Logistics distribution center site selection method based on improved dung beetle optimization algorithm

Abstract

The invention discloses a logistics distribution center site selection method based on an improved dung beetle optimization algorithm. The method comprises the steps of obtaining initial information of a logistics distribution center and demand points; determining a target function based on the obtained initial information, and constructing a logistics distribution center site selection scheme; carrying out coding processing on the logistics distribution center site selection scheme; and solving the objective function by using an improved dung beetle optimization algorithm, including initializing a population by using chaotic mapping and reverse learning, introducing an improved sine algorithm and an adaptive weight coefficient in rolling and stealing behaviors, and obtaining an objective function value and a logistics distribution center site selection scheme output after algorithm iteration is completed. According to the method, the problems that the convergence speed is low and local optimum is likely to happen when a swarm intelligence optimization algorithm is used for site selection planning can be well solved, and meanwhile multi-target optimization is conducted on multiple factors such as transportation cost and construction cost.

Description

Technical Field

[0001] The present invention relates to the field of logistics distribution technology, and in particular to a logistics distribution center site selection method based on an improved dung beetle optimization algorithm. Background Art Major logistics companies and manufacturing industries are building their own logistics distribution centers in cities across China to reduce transportation, warehousing, and information processing costs, shorten delivery times, improve efficiency, and enhance service quality. However, each city's natural environment, transportation conditions, land resources, administrative conditions, and customer and supplier distribution vary. Therefore, the optimal location of a logistics distribution center is crucial for building a successful logistics system. It determines the overall logistics network model, structure, and service level, and, in turn, plays a crucial role in ensuring the effective functioning of the entire logistics system. Currently, approaches to site selection generally fall into two categories: qualitative and quantitative analysis. Qualitative analysis methods, such as the Analytic Hierarchy Process (AHP) and the Fuzzy Comprehensive Evaluation Method (Fuzzy Comprehensive Evaluation Method), are highly subjective and lack objective accuracy. Quantitative analysis methods, including analytical methods, optimal planning methods, intelligent heuristic algorithms, and simulation algorithms, are also considered. For example, patent publication number CN202110799584 discloses a logistics node location planning method based on a clustering algorithm. This method employs a capacity-constrained BIRCH algorithm to cluster demand points layer by layer, deriving the distribution ranges of each intermediate logistics distribution node. The coordinates of local logistics distribution nodes are then calculated using the centroid method, which serves as the optimal location for the nodes. However, this centroid method only considers the transportation distance between adjacent nodes when calculating the coordinates of local logistics distribution nodes, ignoring other factors such as transportation cost, transportation time, and transportation efficiency. Tong Yanfen and Cheng Xianbao published a paper titled "Location of Logistics Distribution Center Based on Improved Bald Eagle Algorithm" in the journal Sustainability. The paper proposes an improved Bald Eagle search algorithm for logistics distribution center location selection, which effectively improves logistics distribution efficiency when applied to logistics distribution center location selection. However, this algorithm is a single-objective optimization algorithm with weak global search capabilities and is prone to falling into local optima, resulting in significant errors in the results. Summary of the Invention

[0002] The present invention provides a logistics distribution center site selection method based on the improved dung beetle optimization algorithm. On the basis of the dung beetle optimization algorithm, a variety of improvement strategies are integrated to better solve the problems of slow convergence and easy falling into local optimality when using swarm intelligence optimization algorithm for site selection planning. At the same time, multi-objective optimization is performed on many factors such as transportation cost and construction cost.

[0003] The present invention provides a logistics distribution center site selection method based on an improved dung beetle optimization algorithm, which includes the following steps: Step (1), obtaining initial information of logistics distribution centers and demand points; Step (2), determine the objective function based on the initial information obtained and construct a logistics distribution center location plan; Step (3), coding the site selection plan of the logistics distribution center; Step (4): Use the improved dung beetle optimization algorithm to solve the objective function and obtain the objective function value and logistics distribution center location plan output after the algorithm iteration is completed.

[0004] Preferably, the initial information obtained about the logistics distribution centers and demand points includes: the number, location, and cargo demand of the demand points, and the number, location, and construction cost of the logistics distribution centers.

[0005] Preferably, the objective function of the logistics distribution center location selection plan in step (2) is: ; in, is the number of alternative distribution centers, is the number of demand points, is the construction cost required to establish a logistics distribution center at location i, , represents the distribution center selection factor, if ,express Select as distribution center, represents the demand for goods at demand point j, represents the distance between demand point j and distribution center i, represents the unit transportation cost between demand point j and distribution center i, , represents the distribution condition selection factor, if , indicating that the goods of demand point j are provided by distribution center i.

