A method applied to warehouse replenishment and storage location collaborative planning

Abstract

A method applied to warehouse replenishment and storage site collaborative planning, comprising: constructing a warehouse replenishment and storage site collaborative model, the target of the warehouse replenishment and storage site collaborative model being minimum total energy consumption of warehouse carrying equipment and minimum warehouse channel load; solving the warehouse replenishment and storage site collaborative model based on an improved non-dominated sorting elitist genetic algorithm (ENSGA-II), to obtain an optimal population solution and corresponding minimum energy consumption value and channel use difference coefficient. The obtained solution is sorted by Pareto frontier level and elite solution is selected based on knee point criteria to find an approximate optimal solution that performs well in multiple target dimensions. Compared with the multi-objective evolutionary algorithm based on index and decomposition, the present application has optimal theoretical support of non-dominated sorting criteria and knee point criteria, ensuring the search performance and stability of the algorithm.

Description

Technical Field

[0001] The present invention relates to the field of intelligent warehousing technology, and in particular to a method for collaborative planning of warehouse replenishment and storage space. Background Art

[0002] With the advent of Intelligent Manufacturing 5.0, smart logistics systems, exemplified by food and pharmaceutical warehousing and picking systems, are evolving to meet customer demand for smaller, more frequent batches of food and pharmaceuticals with shorter delivery windows. This has led to a significant improvement in warehousing system picking efficiency. Scholars define this type of warehouse as a forward-reserve warehouse (FRW). The forward-reserve warehouse comprises an automated storage and retrieval system (AS / RS) and a picking system, while the forward-reserve warehouse comprises a robotic mobile fulfillment system (RMFS). The forward-reserve warehouse provides replenishment for the forward-reserve warehouse. The warehouse system operates as follows: 1) A stacker crane transports pallets loaded with SKUs to the replenishment station at the exit. 2) Automated guided vehicles (AGVs) in the forward-reserve warehouse transport the mobile racks requiring replenishment to the replenishment station. 3) Pickers place SKUs on the mobile racks based on the required replenishment quantity. 4) AGVs transport replenished mobile racks to the forward storage area for storage. 5) Based on order requirements, AGVs transport mobile racks to the picking station for picking. 6) Pickers select SKUs, and AGVs transport the picked mobile racks to the forward storage area. This demonstrates that replenishment decisions and product storage location allocation decisions in the forward storage warehouse (FRW) occur simultaneously, and collisions and deadlocks in transport equipment are significant factors affecting the system's picking efficiency. Appropriate storage location planning can effectively prevent collisions and deadlocks in transport equipment from the outset.

[0003] However, with the development of smart warehouses, existing research technologies can no longer meet the needs of real-world system operation objectives. First, most research technologies only explore storage location allocation problems / batch picking problems / path planning problems in warehouses, and lack research on related replenishment-storage location collaborative planning technologies. Second, most researchers focus on storage location allocation problems with economic efficiency as a single goal, and lack multi-objective collaborative optimization technologies that take into account both economic and green goals. Finally, the extensive use of automated guided vehicles and stackers in forward-storage warehouses has brought about congestion problems, and there is a lack of research on related obstacle avoidance technologies. Therefore, there is an urgent need for a method for warehouse replenishment and storage location collaborative planning to solve this problem. Summary of the Invention

[0004] In view of the above problems, the present invention is proposed to provide a method for warehouse replenishment and storage location collaborative planning that overcomes the above problems or at least partially solves the above problems.

[0005] In order to solve the above technical problems, the embodiments of the present application disclose the following technical solutions:

[0006] In a first aspect, an embodiment of the present invention discloses a method for warehouse replenishment and storage location collaborative planning, comprising:

[0007] S100. Construct a warehouse replenishment and storage coordination model, wherein the objectives of the warehouse replenishment and storage coordination model are to minimize the total energy consumption of warehouse transportation equipment and minimize the warehouse aisle load; the decision variable in the warehouse replenishment and storage coordination model is the variable y of the sub-storage k of shelf l on aisle r assigned to SKUp. pklr SKUp is assigned to the variable of the sub-storage position i on the channel r1 in the pre-register area SKUp is assigned to the variable of sub-storage position j on channel r2 in the pre-address area Number of times SKU p is picked in the front-end aisle r1 Number of times SKU p is picked in storage area aisle r2

[0008] S200. Solve the warehouse replenishment and storage coordination model based on the improved non-dominated sorting elite genetic algorithm, and obtain the optimal population solution and the corresponding minimum energy consumption value and channel usage difference coefficient based on the knee point criterion.

