# Application of Swarm Intelligence Optimization Algorithm in Logistics Delivery Path Optimization under the Background of Big Data

Authors: Guofu Zhao
Journal: Journal of Function Spaces
 (2023)

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## Abstract

Traditional logistics delivery route optimization algorithm has some problems such as long time to find the optimal route. Based on this, this paper discusses swarm intelligence optimization algorithm and logistics delivery route optimization. To solve the logistics vehicle routing problem, considering that the basic ACO (ant colony optimization) has the disadvantages of slow convergence speed and easy to fall into local optimum, this paper proposes a new hybrid population optimization algorithm and applies it to VRPTW (vehicle routing problem with time windows). In addition, the concept of crowding degree in AFSA (artificial fish swarm algorithm) is introduced into ACO. In the early stage of the optimization process, a strong crowding degree limit is set to ensure that most ants are not affected by pheromone concentration to conduct random optimization. The simulation results show that the AC (accuracy rate) of this algorithm is 95.08%, which is higher than the traditional PSO (particle swarm optimization) algorithm and general heuristic algorithm. The hybrid algorithm can effectively improve the optimization efficiency of VRPTW, lay a foundation for solving large-scale VRPTW, and provide new research ideas and methods. At the same time, the results fully show that the algorithm in this paper has certain advantages in performance, and it can be applied to logistics delivery route optimization.


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## Body

## 1. Introduction

The distribution route is very important in the growth of urban economy. Under certain conditions, the most appropriate distribution route can be improved and optimized to effectively reduce the distribution cost and material loss [1, 2]. Shortening the distribution path reduces the transportation expenditure for enterprises and the consumption loss of the masses [3]. IA is an important service industry in the national economy, the logistics industry is developing rapidly all over the world and has gradually become the artery of basic industry and national economic development [4]. At the same time, urban logistics delivery channels are related to the people’s livelihood of the whole city. Therefore, it is necessary to plan transportation routes reasonably and improve logistics delivery efficiency while consuming the lowest cost. VRP (vehicle routing problem) is an important content in logistics system research. Based on this, this paper discusses swarm intelligence optimization algorithm and logistics delivery path optimization. A new optimization algorithm of logistics delivery path is proposed. Now that we have entered the era of big data, we have formed a “big group” space for network interaction under this support. Its collaboration and reliability need to be solved by means of swarm intelligence. The swarm intelligence algorithms represented by particle swarm optimization and ant colony algorithm have good robustness and flexibility, which is the key to solving complex problems. In view of this, the article takes the network swarm intelligence in the age of big data as the research base point, combines the application principle and characteristics of swarm intelligence, explains its application advantages in NP problems, and provides effective support for the security of network information interaction. Through intelligent route planning algorithm, automatically match vehicle data and route information, customer location and driver information, commodity specification and quantity, and loading and unloading points, and combine a large amount of data. Second, calculate the vehicle arrangement route, and finally, formulate an optimized distribution route that meets the transportation and distribution objectives, for example, shorter mileage, less cost, shorter time, and fewer vehicles.Big data is an abstract concept, but at present, the academic circles have not yet formed an exact and unified definition. In this paper, traffic big data is defined as a data set composed of a large quantity of electronic maps, roads, vehicles, and other types of traffic information [5]. According to the vehicle route model, VRP can be converted into TSP (traveling salesman problem). ACO has been applied effectively in solving famous problems such as TSP, but when solving large-scale problems, its convergence speed is slow, and it takes a long time. In this paper, the traditional ACO is improved to build an optimization model. Big data can be used for positioning when building an optimization model. The data needs to be collected from the route collection center about the specific distribution requirements and time of each logistics branch, and based on this information, the data will be uniformly distributed and the distribution route will be planned. In this way, the efficiency of each distribution route can be ensured, while the needs of each customer can be met. The research innovation contribution lies in the discretization of the hybrid algorithm and the introduction of the local path optimization operator. The improved algorithm is applied to solve the VRPTW problem. In the early stage of the optimization process, a strong congestion limit is set. It ensures that most ants are not affected by pheromone concentration, to conduct random optimization. A HSIA model for logistics distribution route optimization is proposed, and its basic principle, mathematical description, parameter analysis, and algorithm flow are analyzed and studied. At the same time, set the distribution target weight, and find the optimal distribution path in the target function according to the different needs of logistics, to complete the optimization of logistics distribution path.According to the research on the application of swarm intelligence optimization algorithm in logistics delivery route optimization and the need of this paper structure, this paper will be divided into five parts; the specific contents are as follows.The first section introduces the research background and significance of logistics distribution path optimization and explains the content of this paper and the organizational structure of the full text. The second section is related work. This section expounds the research status of the research topic of this paper and puts forward the research work of this paper. In the third section, the swarm intelligence optimization algorithm and logistics delivery path optimization are analyzed. A new optimization algorithm of logistics delivery path of mixed population is proposed. In the fourth section, a large quantity of experiments are carried out to explore the performance of the algorithm. The fifth section is summary and prospect. This section makes a comprehensive summary of this research; finally, the shortcomings of the research and the research direction in the future are given.