[0006] Firstly, the constraints of the objective function are as follows: ; Indicates that a total of p logistics distribution centers are established; ; Indicates that the total demand of each demand point should be less than or equal to the total amount of goods in the corresponding logistics distribution center ; ; Indicates that each distribution center delivers to one or more demand points; ; Indicates the distribution relationship between the demand point and the distribution center, that is, one demand point can only be delivered by one distribution center; ; It means that each demand point must be within the reach of the corresponding distribution center, and t is the maximum distance that can be delivered.

[0007] Preferably, the coding process for the logistics distribution center location plan is as follows: Select p final addresses from M alternative distribution center site selection plans, and randomly select p numbers from 1...M to form the code: ,in And there is no repetition; X represents the location selection plan of the logistics distribution center, and a group of codes represents a plan.

[0008] Preferably, the improved dung beetle optimization algorithm in step (4) comprises the following specific steps: In step (4a), whether the initial population distribution has good uniformity has a direct impact on the search accuracy of the swarm intelligence optimization algorithm. The basic dung beetle optimization algorithm uses the random function Rand() to initialize the population, which easily leads to a lack of population diversity and cannot ensure that the initial individuals are evenly distributed throughout the entire search domain, thereby reducing the search accuracy. To this end, the present invention uses an improved Logistic chaotic map instead of a random strategy to initialize the population, which can improve the search breadth of the optimization algorithm and increase the diversity of the initial solution of the population. The expression is: ; in, is the floor function, The value is ( ); It is a control parameter that can control the value range of the function. Can take any non-zero real number; is a control parameter and can be any real number.

[0009] In step (4b), after the chaotic mapping, the reverse learning strategy is used to generate the opposite population. Experiments show that the opposite candidate solution has a higher probability of reaching the global optimum than the random solution. Therefore, the addition of directional learning allows the initial population to approach the optimal solution from multiple directions, increasing the possibility of the algorithm finding the optimal solution. The opposite vector of reverse learning in the multi-dimensional case is defined as follows: ; in, and yes The lower and upper bounds of are , where dim is the dimension of the dataset. After obtaining the opposite population, the fitness function value is calculated for each solution in the chaotic population and the opposite population, and the solutions are arranged in order. Individuals with lower fitness values ​​are selected to enter the final initial population.

[0010] Step (4c) updates the position of the dung beetle by simulating the five behaviors of the dung beetle using five different update rules, and improves the following two behaviors.

[0011] (1) Rolling behavior: The improved sine algorithm is used to replace the formula of the mathematical model of the barrier-free rolling behavior of the dung beetle. The algorithm uses the sine function in mathematics to perform iterative optimization. According to the relationship between the sine function and the unit circle, all values ​​on the sine function can be traversed. At the same time, two specific coefficients are introduced in the position update process to narrow the solution space so as to scan the area that may only produce good results. This greatly improves the search speed and achieves a good balance between search and development to improve the convergence accuracy and speed up the convergence speed. The expression is: ; in is the position information of the i-th dung beetle at the t-th iteration, is the current local optimal position; , determines the distance the dung beetle moves in the next iteration; , determines the direction of movement of the dung beetle in the next iteration; the coefficient and Used to reduce the search space and guide the current individual to reach the global optimum, , ,in , , = .

[0012] (2) Stealing behavior: Based on the original position update, an adaptive weight coefficient is introduced to improve the ability to escape from the local optimum, expand the search space, and maintain a balance between global exploration and local utilization. The expression is: ; in, , , S represents a constant, g is a normal distribution with a size of A random vector of .

[0013] Step (4d) determines whether each dung beetle has exceeded the boundary. If not, the dung beetle position and fitness value are updated. Repeat the above position update steps until the number of iterative updates is met and the optimal solution is output.

[0014] Compared with the prior art, the technical solution of the present invention has the following beneficial effects: 1. The logistics distribution center site selection method based on the improved dung beetle optimization algorithm provided by the present invention can solve the problems existing in the current logistics distribution center, including high logistics costs, long distribution time, low distribution efficiency, etc., reduce the costs of logistics companies in transportation, warehousing, information processing, etc., shorten the distribution time, and improve the distribution efficiency.

