Cold-chain logistics distribution center site selection method based on population expansion

Abstract

The invention discloses a cold-chain logistics distribution center site selection method based on population expansion, and the method comprises the steps: building a site selection model which aims at minimizing the total logistics cost based on the transportation conditions of goods, and taking the traffic conditions around a distribution point and a demand point into consideration; therefore, the site selection of the cold-chain logistics distribution center is more real and reasonable, the optimal address can be selected for the distribution center, and the cost of the whole logistics process is reduced.

Description

Technical Field

[0001] This invention relates to the field of logistics distribution center site selection technology, and specifically to a cold chain logistics distribution center site selection method based on population expansion. Background Technology

[0002] With economic growth and increased purchasing power, the demand for cold chain foods such as vegetables, fruits, and dairy products is constantly increasing, and people's quality requirements for cold chain foods are also rising. Due to the perishable nature of cold chain foods, cold chain logistics differs from the transportation of general goods. To ensure minimal loss during transportation, the entire logistics system must be equipped with infrastructure such as cold storage facilities and refrigerated trucks to maintain consistently low temperatures. However, my country's cold chain industry suffers from uneven market coverage, with urban and rural areas lagging behind large and medium-sized cities in cold chain logistics development. East China has a larger cold storage capacity, while Northwest China has a smaller one. This uneven distribution of cold chain resources leads to problems such as low transportation efficiency, easy food spoilage, and even a lack of cold chain services in some areas. Optimizing the location of cold chain logistics can make transportation more efficient, ensure product quality, reduce damage rates, and make logistics more timely. Therefore, researching and analyzing the location of low-carbon cold chain logistics distribution centers is of great significance for reducing carbon emissions and promoting the healthy development of cold chain logistics.

[0003] Optimizing the location of cold chain logistics can make transportation more efficient, ensure product quality, reduce damage rates, and make logistics more timely. As the most important infrastructure in cold chain logistics, cold chain distribution centers connect supply and demand points, affecting the distribution efficiency of the entire logistics system. This patent aims to study the location problem of distribution centers in cold chain logistics, comprehensively considering factors such as refrigeration, damage, carbon emissions, and traffic conditions. It establishes a low-carbon cold chain logistics distribution center location model with the objective of minimizing total cost and proposes a population expansion optimization algorithm for optimization. This is beneficial for improving distribution efficiency and sales volume of fresh products, thereby reducing costs, increasing enterprise profitability, improving the operational efficiency and economic benefits of the entire logistics system, and enhancing service quality and customer satisfaction. Summary of the Invention

[0004] This invention provides a cold chain logistics distribution center site selection method based on population expansion. It comprehensively considers factors such as refrigeration, cargo damage, carbon emissions, and traffic conditions, establishes a cold chain low-carbon logistics distribution center site selection model with the goal of minimizing total cost, and proposes a population expansion optimization algorithm for optimization solution.

[0005] The technical solution adopted by this invention to solve the technical problem is as follows:

[0006] This invention relates to a method for selecting locations for cold chain logistics distribution centers based on population expansion, which includes the following steps:

[0007] (1) Obtain initial information on raw material supply points, demand points, and distribution centers;

[0008] (2) Obtain historical road condition information around each supply point and demand point in the traffic management system. Based on this, use data-driven methods to predict the traffic conditions around each supply point and demand point over a period of time. Design the corresponding traffic congestion function based on the relationship between its distance and travel time.

[0009] (3) Determine the objective function based on the acquired initial information, and construct the site selection scheme and mathematical model of the warehousing and logistics distribution center;

[0010] (4) Calculate the corresponding transportation time using the traffic congestion function value and the Euclidean distance between the undetermined distribution center and the supply point or demand point;

[0011] (5) A metaheuristic algorithm based on population expansion is proposed. The algorithm parameters are initialized, and the relevant information of supply points and demand points are substituted into the algorithm for solution.

[0012] (6) Each iteration adjusts the population partitioning of the algorithm, and a new leader is selected based on the new population after each adjustment.

[0013] (7) Population members and non-population members perform position iteration updates based on different movement strategies to complete the optimization of the algorithm.

[0014] (8) Provide guidance on site selection based on the location selection results of the warehousing and logistics distribution center after optimization.

[0015] Furthermore, the method for obtaining initial information in step (1) is as follows: construct a supply and demand relationship matrix based on the storage capacity of raw material supply points and the sales volume of demand points; determine the location range and storage area of ​​the distribution center based on the geographical location information around the demand points; determine the total number of cold chain logistics distribution centers to be established based on the quantitative relationship between raw material supply points and demand points; and establish a location information matrix based on the location information of each raw material supply point and demand point. Based on the initial information, calculate the following data: transportation costs from raw material supply points to warehousing and logistics distribution centers, transportation costs from warehousing and logistics distribution centers to manufacturers, and construction costs of warehousing and logistics distribution centers.

[0016] Furthermore, the method for predicting traffic conditions around each supply point and demand point over a relatively long period of time in step (2) is as follows: First, three radius ranges are determined according to the size of the overall solution space: 0 to r1, r1 to r2, and greater than r2. Then, a traffic congestion detection system is established, and a congestion judgment function is designed. Based on the historical traffic conditions around each demand point and supply point, the traffic congestion function values ​​z1, z2, and z3 corresponding to different radius ranges of the demand point and supply point are obtained. The worse the road conditions, the larger the traffic congestion function value. This traffic congestion function value will affect the cold chain delivery time and thus the total cost. The calculation method is as follows: First, the historical road condition information around each supply point and demand point is obtained to obtain the regional travel time data corresponding to each time period. A proxy model is established using this data. The proxy model is continuously optimized through Bayesian optimization to make it approximate the real model. Finally, the regional travel time relationship over a period of time is output through the optimized model. The travel time of each region is substituted into the traffic congestion function to obtain its corresponding traffic congestion function value.