## 2. Related Work

Shukla et al. established a logistics delivery model with rigid requirements for the travel time of distribution vehicles [6]. The model studies how the total cost of delivery will change if the hard time window is considered to be relaxed to a soft time window and takes a delivery task as an example to optimize the delivery route with a heuristic algorithm. Mousavi and Vahdani designed a tabu search algorithm for the most basic model of logistics delivery path optimization in the B2C e-business environment and conducted numerical tests and comparisons at the same time [7]. Ouyang added fuzzy constraints to the close-range open VRPTW and solved it with a hybrid ACO [8]. Raad et al. believe that information technology is a logistics capability that third-party logistics users are particularly concerned about, and users expect third-party logistics to make breakthroughs in services in areas such as integrated supply chain management and e-business. Third-party logistics users have higher and higher requirements for the quality of logistics services [9]. Mardaneh et al. proposed an adaptive multimodal continuous ACO with minimum habitat and extended ACO to solve multimode optimization problems [10]. The algorithm adjusts the ant colony pheromone update strategy and uses the differential evolution operator to construct the initial solution of the ant colony to speed up the convergence rate. To enhance the search, a Gaussian distribution-based local search scheme is adaptively performed around the seeds of the niche, switching between global and local searches. Rodríguez et al. utilized a hybrid algorithm based on tabu search and simulated annealing algorithms to solve VRP with backhaul and time windows [11]. Chu et al. proposed the column generation method to solve the idea of VRP [12]. The idea is to transform the original problem into a simplified problem, and the range that needs to be considered is a subset of all possible feasible solutions, and the shortest path is found by repeatedly solving on this basis. In order to reduce logistics delivery costs and improve customer satisfaction, Oliveira and Hamacher established a distribution system under changing demand and various components of operating costs and formed an integrated model [13]. Kuznietsov et al. proposed a nonlinear programming optimization model aiming at the node construction cost and operating cost of cold chain logistics and used the quantum PSO to solve the model [14, 15]. At the same time, a GA (genetic algorithm) is designed for this problem from the aspects of genetic coding, genetic operator, algorithm termination conditions, etc., to effectively solve the exponential explosion phenomenon when solving combinatorial optimization problems. Rooeinfar et al. explored the logistics delivery system and proposed corresponding development strategies [16]. These include building logistics alliances; third-party logistics models; introducing fourth-party logistics models; and accelerating lean supply chain management. Lang and Shen constructed a multiobjective route optimization model considering customer satisfaction and delivery costs and used an improved GA to simulate the model [17]. Niknejad and Petrovic studied VRP considering customer preference in dynamic environment and gave a solution idea [18]. Xiao and Rao believe that there are many uncertain factors in the real environment, which brings great difficulties to the location selection of logistics delivery [19]. The traditional two-layer objective planning cannot meet the requirements of uncertain conditions. The improved planning model is more suitable for the changing external environment, and then, an example is verified. Gharbi et al. further studied the selection of connection points and the optimization of cold chain logistics delivery paths based on connection points and established a cold chain distribution path optimization model based on transportation big data with connection points [20, 21]. Finally, an example is used to verify the validity of the above model.By summarizing the above algorithms for solving VRP, we can see that there is no best algorithm, only the most suitable one. However, with the increasing scale of VRP and more and more complicated constraints, heuristic algorithm based on swarm intelligence is the main development trend to solve this kind of problems. This paper mainly discusses swarm intelligence optimization algorithm and logistics delivery path optimization. Based on the improvement of ACO, a new optimization algorithm of mixed population logistics delivery path is proposed. At the same time, in order to apply the improved algorithm to solve VRPTW, the hybrid adaptive algorithm is discretized, and a local path optimization operator is introduced. Finally, an example of path optimization test is used to verify the effectiveness and better effect of the algorithm in solving VRPTW.