[0015] 2. In the initialization stage, chaotic mapping combined with reverse learning is used to initialize the dung beetle population. Compared with the random strategy, this method can generate a highly diverse population and has a wider search range.

[0016] 3. A modified sinusoidal algorithm is used during the dung beetle's position update process to enhance the dung beetle optimization algorithm's global and local search capabilities, maintaining a good balance between the two. Furthermore, an adaptive weight coefficient is incorporated to improve the ability to escape local optima and expand the search space. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 The figure is a schematic diagram of a specific process of the logistics distribution center site selection method based on the improved dung beetle optimization algorithm of the present invention.

[0017] Figure 2 : is a location map of the demand points and alternative logistics distribution centers in the embodiment.

[0018] Figure 3 Convergence curve diagram for testing the improved dung beetle optimization algorithm.

[0019] Figure 4 Layout diagram of the logistics distribution center in the embodiment. DETAILED DESCRIPTION The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0020] Refer to the attached Figure 1 As shown, the present invention relates to a logistics distribution center site selection method based on an improved dung beetle optimization algorithm, comprising the following steps: Step (1) is to obtain the initial information of logistics distribution centers and demand points, including: the number, location, and cargo demand of demand points, and the number, location, and construction cost of logistics distribution centers.

[0021] To analyze the performance of the dung beetle optimization algorithm in solving the logistics distribution center location problem, a case study was set up for analysis. There are 27 demand points, of which 6 demand points can be used as alternative logistics distribution centers. Finally, 4 logistics distribution centers are selected to provide distribution services to the other demand points.

[0022] The demand point numbers, coordinates, and demand quantities involved in the calculation example are shown in the following table: Table 1

[0023] Step (2): Determine the objective function based on the initial information obtained and construct a logistics distribution center location selection plan. The objective function of the logistics distribution center location selection plan is: (1) in, is the number of alternative distribution centers, is the number of demand points, is the construction cost required to establish a logistics distribution center at location i, , represents the distribution center selection factor, if ,express Select as distribution center, represents the demand for goods at demand point j, represents the distance between demand point j and distribution center i, represents the unit transportation cost between demand point j and distribution center i, , represents the distribution condition selection factor, if , indicating that the goods of demand point j are provided by distribution center i.

[0024] The constraints of the objective function are as follows: (2) It indicates that a total of p logistics distribution centers are established.

[0025] (3) Indicates that the total demand of each demand point should be less than or equal to the total amount of goods in the corresponding logistics distribution center .

[0026] (4) Indicates that each distribution center delivers to one or more demand points.

[0027] (5) It indicates the distribution relationship between the demand point and the distribution center, that is, one demand point can only be delivered by one distribution center. (6) It indicates that each demand point must be within the reach of the corresponding distribution center, and t is the maximum distance that can be delivered.

[0028] In order to simplify the model and focus on the specific content of the algorithm, the constraints of the objective function are satisfied. The parameters not set in the above steps are as follows: Assume that the unit transportation cost (yuan / cubic meter / km), the number of demand points N=27, the number of alternative logistics distribution centers M=6, the number of logistics distribution centers p=4, and the maximum number of iterations T=100.

[0029] The site selection and construction costs of each alternative logistics distribution center are shown in the following table: Table 2

[0030] According to the coordinates in Table 1 and Table 2, use Matlab to draw a geographical location map, as shown in the attached figure. Figure 2 shown.

[0031] Step (3): Encode the site selection plan for the logistics distribution center: In the process of implementing the algorithm, for the final logistics distribution center site selection plan, the present invention selects p final addresses from M alternative distribution center site selection plans, and randomly selects p numbers from 1...M to form a code as follows: ,in X represents the location selection plan for the logistics distribution center. A set of codes represents a plan. In the iterative process of the algorithm of the present invention, such an individual is a set of codes.

[0032] Step (4) uses the improved dung beetle optimization algorithm to solve the objective function. The specific steps are as follows: In step (4a), whether the initial population distribution has good uniformity has a direct impact on the search accuracy of the swarm intelligence optimization algorithm. The basic dung beetle optimization algorithm uses the random function Rand() to initialize the population, which easily leads to a lack of population diversity and cannot ensure that the initial individuals are evenly distributed throughout the entire search domain. To this end, the present invention uses an improved Logistic chaotic map instead of a random strategy to initialize the population. The expression is: (7) in, is the floor function, The value is ( ); It is a control parameter that can control the value range of the function. You can take any non-zero real number, here we take 1; is the control parameter, which can be any real number, and is 1 here.