[0009] Furthermore, in S100, the minimum total energy consumption function of the warehouse transportation equipment is:

[0010]

[0011] Where R represents the channel set, r=1,…|R|, r∈R; r1∈R1 represents the channel index of the front area, r2∈R2 represents the channel index of the storage area; I represents the sub-storage location set of each channel in the front area, i=1,…|I|, i∈I; J represents the sub-storage location set of each channel in the storage area, j=1,…|J|, j∈J; P represents the SKU set, p=1,…|P|, p∈P; represents the energy consumption required by the AGVs to transport SKU p from storage location i in the front area r1 to the picking platform, Indicates the picking frequency of SKUp in each sub-storage location in the front area. Indicates that SKUp is assigned to the sub-storage position i on the channel r1 in the front area; represents the energy consumption required by the robot to transport SKUp from storage location j in storage area r2 to the picking platform in the front area; Indicates the picking frequency of SKU p in each sub-storage location in the storage area, Indicates that SKU p is assigned to sub-storage location j on storage area channel r2; represents the energy consumption required by the robot to transport SKUp from storage location j in storage area r2 to storage location i in the front area r1; It represents the average replenishment frequency of each sub-storage location allocated to SKU p from the picking platform to the front area, Indicates the average replenishment frequency of each sub-storage location allocated by SKUp from the storage area to the front area to the picking platform.

[0012] Furthermore, in S100, the warehouse channel load minimum function is:

[0013]

[0014] in, is the number of times SKUp is picked in the front area channel r1, is the average number of picking times in all channels of the front area, is the number of times the SKU is picked in the storage area aisle r2, is the average number of picks across all aisles in the storage area.

[0015] Furthermore, in S100, the constraints of the minimum total energy consumption function of the warehouse transportation equipment and the minimum warehouse channel load function include at least: one sub-storage location can only store one SKU, the number of SKU types stored on a single shelf cannot exceed the total sub-storage locations of a single shelf, and the number of sub-storage locations occupied by each SKU cannot exceed the total allocated storage locations.

[0016] Furthermore, in S200, the warehouse replenishment and storage location coordination model is solved based on an improved non-dominated sorting elite genetic algorithm to obtain an optimal population solution and a corresponding minimum energy consumption value and channel usage difference coefficient. The specific method includes:

[0017] S201. Set parameters and initialize the population;

[0018] S202. Generate a selected population based on the initialization population;

[0019] S203. Generate a crossover population based on the crossover method;

[0020] S204. Correct the crossover population using an infeasible solution correction method to obtain a corrected population;

[0021] S205. Mutate the modified population using a mutation method to obtain a mutated population;

[0022] S206. Merge the initial population and the mutated population to form a merged population, perform non-dominated sorting on the merged population, and obtain the Pareto rank of each solution in the merged population;

[0023] S207. Based on the Pareto rank of each solution in the merged population, generate a new offspring, update the number of iterations, and determine whether the current number of iterations has reached the maximum number of iterations. If so, proceed to S208; if not, return to S202.

[0024] S208. The current number of iterations reaches the maximum number of iterations, and the optimal population solution and the corresponding minimum energy consumption value and channel usage difference coefficient are obtained.

[0025] Furthermore, in S201, the parameters are set and the population is initialized. The specific method includes: setting the parameters, which include at least the total number of storage spaces in the front area and the storage area, the number of empty storage spaces and the number of non-empty storage spaces, and the number of sub-storage spaces allocated to each SKU; determining the initial solution population size based on the parameters, randomly selecting a SKU and placing it in the sub-storage spaces in the front area and the storage area until the number of sub-storage spaces allocated to the SKU is allocated, and then allocating the next SKU storage space, and repeating the above steps until all SKUs have completed storage space allocation.

[0026] Furthermore, in S202, a selection population is generated based on the initialization population, and the specific method includes: performing non-dominated sorting on the initialization population to obtain a Pareto front set; judging the quality of the solution according to the quality of the Pareto front set, and selecting elite individuals using a binary tournament technique until the elite individuals reach a preset solution population size. At this time, the population composed of elite individuals is the selection population.

[0027] Furthermore, in S203, a crossover population is generated based on the crossover method, which includes a crossover method based on an optimal target and a two-point crossover method; wherein the crossover method based on an optimal target specifically includes: randomly selecting the optimal chromosome S on two target dimensions based on the selected population best1 and S best2 , respectively select the portion between the preamble and the storage area and the corresponding portion of a parent chromosome Parent1 for crossover to generate a new offspring offspring1; the two-point crossover method specifically includes: randomly selecting genes between the two parent chromosomes for exchange to obtain two new offspring chromosomes offspring2 and offspring3; until all traversals complete all selected population solutions, that is, a crossover population is generated.

[0028] Furthermore, in S204, the crossover population is corrected using a correction method for infeasible solutions to obtain a corrected population. The specific method includes: checking the number of sub-storage positions occupied by each SKU in the chromosome in turn, eliminating redundant SKUs, and replacing SKUs with missing sub-storage positions, until the number of storage positions occupied by all SKUs meets the allocated number of sub-storage positions, at which point the model has a feasible solution.