## 3. Methodology

### 3.1. Logistics Distribution Management Information System

Whether the distribution path is reasonable or not directly affects the speed and cost of logistics delivery, selecting the path optimization goal is the premise of path planning. According to the specific distribution problems of customers, we can design a reasonable distribution scheme to optimize the route. This kind of scheduling belongs to the logistics delivery path optimization problem [22]. According to the different logistics constraints in reality, there are many models of VRP, among which: VRPTW is the most typical problem, and it is also a representative constrained multiobjective problem with the most research value at present. In order to reduce the operating cost of service providers, the logistics system will optimize the vehicle distribution route. Logistics delivery with high timeliness requirements can use the distribution management information system to obtain information such as roads and real-time road conditions through the traffic big data platform to manage and direct vehicles in transit for distribution; at the same time, customers can also inquire about vehicles and goods and feedback information through this platform. The application of big data in logistics delivery is shown in Figure 1.Figure 1
Application of big data in logistics delivery.The application of big data analysis in the freight field is the most common. It is mainly reflected in site selection optimization, inventory scale, supply route, and other activities. Data analysis can group customers of enterprises. Transportation and route selection are the most widely used fields of big data analysis in logistics management. Many enterprises use remote big data information processing technology loaded with GPS navigation to optimize freight transportation routes. The limitations of traditional optimization methods make it impossible to meet the complex requirements of multiconstraints and multiobjectives of path planning problems. At present, heuristic algorithm based on swarm intelligence is the main development trend to solve this kind of problems. Swarm intelligent algorithm is distributed, individual intelligence is not controlled by a unified subject, and it has strong robustness. Moreover, each individual can only perceive local information, so it is relatively simple to follow the rules and easy to implement the algorithm [23]. The intelligent group has the characteristics of self-adaptability, and the group can change its behavior at an appropriate time when the required cost is not too high. Heuristic algorithm is highly sensitive to VRP path, so its solution efficiency is also high. Its VRP is basically the same for different logistics companies. Therefore, heuristic algorithm can be used to plan the path, reduce the cost, consume the least resources, and get the maximum profit. AFSA is a new intelligent bionic algorithm based on the characteristics of fish activities.The optimization of logistics distribution path requires that the vehicle distribution route be arranged quickly and reasonably, so that the goods can be delivered to the customers in time and accurately, and the distribution cost is the lowest. Soft time window means that if the delivery vehicle cannot start service within the time required by the customer, it must be punished accordingly. The meaning of hard time window is that if the delivery vehicle cannot start service within the time required by the customer, the solution is not feasible. The optimization goal is to quickly find a distribution strategy by obtaining real-time road congestion information, building a mathematical model and adopting appropriate algorithms according to the existing resources and customer demand. For the processing of optimization problems, because each logistics delivery route optimization problem faces different situations, it is necessary to design a general optimization algorithm to solve it. Therefore, based on big data, we can simulate the route distribution status in various situations, integrate these distribution statuses, and establish a tracking optimization algorithm to calculate the specific loss of distribution.


