Distribution Path Optimization of Fresh Products in Cold Storage Considering Green Costs

: With the continuous improvement of people’s income level and consumption level, the demand for fresh products is driven by the strong demand, and at the same time, low-carbon and green development puts forward new requirements for the cold chain logistics industry. Starting from the perspective of considering the green cost, by constructing a distribution path optimization model of fresh cold chain products considering green cost with the optimal total distribution cost as the research objective, energy saving and emission reduction are integrated into the path optimization problem so that we can explore how to protect the environment while realizing the ben-eﬁts of the enterprise, and the model is solved by using the ant colony algorithm. By observing the cold chain logistics distribution path arrangement before and after optimization, it is found that the fresh cold chain product distribution path optimization considering green cost can eﬀectively reduce the transportation cost, refrigeration cost, carbon emission cost, and cargo damage cost in the distribution process. Under the optimal distribution strategy, the total cost is reduced by about 16.6% compared to the original route, and the environmental cost is reduced while reducing the distribution cost. It shows that this strategy can improve transportation eﬃciency and customer satisfaction while saving resources and protecting the environment. And this study comprehensively considers the actual operation of logistics enterprises, so this study has a certain signiﬁcance of reference value for the green transformation of enterprises. It further promotes the sustainable development of the cold chain industry and reduces the distribution costs of cold chain logistics companies. It also provides a certain degree of inspiration and reference for other cold chain logistics companies to realize the unification of economic and environmental benefits in actual operation.


Introduction
In recent years, China's economy has developed rapidly, and people have started to pay a ention to health and quality of life on the basis of ensuring basic living.Fresh products contain a variety of proteins, vitamins, and trace elements and have become a common choice in daily family life.In 2021, China's average consumption per person of major fresh food reached 248.7 kg, of which fresh products mainly include fresh vegetables, meat, poultry, aquatic products, eggs, milk, fresh fruits, and vegetables.Due to the special nature of fresh products, fresh products are generally preserved by cold storage and distributed to various demand points.The continuous growth of consumption has put forward high requirements for the distribution of fresh products in cold storage, and the relevant research results are more abundant [1][2][3].
In order to ensure the freshness of fresh products, cold chain products have to use relevant refrigeration equipment to maintain a low-temperature transportation state when distributing them, which will increase fuel loss and pollute the surrounding envi-ronment to a certain extent.According to the statistics of the relevant departments, the exhaust emissions of refrigerated vehicles are more than 30% higher than those of ordinary trucks.At the same time, the distribution path of cold chain vehicles also has unreasonable problems, leading to untimely delivery service, increased loss of goods, and lower customer satisfaction.The issue of how to deliver fresh products in cold storage in a timely manner while considering the green cost has a racted widespread a ention.
The problem of green vehicle delivery and green vehicle fresh produce delivery has been studied by scholars from several perspectives.Kuo Y considered that vehicle speed variation and vehicle load affect the magnitude of carbon emissions and used a simulated annealing algorithm to solve the vehicle path optimization model with the objectives of minimum vehicle fuel consumption, shortest driving distance, and minimum running time, respectively [4].Bektas T, Laporte G studied a multi-objective vehicle path problem that integrates vehicle driving time, vehicle driving distance, and transportation cost, and factors such as vehicle travel distance and driver salary were analyzed, and the results showed that path optimization can reduce carbon emissions [5].Montoya A et al. used a multi-objective distribution path optimization model with multiple vehicle yards to achieve optimal scheduling of vehicles and optimal path arrangement, so as to improve vehicle driving efficiency, reduce energy consumption, and realize green logistics [6].Hariga M et al. delved into the problem of minimizing transportation costs and carbon emissions in a multi-stage supply chain to explore effective solutions to optimize the supply chain while maintaining sustainability [7].Babagolzadeh M et al. developed a two-stage stochastic model to study the impact of cold chain logistics on carbon emissions in response to carbon tax policies and demand uncertainty [8].Xixi Pan and Hongcheng Gan added carbon emission cost to the optimization objective of cold chain logistics distribution and found that the total cost of distribution under the consideration of carbon emission was reduced instead through calculation examples, which provided a driving force for enterprises to realize green logistics [9].Yehong Chen studied the distribution path optimization problem based on the construction of a carbon emission evaluation system [10].Xingxing Huang and Jiankun Hu constructed a cold chain delivery path optimization model with carbon tax and carbon rules to optimize the fresh produce delivery path under the constraints of delivery vehicle load and time window [11].Jie Feng and Li Shi studied the path optimization problem of delivering fresh products to diverse customer points with the same type of pure electric refrigerated delivery vehicles, constructed an algorithm based on the Solomn standard algorithm, and designed an ant colony algorithm to solve the model [12].Yao Zhen and Yi Zhang construct a distribution path optimization model considering the soft time window, customer satisfaction, and carbon emission under the carbon tax system by considering the advantages of IOT technology and the characteristics of cold chain logistics and solve the model with an improved genetic algorithm [13].
At present, scholars have conducted a lot of research on the vehicle path optimization problem of fresh cold chain products and green vehicle path optimization problem and have carried out different degrees of innovation and achieved certain results.However, in the previous research on vehicle path optimization, the total cost optimization model consisting of fixed cost, transportation cost, cargo damage cost, refrigeration cost, elimination cost, and carbon emission cost is not considered comprehensively, and only a few of these costs are often considered, and fewer people combine these six costs for comprehensive analysis.In the current research, the model and the optimization process of the algorithm in much of the literature only use arithmetic examples to support the innovative models and algorithms, and there is a lack of real case support and a lack of relevance for the research on the optimization of the paths of fresh cold chain products in logistics enterprises under the consideration of the impact of green costs.Based on this, this study combines the characteristics of the development of the times, starting from the perspective of green cost, in accordance with the characteristics of fresh products, comprehensively considers the fixed cost of fresh products, transportation costs, refrigeration costs, carbon emission costs, elimination costs, and the cost of cargo damage, and establishes a mathematical model with the goal of minimizing the total cost of distribution, which supplements the consideration of cost in the current research and coincides with the sustainable development advocated nowadays.