[0029] Furthermore, in S205, a mutation method is used to mutate the corrected population to obtain a mutated population. The specific method includes: selecting a parent chromosome in the crossover population according to a preset mutation probability for a mutation operation, and randomly selecting genes in the pre-region and the storage region for exchange to complete the mutation operation, until all crossover population solutions are traversed and completed, that is, a mutated population is generated.

[0030] The beneficial effects of the above technical solutions provided by the embodiments of the present invention include at least:

[0031] The present invention discloses a method for warehouse replenishment and storage space collaborative planning, which searches for an approximate optimal solution that performs well in multiple objective dimensions by sorting the obtained solutions according to the Pareto front rank and selecting elite solutions based on the knee point criterion. Compared with the multi-objective evolutionary algorithm based on indicators and decomposition, the present invention has the optimal theoretical support of the non-dominated sorting criterion and the knee point criterion, which ensures the search performance and stability of the algorithm. The present invention creatively proposes an adaptive mutation technology to enhance the development capability of search individuals, thereby improving the accuracy of the optimal solution. The balance between local search and global search can not only improve the search efficiency of the algorithm, but also improve the search accuracy of the algorithm. The present invention uses an elite solution selection criterion based on congestion and knee point criteria to reduce the difficulty of decision-makers in making decisions due to the large number of Pareto front solutions in the later stages of iteration, thereby enhancing the practical applicability of the algorithm.

[0032] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0034] Figure 1 This is a flow chart of a method for warehouse replenishment and storage space collaborative planning in Example 1 of the present invention;

[0035] Figure 2 This is a schematic diagram of setting commodity information and storage location allocation parameters in a front-storage warehouse in Example 1 of the present invention.

[0036] Figure 3 This is a schematic diagram of the chromosome encoding method in Example 1 of the present invention;

[0037] Figure 4 Schematic diagram of a crossover method based on an optimal target in Example 1 of the present invention;

[0038] Figure 5 Schematic diagram of a two-point intersection method in Example 1 of the present invention;

[0039] Figure 6 Schematic diagram of a method for correcting an infeasible solution in Example 1 of the present invention;

[0040] Figure 7 This is a schematic diagram of the variation method in Example 1 of the present invention;

[0041] Figure 8 This is a comparative analysis chart of Pareto solution sets under different numbers of iterations in Example 2 of the present invention;

[0042] Figure 9 This is a convergence trend diagram of ENSGA-II and NSGA-II in Example 2 of the present invention;

[0043] Figure 10 Schematic diagram of the optimal solution of ENSGA-II and the optimal solution of NSGA-II at a medium scale of s2 in Example 2 of the present invention;

[0044] Figure 11 Schematic diagram of the optimal solution of ENSGA-II and the optimal solution of NSGA-II under large-scale s3 in Example 2 of the present invention;

[0045] Figure 12 Schematic diagram of the optimal solution of ENSGA-II and the optimal solution of NSGA-II under the ultra-large scale of s4 in Example 2 of the present invention. DETAILED DESCRIPTION

[0046] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0047] Example 1

[0048] In order to solve the problems existing in the prior art, an embodiment of the present invention provides a method for warehouse replenishment and storage location collaborative planning, such as Figure 1 ,include:

[0049] S100. Construct a warehouse replenishment and storage coordination model, wherein the goal of the warehouse replenishment and storage coordination model is to minimize the total energy consumption of warehouse transportation equipment and minimize the warehouse channel load; the decision variable in the warehouse replenishment and storage coordination model is the variable y of the sub-storage k of shelf l assigned to channel r. pklr SKUp is assigned to the variable of the sub-storage position i on the channel r1 in the pre-register area SKUp is assigned to the variable of sub-storage position j on channel r2 in the pre-address area Number of times SKU p is picked in the front-end aisle r1 Number of times SKU p is picked in storage area aisle r2

[0050] Specifically, we first introduce the multi-objective optimization problem applied to warehouse replenishment and storage space collaborative planning. Figure 2 As shown, the front-end area consists of low-level mobile racks with different sub-storage locations, each storing a single SKU. The storage area consists of fixed, high-level racks, with each grid representing a storage location, which can only hold a single SKU. The storage area and the front-end area have different storage capacity. A dual-objective optimization approach, minimizing both the green objective (energy consumption) and the efficiency objective (congestion level), determines the appropriate quantity of inventory in the storage area and replenishment in the front-end area, and where to place them on which shelves and storage levels in each system. By ensuring that the number of aisles fluctuates smoothly, excessive congestion in aisles due to frequent use can be avoided, which can reduce picking efficiency. Existing research shows that placing frequently purchased items on the same shelf can reduce energy consumption, and placing frequently purchased items in storage locations close to the picking platform can significantly reduce energy consumption. Furthermore, the product picking locations determine the picking aisles for transport equipment. Planning replenishment-storage location allocation can reduce congestion in picking aisles and improve picking efficiency. Therefore, there are two key issues that need to be addressed in the replenishment-storage allocation synchronization problem in the forward storage warehouse of this embodiment: (1) the automatic storage and retrieval system (AS / AR system) in the storage area needs to decide which area, which channel, and which storage location the incoming goods should be placed in; (2) at the same time, the robotic mobile fulfillment system (RMFS) in the forward area needs to decide which goods need to be replenished, the replenishment quantity, and which shelf and layer the replenished goods should be placed on.