### 3.2. Optimization Algorithm of Mixed Population Logistics Delivery Route

In this paper, the time window of logistics delivery problem is set as a special time window, which is a time interval, and the distribution vehicles need to deliver the materials to the material demand points in advance or on time within this time window. At the same time, this paper adopts the two-population strategy, and the combination of ACO and differential evolution in the first population can solve the parameter optimization problem well. Secondly, the ant colony hybrid PSO is adopted in the population, which enhances the global search ability in a wide range and solves the problems of slow convergence and easy falling into local optimum. The flow chart of logistics and route design is shown in Figure2.Figure 2
Logistics delivery and route design process.A single objective optimization model is established to minimize the total vehicle transportation cost, as shown in(1)Z=min∑i∑j∑kCijxijki≠j,where Z stands for the total cost; i and j represent any two points; k represents any transport vehicle; and Cij represents the transportation cost from point i to point j. The variable xijk is defined as follows:
(2)xijk=1,Thetransportationtaskfromitojiscompletedbyk,0,Otherwise.Considering the actual situation, this paper puts forward three optimization objectives. That is, the shortest delivery time, the shortest driving distance of all delivery vehicles, and the least cost, and the established optimization model is shown in(3)minZ1=∑i∑j∑kTijxijkTheshortesttime,minZ2=∑i∑j∑kDijxijkTheshortestdistance,minZ3=∑i∑j∑kCijxijkTheleastcost.The establishment of the model is based on certain assumptions: the travel time, distance, and the demand of consumers between any two points can be known, that is, the distribution model under certain conditions.Letm be the quantity of ants in the ant colony; dij is the distance between the city i and j; ηijkt=1/dij is the heuristic function; τij is the amount of information on the path i,j at the moment t; pijkt means that the ants k move from city i to city at time t the probability of j. The formula is as follows:
(4)pijkt=τijtα⋅ηijtβ∑s∈allowedkτistα⋅ηistβ,j∈allowedk,0,Otherwise,(5)tabukk=1,2,⋯,m.Among them,j is the city that has not been visited yet; allowedk=C‐tabuk is the city that the ant k is allowed to choose next; α and β are heuristic factors; tabuk is used to record the city that the ant k has walked through at the moment of t. The ant is not allowed to repeatedly pass through this cycle, and the taboo table is cleared after the end of this cycle. The ant completes a cycle and updates each path pheromone:
(6)τijt+n=1−ρ⋅τijt+Δτijt,(7)Δτijt=∑k=1mΔτkijt.Among them,ρ∈0,1 represents the pheromone volatilization coefficient; 1‐ρ represents the pheromone residual factor; Δτij represents the information amount increment on the path ij in this cycle. Initially, Δτij=0; Δτijk represents the amount of information left by the ant k between cities i and j in this cycle. The formula is as follows:
(8)Δτijkt=QLk,Ifthekthantpassesthroughi,jinthiscycle,0,Otherwise.Among them,Lk represents the path length of the ant k to travel around; Q is a constant. In the ACO, the parameter selection method and selection principle directly affect the computational efficiency and convergence of the ACO.In the process of e-business logistics delivery, the weight of the goods is a factor that must be considered. In general, goods with heavy weight should be dispatched first to reduce fuel consumption during the delivery process. The weight index is expressed as:(9)Sg=∑ifg−itu.In the formula,Sg represents the quantity of locations that need to be delivered; ∑if represents the weight of the delivered goods; g is the order of locations for logistics delivery; i is the weight of the goods to be delivered at the i location; and tu is the weight index calculation factor. The establishment of the timeliness index reflects the timeliness requirements of the goods, calculated as follows:
(10)St=1Nta−tiTfs.In the formula,ti represents the preservation time of the goods at the i delivery point; Tfs represents the time required to deliver the goods; ta is the delivery departure time; 1/N represents the impact factor in the delivery process; and St is the arrival time of the goods. The customer importance index is expressed as:
(11)Sj=1NN−imj.In the formula,1/N represents the order of important customer goods; mj is the priority selection factor; N represents the importance degree division factor; and i is the quantity of priority customers.The hybrid intelligent algorithm proposed in this paper adopts a combination of deterministic selection and random selection in the strategy of determining the transfer path. That is, the ants can dynamically adjust the transition probability of the current state during the path search process. The calculation formula of the transition probability is as follows:(12)J=maxh∈Uikτihtα,ηihtβ,Ifq<q0,pijkt,Else.In the formula, a random number with a uniform distribution between (0, 1) is randomly generated before the path selection in(13)q0<0,1.If the random value is less than the thresholdq0, the largest one in τihtα,ηijtβ is selected from the set of feasible cities. The city where this maximum value is located is the next transfer path; otherwise, it is calculated according to the method of calculating the transfer probability in the basic ACO. The process is shown in the following formula:
(14)pijktτijtα⋅ηijtβ∑h∈Uikτijtα⋅ηijtβ.After determining the transition probability, this paper also introduces the concept of crowding degree in AFSA. The calculation formula of crowding degreeqij is shown in the following formula:
(15)qij=2τij∑i≠jτij.The key to the introduction of the congestion degree is to determine a threshold according to the actual situation of the problem and useδt to represent the congestion degree threshold at the moment of t, if the following formula is satisfied:
(16)qij<δt.It means that the current path is not too crowded, and the antk selects this path as the path to move in the next step. Otherwise, the ants reselect a random path within the feasible neighborhood to transfer. Among them, the congestion degree δt is updated as follows:
(17)δt=1−e−ct.At the same time, in the process of evolution, by introducing an information exchange mechanism, the information can be transmitted between the two populations, which helps individuals avoid wrong information judgment and fall into the local optimum point. A nonlinear dynamic adaptive inertia weight strategy is adopted to improve the performance of the algorithm. Its update status is as follows:(18)wt=wend+wstart−wend×exp−k×ttmax2.Among them,k is the control factor; it controls the smoothness of the change curve of w and t. Calculate the total path index:
(19)Sk=1Fn+1hy⋅j.In the formula,Sk represents the distance between the k distribution points; 1/F represents the return distance after the delivery is completed; hy⋅j is the adjustment coefficient of the total path; and n is the total path index value.Build an ant colony of a certain scale. From the starting point, each ant chooses the path to move to the next node according to the pheromone concentration of each path. The advantages and disadvantages of each path are reflected by the amount of pheromone released. Every ant’s transfer process is a solution, repeated and circulated until the best solution is found. In this paper, the pheromone concentration is updated after all ants have completed a complete optimization process. The pheromone-exerting mechanism weakens the influence of ants’ experience earlier in time. Due to the different emphasis on the distribution objectives of goods in logistics delivery centers, the distribution objectives are weighted. Before setting, the obtained objective function is dimensionless.VRP focuses on the path planning between a supplier andK sales points, which can be briefly described as: given one or more centers (central garages), a vehicle set, and a customer set, vehicles and customers have their own attributes, each vehicle has capacity, and the goods carried cannot exceed its capacity. In this paper, the “extreme difference” dimensionless processing method is adopted. By embedding the obtained data into the evaluation function, the comprehensive evaluation value can be obtained. For the problem of logistics delivery route, the smaller the comprehensive evaluation value, the better. However, this method is suitable for the situation where there are many alternatives. In the case of few schemes, the continuous elimination method can be implemented by comparing two schemes, and finally the best scheme can be selected. Minimizing the quantity of vehicles used is the first optimization goal, which has a higher priority. Therefore, the solution with less vehicles is always better than the solution with more vehicles, although this may lead to the increase of vehicle running costs. The delivery service of key users should try to ensure punctuality, so the penalty coefficient of deviation between service time and customer target time in delivery should be higher than that of ordinary users. The introduction of customer importance factors can highlight the important customer value in logistics delivery decision, give priority to ensuring its distribution service, and achieve the balance of customer satisfaction.