[0017] Furthermore, the objective function of the cold chain logistics distribution center site selection scheme in step (3) is:

[0018] minC=C1+C2+C3+C4+C5+C6 (1)

[0019] Equation 1 is the objective function, aiming to minimize the total cost, including fixed costs, transportation costs, cargo damage costs, refrigeration costs, penalty costs, and carbon emission costs. Since most previous researchers did not consider the impact of traffic conditions on costs, we introduce a traffic congestion function to assess the traffic conditions around each demand and supply point, thereby making the vehicle's transportation time t closer to reality and improving the accuracy of cost calculations. The expressions for C1 to C6 are as follows:

[0020] (1) Fixed costs

[0021] Fixed costs refer to costs unrelated to the transportation of goods, including the construction costs of potential distribution centers, vehicle depreciation costs, and operating costs such as employee wages. Assume that in the logistics network, there are I predetermined supply points, J potential distribution centers, and M demand points, where c... j (j=1,2,……,J) represents the fixed cost of the j-th candidate distribution center, then the total fixed cost C1 is:

[0022]

[0023] In the formula,

[0024] (2) Transportation costs

[0025] Transportation costs refer to expenses related to the volume and distance of transportation. Let p2 be the cost required to transport one unit of goods one unit distance, and q be the cost. ij Let q be the volume of transportation from supply point i to the selected distribution center j. jm For the transportation volume from the selected distribution center j to the demand point m, d ij Let d be the distance from supply point i to the candidate distribution center j. jm Let j be the distance from the candidate distribution center to the demand point m. Then the transportation cost C2 is:

[0026]

[0027] In the formula,

[0028] (3) Cost of damaged goods

[0029] Damage costs refer to the losses incurred by cold chain goods during transportation and unloading due to the passage of time and temperature changes. Let p3 be the unit price of the goods, β1 be the spoilage rate of the goods during transportation, β2 be the spoilage rate of the goods during unloading, and t be the unit price of the goods. ij t represents the transportation time of the vehicle from supply point i to the selected distribution center j. jm T is the transportation time for a vehicle from the selected distribution center j to the demand point m. m Let m be the time taken for the vehicle to unload at the demand point m. Then the cargo damage cost is:

[0030]

[0031] (4) Refrigeration cost

[0032] Refrigeration cost refers to the cost incurred by refrigerated trucks during transportation and unloading due to the consumption of refrigerant. Let p be the refrigeration cost incurred by a refrigerated truck per unit time during transportation. 41 During the unloading process, the refrigeration cost incurred by the refrigerated vehicle in unloading goods per unit time is p. 42 The refrigeration cost is:

[0033]

[0034] (5) Penalty Costs

[0035] Penalty costs refer to the costs incurred when a vehicle fails to deliver to a demand point within a specified timeframe. If the vehicle delivers before the earliest time required by the demand point, a waiting cost is incurred; if the vehicle delivers after the latest time required by the demand point, a lateness cost is incurred. Let t... m p is the time it takes for the vehicle to reach the demand point m. w p represents the waiting cost incurred by the vehicle per unit of time. lThe cost of a vehicle's lateness per unit of time, (ET) m LT m (EET) represents the expected time window for demand point m. m LLT m Let m be the acceptable time window for demand point m. Then the penalty cost at demand point m is:

[0036]

[0037] In the formula, inf is an infinitely large positive number;

[0038] The total cost of punishment is

[0039]

[0040] (6) Carbon emission costs

[0041] Carbon emission costs refer to the cost of carbon dioxide emissions resulting from vehicle energy consumption and refrigerant consumption during transportation. A vehicle's fuel consumption is related to factors such as distance traveled, load capacity, and speed; the higher the fuel consumption, the greater the carbon dioxide emissions. Let p... c Let E be the unit carbon tax price, e be the carbon dioxide emission coefficient, E1 be the fuel consumption per unit distance traveled by the refrigerated truck, and E2 be the energy consumption of the refrigeration equipment per unit time. Therefore, the total carbon emission cost of vehicle operation and refrigeration equipment is:

[0042]

[0043] In summary, the site selection model for cold chain low-carbon logistics distribution centers is as follows:

[0044] minC=C1+C2+C3+C4+C5+C6 (1)

[0045] Constraints:

[0046]

[0047]

[0048] Equation (1) is the objective function, aiming to minimize total cost, including fixed costs, transportation costs, damage costs, refrigeration costs, penalties, and carbon emission costs; Equation (8) indicates that each demand point can only be served by one distribution center; Equation (9) indicates that the total transportation volume from the supply point to the distribution center is equal to the total transportation volume from the distribution center to the demand point; Equation (10) indicates that there is no vehicle operation between cold chain distribution centers; Equation (11) indicates that the total amount of goods transported from the distribution center to the demand point is not less than the total demand of the demand point, q mLet V be the demand at demand point m; Equation (12) is a limit on the total number of distribution centers, i.e., a maximum of N distribution centers can be built, n = 1, 2, ..., N; Equation (13) indicates that the capacity of the selected distribution centers must be able to meet all the demands of the demand point, V n This represents the capacity of the nth distribution center.

[0049] Furthermore, to make the transportation time in step (4) closer to reality, a traffic congestion detection system needs to be established, and a congestion judgment function needs to be designed. By analyzing the traffic conditions around each demand point and supply point, the traffic congestion function values ​​corresponding to different radii of the demand and supply points can be obtained. Introducing the traffic congestion function value can make the vehicle transportation time t closer to reality, making cost calculation more accurate. The transportation time calculation process based on traffic conditions is as follows: If d is the distance from the starting point to the destination, and all transport vehicles travel at a constant speed, then the transportation time t in the mathematical model can be expressed as:

[0050]

[0051] Where r1 and r2 represent different radius ranges, and z1, z2, and z3 represent the traffic congestion function values ​​for each radius range.