[0051] This embodiment takes into account picking efficiency and energy consumption and is modeled as a multi-objective optimization problem. The two objective functions are to minimize the total energy consumption of warehouse transportation equipment and to minimize the load on warehouse aisles. Specifically, when constructing a warehouse replenishment and storage location coordination model, based on theoretical and practical foundations, the model must ensure the following assumptions: (1) Only one SKU is stored in a storage location; (2) One SKU can be stored in multiple storage locations; (3) Vacant storage locations are allowed. Before constructing the warehouse replenishment and storage location coordination model, the model parameters and model variables are first defined through Tables 1-3. Specifically, Table 1 is the model parameter set, Table 2 is the model specific parameters, and Table 3 is the model decision variables.

[0052] Table 1

[0053]

[0054]

[0055] Table 2

[0056]

[0057]

[0058] Table 3

[0059]

[0060]

[0061] In this embodiment, the minimum total energy consumption function of the warehouse transportation equipment is obtained by using the parameters in Tables 1-3:

[0062]

[0063] Where R represents the channel set, r=1,…|R|, r∈R; r1∈R1 represents the channel index of the front area, r2∈R2 represents the channel index of the storage area; I represents the sub-storage location set of each channel in the front area, i=1,…|I|, i∈I; J represents the sub-storage location set of each channel in the storage area, j=1,…|J|, j∈J; P represents the SKU set, p=1,…|P|, p∈P; represents the energy consumption required by the AGVs to transport SKU p from storage location i in the front area r1 to the picking platform, Indicates the picking frequency of SKUp in each sub-storage location in the front area. Indicates that SKUp is assigned to the sub-storage position i on the channel r1 in the front area; represents the energy consumption required by the robot to transport SKUp from storage location j in storage area r2 to the picking platform in the front area; Indicates the picking frequency of SKU p in each sub-storage location in the storage area, Indicates that SKU p is assigned to sub-storage location j on storage area channel r2; represents the energy consumption required by the robot to move SKU p from storage location j in storage area r2 to storage location i in the front area r1; Indicates the average replenishment frequency of each sub-storage location allocated by SKUp from the picking platform to the front area. Indicates the average replenishment frequency of SKUp from each sub-storage location allocated to the storage area to the picking platform.

[0064] The warehouse channel load minimum function is:

[0065]

[0066] in, is the number of times SKUp is picked in the front area channel r1, is the average number of picking times in all channels of the front area, is the number of times the SKU is picked in the storage area aisle r2, is the average number of picks across all aisles in the storage area.

[0067] In this embodiment, in S100, the constraints of the total energy consumption minimum function of the warehouse transportation equipment and the warehouse channel load minimum function include at least: one sub-storage location can only store one SKU, the number of SKU types stored on a single shelf cannot exceed the total sub-storage locations of a single shelf, and the number of sub-storage locations occupied by each SKU cannot exceed the total allocated storage locations.

[0068] The specific constraint formula is:

[0069]

[0070] Among them, constraints (1)(2)(3)(4) indicate that a sub-storage location can only store one SKU. Constraints (5)(6)(7)(8) indicate that the number of SKU types stored on a single shelf cannot exceed the total number of sub-storage locations on the single shelf. Constraints (9)(10) ensure that the number of sub-storage locations occupied by each SKU cannot exceed the total number of allocated storage locations. Constraints (11)-(13) define the decision variables.

[0071] S200. Solve the warehouse replenishment and storage coordination model based on the improved non-dominated sorting elite genetic algorithm, and obtain the optimal population solution and the corresponding minimum energy consumption value and channel usage difference coefficient based on the knee point criterion.

[0072] In S200 of this embodiment, the warehouse replenishment and storage location coordination model is solved based on an improved non-dominated sorting elite genetic algorithm to obtain the optimal population solution and the corresponding minimum energy consumption value and channel usage difference coefficient. The specific method includes:

[0073] S201. Set the parameters and initialize the population; specifically, in S201 of this embodiment, set the parameters and initialize the population, and the specific method includes: setting the parameters, and the parameters include at least the total number of storage spaces, the number of empty storage spaces, and the number of non-empty storage spaces in the front area and the storage area, and the number of sub-storage spaces allocated to each SKU; determine the initial solution population size based on the parameters, randomly select a SKU and place it in the sub-storage spaces in the front area and the storage area, until the number of sub-storage spaces allocated to the SKU is allocated, and then allocate the next SKU storage space, and repeat the above steps until all SKUs have completed storage space allocation.