Research Objective
What this paper studies is the optimization problem of the fresh cold chain product distribution path while accounting for green costs, which can be described as follows: Cold chain products are distributed to several customer points through a cold storage distribution center; the cold storage distribution center is equipped with several refrigerated distribution vehicles of uniform specifications; after the vehicles provide services to all customer points of a route, they return to the cold storage distribution center and continue to perform the next distribution task; under the constraints of satisfying the vehicle loading capacity and customer cargo demand, the fixed cost, cargo damage cost, refrigeration cost, transportation cost, extermination cost, and carbon emission cost of the vehicles in the distribution process are considered comprehensively to build a cold chain logistics distribution path optimization model with the optimal total distribution cost and to find the route arrangement with the optimal degree of resource saving, environmental friendliness, and economic benefits.

Basic Assumptions
Through the above problem description, based on a full study of the relevant literature, the problem is abstracted into a model, and the following basic assumptions and constraints are made around distribution vehicles, customers, cold storage distribution centers, etc.
(1) Only one cold storage distribution center provides distribution service work, and the distribution vehicle returns to the cold storage distribution center in time after performing the distribution task and only undertakes the delivery task and no other services.(2) The cold storage distribution center has multiple refrigerated distribution vehicles with uniform specifications, and its refrigeration equipment uses the same refrigerant.(3) The geographical location, product demand, and service time of the customer are known.(4) The weight of goods delivered by each distribution vehicle shall not be greater than the maximum load capacity of the distribution vehicle.(5) The cold storage distribution center has a sufficient supply of goods to fully meet the customer's requirements, and there is no shortage of goods.( 6) Each customer will be served by only one delivery vehicle at a time to complete the delivery service work.(7) The refrigerated vehicles travel at an even speed, the traffic conditions of each transportation path are good, no traffic jams or other phenomena are considered, and the refrigerated vehicles only stop at the delivery place.(8) It is difficult to control and measure unexpected events, such as vehicle breakdown during the delivery process, so this factor is not considered.(9) The demand of the customer point is determined and is smaller than the maximum load capacity of the delivery vehicle, and the goods needed by the same customer or different customers can be mixed in the same delivery vehicle.(10) The vehicle door is closed during the driving process, and the temperature inside and outside the distribution vehicle is constant.(11) Drivers of cold chain distribution vehicles are uniformly and strictly trained with consistent technical experience, and fuel consumption is not affected by subjective factors.( 12) The driver's salary is generally paid monthly, and the next delivery task is carried out immediately after the previous one is completed.
(13) The demand points are all nearby deliveries, with Jinan city as the delivery area, and the delivery time error is small and the customers are not sensitive to time, so the delivery time window problem is not considered.

Parameter Se ing
The symbols and specific meanings of the parameters involved in the mathematical model established are shown in Table 1.
Table 1.Parameter symbols and specific meanings.

Parameter Symbols Specific Meaning ij
Denotes customer point number, where i = 1 denotes cold storage distribution center L1 denotes the set of cold storage distribution center and customer points, where 1 represents the cold storage distribution center and m represents the customer points M denotes the set of all customer points, where m denotes the total number of customer points N denotes the set of all distribution vehicles, where n denotes the total number of cold chain distribution vehicles required Denotes the vehicle travel distance between customer point i and customer point j Q Denotes the dead weight of the cold chain distribution vehicle Denotes the weight of the goods distributed between customer point i to customer point j Indicates the load capacity when arriving at customer point j Indicates the maximum load capacity of the cold chain distribution vehicle Denotes the demand for product at customer point i Denotes the fixed cost per unit of cold chain distribution vehicle Denotes the price per unit of product Denotes the refrigeration cost per unit of cold chain distribution vehicle traveling in unit time Indicates the transportation cost per unit cold chain vehicle for delivering products per unit distance Indicates the cost of extermination of cold chain vehicles and personnel per unit Indicates the inspection cost per unit of goods Indicates the refrigeration cost of loading and unloading goods per unit of cold chain distribution vehicle per unit of time Represents the rate of cargo damage during transportation Represents the rate of cargo damage during unloading Represents the rate of cargo loss during decontamination Indicates carbon tax V Indicates the travel speed of unloading cold chain distribution vehicles K CO2 emission factor H CO2 emissions per unit distance travelled by refrigerant per unit weight of goods delivered Indicates the fuel consumption per unit distance traveled when the vehicle is empty Indicates the fuel consumption per unit distance traveled when the vehicle is fully loaded Indicates the departure time of cold chain distribution vehicle n from the cold storage distribution center Indicates the time required for cold chain distribution vehicle n to travel from customer point i to customer point j Indicates the time required for cold chain distribution vehicle n to serve customer point i, i.e., unloading time Indicates whether the cold chain vehicle n travels from customer point i to customer point j (i ≠ j), where yes is 1, no is 0 Indicates whether the cold chain transportation vehicle n serves customer point i, where yes is 1, no is 0

