Logistics Distribution Path Optimization Using Support Vector Machine Algorithm under Different Constraints

Abstract

Accelerating product flow, improving service level, lowering logistics costs, reducing the possibility of product losses in circulation, and thus optimizing the logistics distribution system are the issues that enterprise managers should consider in logistics distribution. Traditional algorithms can only solve simple problems, while intelligent algorithms can solve the most complex combinatorial optimization problems. The optimization problem of logistics vehicle scheduling path with different constraints is studied in this paper using the SVM algorithm, and the improved algorithm is simulated to verify its effectiveness. The simulation results show that the logistics distribution path optimization method based on the SVM algorithm has good global searching ability, effectively avoids the algorithm falling into local optimum, and reduces total distribution cost, proving the algorithm’s effectiveness. This scheme can optimize vehicle routes, increase distribution efficiency, and reduce logistics costs, and it can be used in a wide range of logistics distribution route optimization applications.

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1. Introduction

With the development of market globalization and economic informatization, international trade exchanges are becoming increasingly prosperous and market competition is becoming increasingly fierce. Higher requirements for resource allocation efficiency are imposed by interregional resource integration [1]. It is the storage, transportation, and distribution of goods, or the movement or circulation of goods. Traditional logistics and distribution methods are inefficient, but they have high distribution costs, and meeting people’s demands for fast and efficient distribution is difficult [2]. The physical displacement of transporting goods to customers by vehicles and other modes of transportation at a specified time is the central task of logistics distribution [3]. The upstream suppliers in a logistics system can be factories, for example, and the downstream users can include wholesalers and retailers. Upstream and downstream businesses can be effectively connected through distribution. Because of its ability to tap the third profit of enterprises and its important role in improving service quality, modern logistics has become a key factor in improving core competitiveness of businesses [4]. With the acceleration of the process of urban modernization, the scale of the city is constantly expanding, and the number of motor vehicles and road traffic are rapidly increasing, which brings about a series of urban traffic problems such as traffic congestion, congestion, and environmental pollution [5]. In today’s society, the rapid development of information technology has accelerated the pace of economic globalization and made more and more economic cooperation close and diversified. Information-based logistics technology can help logistics enterprises make decisions, thus shortening the distribution time, improving the distribution efficiency, and reducing the transportation cost.

The essence of logistics is the transportation process of commodities. It plays a very important role in the logistics system by allocating all links of transportation to deliver commodities from producers to consumers [6]. The quality of distribution service is directly related to the interests of consumers, thus affecting consumers’ satisfaction with enterprises, and has an invisible influence on the market competitiveness of enterprises [7]. Reasonable optimization of logistics distribution path can save costs, speed up the circulation of goods, and increase the profits of logistics enterprises. The good development of logistics industry cannot be separated from logistics planning, which is based on the analysis and prediction of logistics demand [8]. In the logistics system, accelerating the flow of products, improving the service level, reducing the logistics cost, reducing the possible losses of various products in circulation, and thus optimizing the logistics distribution system are the issues that enterprise managers should consider in logistics distribution [9]. Informatization and systematic distribution mode can save logistics transportation and distribution costs, save distribution resources, reduce costs, and create good economic benefits [10]. As far as the current logistics system is concerned, in the process of distribution, the unreasonable vehicle configuration and distribution path make the logistics system work inefficiently, and, at the same time, it also affects the benefit distribution of enterprises [11]. In this paper, based on the Support Vector Machine (SVM) algorithm, the logistics Vehicle Routing Problem (VRP) with different constraints is studied, and the improved algorithm is simulated to verify the effectiveness of the algorithm.