[0074] For example, Figure 2 The total number of storage spaces, empty storage spaces, and non-empty storage spaces in the pre-position and storage areas, as well as the number of sub-storage spaces allocated to each SKU are given. Based on the above parameters, the initial solution population of the present invention is set to 100. The initial solution chromosome is as follows: Figure 3 The figure shows a 2x28 matrix, coded according to the total number of sub-storage slots in the pre-storage warehouse. There are 28 sub-storage slots, or 28 genes (a 2x1 matrix). The first 16 columns encode the pre-storage area, and the last 12 columns encode the storage area. The numbers in the first row of squares represent the SKU numbers, and the column corresponding to the SKU number represents the number of sub-storage slots. "0" indicates an empty slot. The second row shows the number of SKUs stored in the corresponding sub-storage slot.

[0075] S202. A selection population is generated based on the initialization population. In S202 of this embodiment, a selection population is generated based on the initialization population. The specific method includes: performing non-dominated sorting on the initialization population to obtain a Pareto front set; determining the quality of the solution based on the quality of the Pareto front set, and selecting elite individuals using a binary tournament technique until the number of elite individuals reaches a preset solution population size. At this time, the population composed of elite individuals is the selection population.

[0076] S203. Generate a cross population based on the cross method; in S203 of this embodiment, Figure 4 , generating a crossover population based on the crossover method, the crossover method includes a crossover method based on the optimal target and a two-point crossover method; wherein the crossover method based on the optimal target specifically includes: randomly selecting the optimal chromosome S on two target dimensions based on the selected population best1 and S best2, respectively select the part between the preamble area and the storage area and the corresponding part of a parent chromosome Parent1 to cross over and generate a new offspring offspring1; Figure 5 The two-point crossover method specifically includes: randomly selecting genes between two parent chromosomes for exchange to obtain two new offspring chromosomes, offspring2 and offspring3; until all traversals complete all selected population solutions, that is, a crossover population is generated.

[0077] S204. Use the correction method of the infeasible solution to correct the cross population to obtain the corrected population; since the cross technology changes the total number of sub-storages occupied by each SKU, it will produce a solution that violates the model constraints, which is called an infeasible solution. In order to make the infeasible solution a feasible solution, in S204 of this embodiment, Figure 6 , the crossover population is corrected by using the correction method of the infeasible solution to obtain the corrected population. The specific method includes: checking the number of sub-storage bits occupied by each SKU in the chromosome in turn, eliminating the redundant SKUs, and replacing the SKUs with missing sub-storage bits, until the number of storage bits occupied by all SKUs meets the allocated sub-storage bits, at which point the model has a feasible solution.

[0078] S205. Mutate the modified population using a mutation method to obtain a mutated population. In S205 of this embodiment, the modified population is mutated using a mutation method to obtain a mutated population. The specific method includes: selecting a parent chromosome in the crossover population according to a preset mutation probability to perform a mutation operation, and randomly selecting genes in the preamble region and the storage region to exchange and complete the mutation operation until the generated new chromosome reaches the population size, that is, a mutated population is generated. Specifically, Figure 7 As shown, a parent chromosome is selected from the crossover population with a mutation probability of 0.1 for mutation. Genes in the prefix bit 1 and bit 2, and the storage bit 3 and bit 4 are randomly swapped to complete the mutation. Because the mutation occurs within the same chromosome, no infeasible solutions are generated. This process continues until all crossover-corrected population solutions are traversed, resulting in a mutant population. At this point, the entire evolution process is complete, and the process proceeds to S206.

[0079] S206. Merge the initial population and the mutated population to form a merged population, perform non-dominated sorting on the merged population, and obtain the Pareto rank of each solution in the merged population;

[0080] S207. Based on the Pareto rank of each solution in the merged population, a new offspring is generated, the number of iterations is updated, and a determination is made as to whether the current number of iterations has reached the maximum number of iterations. If so, the process proceeds to S208; if not, the process returns to S202. Specifically, excellent solutions are selected from the solutions in the merged population based on their Pareto ranks to be added to the offspring. If the ranks are the same, the solution with the largest crowding distance is selected to be added to the offspring. This continues until the population size is reached, at which point a new offspring is generated.

[0081] S208. The current number of iterations reaches the maximum number of iterations, and the optimal population solution and the corresponding minimum energy consumption value and channel usage difference coefficient are obtained.

[0082] This embodiment discloses a method for warehouse replenishment and storage space collaborative planning, which searches for an approximate optimal solution that performs well in multiple objective dimensions by sorting the obtained solutions according to the Pareto front rank and selecting elite solutions based on the knee point criterion. Compared with the multi-objective evolutionary algorithm based on indicators and decomposition, the present invention has the support of the multi-objective evolutionary algorithm and the Pareto optimal theory of economics, which ensures the search performance and stability of the algorithm. The present invention creatively proposes an adaptive mutation technology to enhance the development capability of search individuals, thereby improving the accuracy of the optimal solution. The balance between local search and global search can not only improve the search efficiency of the algorithm, but also improve the search accuracy of the algorithm. The present invention is based on the optimal theoretical support of the non-dominated sorting criterion and the knee point criterion, which ensures the search performance and stability of the algorithm.