## 3.1. Logistics Distribution Management Information System

Whether the distribution path is reasonable or not directly affects the speed and cost of logistics delivery, selecting the path optimization goal is the premise of path planning. According to the specific distribution problems of customers, we can design a reasonable distribution scheme to optimize the route. This kind of scheduling belongs to the logistics delivery path optimization problem [22]. According to the different logistics constraints in reality, there are many models of VRP, among which: VRPTW is the most typical problem, and it is also a representative constrained multiobjective problem with the most research value at present. In order to reduce the operating cost of service providers, the logistics system will optimize the vehicle distribution route. Logistics delivery with high timeliness requirements can use the distribution management information system to obtain information such as roads and real-time road conditions through the traffic big data platform to manage and direct vehicles in transit for distribution; at the same time, customers can also inquire about vehicles and goods and feedback information through this platform. The application of big data in logistics delivery is shown in Figure 1.Figure 1
Application of big data in logistics delivery.The application of big data analysis in the freight field is the most common. It is mainly reflected in site selection optimization, inventory scale, supply route, and other activities. Data analysis can group customers of enterprises. Transportation and route selection are the most widely used fields of big data analysis in logistics management. Many enterprises use remote big data information processing technology loaded with GPS navigation to optimize freight transportation routes. The limitations of traditional optimization methods make it impossible to meet the complex requirements of multiconstraints and multiobjectives of path planning problems. At present, heuristic algorithm based on swarm intelligence is the main development trend to solve this kind of problems. Swarm intelligent algorithm is distributed, individual intelligence is not controlled by a unified subject, and it has strong robustness. Moreover, each individual can only perceive local information, so it is relatively simple to follow the rules and easy to implement the algorithm [23]. The intelligent group has the characteristics of self-adaptability, and the group can change its behavior at an appropriate time when the required cost is not too high. Heuristic algorithm is highly sensitive to VRP path, so its solution efficiency is also high. Its VRP is basically the same for different logistics companies. Therefore, heuristic algorithm can be used to plan the path, reduce the cost, consume the least resources, and get the maximum profit. AFSA is a new intelligent bionic algorithm based on the characteristics of fish activities.The optimization of logistics distribution path requires that the vehicle distribution route be arranged quickly and reasonably, so that the goods can be delivered to the customers in time and accurately, and the distribution cost is the lowest. Soft time window means that if the delivery vehicle cannot start service within the time required by the customer, it must be punished accordingly. The meaning of hard time window is that if the delivery vehicle cannot start service within the time required by the customer, the solution is not feasible. The optimization goal is to quickly find a distribution strategy by obtaining real-time road congestion information, building a mathematical model and adopting appropriate algorithms according to the existing resources and customer demand. For the processing of optimization problems, because each logistics delivery route optimization problem faces different situations, it is necessary to design a general optimization algorithm to solve it. Therefore, based on big data, we can simulate the route distribution status in various situations, integrate these distribution statuses, and establish a tracking optimization algorithm to calculate the specific loss of distribution.