Methodology
Methods for solving the VRP problem mainly include exact algorithms and heuristic algorithms.The exact algorithms mainly include the branching branch-and-bound method, network flow algorithm, dynamic programming method, cu ing plane method, etc.It is a method to find the optimal solution through strict mathematical logic.It is a kind of algorithm to find the optimal solution through a strict mathematical logic algorithm, but due to its complexity and low solving efficiency and other shortcomings, it is less studied and used.Heuristic algorithms mainly include the economizing method, scanning method, two-stage algorithm, ant colony algorithm, genetic algorithm, forbidden search method, particle swarm algorithm, Simulated Annealing Algorithm, Bat Algorithm, Cuckoo Algorithm, etc., which is simulated by computer simulation to obtain the feasible solution with good reference.It is a feasible solution with good reference value obtained through computer simulation, which has high global optimization ability, fast solving speed, and strong reference.Due to its high global optimization ability, fast solution speed, strong referability, and generality, it is suitable for complex and large-scale problems, and scholars are constantly improving it and designing new heuristic algorithms.
With the development of artificial intelligence technology and computer technology, researchers have put forward higher requirements for solving large-scale nonlinear constrained planning problems, such as fast convergence, global optimization, etc. Maxim A. D, in solving the problem of scheduling CDT trucks, proposes a new adaptive polyploid modulo algorithm, which facilitates the search process through the use of a number of problem-specific hybridization techniques that can greatly improve the quality of the solution at convergence, and which has outperformed some of the meta-heuristic algorithms in some respects [14].Maiyue Chen and Ying Tan have proposed an adaptive fast fireworks algorithm for large-scale black-box optimization, and the results also show that this algorithm outperforms the state-of-the-art large-scale global optimization algorithms, which proves the great potential of this algorithm to be applied to other practical problems [15].Junayed P et al., in their study of the vehicle path optimization problem, proposed a novel multi-objective optimization model for cost reduction, which is solved with a customized multi-objective hybrid meta-heuristic algorithm that directly takes into account the specific a ributes of the problem and completes the decision making about the optimal routes in the supply chain in question, comprising of the warehouse, the supplier, the manufacturer, and the customer [16].Emilio S and Nelishia P proposed a new ant-based generative constructive hyper-heuristic approach, extending the existing body of research, and then investigated how 2D and 3D pheromone graphs affect its performance.Although research on the applicability of ant-based optimization techniques to hyper-heuristic algorithms has been largely limited, it has also been found that different pheromone graphs work differently for different types of optimization problems [17].
The ant colony algorithm is one of the heuristic algorithms used below, due to its simpler implementation process and more effective search and optimization results.
The essence of the ant colony algorithm is the simulation of the foraging behavior of ants in nature.In the ant colony algorithm, ants release pheromones along the paths they walk and pass information to each other through pheromones.In the process of foraging, ants tend to choose the route with a large amount of pheromone, which makes the pheromone content on this route larger and larger, forming a positive feedback mechanism, and the algorithm is close to the optimal solution after a period of iteration.The ant colony algorithm is characterized by strong parallelism, robustness, and global optimization search.The main advantage of the ACO algorithm is that it can handle large-scale optimization problems with strong global search capability and good robustness [18].Its disadvantage is that it is greatly affected by parameters.
By analyzing the advantages and disadvantages of the algorithm, after reviewing the research results of many scholars on the optimization problem of logistics distribution routes, we finally choose to use the ant colony algorithm to solve the distribution path optimization problem of fresh cold chain products considering green cost.
In this study, we simulate the crawling path of each ant in the ant colony and set the parameters according to the specific situation in order to solve the ant path planning problem effectively.Let denote the colony size, denote the distance between node and node , denote the pheromone strength between node and node , h denote the degree of inspiration between node and node , denote the information inspiration factor, denote the expectation inspiration factor, denote the set of ants at node that choose to visit the node next, and ∆ ( , + 1) denote the paths of ants at ( , + 1), which denotes the pheromone increment between node and node in the time period of ( , + 1), denote the pheromone volatilization coefficient, and NC denote the number of iterations.The basic steps of the ACO algorithm are shown below.
(2) The crawling direction of each ant is determined by the pheromone concentration, and the set of all the ants' next action nodes at node i is stored in the table with contraindications.
(3) In the path search process, the probability of an ant choosing the next node is calculated by the state transfer probability formula.Assume that the state transfer probability expression for ant k to select node j at time t from node i with a certain probability is The ant completes a traversal and updates the pheromone concentration on the path.t + 1 time pheromone concentration is updated with the following formula: ( , + 1) = (1 − ) ( ) + Δ ( , + 1) (5) When the number of searches reaches the maximum, the shortest path can be found accurately.