[0083] Example 2

[0084] To verify the effectiveness of the non-dominated elite sorting genetic algorithm (ENSGA-II) disclosed in Example 1, a comparison scheme using the second generation non-dominated elite sorting genetic algorithm (NSGA-II) was designed. Table 4 shows the basic data settings for the multi-objective model of replenishment-slot allocation collaborative planning. The second generation non-dominated elite sorting genetic algorithm has a crossover probability of 0.8, a mutation probability of 0.1, a population size of 50, and a maximum number of iterations of 50.

[0085] Table 4 Basic data range

[0086]

[0087]

[0088] In the embodiment, the above fixed scale setting will be used to analyze and compare the visualization results of the Pareto frontier solutions of the two algorithms at different iterations. Figure 8As shown in the figure, these four figures describe the Pareto optimal solutions when the number of iterations is 10, 20, 30 and 50 respectively. The vertical axis represents the first target value (total energy consumption), and the horizontal axis represents the second target value (total balance factor). Since the minimum value of the objective function is sought, the closer the scattered point solution is to the lower right corner area, the higher the quality of the solution. The wider the distribution of the scattered points on the horizontal and vertical axes, the better the diversity of solutions obtained by the algorithm. The red triangle represents the Pareto optimal solution obtained by ENSGA-II, and the blue circle represents the Pareto optimal solution obtained by NSGA-II. Figure 7 As shown in the figure, when the number of iterations is 10, 20, or 30, the red triangle's scattered points are closer to the lower left corner, indicating that the optimal solution of ENSGA-II is superior to that of NSGA-II. When the number of iterations is 50, both algorithms achieve the optimal solution. Therefore, the above analysis results show that ENSGA-II can obtain a better Pareto optimal solution in a shorter time.

[0089] In this embodiment, we analyze in detail the convergence speed of the dual objective values ​​obtained by the two algorithms. Figure 9 The convergence trends of ENSGA-II and NSGA-II are shown in the upper and lower panels, respectively. The left panel shows the convergence trend of the first target value (total energy consumption), and the right panel shows the convergence trend of the second target value (total channel balance factor). The vertical axis represents the ratio of the target value, and the horizontal axis represents the change in the number of iterations. Figure 9 The results of a) show that the target value of total energy consumption reaches stability after 5 iterations, while the target value of total channel balance factor reaches stability after 3 iterations. The Pareto optimal solution obtained by ENSGA-II algorithm reaches stability after 5 iterations. Figure 9 As shown in Figure b), after 11 iterations, NSGA-II achieves the same total energy consumption target as ENSGA-II and reaches stability, while the target value for the total channel balancing factor requires four iterations. After 11 iterations, the Pareto optimal solution obtained by NSGA-II is stable. These analysis results demonstrate that ENSGA-II can achieve a better Pareto optimal solution in a shorter time and achieve stability first.

[0090] Visual analysis of Pareto fronts of different scales under different iterations. In the embodiment, the performance of the algorithm will be verified by comparative analysis of medium-scale, large-scale and ultra-large-scale examples. Figure 10-12As shown in the figure, these four figures describe the Pareto optimal solutions when the number of iterations is 10, 20, 30 and 50 respectively. The vertical axis represents the first target value (total energy consumption), and the horizontal axis represents the second target value (total channel balance factor). Since the minimum value of the objective function is sought, the closer the scattered point solution is to the lower left corner area, the higher the quality of the solution. The wider the distribution of the scattered points on the horizontal and vertical axes, the better the diversity of the solutions obtained by the algorithm. The red triangle represents the Pareto optimal solution obtained by ENSGA-II, and the blue circle represents the Pareto optimal solution obtained by NSGA-II. Figure 8 As shown, in the medium-scale case s2, regardless of the number of iterations, the red triangles are closer to the lower right corner (high solution quality) and are widely distributed (good diversity). Therefore, the optimal solution of ENSGA-II is significantly better than that of NSGA-II. In the large-scale case s3 and the ultra-large-scale case s4, when the number of iterations is 30 / 50, the red triangles are closer to the lower right corner (high solution quality) and are widely distributed (good diversity). The optimal solution of ENSGA-II is better than that of NSGA-II. This shows that ENSGA-II has a clear advantage in small-scale cases. In large-scale cases, as the number of iterations increases, higher-quality solutions are obtained that exceed those of NSGA-II. Therefore, these analysis results show that ENSGA-II can obtain a good Pareto optimal solution in a shorter time.

