A city logistics vehicle path optimization method considering driver dynamic efficiency

Abstract

The application discloses a city logistics vehicle path optimization method considering driver dynamic efficiency, and comprises the following steps: determining the relationship between driver fatigue and performance; introducing a fatigue curve model and analyzing the relationship between driver fatigue and performance; establishing a vehicle path optimization model; determining problem objectives and constraint conditions, determining the symbolic representation of parameters and variables, and establishing a mathematical model; solving the above model; and encoding and evaluating the solution, designing an initialization stage, designing an employed bee stage, designing a following bee stage, and designing a scout bee stage. The application can not only make logistics enterprises more reasonably plan the distribution path of drivers under the condition of limited resources, help enterprises improve distribution efficiency and save distribution cost, but also make the path planning process take into account the interests of drivers, relieve the accumulation of driver fatigue, and improve the work experience of drivers. The two aspects are of great significance to improving the competitiveness of enterprises.

Description

Technical Field

[0001] This invention belongs to the field of logistics optimization technology and relates to a method for optimizing urban logistics vehicle routes that takes into account driver dynamic efficiency. Background Technology

[0002] In recent years, driven by the continuous growth of e-commerce, urban logistics has become an indispensable part of people's lives. In urban logistics activities, drivers, as the link between businesses and customers, directly impact a company's delivery costs, efficiency, and customer satisfaction. To improve driver efficiency, logistics dispatchers often devise optimal delivery routes before drivers depart; however, actual delivery conditions often differ. Due to external factors such as weather and traffic, as well as internal factors like driver fatigue, the actual route and time taken by drivers to complete delivery tasks often differ significantly from the dispatcher's initial plan.

[0003] To date, researchers have focused more on the impact of external factors on optimal delivery routes, neglecting the influence of drivers' intrinsic characteristics, especially driver fatigue. In today's high-intensity work environment, fatigue during delivery inevitably affects driver performance, leading to reduced delivery efficiency. Therefore, how companies can effectively optimize delivery plans to provide better delivery services to customers while taking into account driver performance fluctuations caused by fatigue has become a pressing issue.

[0004] The optimization of delivery services for express delivery, food delivery, and fresh produce in urban logistics can be collectively referred to as the vehicle routing problem. The vehicle routing problem is a typical NP-hard problem, and current research on solution methods mainly focuses on metaheuristic methods. Among these, the Artificial Bee Colony Algorithm (ASA), a classic metaheuristic algorithm, was first formally proposed by Karaboga in 2005. This algorithm simulates the collective intelligent behavior of bee colonies collecting nectar in nature. It finds better nectar sources by dividing tasks into three roles: hired bees, follower bees, and scout bees, and by three basic behavioral patterns: searching for nectar sources, gathering bees for nectar sources, and abandoning nectar sources. In practical optimization problems, the process of bees searching for the optimal nectar source is the process of finding the optimal solution to the problem. The original ASA is suitable for solving continuous problems, while the vehicle routing problem is a discrete problem. Furthermore, the ASA itself has the drawback of strong exploration ability but weak extraction ability. Therefore, it is necessary to design and improve the ASA to make it applicable to solving the vehicle routing problem. Summary of the Invention

[0005] This invention specifically considers the direct impact of driver fatigue on driver performance during delivery. The method employs an improved artificial bee colony algorithm to solve this problem, proposing a route optimization method for urban logistics vehicles that considers driver dynamic efficiency, including the following steps:

[0006] S1, determine the relationship between driver fatigue and performance;

[0007] S2, Establish a vehicle routing optimization model;

[0008] S3, Solve the established model.

[0009] Preferably, step S1, determining the relationship between driver fatigue and performance, specifically includes the following steps:

[0010] S11, introduce the fatigue curve model;

[0011] S12, analyze the relationship between driver fatigue and performance.