[0052] Furthermore, the basic idea of ​​the population expansion-based optimization algorithm proposed in step (5) is as follows:

[0053] The algorithm establishes a population centered on the individual with the highest fitness. The population gradually expands with each iteration, and the number of members continuously increases. Simultaneously, the best individual is updated as the leader based on fitness in each iteration. Population members, guided by the leader, act around the leader (local exploitation), while non-population members engage in random activities (global search). In the early stages of iteration, the population size is small, with few members but a large number of followers, resulting in weak local exploitation but strong global search capabilities, which is beneficial for escaping local optima. In the later stages of iteration, the population size is large, with many members but fewer followers, and the algorithm gradually shifts from global search to local exploitation, which is beneficial for further finding the optimal value.

[0054] Furthermore, the population division method proposed in step (6) is as follows:

[0055]

[0056] P′ i =D Li

[0057] In the formula X * X(t) represents the position of the leader in the j-th dimension, X(t) represents the position of a population member in the j-th dimension, and D... Li Let P' be the Euclidean distance between the leader and group member i.i Store D in location Li The algorithm calculates the Euclidean distance between members and the leader, classifying individuals closer to the leader as population members.

[0058] Inspired by bio-logic heuristic computing algorithms, this patent proposes a population expansion method to balance the algorithm's global search capability and local utilization capability. The specific population expansion strategy is as follows:

[0059]

[0060] In the formula, S is the total number of individuals, M is the maximum number of iterations, t is the current number of iterations, the parameter g takes values ​​in the range of [0,1], the algorithm initializes the population with the number of individuals S*g, and then gradually expands it as the number of iterations increases, N is the current population size.

[0061] Furthermore, in step (7), population members and non-population members should update their positions based on different movement strategies to ensure population diversity and the balance between global search and local utilization. Therefore, this patent proposes a spiral approach strategy, according to which population members update their positions. The characteristic of this movement strategy is that as the number of iterations increases, the spiral trajectory gradually approaches the leader, enhancing the algorithm's local utilization capability and facilitating convergence to the optimal value. The specific movement strategy is as follows:

[0062] When probability p < 0.5

[0063] D L =|C*X * (t)-X(t)|

[0064] X(t+1)=X * (t)-A*D L (17)

[0065] When probability p>=0.5

[0066] D L2 =|C*X * (t)-X(t)|

[0067] X(t+1)=D L2 *e bl *cos(2πl)+X * (t) (18)

[0068] In the formula X *Let X(t) be the position of the leader in the j-th dimension at the t-th iteration, X(t) be the position of the population member in the j-th dimension at the t-th iteration, X(t+1) be the position of the population member in the j-th dimension at the (t+1)-th iteration, and C, A, b, l be relevant parameters. Let the function f(x,y) represent the value taken in the interval [x,y], where

[0069] A = 2*a*r1 - a

[0070] C = 2 * r²

[0071] b=1

[0072] l=(a2-1)*f(0,1)+1

[0073] The movement strategy for non-population members is to randomly initialize their positions:

[0074] X(t+1)=f(0,1)*(ub-lb)+lb; (19)

[0075] In the formula, X(t+1) is the position of the population member in the j-th dimension at the (t+1)-th iteration, the function f(x,y) represents the value taken in the interval [x,y], ub is the upper limit of the value given in the current dimension, and lb is the lower limit of the value given in the current dimension.

[0076] Furthermore, the specific method for selecting the location of the cold chain warehousing and logistics distribution center in step (8) is as follows:

[0077] First, obtain the initial information matrix, then establish a traffic congestion detection system, input the traffic conditions around each demand point and supply point, obtain the corresponding traffic congestion function value, substitute it into equation (14) to calculate the transportation time, and then substitute it into equation (1).

[0078] This model is set as the objective function, and the optimization algorithm is initialized using the information provided at the beginning, including the solution space range, the number of search agents, the initial population size, and the number of iterations. Then, the fitness of each individual is calculated, a leader is selected to form the initial population, and then non-population members and population members update their positions iteratively according to different movement strategies, and the population is updated according to the population expansion strategy.

[0079] The fitness of parent and offspring individuals is compared, and the individual with better fitness is selected as the new offspring. The fitness of the new population individuals is then compared, and the best individual is selected as the new leader for the next generation iteration.

[0080] Compared with the prior art, the technical solution of the present invention has the following advantages:

[0081] 1. The cold chain logistics distribution center site selection method based on population expansion of the present invention is based on the transportation conditions of goods and takes into account the traffic conditions around the distribution point and the demand point. It constructs a site selection model with the goal of minimizing the total logistics cost, which makes the site selection of cold chain logistics distribution centers more realistic and reasonable, helps to select the optimal address for the distribution center, and thus reduces the cost of the entire logistics process.

[0082] 2. The present invention relates to a population expansion-based cold chain logistics distribution center location method, which proposes a population expansion optimization algorithm. Compared with traditional optimization algorithms, the population expansion optimization algorithm has improved accuracy in high dimensions. For complex functions, the algorithm can effectively avoid getting trapped in local optima, while the convergence speed is similar to other optimization algorithms. Applying it to the cold chain logistics distribution center location problem can effectively avoid the shortcomings of slow convergence speed and low convergence accuracy, thereby optimizing the algorithm. Attached Figure Description

[0083] Figure 1 A schematic diagram illustrating the overall process of a population expansion-based cold chain logistics distribution center site selection method.

[0084] Figure 2 A schematic diagram of the algorithm flow for a cold chain logistics distribution center site selection method based on population expansion.