[0033] In step (4b), after the chaotic mapping, the reverse learning strategy is used to generate the opposite population. Experiments show that the opposite candidate solution has a higher probability of reaching the global optimum than the random solution. Therefore, the addition of directional learning allows the initial population to approach the optimal solution from multiple directions, increasing the possibility of the algorithm finding the optimal solution. The opposite vector of reverse learning in the multi-dimensional case is defined as follows: (8) in, and yes The lower and upper bounds of are , where dim is the dimension of the dataset. After obtaining the opposite population, the fitness function value (i.e., the target cost function value) is calculated for each solution in the chaotic population and the opposite population, and the solutions are arranged in order. Individuals with lower fitness values ​​are selected to enter the final initial population.

[0034] In step (4c), the positions of dung beetles are updated using five different update rules by simulating their five behaviors. The initial population is set to 90, with the proportions of rolling dung beetles, breeding dung beetles, foraging dung beetles, and stealing dung beetles being 6:6:7:11. Each role of dung beetles corresponds to a different position update rule.

[0035] (1) Rolling behavior: The improved sine algorithm is used to replace the formula of the mathematical model of the barrier-free rolling behavior of the dung beetle. The algorithm uses the sine function in mathematics to perform iterative optimization. According to the relationship between the sine function and the unit circle, all values ​​on the sine function can be traversed. At the same time, two specific coefficients are introduced in the position update process to narrow the solution space so as to scan the area that may only produce good results. This greatly improves the search speed and achieves a good balance between search and development to improve the convergence accuracy and speed up the convergence speed. The expression is: (9) in is the position information of the i-th dung beetle at the t-th iteration, is the current local optimal position; , determines the distance the dung beetle moves in the next iteration; , determines the direction of movement of the dung beetle in the next iteration; the coefficient and Used to reduce the search space and guide the current individual to reach the global optimum, , ,in , , = .

[0036] (2) Dancing behavior: When a dung beetle encounters an obstacle, it reorients itself through dancing. The position update formula is defined using the tangent function: (10) in, ,if 、 or , then the dung beetle position is not updated. The rolling ball dung beetle updates its position based on method a and method b. It uses random numbers to determine which behavior method to use for position update and generates random numbers. , ; (3) Breeding behavior: The boundary selection strategy is used to simulate the egg-laying area of ​​female dung beetles, which is expressed as: (11) (12) and They represent the lower and upper limits of the spawning area respectively; , t is the current iteration number, T is the maximum iteration number; and denote the lower and upper bounds of the optimization problem, respectively.

[0037] As the spawning area changes, the breeding ball also updates dynamically. The expression is: (13) in, is the position information of the i-th breeding ball at the t-th iteration, and Indicates that two sizes are The position of the nest ball needs to be limited to the spawning area. If it exceeds, it is converted as follows:

[0038] (4) Foraging behavior: The optimal foraging area of ​​the dung beetle is expressed as: (14) (15) in and denote the lower and upper bounds of the optimal foraging area, is the global best position.

[0039] The position update expression of the dung beetle is: (16) represents a random number that follows a normal distribution, Indicates belonging A random vector of .

[0040] (5) Stealing behavior: Based on the original position update, an adaptive weight coefficient is introduced to improve the ability to escape from the local optimum, expand the search space, and maintain a balance between global exploration and local utilization. The expression is: (17) in, , , S represents a constant, g is a normal distribution with a size of A random vector of .

[0041] Step (4d) determines whether each dung beetle has exceeded the boundary. If not, the dung beetle position and fitness value are updated. Repeat the above position update steps until the number of iterative updates is met and the optimal solution is output.

[0042] The convergence curve of the test algorithm is shown in the attached Figure 3 As shown in the figure, the results show that the improved dung beetle optimization algorithm can not only converge quickly, but also has the ability to balance exploration and development, and has the ability to jump out of the local optimal solution. Solving the above case, the alternative logistics distribution centers numbered 13, 24, 5, and 27 are finally selected as the final addresses. At this time, the investment and construction cost is 1404, the transportation cost from the distribution center to the demand point is 4650, and the minimum value of the objective function is 6054. The distribution center layout diagram is shown in the attached figure. Figure 4 shown.