## 3.2. Optimization Algorithm of Mixed Population Logistics Delivery Route

In this paper, the time window of logistics delivery problem is set as a special time window, which is a time interval, and the distribution vehicles need to deliver the materials to the material demand points in advance or on time within this time window. At the same time, this paper adopts the two-population strategy, and the combination of ACO and differential evolution in the first population can solve the parameter optimization problem well. Secondly, the ant colony hybrid PSO is adopted in the population, which enhances the global search ability in a wide range and solves the problems of slow convergence and easy falling into local optimum. The flow chart of logistics and route design is shown in Figure2.Figure 2
Logistics delivery and route design process.A single objective optimization model is established to minimize the total vehicle transportation cost, as shown in(1)Z=min∑i∑j∑kCijxijki≠j,where Z stands for the total cost; i and j represent any two points; k represents any transport vehicle; and Cij represents the transportation cost from point i to point j. The variable xijk is defined as follows:
(2)xijk=1,Thetransportationtaskfromitojiscompletedbyk,0,Otherwise.Considering the actual situation, this paper puts forward three optimization objectives. That is, the shortest delivery time, the shortest driving distance of all delivery vehicles, and the least cost, and the established optimization model is shown in(3)minZ1=∑i∑j∑kTijxijkTheshortesttime,minZ2=∑i∑j∑kDijxijkTheshortestdistance,minZ3=∑i∑j∑kCijxijkTheleastcost.The establishment of the model is based on certain assumptions: the travel time, distance, and the demand of consumers between any two points can be known, that is, the distribution model under certain conditions.Letm be the quantity of ants in the ant colony; dij is the distance between the city i and j; ηijkt=1/dij is the heuristic function; τij is the amount of information on the path i,j at the moment t; pijkt means that the ants k move from city i to city at time t the probability of j. The formula is as follows:
(4)pijkt=τijtα⋅ηijtβ∑s∈allowedkτistα⋅ηistβ,j∈allowedk,0,Otherwise,(5)tabukk=1,2,⋯,m.Among them,j is the city that has not been visited yet; allowedk=C‐tabuk is the city that the ant k is allowed to choose next; α and β are heuristic factors; tabuk is used to record the city that the ant k has walked through at the moment of t. The ant is not allowed to repeatedly pass through this cycle, and the taboo table is cleared after the end of this cycle. The ant completes a cycle and updates each path pheromone:
(6)τijt+n=1−ρ⋅τijt+Δτijt,(7)Δτijt=∑k=1mΔτkijt.Among them,ρ∈0,1 represents the pheromone volatilization coefficient; 1‐ρ represents the pheromone residual factor; Δτij represents the information amount increment on the path ij in this cycle. Initially, Δτij=0; Δτijk represents the amount of information left by the ant k between cities i and j in this cycle. The formula is as follows:
(8)Δτijkt=QLk,Ifthekthantpassesthroughi,jinthiscycle,0,Otherwise.Among them,Lk represents the path length of the ant k to travel around; Q is a constant. In the ACO, the parameter selection method and selection principle directly affect the computational efficiency and convergence of the ACO.In the process of e-business logistics delivery, the weight of the goods is a factor that must be considered. In general, goods with heavy weight should be dispatched first to reduce fuel consumption during the delivery process. The weight index is expressed as:(9)Sg=∑ifg−itu.In the formula,Sg represents the quantity of locations that need to be delivered; ∑if represents the weight of the delivered goods; g is the order of locations for logistics delivery; i is the weight of the goods to be delivered at the i location; and tu is the weight index calculation factor. The establishment of the timeliness index reflects the timeliness requirements of the goods, calculated as follows:
(10)St=1Nta−tiTfs.In the formula,ti represents the preservation time of the goods at the i delivery point; Tfs represents the time required to deliver the goods; ta is the delivery departure time; 1/N represents the impact factor in the delivery process; and St is the arrival time of the goods. The customer importance index is expressed as:
(11)Sj=1NN−imj.In the formula,1/N represents the order of important customer goods; mj is the priority selection factor; N represents the importance degree division factor; and i is the quantity of priority customers.The hybrid intelligent algorithm proposed in this paper adopts a combination of deterministic selection and random selection in the strategy of determining the transfer path. That is, the ants can dynamically adjust the transition probability of the current state during the path search process. The calculation formula of the transition probability is as follows:(12)J=maxh∈Uikτihtα,ηihtβ,Ifq<q0,pijkt,Else.In the formula, a random number with a uniform distribution between (0, 1) is randomly generated before the path selection in(13)q0<0,1.If the random value is less than the thresholdq0, the largest one in τihtα,ηijtβ is selected from the set of feasible cities. The city where this maximum value is located is the next transfer path; otherwise, it is calculated according to the method of calculating the transfer probability in the basic ACO. The process is shown in the following formula:
(14)pijktτijtα⋅ηijtβ∑h∈Uikτijtα⋅ηijtβ.After determining the transition probability, this paper also introduces the concept of crowding degree in AFSA. The calculation formula of crowding degreeqij is shown in the following formula:
(15)qij=2τij∑i≠jτij.The key to the introduction of the congestion degree is to determine a threshold according to the actual situation of the problem and useδt to represent the congestion degree threshold at the moment of t, if the following formula is satisfied:
(16)qij<δt.It means that the current path is not too crowded, and the antk selects this path as the path to move in the next step. Otherwise, the ants reselect a random path within the feasible neighborhood to transfer. Among them, the congestion degree δt is updated as follows:
(17)δt=1−e−ct.At the same time, in the process of evolution, by introducing an information exchange mechanism, the information can be transmitted between the two populations, which helps individuals avoid wrong information judgment and fall into the local optimum point. A nonlinear dynamic adaptive inertia weight strategy is adopted to improve the performance of the algorithm. Its update status is as follows:(18)wt=wend+wstart−wend×exp−k×ttmax2.Among them,k is the control factor; it controls the smoothness of the change curve of w and t. Calculate the total path index:
(19)Sk=1Fn+1hy⋅j.In the formula,Sk represents the distance between the k distribution points; 1/F represents the return distance after the delivery is completed; hy⋅j is the adjustment coefficient of the total path; and n is the total path index value.Build an ant colony of a certain scale. From the starting point, each ant chooses the path to move to the next node according to the pheromone concentration of each path. The advantages and disadvantages of each path are reflected by the amount of pheromone released. Every ant’s transfer process is a solution, repeated and circulated until the best solution is found. In this paper, the pheromone concentration is updated after all ants have completed a complete optimization process. The pheromone-exerting mechanism weakens the influence of ants’ experience earlier in time. Due to the different emphasis on the distribution objectives of goods in logistics delivery centers, the distribution objectives are weighted. Before setting, the obtained objective function is dimensionless.VRP focuses on the path planning between a supplier andK sales points, which can be briefly described as: given one or more centers (central garages), a vehicle set, and a customer set, vehicles and customers have their own attributes, each vehicle has capacity, and the goods carried cannot exceed its capacity. In this paper, the “extreme difference” dimensionless processing method is adopted. By embedding the obtained data into the evaluation function, the comprehensive evaluation value can be obtained. For the problem of logistics delivery route, the smaller the comprehensive evaluation value, the better. However, this method is suitable for the situation where there are many alternatives. In the case of few schemes, the continuous elimination method can be implemented by comparing two schemes, and finally the best scheme can be selected. Minimizing the quantity of vehicles used is the first optimization goal, which has a higher priority. Therefore, the solution with less vehicles is always better than the solution with more vehicles, although this may lead to the increase of vehicle running costs. The delivery service of key users should try to ensure punctuality, so the penalty coefficient of deviation between service time and customer target time in delivery should be higher than that of ordinary users. The introduction of customer importance factors can highlight the important customer value in logistics delivery decision, give priority to ensuring its distribution service, and achieve the balance of customer satisfaction.