[0085] Figure 3 The test results show the population expansion optimization algorithm proposed in this invention.

[0086] Figure 4 The diagram shows the iterative processes of each algorithm used to test examples of the present invention.

[0087] Figure 5 This invention provides a cold chain logistics distribution center location scheme based on a population expansion optimization algorithm. Detailed Implementation

[0088] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0089] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0090] See attached document Figure 1 As shown, this invention relates to a method for selecting a cold chain logistics distribution center based on population expansion, which includes the following steps:

[0091] (1) Obtain initial information on raw material supply points, demand points and distribution centers.

[0092] (2) Obtain historical road condition information around each supply point and demand point in the traffic management system, use data-driven methods to predict the traffic conditions around them for a long period of time in the future based on historical data, and design corresponding traffic congestion functions based on the relationship between their distance and travel time.

[0093] (3) Determine the objective function based on the acquired initial information, and construct the site selection scheme and mathematical model of the warehousing and logistics distribution center.

[0094] (4) Calculate the corresponding transportation time using the traffic congestion function value and the Euclidean distance between the undetermined distribution center and the supply or demand point.

[0095] (5) A metaheuristic algorithm based on population expansion is proposed. The algorithm parameters are initialized, and the relevant information of supply points and demand points are substituted into the algorithm for solution.

[0096] (6) Each iteration adjusts the population partitioning of the algorithm, and a new leader is selected based on the new population after each adjustment.

[0097] (7) Population members and non-population members perform position iteration updates based on different movement strategies to complete the optimization of the algorithm.

[0098] (8) Provide guidance on site selection based on the location selection results of the warehousing and logistics distribution center after optimization.

[0099] First, the mathematical modeling for the location selection of this cold chain logistics distribution center is based on the following assumptions:

[0100] a. The demand volume, geographical location, and time window for each demand point must be known, and the demanded goods must be delivered in one go;

[0101] b. The fixed costs of each potential distribution center are known;

[0102] c. The distances from the supply point to the candidate distribution center and from the candidate distribution center to the demand point are known;

[0103] d. The variety of cold chain products is limited;

[0104] e. The unit transportation cost of the goods is known, and the transportation costs between the supply point and the candidate distribution center, and between the candidate distribution center and the demand point, increase with the increase of the distance between them;

[0105] f. There is no limit to the number of vehicles, and they must be of a single model.

[0106] The initial information on raw material supply points and demand points obtained in step (1) includes a supply-demand relationship matrix of raw material supply points and demand points, a general storage area of ​​the cold chain logistics distribution center, the quantitative relationship between raw material supply points and demand points within the region, the total number of planned cold chain logistics distribution centers, and a location information matrix of each raw material supply point and demand point. Based on the initial information, the transportation costs from the raw material supply points to the warehousing and logistics distribution center, the transportation costs from the warehousing and logistics distribution center to the manufacturer, and the construction costs of the warehousing and logistics distribution center are calculated. In this example, assume there is a given supply point located at (100, 70). The distribution center can take any value within the one-dimensional interval [0, 100] and the two-dimensional interval [0, 100]. A distribution center to be selected provides delivery services to 15 demand points. The fixed cost of the distribution center is 100,000. Assume that the vehicle departs from the selected distribution center at 7:00, the vehicle speed is 50 km / h, the unloading time is proportional to the unloading volume at this point, the proportionality coefficient is 1 / 15, the unit price of cold chain products is 4,000 yuan / t, the transportation price is 0.5 yuan / km*t, the spoilage rate during transportation is 0.02, the spoilage rate during unloading is 0.05, the refrigeration cost of transporting goods is 20 yuan / h, the refrigeration cost of unloading goods is 25 yuan / h, and the waiting cost and lateness cost of the vehicle are 10 yuan / h and 15 yuan / h, respectively. The vehicle's fuel consumption is 0.25 L / ton, the refrigeration equipment's energy consumption is 0.003 L / t·km, the unit carbon tax price is 25 yuan / kg, and the carbon dioxide emission coefficient is 2.6 kg / L. Relevant data for the demand points are shown in Table 1.

[0107] Table 1. Data related to demand points

[0108]

[0109]

[0110] In step (2), historical road condition information around each supply point and demand point is obtained from the traffic management system. The data-driven optimization method is used to predict the traffic conditions around the surrounding area for a relatively long period of time based on historical data. Since the location of the distribution center is not given in advance in the central location problem, and the path is also uncertain, it is difficult to determine the congestion situation of each path. This solution first determines three radius ranges according to the size of the overall solution space: 0 to r1, r1 to r2, and greater than r2. Then, a traffic congestion detection system is established. The traffic conditions around each demand point and supply point are input, and the corresponding congestion calculation function is substituted. Finally, the traffic congestion function values ​​z1, z2, and z3 of the three ring areas corresponding to the three radius ranges of each point are obtained (the worse the road conditions, the larger the traffic congestion function value). This traffic congestion function value will affect the cold chain delivery time and thus affect the total cost. The calculation method is as follows: First, obtain historical road condition information around each supply point and demand point to obtain the area-travel time data corresponding to each time period. Use this data to build a surrogate model, and continuously optimize the surrogate model through Bayesian optimization to make it approximate the real model. Finally, output the area-travel time relationship for a subsequent period through the optimized model. Substitute the travel time of each area within the three radii into the congestion calculation function to give the corresponding traffic congestion function value. In this example, let r1 = 5km, r2 = 20km, and the traffic congestion function values ​​of each demand point and delivery point are shown in Table 2.