Green Cost Variables (1) Cooling cost
Refrigeration cost mainly refers to the cost of cold chain vehicles to maintain the internal temperature of the carriage by consuming refrigerant during transportation to ensure the quality of the products, which is mainly affected by the driving time of the vehicle.Set the time required for vehicle n to travel from customer point i to customer point j as , the unloading time as , the refrigeration cost of the unit cold chain distribution vehicle when traveling in unit time as , and the refrigeration cost of the unit cold chain distribution vehicle when loading and unloading goods in unit time as .
The refrigeration cost during transportation is The cost of refrigeration during loading and unloading is The total cost of refrigeration is (2) Carbon emission cost Carbon emissions in the cold chain distribution process mainly originate from two aspects.One is the carbon emissions generated by fuel consumption during vehicle transportation due to normal driving and refrigeration, and the other is the carbon emissions generated by refrigerant consumption in the operation and unloading phases [19].The carbon dioxide content of the vehicle is the highest after the full combustion of fuel and the use of refrigerant during the driving process, so we focus on the carbon emission cost to be paid for the emissions.
The cost of carbon emissions is related to carbon tax, CO emission factor, and fuel consumption, using the following formula: carbon emissions = fuel consumption × CO emission factor, carbon cost = carbon emissions × carbon tax.
The amount of cargo carried by the transport vehicle and the transport distance are important factors affecting the fuel consumption.The larger the amount of cargo carried and the longer the transport distance, the more fuel will be consumed.Conversely, if the amount of cargo carried is small and the transport distance is short, the fuel consumption will be less.Some scholars found a significant linear relationship between the fuel consumption per unit distance and the load capacity of distribution vehicles through regression analysis [20].Set the carbon tax as , the self-weight of the cold chain distribution vehicle as Q, the maximum cargo capacity as , the CO emission factor as K, and the distance between customer point i and customer point j as .The fuel consumption per unit distance is The fuel consumption per unit distance when the vehicle is unladen is The fuel consumption per unit distance when the vehicle is fully loaded is We obtain = − So the fuel consumption per unit distance can be expressed as If the weight of the goods delivered between customer point i and customer point j is , then the carbon emissions generated by the vehicle traveling between customer point ij can be expressed as = ( ) In the process of distribution, the refrigerant used will produce CO , and its emissions are related to the amount of cargo carried by the distribution vehicle and the dis-tance of distribution, and the emissions will increase as the amount of cargo carried and the distance of distribution increase.If the weight of the goods delivered between customer point i and customer point j is , and the emissions generated by the refrigerant used to deliver the unit weight of goods traveling the unit distance are represented by H, then the emissions generated by refrigeration when the vehicle is traveling between customer points i and j can be expressed as follows: When the vehicle completes the distribution task, all products have been delivered to the customer safely and on time, that is = 0, and the distribution vehicle returns to the cold storage distribution center without refrigeration.Carbon emissions are only generated by the combustion of fuel when the vehicle is driving, as can be seen from Equation (9), and the carbon emissions generated during the return of the vehicle to the cold storage distribution center are represented by In summary, the CO emissions generated in the distribution process of refrigerated vehicles are represented by = + , and the total cost of carbon emissions to be paid in the distribution process is (3) Transportation cost The transportation cost of cold chain vehicles mainly refers to the cost of fuel consumed in the transportation process, which is closely related to the transportation distance, transportation speed, and engine emissions of the vehicle.We choose the same type of cold chain vehicle for distribution service and assume that the cold chain distribution vehicle travels at a uniform speed during the whole transportation process, so the distance of the vehicle is the main factor affecting the transportation cost.Set the distance between customer point i and customer point j as , the transportation cost per unit cold chain distribution vehicle per unit distance as , and the total transportation cost generated by all cold chain distribution vehicles in the transportation process as