[0012] Preferably, step S2, establishing a vehicle route optimization model, specifically includes the following steps:

[0013] S21, Define the problem objectives and constraints;

[0014] S22, Determine the symbolic representation of parameters and variables;

[0015] S23, Establish a mathematical model.

[0016] Preferably, step S3, solving the established model, specifically includes the following steps:

[0017] S31, Encoding and evaluation of the solution;

[0018] S32, Initialization Phase Design;

[0019] S33, Employed Bee Phase Design;

[0020] S34, designed to follow the bee's stage;

[0021] S35, reconnaissance bee phase design.

[0022] Preferably, the fatigue curve model introduced is a classic fatigue curve model from the field of ergonomics, with the specific function expression as follows:

[0023] f t =1-e -λt

[0024] Among them, f t Let t represent the driver's fatigue level at time t, and λ be the fatigue index, representing the rate of fatigue accumulation.

[0025] Preferably, in the analysis of the relationship between driver fatigue and performance, the fatigue curve model is transformed to determine the driver delivery speed function under the influence of fatigue, as shown in the formula:

[0026] v t =v0(1-f t )=v0e -λt

[0027] Among them, v t Let v0 be the driver's delivery speed at time t, and v0 be the initial speed.

[0028] Preferably, as can be seen from the driver's delivery speed function, the driver's delivery speed changes non-linearly; therefore, the relationship between delivery speed and distance is expressed as follows:

[0029]

[0030] Where, d ij Let s be the distance between customer i and customer j. i With s j These are the arrival times for customer i and customer j, respectively;

[0031] The time t taken by the driver to travel from customer point i to customer point j is calculated. ij The formula is:

[0032]

[0033] Preferably, in determining the problem objective and constraints, the problem is described as follows: A distribution center has several vehicles providing logistics delivery services to multiple customers, where the customer's location and needs are known; each customer can only be served by one vehicle and only once, and the number of vehicles dispatched cannot exceed the number of vehicles owned by the distribution center; each vehicle has a capacity limit, so the sum of customer needs on each delivery route cannot exceed the vehicle's maximum capacity; each vehicle departs from the distribution center and must return to the distribution center after serving all customers on the route; it is assumed that driver fatigue is not present at the initial moment, but fatigue accumulates over time, and the driver's performance changes due to fatigue during the delivery process; furthermore, the driver's continuous delivery time is limited to a preset time.

[0034] Preferably, the symbolic representation of the determined parameters and variables includes the following parameters and their descriptions:

[0035] G is the city's logistics and distribution network, where G = (V, A);

[0036] V is a set of nodes, V = {0, 1, 2, ..., n}, where 0 is a distribution center and 1 to n are customer points;

[0037] A set of arcs, consisting of routes between nodes, A = {(i,j)|i,j∈V,i≠j};

[0038] A set of K vehicles, K = {1,2,...,m}, where each vehicle corresponds to a driver;

[0039] d ij The distance between node i and node j;

[0040] Q represents the maximum capacity of the vehicle.

[0041] q i Customer i's demand;

[0042] t ij The travel time of the vehicle from node i to node j;

[0043] s i The time it takes for the vehicle to arrive at node i;

[0044] The longest continuous delivery time allowed for driver T;

[0045] x ijk A 0-1 variable, which is 1 when vehicle k travels from node i to node j, and 0 otherwise;

[0046] y ik A 0-1 variable, which is 1 when vehicle k is at node i, and 0 otherwise.

[0047] Preferably, establishing the mathematical model includes establishing a mathematical model for vehicle routing optimization based on the problem objective, constraints, and symbolic representation:

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[0059] Equation (1) is the objective function, representing minimizing the total delivery time; Equation (2) indicates that each customer can only be served by one vehicle; Equation (3) indicates that if vehicle k provides service to customer j, it must visit node j; Equation (4) indicates that if vehicle k provides service to customer i, it must leave customer i after the service is completed; Equation (5) indicates that all vehicles start from the distribution center, must return to the distribution center after serving all customers on the route, and each vehicle travels along only one delivery route; Equation (6) indicates that the sum of all customer demands on each delivery route cannot exceed the maximum capacity of the vehicle; Equation (7) indicates that the number of vehicles used cannot exceed the number of vehicles owned by the distribution center; Equation (8) indicates the time relationship between two customers arriving in succession; Equation (9) indicates that the delivery time of each vehicle does not exceed the allowed continuous delivery time; Equations (10) and (11) are constraints on the values ​​of decision variables.