[0111] Table 2 Traffic congestion function values ​​at various points

[0112]

[0113] The objective function of the cold chain logistics distribution center site selection scheme in step (3) is:

[0114] minC=C1+C2+C3+C4+C5+C6 (1)

[0115] Equation 1 is the objective function, aiming to minimize the total cost, including fixed costs, transportation costs, cargo damage costs, refrigeration costs, penalty costs, and carbon emission costs. Since most previous researchers did not consider the impact of traffic conditions on costs, we introduce a traffic congestion function to assess the traffic conditions around each demand and supply point, thereby making the vehicle's transportation time t closer to reality and improving the accuracy of cost calculations. The expressions for C1 to C6 are as follows:

[0116] (1) Fixed costs

[0117] Fixed costs refer to costs unrelated to the transportation of goods, including the construction costs of potential distribution centers, vehicle depreciation costs, and operating costs such as employee wages. Assume that in the logistics network, there are I predetermined supply points, J potential distribution centers, and M demand points, where c...j (j=1,2,……,J) represents the fixed cost of the j-th candidate distribution center, then the total fixed cost C1 is:

[0118]

[0119] In the formula,

[0120] In this example, there is only one alternative distribution center, C1 = 100,000.

[0121] (2) Transportation costs

[0122] Transportation costs refer to expenses related to the volume and distance of transportation. Let p2 be the cost required to transport one unit of goods one unit distance, and q be the cost. ij Let q be the volume of transportation from supply point i to the selected distribution center j. jm For the transportation volume from the selected distribution center j to the demand point m, d ij Let d be the distance from supply point i to the candidate distribution center j. jm Let j be the distance from the candidate distribution center to the demand point m. Then the transportation cost C2 is:

[0123]

[0124] In the formula,

[0125] (3) Cost of damaged goods

[0126] Damage costs refer to the losses incurred by cold chain goods during transportation and unloading due to the passage of time and temperature changes. Let p3 be the unit price of the goods, β1 be the spoilage rate of the goods during transportation, β2 be the spoilage rate of the goods during unloading, and t be the unit price of the goods. ij t represents the transportation time of the vehicle from supply point i to the selected distribution center j. jm T is the transportation time for a vehicle from the selected distribution center j to the demand point m. m Let m be the time taken for the vehicle to unload at the demand point m. Then the cargo damage cost is:

[0127]

[0128] (4) Refrigeration cost

[0129] Refrigeration cost refers to the cost incurred by refrigerated trucks during transportation and unloading due to the consumption of refrigerant. Let p be the refrigeration cost incurred by a refrigerated truck per unit time during transportation. 41 During the unloading process, the refrigeration cost incurred by the refrigerated vehicle in unloading goods per unit time is p. 42 The refrigeration cost is:

[0130]

[0131] (5) Penalty Costs

[0132] Penalty costs refer to the costs incurred when a vehicle fails to deliver to a demand point within a specified timeframe. If the vehicle delivers before the earliest time required by the demand point, a waiting cost is incurred; if the vehicle delivers after the latest time required by the demand point, a lateness cost is incurred. Let t... m p is the time it takes for the vehicle to reach the demand point m. w p represents the waiting cost incurred by the vehicle per unit of time. l The cost of a vehicle's lateness per unit of time, (ET) m LT m (EET) represents the expected time window for demand point m. m LLT m Let m be the acceptable time window for demand point m. Then the penalty cost at demand point m is:

[0133]

[0134] In the formula, inf is an infinitely large positive number;

[0135] The total cost of punishment is:

[0136]

[0137] In this example, the correlation matrix TD is generated by subtracting the vehicle departure time from the time window, as shown in Table 3.

[0138] Table 3 Matrix TD

[0139]

[0140]

[0141] (6) Carbon emission costs

[0142] Carbon emission costs refer to the costs of carbon dioxide emissions resulting from vehicle energy consumption and refrigerant consumption during transportation. A vehicle's fuel consumption is related to factors such as distance traveled, load capacity, and speed; the higher the fuel consumption, the greater the carbon dioxide emissions. Let p... c Let E be the unit carbon tax price, e be the carbon dioxide emission coefficient, E1 be the fuel consumption per unit distance traveled by the refrigerated truck, and E2 be the energy consumption of the refrigeration equipment per unit time. Therefore, the total carbon emission cost of vehicle operation and refrigeration equipment is:

[0143]

[0144] In summary, the site selection model for cold chain low-carbon logistics distribution centers is as follows:

[0145] minC=C1+C2+C3+C4+C5+C6 (1)

[0146] Constraints:

[0147]

[0148]

[0149] Equation (1) is the objective function, aiming to minimize the total cost, including fixed costs, transportation costs, cargo damage costs, refrigeration costs, penalty costs, and carbon emission costs; Equation (8) indicates that each demand point can only be served by one distribution center; Equation (9) indicates that the total transportation volume from the supply point to the distribution center is equal to the total transportation volume from the distribution center to the demand point; Equation (10) indicates that there is no vehicle operation between cold chain distribution centers; Equation (11) indicates that the total amount of goods transported from the distribution center to the demand point is not less than the total demand of the demand point, q m Let V be the demand at demand point m; Equation (12) is a limit on the total number of distribution centers, i.e., a maximum of N distribution centers can be built, n = 1, 2, ..., N; Equation (13) indicates that the capacity of the selected distribution centers must be able to meet all the demands of the demand point, V n This represents the capacity of the nth distribution center.