Diversified customer demand, traffic and transportation road conditions, and other factors all influence logistics and distribution vehicle route optimization [12]. Logistics cost [13] is the necessary cost of the logistics distribution process, which is primarily composed of transportation cost, classification processing cost, and distribution cost H. The transportation cost, which includes the related transportation cost as well as the driving cost of the vehicles involved in the distribution, is the most significant logistics cost. As a result, lowering the transportation cost of vehicles participating in distribution lowers the logistics cost of the logistics distribution process, improving enterprise operation efficiency [14]. It is a realistic problem that enterprise managers should first consider to adopt a reasonable logistics distribution scheme to improve the operational efficiency of enterprises. The routing optimization of distribution vehicles in the logistics system can be simplified to VRP through certain ideal assumptions [15]. The goal of logistics is to pursue efficient, low-cost, and rational use of resources, manage logistics management with dynamic information, and guide the logistics industry to make reasonable decisions. Compared with traditional learning methods, SVM has no local minimum problem, and it is difficult to choose the number of hidden nodes. Moreover, this method does not depend on the mathematical model of the system and at the same time has the characteristics of self-learning and self-adjusting model, which can produce better prediction results for various chaotic systems. Effective logistics distribution can save transport vehicles, ease urban traffic, reduce air pollution caused by transport vehicles, and contribute to the protection of ecological balance.

2. Related Work

The method of stepwise linear regression was used to forecast highway freight volume in the literature [16], and the model’s validity was verified through examples. The method of minimum description length was used in literature [17] to determine the best Neural Network (NN) forecasting model, which provided more accurate logistics demand forecasting and proved that the model is suitable for any data. The vehicle scheduling problem with specified requirements is studied in [18, 19], and particle swarm optimization is used to solve it. From the perspective of traditional VRP, literature [20] proposes a model based on the dual satisfaction of employees and customers and devises a hybrid algorithm to solve it. The vehicle route optimization model of urban distribution is proposed in literature [21] based on the calculation of vehicle travel time between nodes of the distribution network. The example solution demonstrates that, in the vehicle route model, considering the time and space of vehicle speed can better describe the practice of urban logistics distribution. Literature [22] compares the requirement that VRP can be split continuously with the requirement that demand points’ requirements are composed in discrete form and establishes a mathematical model of discrete split VRP. The number of vehicles and the driving distance are chosen as the objectives in literature [23], and the open VRP, multiyard, and multiobjective logistics distribution problem is solved using a genetic algorithm and a saving algorithm. The results show that the improved algorithm outperforms the genetic algorithm in terms of robustness. In the literature [24], tabu search was used in parallel to achieve VRP with similar clustering solutions, and each optimal solution was essentially obtained by asynchronous cooperation between tabu search and a basic solution set. In literature [25], considering the fuel consumption of vehicles, the mathematical model with the minimum fuel consumption as the objective was solved by particle swarm optimization. Literature [26] studies the common Vehicle Routing Problems in road freight transportation, especially those related to reverse logistics, considering the fuel consumption and carbon emission costs in the model.

Through the study of the previous vehicle scheduling problems, it is found that basically the number of cargo delivery points is fixed, and a vehicle only passes through one cargo transportation point. In this paper, a vehicle routing optimization model based on SVM algorithm is established by imposing constraints on standard VRP, in order to shorten the solution time and improve the solution quality, and the correctness and effectiveness of the algorithm are analyzed by simulation results.

3. Materials and Methods

3.1. Distribution of VRP in Logistics System

Logistics demand is a derivative demand. However, social development cannot be separated from economic activities [27]. Logistics demand widely exists in daily activities such as economic development, population increase, consumption level improvement, and technology upgrading, resulting in various forms of movement of personnel, materials, funds, information, and so forth, which forms the objective basis for the universal existence of logistics. The basic elements of logistics are shown in Figure 1.

