

for the second objective function:

F ₂ (x ₍₁₎ )≤F ₂ (x ₍₂₎ )≤F ₂ (x _(N) )

for the third objective function:

F ₃ (x ₍₁₎ )≤F ₃ (x ₍₂₎ )≤F ₃ (x _(N) )

distance on three objective functions:

d _i,j,k ＝|F _l (x _(i) )-F _l (x _(j) )|,l∈{1,2,3}

degree of congestion between each individual:

wherein x is _(i) ，x _(j) ，x _(k) Represents the ith, jth and kth individuals ranked on the first, second and third objective functions, N represents the total number of individuals, F _l (x _(i) )，F ₂ (x _(i) )，F ₃ (x _(i) ) Respectively represent individual x _(i) The values on the three objective functions, l.epsilon. {1,2,3} represent the objective function number d _i,j1 ，d _i,j2 ，d _i,j3 Representing individual x _(i) And x _(j) Distances on three objective functions;

step5.4, selection: tournament selection, sorting the selected rows according to Pareto hierarchy and congestion level;

selecting the Popsize times, randomly selecting and comparing the Popsize/2, firstly, giving priority to the Popsize/2 which is smaller than the Pareto level, then, giving priority to the crowding degree, and if the priority to the crowding degree is large, selecting more than one individual at random after the selection is finished;

step5.5, crossover: the crossing mode adopts single-point crossing and sequential crossing, determines the position of the crossing point and the front half part or the rear half part of the crossing, and then exchanges line by line;

firstly generating Popsize filial generation, selecting two different individuals for crossing to obtain codes of the two individuals, crossing, adopting single-point crossing and sequential crossing, wherein the crossing probability is P _c Firstly, obtaining the position of an intersection point and intersecting the front half part or the rear half part, and intersecting the intersection point line by line to obtain an intersecting individual;

step5.6, variation: inversion mutation, namely selecting a mutation position through a random number, and then exchanging genes before and after the position;

first by random numbersSelecting a mutation position, and then exchanging genes before and after the position; where the mutation probability is P _m During this process, the genetic information of each individual in the population is stored and then checked twice to ensure that there are no duplicate genes;

step5.7, merging the newly generated solution set with the original population, and sequencing the crowding degree;

the obtained solutions are ranked according to Pareto, and the previous individuals are screened out to determine the range of the Pareto optimal solution so as to obtain the final Pareto optimal solution set;

step5.8, selecting the previous pop solutions from the pooled set as a new population;

step5.9, if the termination condition is met, returning to the optimal solution set; otherwise, go to Step2.