[0150] In step (4), the calculation process for the corresponding transportation time based on the congestion coefficient and the distance between the undetermined distribution center and the supply or demand point is as follows: If d is the distance from the starting point to the destination, and all transport vehicles travel at a constant speed, then the transportation time t in the mathematical model can be expressed as:

[0151]

[0152] The basic idea of ​​the optimization algorithm based on population expansion proposed in step (5) is as follows:

[0153] The algorithm establishes a population centered on the individual with the highest fitness. The population gradually expands with each iteration, and the number of members continuously increases. Simultaneously, the best individual is updated as the leader based on fitness in each iteration. Population members, guided by the leader, act around the leader (local exploitation), while non-population members engage in random activities (global search). In the early stages of iteration, the population size is small, with few members but a large number of followers, resulting in weak local exploitation but strong global search capabilities, which is beneficial for escaping local optima. In the later stages of iteration, the population size is large, with many members but fewer followers, and the algorithm gradually shifts from global search to local exploitation, which is beneficial for further finding the optimal value.

[0154] The method for adjusting the population division in step (6) is as follows:

[0155]

[0156] P′ i =D Li

[0157] In the formula X * X(t) represents the position of the leader in the j-th dimension, X(t) represents the position of a population member in the j-th dimension, and D... Li Let P' be the Euclidean distance between the leader and group member i. i Store D in location Li The algorithm calculates the Euclidean distance between members and the leader, classifying individuals closer to the leader as population members.

[0158] The population expansion process is as follows:

[0159]

[0160] In the formula, S is the total number of individuals, M is the maximum number of iterations, t is the current number of iterations, the algorithm initializes the population with 1 / 10 of the number of individuals, and then gradually expands it as the number of iterations increases, and N is the current population size.

[0161] In step (7), population members and non-population members should update their positions based on different movement strategies to ensure population diversity and balance between global search and local utilization. Therefore, this patent proposes a spiral approach strategy, which population members use to update their positions. The characteristic of this movement strategy is that as the number of iterations increases, the spiral trajectory gradually approaches the leader, enhancing the algorithm's local utilization capability and facilitating convergence to the optimal value. The specific movement strategy is as follows:

[0162] When probability p < 0.5

[0163] D L =|C*X * (t)-X(t)|

[0164] X(t+1)=X * (t)-A*D L (17)

[0165] When probability p>=0.5

[0166] D L2 =|C*X * (t)-X(t)|

[0167] X(t+1)=D L2 *e bl *cos(2πl)+X * (t) (18)

[0168] In the formula X * Let X(t) be the position of the leader in the j-th dimension at the t-th iteration, X(t) be the position of the population member in the j-th dimension at the t-th iteration, X(t+1) be the position of the population member in the j-th dimension at the (t+1)-th iteration, and C, A, b, l be relevant parameters. Let the function f(x,y) represent the value taken in the interval [x,y], where

[0169] A = 2*a*r1 - a

[0170] C = 2 * r²

[0171] b=1

[0172] l=(a2-1)*f(0,1)+1

[0173] The movement strategy for non-population members is to randomly initialize their positions:

[0174] X(t+1)=f(0,1)*(ub-lb)+lb; (19)

[0175] In the formula, X(t+1) is the position of the population member in the j-th dimension at the (t+1)-th iteration, the function f(x,y) represents the value taken in the interval [x,y], ub is the upper limit of the value given in the current dimension, and lb is the lower limit of the value given in the current dimension.

[0176] The algorithm was tested, and the test functions are shown in Table 4. The test results are attached. Figure 3 As shown, compared with traditional optimization algorithms, the Population Expansion Optimization Algorithm (SEOA) has improved its accuracy in high dimensions. For complex functions, the algorithm can effectively avoid getting trapped in local optima, while its convergence speed is similar to other optimization algorithms. Applying it to the location problem of cold chain logistics distribution centers can effectively avoid the disadvantages of slow convergence speed and low convergence accuracy.

[0177] Table 4 Algorithm Test Functions

[0178]

[0179] The specific method for selecting the location of the cold chain warehousing and logistics distribution center in step (8) is as follows:

[0180] First, obtain the initial information matrix, then establish a traffic congestion detection system, input the traffic conditions around each demand point and supply point, obtain the corresponding traffic congestion function value, substitute it into equation (14) to calculate the transportation time, and then substitute it into equation (1).

[0181] This model is set as the objective function, and the optimization algorithm is initialized using the information provided at the beginning, including the solution space range, the number of search agents, the initial population size, and the number of iterations. Then, the fitness of each individual is calculated, a leader is selected to form the initial population, and then non-population members and population members update their positions iteratively according to different movement strategies, and the population is updated according to the population expansion strategy.

[0182] The fitness of parent and offspring individuals is compared, and the individual with the better fitness is selected as the new offspring. The fitness of the new population is then compared, and the optimal individual is selected as the new leader for the next generation iteration. The iteration process of each algorithm in this example is as follows: Figure 4 As shown in the test output data, SEOA converges faster than other traditional algorithms, second only to WOA, while its accuracy is higher than other algorithms. It can be well applied in the location problem of cold chain logistics distribution centers.

[0183] MV0 Solution:[58.2167 60.7473] Value:[116361.5938]

[0184] AL0 Solution:[58.179 60.7466] Value:[116361.579]

[0185] SCA Solution:[57.4524 60.7444] Value:[116363.4476]

[0186] WOA Solution:[58.0538 60.7439] Value:[116361.6325]

[0187] SEOA Solution:[58.2518 60.7496] Value:[116361.5777]

[0188] In this example, the instance data is substituted into the improved algorithm, and the final coordinates and minimum cost of the cold chain warehousing and logistics distribution center are shown below. The optimal location coordinates of the cold chain warehousing and logistics distribution center are [58.2518, 60.7496], and the calculated minimum cost is 116361.5777 yuan. A schematic diagram of the obtained solution is shown below. Figure 5 As shown.

[0189] SEOA Solution:[58.2518 60.7496] Value:[116361.5777]

[0190] As can be seen from the above examples, the metaheuristic algorithm based on population expansion in this invention has a certain scientific validity when applied to the site selection problem of cold chain logistics distribution centers. This algorithm can reduce the expenses of enterprises in the site selection of cold chain logistics distribution centers, improve the service quality of logistics, and reduce the transportation and construction costs of enterprises.