[figure omitted; refer to PDF]

There are many vehicles, road sections, intersections, and traffic engineering facilities in the urban traffic system. People and vehicles moving in traffic have the ability to self-organize, adapt, and drive themselves. The urban traffic system is a complex network system because there is nonlinear interaction between moving vehicles in the road network. Theoretically, distribution of VRP in a logistics system is as follows: given the location of a distribution center and the specific locations of a series of customers with specific demands, the number of vehicles in the distribution center and the maximum capacity of each vehicle are known. Vehicles depart from the distribution center under the condition that they meet constraints such as customer demand, and each vehicle returns to the distribution center after visiting the customer points corresponding to the goods it transports [28]. We are going to assume that each car’s speed is the same. This process necessitates making reasonable design arrangements in order to achieve the goals of shortest distance and fewest vehicles used, thereby lowering enterprise logistics and distribution costs. Calculating the road weight in a traffic network and obtaining information that can represent the characteristics of an urban traffic network can be used as a reference for logistics distribution and distribution route planning. Therefore, the determination of road weight is an important research issue of traffic route optimization. The multistage response cycle model of logistics supply chain is shown in Figure 2.

[figure omitted; refer to PDF]

Scientific vehicle routing can speed up the response of service to meet customer demand and improve customer satisfaction with logistics, thereby improving the service quality and reducing the operating cost of service providers. If the vehicle route or scheduling scheme is unreasonable, it will have a negative impact on the production and operation of enterprises, such as the slow response speed and the decline of customer satisfaction, as well as low vehicle load rate and high logistics cost. Excellent vehicle dispatching system can not only improve the execution efficiency and service quality but also play an important role in the utilization and allocation of social resources. By abstracting practical problems and based on certain assumptions, we set up various mathematical models of VRP. Through the analysis and solution of the model, a scientific and reasonable vehicle path planning can be worked out, so as to improve the whole logistics transportation speed, effectively link production and consumption, and solve the contradiction in space.

The standard VRP is the Capacitated Vehicle Routing Problem (CVRP), and each service vehicle is equipped with a load attribute, which specifies the maximum transportation capacity of the vehicle. Each vehicle has a maximum load limit. CVRP is one of the basic models of VRP, from which VRP with different conditions can be derived, which is suitable for different practical problems of enterprises. For the whole logistics system, there are many factors that affect the optimization of distribution vehicle scheduling. Therefore, VRP in the logistics system can be divided into different types according to its influencing factors. The relationship between logistics capability and supply chain performance is shown in Figure 3.

[figure omitted; refer to PDF]

Non-full-load problem means that the customer demand is far less than the transportation capacity limit of the vehicle, the same vehicle can provide distribution services for multiple customers, and the vehicle is in a non-full-load state during the distribution process. Full-load type means that the customer’s demand is greater than or equal to the cargo capacity of the vehicle, and one or more vehicles need to cooperate to complete a task, and the vehicle is in a full-load state during the distribution process. The problem model of the two situations mentioned above is the mixed problem of nonfull load and full load. The transportation capacity of vehicles can only meet the needs of some customers, so some vehicles are not full load while others are full load, and the two states exist at the same time.,

VRP is a complex combinatorial optimization problem with many components and types which is difficult to solve. It can only solve the global optimization of small-scale VRP optimally at the moment. Although different from precise mathematical means, heuristic algorithms based on specific information from specific problems or natural metaphors can obtain suboptimal or feasible VRP solutions in a short amount of time and have gradually become the focus of scholars’ research.

Multiple distribution centers as a VRP problem mean that multiple distribution centers are distributed according to certain conditions in the logistics system, and multiple distribution centers coordinate and dispatch distribution tasks in the logistics system. In theory, the method of creating virtual distribution centers and merging multiple distribution centers into a single distribution center is commonly used to solve such problems. The main principles of urban logistics distribution traffic path planning simulation are creating a road weight function model that accounts for traffic flow and driving time, predicting the traffic flow of the distribution path, and determining the road weight by substituting the predicted value of traffic flow into the road weight function model.

3.2. Optimization of Logistics Distribution Path Based on SVM Algorithm

Compared with traditional learning methods, SVM has no local minimum problem, and it is difficult to choose the number of hidden nodes. This method does not depend on the mathematical model of the system and at the same time has the characteristics of self-learning and self-adjusting model, which can produce good prediction results for various chaotic systems. Besides robustness, SVM is globally unique and sparse, which avoids the problem that there may be multiple local optimization solutions in NN. Moreover, the complexity of the problem does not depend on the dimension of features, and it has better generalization ability than NN, so it is becoming a research hotspot after NN.