Other Cost Variables (1) Extermination cost
Extermination cost refers to the cost paid by the logistics company for the distribution vehicles and goods for extermination and inspection activities during an epidemic to meet the consumer's shopping needs and reduce the risk of infection.If the extermination cost per unit of cold chain vehicles and personnel is , and the inspection cost per unit of goods is , the extermination cost is = ∑ ( + ) (13) (2) Cargo damage cost Due to the perishable nature of fresh products during cold chain transportation, they will be affected by factors such as temperature, humidity, and oxygen concentration in the storage environment and will produce certain losses over time [19].The cost of goods damage refers to the cost paid by the logistics company for the contamination of the disinfectant during the disinfection process and the impact on the quality of the product caused by collision and extrusion during transportation.The cost of goods loss discussed in this study mainly includes the following three cases.The first case is the loss of goods arising from the disinfection work before transportation; the use of disin-fectants in the disinfection process may affect the quality of products and even cause damage to goods, affecting customer satisfaction, so the impact of the disinfection process on the quality of goods should not be ignored.The second case is the loss of goods arising in transit, due to the distribution process.Because the distribution process uses a distribution vehicle with refrigerated and frozen equipment, it is assumed that the ambient temperature of the goods in the transportation process is constant, and only the decline in product quality caused by the accumulation of the distribution time is considered.The third case is the loss of goods when unloading, because during unloading, the car door is opened, and when the door is opened, the air inside and outside undergoes convection, causing the temperature inside the car to rise, which will also cause a loss of product quality [21].Assume that the price per unit of product is , the weight of goods distributed between customer point i to customer point j is , denotes the load when arriving at customer point j, the cargo loss rate during transportation is , the cargo loss rate during unloading is , the unloading time is , and the cargo loss rate during elimination is .
The cost of cargo damage incurred during abatement prior to transportation is The cost of goods damage during transportation is The cost of cargo damage at the time of unloading is Then, the total cost of cargo damage is (3) Fixed cost Cold chain distribution vehicles in the process of completing transport incur relatively fixed costs of consumption, including the driver's wages, vehicle depreciation costs, etc.The fixed cost of distribution vehicles is usually a constant, and with the increase in the number of distribution vehicles, the fixed cost of distribution vehicles will also increase.The current cold storage distribution center has N cold chain distribution vehicles, the fixed cost of the unit cold chain distribution vehicles is , and the total fixed cost generated by all cold chain distribution vehicles in the distribution process is shown below.

=
The combined costs are

Construction of Path Optimization Model
In summary, the fresh cold chain product distribution path optimization objective function can be established as The constraints are as follows: ∑ ≤ ∑ ∑ ≤ , = 1 ∑ ∑ ∑ = 1 Equation ( 20) is a comprehensive cost function consisting of fixed cost, transportation cost, refrigeration cost, carbon emission cost, extermination cost, and cargo damage cost of distribution vehicles.Equation (21) indicates that the cold storage distribution center has N vehicles, and only one vehicle provides distribution service work at each customer point.Equation (22) indicates that the distribution vehicle departs from the cold storage distribution center, delivers the goods on time according to the customer's demand, and returns to the cold storage distribution center safely after the task is completed.Equation (23) indicates that the maximum load capacity of the distribution vehicle shall not exceed its maximum load capacity range to ensure safety and reliability.Equation (24) indicates that the number of vehicles performing distribution operations is not greater than the number of vehicles at the disposal of the cold storage and distribution center.Equation (25) indicates that the whole distribution process does not carry the new corona virus.

Parameters Related to Customer Point Demand and Service Time
The specific data of customer number, demand, and service time of the cold storage distribution center are shown in Table 2. Jinan city is taken as the distribution area and determines the location of each customer point, the distance between the cold storage distribution center and each customer point, and the distance between each customer by collecting and organizing relevant data and field visits.For the convenience of the study, the shortest straight-line distance in the map is used as the distribution distance without considering the actual traffic conditions and other factors.The specific distribution distance matrix is shown in Appendix A.

Model-Related Parameters
The model-related parameters are shown in Table 3.

Ant Colony Algorithm Parameter Se ing
According to the formula of the ant colony algorithm, it can be seen that the parameter se ing of the ant colony algorithm has a greater impact on the performance of the algorithm.By conducting simulation experiments on the data of 36 customer points, the number of iterations NC is set to a fixed value of 200, and other parameters default to the initial value.By adjusting a certain parameter, conducting sub-operations on each group of experiments, the final suitable parameter combination is determined by performing sub-operations for each group of experiments and comparing the results of each operation.

Selection of Ant Colony Size
To analyze the effect of ant colony size on the performance of the algorithm, we set other parameters α = 2, β = 1, ρ = 0.1, Q = 400, adjusting the value of parameter m, combined with considering the characteristics of the green cost path optimization model.After 10 experiments, five groups of data were selected for the comparison of algorithm convergence effect after screening, and the comparison results are shown in Figure 1.From Figure 1, we can see that after 200 iterations, the algorithm finds a distribution path for different ant colony size states.By comparing the convergence effect of the algorithm under different ant colony sizes, we can find that when the ant colony size is 20, the convergence effect of the algorithm is the fastest, and the first one reaches the stable state after 90 iterations.At this time, the algorithm converges too fast, and it is difficult to jump out of the local optimal solution.When the ant colony size is 5, the algorithm tends to be stable after 133 iterations; at this time, the algorithm converges too slowly, and it is easy to fall into the defect of local search.When the ant colony size is 30, the algorithm enters the initial equilibrium state after three iterations, indicating that the algorithm enters a local optimum state at this time.Because the pheromone generated by the ant colony algorithm has a self-feedback mechanism, the ant colony algorithm is influenced by positive feedback to jump out of the local search and find the optimal solution after 111 iterations; at this time, the total cost after optimization is the lowest among the above five datasets, and the solution quality is be er.
In summary, in the path optimization model of fresh cold chain products considering green cost, when the ant colony size is set to 30, the algorithm can effectively balance the local search and global detection ability of the algorithm, the convergence effect is be er, and the search ability is stronger.