[0060] The beneficial effects of this invention include at least the following:

[0061] 1) When optimizing vehicle routes, this invention considers the dynamic changes in driver delivery performance caused by fatigue from a humanistic perspective, and introduces a delivery speed function based on fatigue level to measure this important change. A vehicle route optimization model is constructed with the goal of minimizing the total delivery time, and an improved artificial bee colony algorithm is used to solve the optimization model.

[0062] 2) This invention not only enables logistics companies to plan driver delivery routes more rationally when resources are limited, helping them improve delivery efficiency and save delivery costs, but also ensures that the route planning process takes into account the interests of drivers, alleviates driver fatigue, and improves their work experience. Both of these aspects are of great significance for enhancing the competitiveness of enterprises. Attached Figure Description

[0063] Figure 1 This is a flowchart illustrating the steps of the urban logistics vehicle route optimization method considering driver dynamic efficiency according to an embodiment of the present invention.

[0064] Figure 2 This is a flowchart of step S3 of the urban logistics vehicle route optimization method considering driver dynamic efficiency according to an embodiment of the present invention.

[0065] Figure 3 This is a coding diagram of the urban logistics vehicle route optimization method considering driver dynamic efficiency according to an embodiment of the present invention.

[0066] Figure 4This is a schematic diagram of the operator for the urban logistics vehicle route optimization method considering driver dynamic efficiency according to an embodiment of the present invention.

[0067] Figure 5 This diagram shows a comparison between the urban logistics vehicle route optimization method considering driver dynamic efficiency in this invention and the prior art.

[0068] Figure 6 This is a vehicle routing diagram for an urban logistics vehicle routing optimization method that considers driver dynamic efficiency, as described in an embodiment of the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0070] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0071] See Figure 1 Here is a flowchart of the method, including the following steps:

[0072] S1, determine the relationship between driver fatigue and performance;

[0073] S11, introduce the fatigue curve model;

[0074] In this invention, the driver's performance during delivery is directly affected by the significant factor of driver fatigue. Fatigue is a physiological phenomenon, and current research on it primarily focuses on the field of ergonomics. In urban logistics delivery, drivers maintain the same driving posture for extended periods, leading to fatigue. Furthermore, fatigue accumulates over time. According to relevant research, fatigue is generally described as a function of time, meaning that the degree of fatigue increases over time. Therefore, this invention introduces the classic fatigue curve model from the field of ergonomics, with the specific functional expression as follows:

[0075] f t =1-e -λt

[0076] Where f t Let t represent the driver's fatigue level at time t, and λ be the fatigue index, representing the rate of fatigue accumulation.

[0077] S12, analyze the relationship between driver fatigue and performance.

[0078] Dispatchers often assume that driver delivery efficiency remains constant when planning vehicle routes. However, research shows that fatigue during delivery reduces driver productivity, negatively impacting performance and leading to a decrease in driving speed. In this invention, driver delivery speed variation serves as an indicator of driver dynamic performance. Therefore, as driver fatigue accumulates, delivery speed can be characterized as a downward trend. This invention transforms the fatigue curve model to determine the driver delivery speed function under fatigue influence, as shown in the following formula:

[0079] v t =v0(1-v t )=v0e -λt

[0080] Where v t Let v0 be the driver's delivery speed at time t, and v0 be the initial speed.

[0081] Generally, changes in driver speed ultimately affect delivery time. As shown in the delivery speed function above, the driver's delivery speed changes non-linearly; therefore, the relationship between delivery speed and distance can be expressed as:

[0082]

[0083] Where d ij Let s be the distance between customer i and customer j. i With s j These are the arrival times for customer i and customer j, respectively.