[0191] The present invention has been described in detail above with reference to the embodiments, but the content described is only a preferred embodiment of the present invention and should not be considered as limiting the scope of the present invention. All equivalent changes and improvements made in accordance with the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. A method for selecting a cold chain logistics distribution center based on population expansion, characterized in that: Includes the following steps: (1) Obtain initial information on raw material supply points, demand points, and distribution centers; (2) Obtain historical road condition information around each supply point and demand point in the traffic management system, use data-driven methods to predict the traffic conditions around each supply point and demand point over a period of time, and determine the traffic congestion function through the relationship between its distance and travel time. (3) Determine the objective function based on the acquired initial information, and construct the site selection scheme and mathematical model of the warehousing and logistics distribution center; (4) Calculate the corresponding transportation time using the traffic congestion function value and the Euclidean distance between the undetermined distribution center and the supply point or demand point; (5) Based on the population expansion optimization algorithm, initialize the algorithm parameters and substitute the relevant information of the supply point and demand point into the algorithm for solution; (6) Adjust the population partitioning of the algorithm in each iteration, and select a new leader based on the new population after each adjustment; (7) Population members and non-population members perform position iteration updates based on different movement strategies to complete the algorithm optimization; (8) Provide guidance on site selection based on the location selection results of the warehousing and logistics distribution center after optimization.

2. The cold chain logistics distribution center site selection method based on population expansion according to claim 1, characterized in that: Step (1) of obtaining initial information includes: A supply-demand matrix is ​​constructed based on the reserves at raw material supply points and the sales volume at demand points. The location range and storage area of ​​the distribution center are determined based on the geographical location information around the demand points. The total number of cold chain logistics distribution centers to be established is determined based on the quantitative relationship between raw material supply points and demand points. A location information matrix is ​​constructed based on the location information of each raw material supply point and demand point. Based on the initial information, the following data are calculated: transportation costs from raw material supply points to warehousing and logistics distribution centers, transportation costs from warehousing and logistics distribution centers to manufacturers, and construction costs of warehousing and logistics distribution centers.

3. The cold chain logistics distribution center site selection method based on population expansion according to claim 2, characterized in that: The prediction of traffic conditions around each supply point and demand point in step (2) for a period of time includes: Based on the size of the overall solution space, three radius ranges are determined: 0 to r1, r1 to r2, and greater than r2. Establish a traffic congestion detection system, determine the traffic congestion function, and obtain the traffic congestion function values ​​z1, z2, and z3 corresponding to different radii of the demand and supply points by using the historical traffic conditions around each demand point and supply point. The worse the road conditions, the larger the traffic congestion function value. The traffic congestion function is calculated as follows: Obtain historical traffic information around each supply and demand point to obtain data on regional travel time for each time period; Using this data, we build a proxy model and continuously optimize it through Bayesian optimization to make it approximate the real model. By outputting the optimized model, the travel time relationship between districts over a period of time is obtained. The travel time of each district is then substituted into the traffic congestion function to obtain its corresponding traffic congestion function value.

4. The cold chain logistics distribution center site selection method based on population expansion according to claim 2 or 3, characterized in that: The objective function for constructing the site selection scheme and mathematical model of the warehousing and logistics distribution center in step (3) is: minC=C1+C2+C3+C4+C5+C6 (1) Equation 1 aims to minimize total cost, including fixed costs, transportation costs, cargo damage costs, refrigeration costs, penalties, and carbon emission costs. The expressions for C1 to C6 are as follows: (1) Fixed costs Fixed costs are those unrelated to the transportation of goods, including the construction costs of potential distribution centers, vehicle depreciation costs, and employee wages and operating costs. Assume the logistics network has I predetermined supply points, J potential distribution centers, and M demand points, where c... j (j=1,2,……,J) represents the fixed cost of the j-th candidate distribution center, then the total fixed cost C1 is: In the formula, (2) Transportation costs Transportation costs are expenses related to the volume and distance of transport; let p2 be the cost required to transport one unit of goods one unit distance, and q be the cost. ij Let q be the volume of transportation from supply point i to the selected distribution center j. jm For the transportation volume from the selected distribution center j to the demand point m, d ij Let d be the distance from supply point i to the candidate distribution center j. jm Let j be the distance from the candidate distribution center to the demand point m. Then the transportation cost C2 is: In the formula, (3) Cost of damaged goods The cost of spoilage is the loss incurred by cold chain goods during transportation and unloading due to the passage of time and temperature changes; let p3 be the unit price of the goods, β1 be the spoilage rate of the goods during transportation, β2 be the spoilage rate of the goods during unloading, and t be the spoilage cost of the goods. ij t represents the transportation time of the vehicle from supply point i to the selected distribution center j. jm T is the transportation time for a vehicle from the selected distribution center j to the demand point m. m Let m be the time taken for the vehicle to unload at the demand point; then the cost of cargo damage is: (4) Refrigeration cost Refrigeration costs are the costs incurred during transportation and unloading due to the consumption of refrigerant by refrigerated trucks. Let p be the refrigeration cost incurred by the refrigerated truck in transporting products per unit time during the transportation process. 41 During the unloading process, the refrigeration cost incurred by the refrigerated vehicle in unloading goods per unit time is p. 42 The refrigeration cost is: (5) Penalty Costs The penalty cost is the cost incurred when a vehicle fails to deliver to the demand point within the specified time period. If the vehicle delivers before the earliest time required by the demand point, a waiting cost is incurred; if the vehicle delivers after the latest time required by the demand point, a lateness cost is incurred. Let t... m p is the time it takes for the vehicle to reach the demand point m. w p represents the waiting cost incurred by the vehicle per unit of time. l The cost of a vehicle's lateness per unit of time, (ET) m LT m (EET) represents the expected time window for demand point m. m LLT m Let m be the acceptable time window for demand point m; then the penalty cost at demand point m is: In the formula, inf is an infinitely large positive number; The total cost of punishment is: (6) Carbon emission costs Carbon emission cost refers to the cost of carbon dioxide emissions resulting from vehicle energy consumption and refrigerant consumption during transportation; let p c Let E1 be the unit carbon tax price, e be the carbon dioxide emission coefficient, E1 be the fuel consumption per unit distance traveled by the refrigerated truck, and E2 be the energy consumption of the refrigeration equipment per unit time. Therefore, the total carbon emission cost of vehicle operation and refrigeration equipment is: Constraints of the cold chain low-carbon logistics distribution center site selection model: Equation (8) indicates that each demand point can only be provided with delivery services by one distribution center; Equation (9) indicates that the total transportation volume from the supply point to the distribution center is equal to the total transportation volume from the distribution center to the demand point; Equation (10) indicates that there is no vehicle operation between cold chain distribution centers; Equation (11) indicates that the total amount of goods transported from the distribution center to the demand point is not less than the total demand at the demand point, q m Let m be the quantity demanded at demand point; Equation (12) is a limit on the total number of distribution centers, that is, a maximum of N distribution centers can be built, n = 1, 2, ..., N; Equation (13) indicates that the capacity of the selected distribution center must be able to meet all the demands of the demand points, V n This represents the capacity of the nth distribution center.