## 4. Result Analysis and Discussion

The urban logistics distribution path planning problem is essentially a vehicle path optimization problem, which can be defined as: under the condition that the distribution center and the customer point are known, find an optimal vehicle distribution path scheme, and deliver the goods to the customer within the specified time, usually with the goal of minimizing the distribution cost. In order to verify the rationality of the proposed model and the effectiveness of the solution algorithm, this section simulates the proposed model and algorithm. Test question bank by simulating VRPTW standard. In VRPTW, test data including 25, 50, and 100 customer nodes are set according to the scale of problem solving, and it is agreed that each demand point of goods has corresponding time window constraint and corresponding demand of goods. Moreover, it is assumed that each cargo transportation task point in the distribution network has corresponding time window constraints and certain demand, and the maximum load capacity of each vehicle is given. The actual running time of vehicles between customers is completely determined by the physical distance between customers. Firstly, the performance of the two-population hybrid algorithm is tested by using 10 city outlets. The quantity of ants is 100, the quantity of iterations is 500, the heuristic factors are 1 and 2, and the pheromone volatilization coefficient is 0.3. In this section, under the Windows operating system, the simulation experiment of model realization and algorithm solution is carried out with Matlab software. The specific experimental environment is shown in Table1.Table 1
Experimental environment.
Hardware environmentPentium DOperating systemWindowsImplementation softwareMatlabWeb serverIIS5.1Programming languageC#Database systemAccessHard disc1 TDisplay card512 GThe soft time window means that if the delivery vehicle fails to start service within the time required by the customer, a certain amount of compensation will be paid; the longer the delay, the more compensation you have to pay. If the delivery vehicle is earlier than the earliest start time required by the customer, additional waiting time will be generated, which will affect the rest of the delivery staff’s work arrangement and their salary. In this paper, the total transportation area is divided according to the constraints such as vehicle load, and then, the optimal transportation route is designed in the divided subareas. This can reduce the space of single optimization search, greatly reduce the amount of calculation, and improve the speed and accuracy of solution. The convergence curve pairs of the algorithm are shown in Figure3 below.Figure 3
Comparison of convergence curves of algorithms.The distance between customer nodes in the distribution network is calculated by the Euclid distance formula of two-point coordinates, and it is assumed that the running time of vehicles between two points is equal to the transportation distance. The purpose of the test is to test whether the HSIA proposed in this paper can achieve the optimal distribution path and test the related performance of the HSIA. The MSE (mean-squared error) of the algorithm is shown in Figure4. RMSE (root mean square error) of the algorithm is shown in Figure 5. The MAE (mean absolute error) of the algorithm is shown in Figure 6.Figure 4
MSE test results.Figure 5
RMSE test results.Figure 6
MAE test results.In order to reflect the test results more intuitively, this paper draws the test results of various errors in the above figure into tables. Table2 shows the error comparison of each algorithm.Table 2
Comparison of errors of each algorithm.
AlgorithmMSERMSEMAEPSO5.1890.5511.578Tabu search algorithm6.2540.7682.754Simulated annealing algorithm6.1920.6512.657Algorithm in this paper4.0540.5091.465In this paper, a delivery route optimization model based on differentiated satisfaction is proposed. Through customer set division, key customers, ordinary customers, and both customers are distinguished. The differentiated satisfaction of different customer roles is used to participate in the decision-making in route optimization to improve the satisfaction of key customers of enterprises, and a balanced route scheme with lower transportation cost is produced. The calculation results of the algorithm are shown in Figure7.Figure 7
Calculation results of the algorithm.In this paper, the hybrid population algorithm absorbs the advantages of different algorithms, and it reaches the best solution the most times, which increases the probability of the best solution. In addition, because of the communication mechanism in different populations, the algorithm improves the search efficiency of populations.The algorithm proposed in this paper is carefully tested on other examples in Solomon standard test data source. In order to make the test results more accurate and reliable, each instance is operated 20 times under the same hardware and software configuration, and the average of these operation results is taken as the running result of the algorithm and compared with the settlement results of other algorithms. The comparison of search efficiency of the algorithm is shown in Figure8.Figure 8
Comparison of search efficiency of algorithms.It can be seen that there is a big difference in running time between HSIA and PSO for path optimization. At the same time, the PSO has some shortcomings, such as slightly insufficient search precision and accuracy, and high-dependence on parameter setting. As a result, the total length of the optimal path searched by the PSO is farther than the search result of the hybrid algorithm.An example is used to test the performance of the HSIA, and the results are compared with those of other algorithms. The experiment was conducted independently for 50 times, and the statistical results are shown in Table3.Table 3
Comparison of time consumption of different algorithms.
IndexPSOTabu search algorithmSimulated annealing algorithmAlgorithm in this paperBest solution676662669672Worst solution689697696681Average value681690688678The quantity of times to reach the best solution155921The results show that, although other algorithms can improve the convergence speed, there are many worst solutions obtained by the algorithm, which indicates that the algorithm is easy to converge to the local minimum solution. This paper can improve the global optimization ability of the algorithm, get a better solution, and be relatively stable. The AC comparison of the algorithm is shown in Figure9.Figure 9
AC comparison of algorithms.Test results show that the AC of this algorithm is 95.08%, which is higher than that of traditional PSO and general heuristic algorithm. In this paper, the advantages of different algorithms are taken into account at the same time, and the crowding degree of fish school is introduced into the iterative process of ACO. When the initial feasible solution is obtained by using artificial fish school, the ability of the algorithm to obtain the global optimal solution is improved by gradually changing the crowding degree. Therefore, the HSIA proposed in this paper does have strong global optimization ability. The test results in this section fully demonstrate that our algorithm has certain advantages in performance. It can be completely applied to the optimization of logistics delivery path.Based on the above experimental results, it can be seen that the e-commerce logistics distribution path optimization algorithm under the big data background designed this time can save a lot of logistics distribution costs compared with the traditional algorithm. It conforms to the economic effectiveness of e-commerce logistics distribution path optimization. Compared with the actual optimal path, the error values of the path optimized by the e-commerce logistics distribution path optimization algorithm are lower than those of the traditional algorithm. The above experimental results show that the path optimized by the e-commerce logistics distribution path optimization algorithm is more consistent with the actual optimal path. The accuracy of the e-commerce logistics distribution path optimization algorithm is verified.


## 5. Conclusions

With the growth of the Internet, the growth of e-business has also been advanced by leaps and bounds. In the current environment, the logistics industry must keep pace with the growth of the Internet and actively innovate and shorten the distribution route, which can significantly reduce the logistics cost. This plays an important role in reducing material loss and improving benefits. Based on this, this paper deeply discusses the application of swarm intelligence optimization algorithm in logistics delivery path optimization under the background of big data. In this paper, under the constraints of time window, delivery vehicles, and customer demand, the specific delivery requirements and delivery time of each logistics branch are obtained through big data, and based on this information, the distribution is unified, and the distribution route is planned. In this paper, in order to apply the improved algorithm to solve VRPTW, the hybrid algorithm is discretized, and a local path optimization operator is introduced. At the same time, the concept of crowding degree in the AFSA is introduced into the ACO. In the early stage of the optimization process, a strong crowding degree limit is set to ensure that most ants are not affected by the pheromone concentration to conduct random optimization. Test results show that the AC of this algorithm is 95.08%, which is higher than that of traditional PSO and general heuristic algorithm. The algorithm achieves the best solution the most times and increases the probability of the best solution. The test results of this paper fully show that the algorithm in this paper has certain advantages in performance. It can be completely applied to the optimization of logistics delivery path. However, when the algorithm is applied in practice, it should be constantly updated with the growth of urban roads.



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