Selection of Pheromone Volatilization Coefficient
When analyzing the effect of the pheromone volatility coefficient on the performance of the algorithm, se ing other parameters α = 2, β = 1, m = 30, Q = 400, adjusting the value of parameter ρ and combining the characteristics of the path optimization model considering green cost, after 10 experiments, five groups of data were selected after screening to compare the convergence effect of the algorithm, and the comparison results are shown in Figure 2. Figure 2 reflects the effect of pheromone volatilization coefficient ρ on algorithm performance.In the ant colony algorithm, the value of the pheromone volatility coefficient ρ has an impact on the global search ability and convergence speed of the algorithm.When the value of ρ is made smaller, the difference in pheromone concentration after iteration is larger and the convergence speed is faster.However, when the value of ρ is made too small, it will affect the pheromone accumulation and weaken the positive feedback effect.When the value of ρ is made larger, the volatility of pheromone on the path is accelerated, which will make the algorithm search the previously searched path again due to the faster volatility of the pheromone on the previously searched path, which has a greater impact on the global search ability of the algorithm.
As can be seen from Figure 2, when the information volatility coefficient is 0.4, the algorithm first starts to converge to a stable state at 19 iterations, at which time the algorithm converges quickly and the search randomness weakens and easily falls into the local optimum.When the information volatility coefficient is 0.1, it can be observed that the algorithm starts to converge at 60 iterations, at which time the algorithm converges more slowly, and this affects the algorithm's ability to find the best path.When the information volatility coefficient is 0.2, the algorithm reaches the convergence state at 40 iterations, at which time the convergence curve is the lowest and the solution quality is better.
Therefore, in solving the fresh cold chain product path optimization model considering green cost, the algorithm has a stronger optimization-seeking ability when the information volatility coefficient is set to 0.2.

Selection of Information Heuristic Factor and Expectation Heuristic Factor
The parameters α and β are strongly coupled, and the combination of the values of these two also has a large impact on the overall algorithm performance of the ant colony algorithm.In order to analyze the influence of these two on the performance of the algorithm, se ing other parameters m = 30, ρ = 0.2, Q = 400 and adjusting the values of the combination of parameters α and β, combined with the characteristics of the path optimization model considering green cost, after 10 experiments, five groups of screened high-quality factor combinations were taken for the comparison of algorithm convergence effects, and the comparison results are shown in Figure 3. Figure 3 reflects the effect of the combination of parameters α and β on the performance of the algorithm.The parameter α is the information heuristic factor.The larger the value of α, the more pheromones the ants accumulate in the transfer process, which will weaken the randomness of the ants' path search and make the algorithm easily trapped in a local optimum.The parameter β is the expectation heuristic factor, which reflects the importance of the heuristic information.The larger the value of β, the greater the probability that the ant will choose the path with a shorter distance.The combination of these two values has a large impact on the overall performance of the ant colony algorithm.
According to the experimental results in Figure 3, when the combination of information heuristic factor and expectation heuristic factor is set to 3 and 5, the algorithm solution process starts to converge first among the five combinations and reaches the equilibrium state at the 32nd iteration, at which time the algorithm converges too fast and the solution searched is not the optimal solution.When the combination of information heuristic factor and expectation heuristic factor is set to 2 and 3, the algorithm converges at the 174th iteration, and at this time the total cost of optimization is the least among the above five datasets, the number of iterations is acceptable, and the solution quality is be er.
Therefore, in solving the fresh cold chain product path optimization model considering green cost, the algorithm has a strong optimization-finding ability and good convergence effect when the combination of information heuristic factor and expectation heuristic factor is set to 2 and 3.

Selection of Pheromone Intensity
To analyze the effect of pheromone intensity on the performance of the algorithm, other parameters are set as m = 30, ρ = 0.2, α = 2, β = 3, adjusting the size of the parameter Q and combining the characteristics of the path optimization model considering the green cost.After 10 experiments, five groups of data were selected for the comparison of the convergence effect of the algorithm after screening, and the comparison results are shown in Figure 4. Figure 4 reflects the effect of total pheromone release Q on algorithm performance.The pheromone intensity is the concentration of elements on the path that a racts ants.The greater the pheromone intensity on a path point, the greater the possibility that the point will be selected; the smaller the pheromone intensity, the lower the possibility that the point will be selected, which affects the convergence speed of the ant colony algorithm.
As shown in Figure 4, after 200 iterations, by comparing the convergence effect of the algorithm under different information strengths, it can be seen that the algorithm starts to converge first when the pheromone strength is 100.At this time, there is the problem of premature convergence, and the algorithm easily falls into local search, which affects the global detection ability.When the pheromone intensity is 300, the algorithm starts to converge after the 132nd iteration, at which time the total cost of the model solution is the lowest among the five datasets in the above figure, the number of iterations is acceptable, and the quality of the algorithm solution is the best.
Therefore, in solving the fresh cold chain product path optimization model considering green cost, the algorithm has a be er convergence speed and optimal finding ability when the pheromone intensity is set to 300.