[0091] In summary, this implementation first builds on the theoretical foundation of multi-objective evolutionary algorithms. Multi-objective evolutionary algorithms are a mature and well-established technology, and NSGA-II has achieved outstanding performance in numerous fields. The proposed ENSGA-II algorithm, building on the principles of NSGA-II, searches for near-optimal solutions that excel across multiple objective dimensions by ranking the obtained solutions on the Pareto front and selecting elite solutions based on the knee point criterion. Compared to multi-objective evolutionary algorithms based on indicators and decomposition, the ENSGA-II algorithm possesses the optimal theoretical support of multi-objective evolutionary algorithms and the knee point criterion, ensuring the algorithm's search performance and stability. A novel crossover technique is proposed to help search individuals conduct extensive exploration in the early stages of iteration, while a creative adaptive mutation technique is proposed to enhance the development capabilities of search individuals, thereby improving the accuracy of the optimal solution. This balance between local and global search improves not only the algorithm's search efficiency but also its search accuracy. This embodiment uses the elite solution selection criteria based on congestion and the knee point criterion to reduce the difficulty in decision-making caused by a large number of Pareto front solutions in the later stages of iteration, thereby enhancing the algorithm's practical application.

[0092] It should be understood that the specific order or hierarchy of steps in the disclosed processes is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process can be rearranged without departing from the scope of the present disclosure. The accompanying method claims present elements of the various steps in an exemplary order and are not intended to be limited to the specific order or hierarchy described.

[0093] In the foregoing detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that embodiments of the claimed subject matter require more features than are expressly recited in each claim. On the contrary, as reflected in the appended claims, the invention comprises less than all the features of any individual disclosed embodiment. The appended claims are therefore hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.

[0094] Those skilled in the art will also appreciate that the various illustrative logic blocks, modules, circuits, and algorithmic steps described in conjunction with the embodiments herein may be implemented as electronic hardware, computer software, or a combination thereof. In order to clearly illustrate the interchangeability between hardware and software, the various illustrative components, blocks, modules, circuits, and steps described above are generally described around their functions. Whether such functions are implemented as hardware or software depends on the specific application and the design constraints imposed on the entire system. A skilled person may implement the described functions in an adaptable manner for each specific application, but such implementation decisions should not be interpreted as departing from the scope of protection of this disclosure.

[0095] The steps of the methods or algorithms described in conjunction with the embodiments herein may be directly embodied as hardware, software modules executed by a processor, or a combination thereof. The software module may be located in a RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, register, hard disk, removable disk, CD-ROM, or any other form of storage medium well known in the art. An exemplary storage medium is connected to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium may also be an integral part of the processor. The processor and storage medium may be located in an ASIC. The ASIC may be located in a user terminal. Of course, the processor and storage medium may also be present in a user terminal as discrete components.

[0096] For software implementation, the techniques described in this application can be implemented using modules (e.g., procedures, functions, etc.) that perform the functions described in this application. These software codes can be stored in a memory unit and executed by a processor. The memory unit can be implemented within the processor or external to the processor. In the latter case, it is communicatively coupled to the processor via various means, which are well known in the art.

[0097] The foregoing description includes examples of one or more embodiments. Of course, it is not possible to describe all possible combinations of components or methods for the purposes of describing the above embodiments, but one of ordinary skill in the art will recognize that the various embodiments may be further combined and arranged. Therefore, the embodiments described herein are intended to encompass all such changes, modifications and variations that fall within the scope of the appended claims. Furthermore, to the extent the term "comprising" is used in the specification or claims, the term is intended to be encompassed in a manner similar to the term "including," as explained in terms of "including," used as a transitional word in the claims. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or."

Claims

1. A method for warehouse replenishment and storage space collaborative planning, characterized in that: include: S100. Construct a warehouse replenishment and storage coordination model, wherein the goal of the warehouse replenishment and storage coordination model is to minimize the total energy consumption of warehouse transportation equipment and minimize the warehouse channel load; the decision variable in the warehouse replenishment and storage coordination model is SKU Assigned to channel On the shelf Sub-storage , SKU Assigned to the front channel on Variables , SKU Assigned to the front channel on Variables SKU In the front channel Number of picks on , SKU In the storage area channel Number of picks on ; S200. Solve the warehouse replenishment and storage coordination model based on an improved non-dominated sorting elite genetic algorithm, and obtain the optimal population solution and the corresponding minimum energy consumption value and channel usage difference coefficient based on the knee point criterion; In S200, the warehouse replenishment and storage location coordination model is solved based on an improved non-dominated sorting elite genetic algorithm to obtain the optimal population solution and the corresponding minimum energy consumption value and channel usage difference coefficient. The specific method includes: S201. Set parameters and initialize the population; S202. Generate a selected population based on the initialization population; S203. Generate a crossover population based on a crossover method; S204. Correcting the crossover population using a correction method for infeasible solutions to obtain a corrected population. In S204, correcting the crossover population using a correction method for infeasible solutions to obtain a corrected population includes sequentially verifying the number of sub-storage slots occupied by each SKU in the chromosome, eliminating redundant SKUs, and replacing SKUs with missing sub-storage slots until the number of slots occupied by all SKUs meets the allocated number of sub-storage slots, at which point the model has a feasible solution. S205. Mutate the modified population using a mutation method to obtain a mutated population; S206. Merge the initial population and the mutated population to form a merged population, perform non-dominated sorting on the merged population, and obtain the Pareto rank of each solution in the merged population; S207. Based on the Pareto rank of each solution in the merged population, generate a new offspring, update the number of iterations, and determine whether the current number of iterations has reached the maximum number of iterations. If so, proceed to S208; if not, return to S202. S208. The current number of iterations reaches the maximum number of iterations, and the optimal population solution and the corresponding minimum energy consumption value and channel usage difference coefficient are obtained.