[0043] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A logistics distribution center site selection method based on an improved dung beetle optimization algorithm, characterized in that: The steps include: Step (1), obtaining initial information of logistics distribution centers and demand points; Step (2), determine the objective function based on the initial information obtained and construct a logistics distribution center location plan; Step (3), coding the site selection plan of the logistics distribution center; Step (4): Use the improved dung beetle optimization algorithm to solve the objective function and obtain the objective function value and logistics distribution center location plan output after the algorithm iteration is completed.

2. The method for selecting a logistics distribution center site based on the improved dung beetle optimization algorithm according to claim 1, characterized in that: The initial information obtained about logistics distribution centers and demand points includes: the number, location, and cargo demand of demand points, and the number, location, and construction cost of logistics distribution centers.

3. The method for selecting a logistics distribution center site based on the improved dung beetle optimization algorithm according to claim 1, wherein: The objective function of the logistics distribution center location selection plan in step (2) is: ； in, is the number of alternative distribution centers, is the number of demand points, is the construction cost required to establish a logistics distribution center at location i, , represents the distribution center selection factor, if ,express Select as distribution center, represents the demand for goods at demand point j, represents the distance between demand point j and distribution center i, represents the unit transportation cost between demand point j and distribution center i, , represents the distribution condition selection factor, if , indicating that the goods of demand point j are provided by distribution center i.

4. The method for selecting a logistics distribution center site based on the improved dung beetle optimization algorithm according to claim 3, wherein: The constraints of the objective function are as follows: ； Indicates that a total of p logistics distribution centers are established; ； Indicates that the total demand of each demand point should be less than or equal to the total amount of goods in the corresponding logistics distribution center ; ； Indicates that each distribution center delivers to one or more demand points; ； Indicates the distribution relationship between the demand point and the distribution center, that is, one demand point can only be delivered by one distribution center; ； It means that each demand point must be within the reach of the corresponding distribution center, and t is the maximum distance that can be delivered.

5. The method for selecting a logistics distribution center site based on an improved dung beetle optimization algorithm according to claim 1, wherein: The coding method for the logistics distribution center site selection plan is as follows: Select p final addresses from M alternative distribution center site selection plans, and randomly select p numbers from 1...M to form the code: ,in And there is no repetition; X represents the location selection plan of the logistics distribution center, and a group of codes represents a plan.

6. The method for selecting a logistics distribution center site based on an improved dung beetle optimization algorithm according to claim 1, wherein: The specific steps of the improved dung beetle optimization algorithm in step (4) are: In step (4a), the improved Logistic chaotic map is used instead of the random strategy to initialize the population, and the expression is: ; in, is the floor function, The value is ( ); It is a control parameter that can control the value range of the function. Can take any non-zero real number; is a control parameter, which can be any real number; In step (4b), after the chaotic mapping, the reverse learning strategy is used to generate the opposite population. The opposite vector of reverse learning in the multidimensional case is defined as follows: ; in, and yes The lower and upper bounds of dim are the dimensions of the data set. After obtaining the opposite population, the fitness function value of each solution in the chaotic population and the opposite population is calculated and arranged in order. The individuals with lower fitness values ​​are selected to enter the final initial population. In step (4c), the positions of the dung beetles are updated using five different update rules by simulating their rolling, dancing, breeding, stealing, and foraging behaviors. In step (4d), it is determined whether each dung beetle has exceeded the boundary. If not, the position and fitness value of the dung beetle are updated. The above position update steps are repeated until the number of iterative updates is met and the optimal solution is output.

7. The method for selecting a logistics distribution center site based on the improved dung beetle optimization algorithm according to claim 6, wherein: In step (4c), the position of the dung beetle is updated using five different update rules by simulating the dung beetle's rolling behavior, dancing behavior, breeding behavior, stealing behavior, and foraging behavior. The rolling behavior and stealing behavior include: (1) Rolling behavior: The improved sine algorithm is used to replace the formula of the mathematical model of the barrier-free rolling behavior of the dung beetle. The expression is: ; in, is the position information of the i-th dung beetle at the t-th iteration, is the current local optimal position; , determines the distance the dung beetle moves in the next iteration; , determines the direction of movement of the dung beetle in the next iteration; the coefficient and Used to reduce the search space and guide the current individual to reach the global optimum, , ,in , , = ; (2) Stealing behavior: Based on the original position update, an adaptive weight coefficient is introduced, which is expressed as: ; in, , , S represents a constant, g is a normal distribution with a size of A random vector of .

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