Certain principles usually guide the distribution route (such as the principle of reducing cost, economic benefit, and improving customer service level). Some schemes are preselected and then compared using various methods, and, finally, one or more satisfactory schemes are chosen as the new distribution route. The travel time is one of the many indicators used by relevant professionals and the general public to reflect the logistics distribution route because it is simple to comprehend and calculate. As a result of the important metric of travel time, the optimal goal is determined as the delivery personnel’s shortest travel time. If the length of the road section under consideration is L and the road section’s driving time is the road weight, the road section’s road weight function is as follows:$$\begin{array}{}\text{(1)}& T=\frac{L}{VQ}.\end{array}$$

In the above equation, Q is the traffic volume, and $VQ$ is the average driving speed of the road section corresponding to the traffic volume Q. T is the time required to pass through section L when the traffic volume is Q.

The key to solving this model is to find the relationship between the traffic volume Q and the average road speed $V$. Traffic flow Q, driving speed $V$, and traffic density K are three basic parameters that characterize the characteristics of traffic flow, and the relationship is as follows:$$\begin{array}{}\text{(2)}& Q=V\ast K.\end{array}$$

Under normal traffic conditions, the relationship between speed and density can be expressed by the following formula:$$\begin{array}{}\text{(3)}& K=K_m-\frac{K_m}{V_m}V,\end{array}$$

where $V_m$ is the unobstructed speed and $K_m$ is the blocking density. It can be derived from the above formula that$$\begin{array}{}\text{(4)}& Q=K_{m}V-\frac{K_m}{V_m}{V}^2,\end{array}$$

and when the flow rate Q satisfies $0\le Q\le K_m{V}_m/4$, the relationship between the speed $V$ and the flow rate Q can be deduced.$$\begin{array}{}\text{(5)}& V=\frac{V_m}{2}\pm \frac{1}{2}\sqrt{V_m^2-\frac{4V_m}{K_m}Q}.\end{array}$$

The difficulty of the simulation principle model can be seen through analysis in the prediction of traffic flow. The road weight can be calculated when the traffic flow in a given period can be predicted. The specific algorithm is presented in the following section.

Using the relationship between travel time and traffic flow, a road weight function model for the logistics distribution section is created. The residual error is used to correct the predicted value after the model has predicted the traffic flow. The SVM model is proposed to predict the positive and negative residual error during the correction process.

Given the sample data set ${x_i,y_i}_{i=1}^N$, $x_i\in R$ is the input vector, $y_i\in R$ is the output vector, and N is the number of training samples. The goal is to find a function $fx$ that can better approximate all sample points. By defining an appropriate kernel function $k{x}_i,x_j=\varphi x_i•\varphi x_j$, the input sample space is nonlinearly transformed into the feature space for linear regression estimation. The estimation function of the support vector regression machine is expressed as$$\begin{array}{}\text{(6)}& fx={\omega }^T•\varphi x+b.\end{array}$$

In the above equation,, ω is the weight vector, b is the threshold, and $•$ represents the inner product operation. The standard SVM regression algorithm can be described as the following problem:$$\begin{array}{c}\text{(7)}& \underset{\omega ,b,{\xi }_i{\xi }_i^{\ast }}{{\displaystyle \min }}\frac{1}{2}{\omega }^T\omega +c{\displaystyle \sum _{i=1}^n{\xi }_i+{\xi }_i^{\ast }},\text{(8)}& s.t.y_i-{\omega }^T•\varphi x_i+b\le \epsilon +{\xi }_i,{\omega }^T•\varphi x_i+b-y_i\le \epsilon +{\xi }_i,\\ {\xi }_i,{\xi }_i^{\ast }\ge 0,\hspace{1em}i=\mathrm{1,2},\dots ,i.\end{array}$$