Analysis of the Optimization Results of the Ant Colony Algorithm
The ant colony algorithm is designed for solving by MATLAB R2022b simulation software, where the algorithm parameters are set according to the experimental results of algorithm parameters.The number of ants m is set to 30, the pheromone volatility coefficient ρ is set to 0.2, the information heuristic factor α is set to 2, the expectation heuristic factor β is set to 3, the pheromone intensity Q is set to 300, and the number of iterations NC is set to 200, and the simulation experiment is conducted for the fresh cold chain product distribution path optimization model considering the green cost.
After 20 iterations, the algorithm achieves a good result in the local optimum, but with the adjustment of the self-feedback mechanism of the ant colony algorithm, it jumps out of the local search, which makes it possible to solve more complex problems with higher efficiency and accuracy.After more iterations, the global optimal solution, which is the optimal solution of the whole algorithm, is finally determined.At this time, the optimal solution of the objective function of the fresh cold chain product distribution path optimization model considering the green cost is USD 8889.3, in which the carbon emission cost is USD 69.3, the refrigeration cost is USD 204.3, the fixed cost is USD 2660, and the extermination cost is USD 288.5.The optimal path of the MATLAB R2022b simulation is shown in Figure 5.The optimal path diagram obtained by the MATLAB R2022b simulation experiment shows that there are seven delivery vehicles providing delivery service from the cold storage distribution center, and the order of customer point access and delivery mileage before and after optimization for each refrigerated vehicle as well as the comparison of delivery mileage before and after optimization are shown in Tables 4-6.As known from Table 5, with the optimized vehicle distribution path scheme, the cold storage distribution center still needs to send seven vehicles to complete the distribution task, but the distribution path of each vehicle is changed compared with that before optimization, and the distribution vehicles will provide distribution service for the customer points with more demand for goods first as far as possible, which can reduce the vehicle load, lower the fuel consumption, and reduce the emission of pollutants.The first vehicle serves 28, 12, 14, 10, 27, and 2 customer points in order, with a delivery mileage of 59.3 km; the second vehicle serves 34, 33, 6, 7, and 21 customer points in order, with a delivery mileage of 47.1 km; the third vehicle serves 4, 19, 37, and 31 customer points in order, with a delivery mileage of 42.0 km; the fourth vehicle serves 25, 8, 5, 32, and 20 customer points in order, with a delivery mileage of 3.0 km; the fifth vehicle serves 26, 3, 11, 15, 30, and 13 customer points in order, with a delivery distance of 80.5 km; the sixth vehicle serves 35, 29, 9, 36, 23, and 22 customer points in order, with a delivery distance of 138.9 km; the seventh vehicle serves 17, 16, 18, and 24 customer points in order, with a delivery distance of 73.9 km.After the service is completed, all seven vehicles return to the cold storage distribution center.
Compared with the original route before optimization, the optimal distribution strategy given by the ant colony algorithm, as shown in Table 6, the distribution mileage is optimized from 701 km in the original distribution plan to 493.7 km, and the transportation route is significantly shortened, saving 29.6% of the distance traveled.The optimized path has faster distribution speed, higher distribution efficiency, and shorter total distribution distance, which saves fuel consumption and reduces carbon emission for the enterprise and realizes the purpose of cost reduction and green development.
In the comparison of the cost of the optimized distribution path and the original distribution path, it is mainly reflected in the carbon emission cost, cooling cost, fixed cost, extermination cost, cargo damage cost, and transportation cost.Table 7 shows the comparison of the cost components before and after optimization.As shown in Table 7, the total distribution cost of the original distribution scheme before optimization is USD 10,658.0, of which the carbon emission cost is USD 83.1, accounting for about 0.8%, the refrigeration cost is USD 252.7, accounting for about 2.4%, and the fixed cost is USD 2660, accounting for about 25.0%.The cost of elimination is USD 288.5, or 2.7%, and the cost of damage is USD 2116.1, or 19.8%.The total distribution cost of the optimized distribution plan is USD 8889.3, of which the carbon emission cost is USD 69.3, accounting for about 0.8%, the refrigeration cost is USD 204.3, account-ing for about 2.3%, the fixed cost is USD 2660, accounting for about 29.9%, the extermination cost is USD 288.5, accounting for about 3.2%, and the cost of transportation is CNY 3703.1, accounting for 41.6%.From the above table, it can be seen that the transportation cost, carbon emission cost, cooling cost, and damage cost are all reduced to different degrees in the optimized scheme.
(1) Transportation cost After the calculation before and after optimization, it can be seen that among these six costs, the transportation cost accounts for the largest proportion and has a greater impact on the total cost.The daily transportation cost of the original distribution solution is CNY 10,658, and the optimized solution is CNY 8889.3 per day, which is about 29.6% less than that before optimization.The significant reduction in transportation cost not only means the reduction in enterprise operation cost, but also means that the optimized distribution path of fresh cold chain products considering green cost has effectively planned the distribution time, cargo capacity, and transportation mileage, which verifies the reliability of the model. (