2. The method for warehouse replenishment and storage space collaborative planning according to claim 1, characterized in that: In S100, the minimum total energy consumption function of the warehouse transportation equipment is: ； in, represents a channel set, ; Indicates the channel index of the preamble area. Indicates the storage area channel index; Represents the sub-storage set of each channel in the preamble area, ; Represents the sub-storage bit set of each channel in the storage area, ; Represents a SKU set, ; Indicates AGVs handling SKU From the front area Storage space The energy consumption required to reach the picking station, Indicates SKU The picking frequency of each sub-storage location in the front area, Indicates SKU Assigned to the front channel on ; Indicates the robot handling SKU From the storage area Storage space Energy consumption required to reach the picking platform in the front area; Indicates SKU The picking frequency of each sub-storage location in the storage area, Indicates SKU Assigned to the storage channel on ; Indicates the robot handling SKU From the storage area Storage space To the front area Storage space required energy expenditure; Indicates SKU The average replenishment frequency of each sub-storage location allocated from the picking platform to the front area, Indicates SKU The average replenishment frequency from each sub-location allocated to the storage area to the picking station.

3. The method for warehouse replenishment and storage space collaborative planning according to claim 2, characterized in that: In S100, the warehouse channel load minimum function is: ； in, SKU In the front channel The number of selections on , is the average number of picking times in all channels of the front area, For SKU in store aisle The number of selections on , is the average number of picks across all aisles in the storage area.

4. The method for warehouse replenishment and storage space collaborative planning according to claim 3, characterized in that: In S100, the constraints of the minimum total energy consumption function of the warehouse transportation equipment and the minimum warehouse channel load function include at least: one sub-storage location can only store one SKU, the number of SKU types stored on a single shelf cannot exceed the total sub-storage locations of a single shelf, and the number of sub-storage locations occupied by each SKU cannot exceed the total allocated storage locations.

5. The method for warehouse replenishment and storage space collaborative planning according to claim 1, characterized in that: In S201, the parameters are set and the population is initialized. The specific method includes: setting the parameters, which include at least the total number of storage spaces, the number of empty storage spaces and the number of non-empty storage spaces in the front area and the storage area, and the number of sub-storage spaces allocated to each SKU; determining the initial solution population size based on the parameters, randomly selecting a SKU and placing it in the sub-storage spaces in the front area and the storage area until the number of sub-storage spaces allocated to the SKU is allocated, and then allocating the next SKU storage space, and repeating the above steps until all SKUs have completed storage space allocation.

6. The method for warehouse replenishment and storage space collaborative planning according to claim 1, characterized in that: In S202, a selection population is generated based on the initialization population. The specific method includes: performing non-dominated sorting on the initialization population to obtain a Pareto front set; judging the quality of the solution according to the quality of the Pareto front set, and selecting elite individuals using a binary tournament technique until the elite individuals reach a preset solution population size. At this time, the population composed of elite individuals is the selection population.

7. The method for warehouse replenishment and storage space collaborative planning according to claim 1, characterized in that: In S203, a crossover population is generated based on the crossover method, which includes a crossover method based on an optimal target and a two-point crossover method; wherein the crossover method based on an optimal target specifically includes: randomly selecting the optimal chromosomes on two target dimensions based on the selected population and , respectively select the part between the preamble area and the storage area and a parent chromosome Cross the corresponding parts to produce new offspring The two-point crossover method specifically includes: randomly selecting genes between two parent chromosomes for exchange, and obtaining two new daughter chromosomes , ; Until all traversals complete all selected population solutions, a crossover population is generated.

8. The method for warehouse replenishment and storage space collaborative planning according to claim 1, characterized in that: In S205, a mutation method is used to mutate the corrected population to obtain a mutated population. The specific method includes: selecting a parent chromosome in the crossover population according to a preset mutation probability to perform a mutation operation, and randomly selecting genes in the preamble area and the storage area to exchange and complete the mutation operation, until all crossover population solutions are traversed and completed, that is, a mutated population is generated.

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