In formula (7), ${\xi }_i$ and ${\xi }_i^{\ast }$ are slack variables, which indicate the degree of deviation of the data points. C > 0 is the penalty coefficient, and ε is the loss function. By introducing the auxiliary variable Lagrangian multiplier ${\alpha }_i$, ${\alpha }_j$ transforms the above-mentioned constrained optimization problem into an unconstrained optimization problem. At the same time, the kernel function $k{x}_i,x_j=\varphi x_i·\varphi x_j$ is introduced, and the solution of (7) is transformed into the following dual problem:$$\begin{array}{}\text{(9)}& \max Q\alpha ,\varphi x_i={\displaystyle \sum _{i=1}^l{\alpha }_i{\alpha }_j{y}_i{y}_{j}k{x}_i,x_j},\text{(10)}& s.t.0\le {\alpha }_i\le C& {\displaystyle \sum _{i=1}^n{\alpha }_i{y}_i=0}.\end{array}$$

Equation (9) is a quadratic optimization problem under inequality constraints, with a unique solution ${\alpha }_i$, and ${\alpha }_j$ is the solution to the quadratic optimization problem.

The evaluation function is used to evaluate the further optimized solution. In SVM algorithm, the evaluation function is used by memory criterion and amnesty criterion to select the new current state. In practical application, the evaluation function is selected according to the constraints and objectives of the research problem. Generally, the objective function of solving the problem and its deformation can be used as the evaluation function. If the calculation of the objective function is difficult or time-consuming, an integral eigenvalue reflecting the problem objective can also be used as the evaluation value. At this time, it is necessary to ensure the consistency between the optimal eigenvalue and the optimal objective function.

4. Result Analysis and Discussion

Neighborhood structure design is frequently required to address specific issues. Insertion, exchange, and reverse order are commonly used in adaptive memory algorithms. Different operations will result in a different number of neighborhood solutions or even different changes, which will have a significant impact on the efficiency of search quality. The candidate solution is chosen based on its proximity to the current state; however, too many options will increase the amount of computation required, whereas too few options will easily lead to premature convergence. To optimize the entire neighborhood, however, a lot of calculations are often required. As a result, the size of specific data, the characteristics of visual problems, and algorithm requirements all play a role in the selection of candidate solutions in some neighborhoods.

In the experimental section, two groups of data are chosen based on different traffic flow data characteristics in order to verify the effectiveness of the improved road weight determination method presented in this paper. Training and test sets are created from the experimental data. The training set consists of the first 20 data items, the test set of the last 20 data items, and the 21st data item is mostly predicted. Figure 4 shows the results of the tests.

[figure omitted; refer to PDF]

The first 19 data items are used as training sets and the last 2 data items are used as test sets, and the 20th and 21st data items are mainly predicted. The test results are shown in Figure 5.

[figure omitted; refer to PDF]

It can be seen from Figures 4 and 5 that SVM prediction model can obtain more effective prediction results than CM(1,1) model, and the predicted value is closer to the actual value. The experimental results of this algorithm under different combination parameters are studied, and the algorithm evolution curve is obtained, as shown in Figure 6.

[figure omitted; refer to PDF]

Experiments show that the optimal path obtained by the adaptive ant colony algorithm is better than the basic ant colony algorithm under various parameters. Moreover, the global searching ability and convergence speed of this algorithm are improved, and it is an effective solution method.

In an information system, all attributes are not equally important, and some are even redundant. Therefore, removing redundant attributes and obtaining simpler decision rules is one of the basic problems of rough set theory. The results show that it is necessary to reduce attributes before SVM regression. Eliminating redundant attributes from the sample matrix can effectively reduce the root mean square error, increase the square correlation coefficient, and reduce the program operation time. In this paper, some cases are selected for experiments, and the evolutionary process of this algorithm is shown in Figure 7.