2) Carbon emission cost
The carbon emission cost of the original distribution plan is CNY 83.1 per day, and the optimized plan is CNY 69.3 per day, which is about 16.6% less than that before the optimization.The significant reduction in carbon emission cost not only means that the total cost of distribution is reduced, but also means that the environmental cost paid by the enterprise for distribution is reduced, which can provide support for the enterprise to truly realize the unity of economic and environmental benefits.
(3) Refrigeration cost Refrigeration cost is mainly generated by refrigerant consumption.In the original distribution plan, the daily refrigeration cost is CNY 252.7, but after continuous optimization, the daily refrigeration cost is reduced to CNY 204.3, which is about 19.1% less than before optimization.The reduction in refrigeration cost not only means the reduction in the total cost of distribution, but also means the saving of energy loss, which means the distribution strategy given by the ant colony algorithm is in line with the development theme of energy saving and emission reduction in the current era.

(4) Cost of goods loss
The cost of cargo damage refers to the cost of cargo damage caused by the change in temperature in the refrigerated carriage during the distribution process.The cost of goods damage is CNY 2116.1 per day in the original distribution plan and CNY 1964 per day in the optimized plan, which is about 7.2% less than before the optimization.The significant reduction in the cost of goods damage not only means that the enterprise pays less, but also means that the freshness of goods delivered to customers is guaranteed, which improves customer satisfaction.
In summary, the fresh cold chain product distribution path optimization model proposed is feasible.Therefore, when formulating the distribution path, the influence of multiple parties should be considered, and the distribution path should be planned scientifically and reasonably, which can not only reduce the negative impact of cold chain transportation on the ecological environment, but also help to reduce the total cost of distribution, and can guarantee the quality of fresh products to a greater extent, improve customer satisfaction, and bring more competitive advantages to enterprises.

Conclusions
This study mainly focuses on the fresh cold chain product distribution path optimization problem, constructs a fresh cold chain product distribution path optimization model considering the green cost, and solves the model by using ant colony algorithm, so that the fresh product enterprises can obtain the relative maximization of economic benefits, while responding to the national policy of low-carbon practices and environ-mental protection, reducing the negative impact on the environment and establishing a good corporate image.It is also conducive to the long-term development of cold storage and similar enterprises.
The concept of green development has become more and more industry consensus; therefore, the cold chain logistics industry enterprises which mainly emit carbon emissions should strengthen green reform in their daily operation processes, and the enterprise managers should focus on reducing carbon emissions.From the results of this thesis, it can be seen that in the process of fresh cold chain product distribution path planning, enterprises should consider the total cost and carbon emission optimization from the economic, environmental, and social perspectives and formulate an optimal distribution plan that takes into account the internal economic benefits and external eco-efficiency of the enterprise from the economic, environmental, and social perspectives, in order to obtain the maximum benefits for the enterprise and provide the society with more.Only by doing so can we maximize the benefits for enterprises, provide more safe, green, and efficient logistics services for the society, and effectively put the idea of green development strategy into practice.
It can also provide a decision-making basis for government departments to introduce relevant policies and supporting measures.By analyzing the impact of cold chain logistics on the ecological environment, it can provide certain references for the government to formulate evaluation standards for green logistics and support and incentives for enterprises according to the actual results.

Figure 1 .
Figure 1.Effect of ant colony size m on the performance of the algorithm.

Figure 1
Figure 1 reflects the effect of ant colony size m on the performance of the algorithm.From Figure1, we can see that after 200 iterations, the algorithm finds a distribution path for different ant colony size states.By comparing the convergence effect of the algorithm under different ant colony sizes, we can find that when the ant colony size is 20, the convergence effect of the algorithm is the fastest, and the first one reaches the stable state after 90 iterations.At this time, the algorithm converges too fast, and it is difficult to jump out of the local optimal solution.When the ant colony size is 5, the algorithm tends to be stable after 133 iterations; at this time, the algorithm converges too slowly, and it is easy to fall into the defect of local search.When the ant colony size is 30, the algorithm enters the initial equilibrium state after three iterations, indicating that the algorithm enters a local optimum state at this time.Because the pheromone generated by the ant colony algorithm has a self-feedback mechanism, the ant colony algorithm is influenced by positive feedback to jump out of the local search and find the optimal solution after 111 iterations; at this time, the total cost after optimization is the lowest among the above five datasets, and the solution quality is be er.In summary, in the path optimization model of fresh cold chain products considering green cost, when the ant colony size is set to 30, the algorithm can effectively balance the local search and global detection ability of the algorithm, the convergence effect is be er, and the search ability is stronger.

Figure 2 .
Figure 2. Effect of pheromone volatility coefficient ρ on algorithm performance.

Figure 3 .
Figure 3.Effect of the combination of parameters α and β on the performance of the algorithm.

Figure 4 .
Figure 4. Effect of total pheromone release Q on algorithm performance.

Table 2 .
Statistics of demand and service time information of each customer point.

Table 3 .
Table of relevant parameters.

Table 4 .
Customer point access order and delivery mileage before optimization.

Table 5 .
Optimized customer point access order and delivery mileage.

Table 6 .
Comparison of total distribution mileage before and after optimization.

Table 7 .
Comparison of cost components before and after optimization.