5. The cold chain logistics distribution center site selection method based on population expansion according to claim 4, characterized in that: The corresponding transportation time is calculated using traffic congestion function values ​​and the Euclidean distance between the pending distribution center and the supply or demand point, including: By analyzing the traffic conditions around each demand and supply point, the traffic congestion function values ​​corresponding to different radii of the demand and supply points are obtained. The transportation time calculation process based on traffic conditions is as follows: If d is the distance from the starting point to the destination, and all transport vehicles travel at a constant speed, then the transport time t in the mathematical model can be expressed as: t=[r1*z1+(d-r1)*z2] / v, r2≥d≥r1(14) t = d * z1 / v, d <r1 Where r1 and r2 represent different radius ranges, and z1, z2, and z3 represent the traffic congestion function values ​​for each radius range.

6. The cold chain logistics distribution center site selection method based on population expansion according to claim 4, characterized in that: The optimization algorithm based on population expansion in step (5) includes: A population is established centered around the individual with the highest fitness. The population gradually expands with each iteration, and the number of population members increases continuously. At the same time, the best individual is updated as the leader based on fitness in each iteration. Population members act around the leader under the leader's guidance, while non-population members engage in random activities.

7. The cold chain logistics distribution center site selection method based on population expansion according to claim 6, characterized in that: The population division in step (6) includes: P i '=D Li In the formula X * X(t) represents the position of the leader in the j-th dimension, X(t) represents the position of a population member in the j-th dimension, and D... Li Let P' be the Euclidean distance between the leader and group member i. i Store D in location Li The location of the individual is determined by calculating the Euclidean distance between the individual and the leader, and individuals closer to the leader are classified as members of the population. The population expansion method is used to balance global search capability and local exploitation capability. The specific population expansion strategy is as follows: In the formula, S is the total number of individuals, M is the maximum number of iterations, t is the current number of iterations, the parameter g takes values ​​in the range of [0,1], the population is initialized with the number of individuals S*g, and then gradually expands as the number of iterations increases, and N is the current population size.

8. The cold chain logistics distribution center site selection method based on population expansion according to claim 7, characterized in that: In step (7), population members and non-population members perform iterative position updates based on different movement strategies to optimize the algorithm, including: When probability p < 0.5 D L =|C*X * (t)-X(t)| X(t+1)=X * (t)-A*D L (17) When probability p>=0.5 D L2 =|C*X * (t)-X(t)| X(t+1)=D L2 *e bl *cos(2πl)+X * (t) (18) In the formula X * X(t) represents the position of the leader in the j-th dimension at the t-th iteration, X(t) represents the position of the population member in the j-th dimension at the t-th iteration, X(t+1) represents the position of the population member in the j-th dimension at the (t+1)-th iteration, C, A, b, and l are relevant parameters, and let the function f(x,y) represent the value taken in the interval [x,y], where: A = 2*a*r1 - a C＝2*r2 b＝1 l=(a2-1)*f(0,1)+1 The movement strategy for non-population members is to randomly initialize their positions: X(t+1)=f(0,1)*(ub-lb)+lb; (19) In the formula, X(t+1) is the position of the population member in the j-th dimension at the (t+1)-th iteration, the function f(x,y) represents the value taken in the interval [x,y], ub is the upper limit of the value given in the current dimension, and lb is the lower limit of the value given in the current dimension.

9. The cold chain logistics distribution center site selection method based on population expansion according to claim 5, characterized in that: The specific method for selecting the location of the warehousing and logistics distribution center in step (8) is as follows: First, obtain the initial information matrix, then establish a traffic congestion detection system, input the traffic conditions around each demand point and supply point, obtain the corresponding traffic congestion function value, substitute it into equation (14) to calculate the transportation time, then substitute it into equation (1) to calculate the fitness of each individual, select the leader, form the initial population, and then non-population members and population members perform position iteration updates according to different movement strategies, and perform population updates according to the population expansion strategy; The fitness of parent and offspring individuals is compared, and the individual with better fitness is selected as the new offspring. The fitness of the new population individuals is then compared, and the best individual is selected as the new leader for the next generation iteration.

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