[figure omitted; refer to PDF]

The customer nodes are clustered using a density-based clustering algorithm, which means that customer nodes with a higher density in spatial distribution form a cluster and are delivered by the same car. A virtual customer, whose customer demand is the sum of the actual customer node demand in the corresponding cluster, and whose position coordinates are the geometric center of the actual customer node positio, can be used to replace a cluster. A small number of virtual customers replace a sample of large-scale actual customer nodes, greatly reducing the scale of problem solving. Figure 8 depicts an evolutionary comparison of the basic ant colony algorithm, MMAS algorithm, and this algorithm’s calculation process.

[figure omitted; refer to PDF]

It can be concluded from Figures 7 and 8 that the algorithm in this paper can get the optimal solution in a short time, and it takes less time to search the optimal path. When solving VRP with soft time window constraints, we need to consider one more variable-penalty cost. In VRP with hard time window, the service time of vehicles to customers must start within the time window, and opportunity cost and late penalty are not allowed. On this basis, we should consider the actual situation and complete all tasks with the minimum number of vehicles and the minimum total distance of vehicles.

The experimental data in Figure 9 comes from the statistics of the traffic volume of a certain place in one day. The traffic volume of motor vehicles in rush hour is observed by manual counting method, and the traffic volume observation table of this road section in different periods is established according to the flow direction. With a time interval of 10 minutes, it is divided into 8 investigation periods to record the traffic volume for 1 hour. The first six groups of data are used to predict the second two groups of data, and the test results are shown in Figure 9.

[figure omitted; refer to PDF]

The experimental results show that the predicted results of the optimized model are closer to the distribution of the actual values. The predicted value of this algorithm shows the same change rule as the actual value, and it is closer to the real value.

There are many influencing factors on the location of distribution center. According to the principles of logistics and the actual situation, some of the more important factors can be selected as decision indicators. These factors can be roughly divided into natural environment, transportation conditions, business environment, candidate site conditions, and public facilities. The quality of index selection is very important for correct decision-making. In logistics and distribution, distribution personnel are often unable to grasp a large number of effective and referential historical data, which makes the regression model often ineffective. How to effectively predict the road condition has become an important research topic. At the same time, the process of logistics and distribution is easily affected by various disturbances, which makes the logistics and distribution system highly uncertain.

In this paper, starting from practical problems, under the constraints, vehicles start from one or more distribution centers and pass through several randomly distributed distribution points in turn, so that each distribution point has only one vehicle to provide services. The solution of VRP aims at designing the most reasonable path and making the distribution cost the lowest. This paper compares and analyzes the optimal path, path length, driving route map, and so forth. In the same maximum number of iterations, the algorithm in this paper has higher full load rate and shorter total distance, and the driving route can intuitively reflect that the optimal path found by the improved algorithm is more reasonable. The experimental results fully show that the algorithm in this paper has stronger global searching ability and higher execution efficiency and can find a better vehicle route on the basis of satisfying the constraint conditions. From a realistic point of view, this algorithm can save the distribution cost to the greatest extent and improve customer satisfaction.

5. Conclusions

The demand for regional logistics will almost certainly increase rapidly as a result of the national policy of revitalizing the logistics industry. The goal of urban logistics distribution traffic path planning is to choose the most efficient distribution route, reducing distribution time and cost. In the selection of urban logistics distribution routes, establishing the road weight function model is crucial. The distribution route features are not fixed because of the uncertainty of traffic flow in the distribution section. In the case of small samples, the traditional modeling method of predicting traffic flow and road weight is difficult, resulting in large modeling errors. In this paper, the logistics distribution path optimization problem and its solution method are systematically studied, and preliminary research results are obtained. The model in this paper is used to predict the traffic flow, and the road weight function model reflecting the traffic flow and driving time is established. The predicted value of traffic flow is substituted into the road weight function model to determine the road weight. Moreover, the model in this paper has incomparable advantages compared with traditional models; it can quickly converge to a narrow range, and it has strong learning performance, high accuracy, and strong adaptability to different samples, which proves that the model is scientific and objective. However, in the process of logistics and distribution, the traffic flow in the road network is constantly changing, and SVM model has a good prediction effect on short-term traffic flow. How to further improve the existing model, so that it can better predict the long-term traffic flow, has become the focus of next research.

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