[0084] Ultimately, this invention yields the time t that the driver spends traveling from customer point i to customer point j. ij The formula is shown below:

[0085]

[0086] By introducing the driver fatigue curve model and analyzing and deriving the formulas for driver delivery speed and driving time, the dynamic performance of drivers during the delivery process can be expressed by a clear functional relationship, which is conducive to quantifying the dynamic performance under the complex influence of driver fatigue.

[0087] S2, Establish a vehicle routing optimization model;

[0088] S21, Define the problem objectives and constraints;

[0089] The optimization objective of this invention is to minimize the total delivery time. The specific problem is described as follows: A distribution center has several vehicles providing logistics delivery services to multiple customers, whose locations and needs are known. Each customer can only be served by one vehicle and only once; the number of vehicles dispatched cannot exceed the number of vehicles owned by the distribution center. Each vehicle has a capacity limit, therefore the sum of customer demands on each delivery route cannot exceed the vehicle's maximum capacity. Each vehicle departs from the distribution center and must return to the distribution center after serving all customers on its route. It is assumed that driver fatigue is not present initially, but accumulates over time. Due to the effects of fatigue during delivery, the driver's performance changes. Furthermore, in accordance with relevant regulations, the driver's continuous delivery time should be limited to a reasonable period.

[0090] S22, Determine the symbolic representation of parameters and variables;

[0091] To facilitate the establishment of the subsequent mathematical model, it is necessary to first explain the parameters and variables involved in the model.

[0092] G is the city's logistics and distribution network, where G = (V, A);

[0093] V is a set of nodes, V = {0, 1, 2, ..., n}, where 0 is a distribution center and 1 to n are customer points;

[0094] A set of arcs, consisting of routes between nodes, A = {(i,j)|i,j∈V,i≠j};

[0095] A set of K vehicles, K = {1,2,...,m}, where each vehicle corresponds to a driver;

[0096] d ij The distance between node i and node j;

[0097] Q represents the maximum capacity of the vehicle.

[0098] q i Customer i's demand;

[0099] t ij The travel time of the vehicle from node i to node j;

[0100] s i The time it takes for the vehicle to arrive at node i;

[0101] The longest continuous delivery time allowed for driver T;

[0102] x ijk A 0-1 variable, which is 1 when vehicle k travels from node i to node j, and 0 otherwise;

[0103] yik A 0-1 variable, which is 1 when vehicle k asks node i, and 0 otherwise;

[0104] S23, Establish a mathematical model.

[0105] Based on the above problem objectives, constraints, and symbolic representations, this invention ultimately establishes a mathematical model for vehicle routing optimization:

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[0117] Equation (1) is the objective function, representing minimizing the total delivery time; Equation (2) indicates that each customer can only be served by one vehicle; Equation (3) indicates that if vehicle k provides service to customer j, it must visit node j; Equation (4) indicates that if vehicle k provides service to customer i, it must leave customer i after the service is completed; Equation (5) indicates that all vehicles start from the distribution center, must return to the distribution center after serving all customers on the route, and each vehicle travels along only one delivery route; Equation (6) indicates that the sum of all customer demands on each delivery route cannot exceed the maximum capacity of the vehicle; Equation (7) indicates that the number of vehicles used cannot exceed the number of vehicles owned by the distribution center; Equation (8) indicates the time relationship between two customers arriving in succession; Equation (9) indicates that the delivery time of each vehicle does not exceed the allowed continuous delivery time; Equations (10) and (11) are constraints on the values ​​of decision variables.

[0118] S3, Solve the established model.

[0119] Artificial bee colony algorithms simulate the behavior of bee colonies foraging for nectar, which mainly involves the following four processes:

[0120] (1) Initially, the scout bee randomly searches for nectar sources, and after finding a nectar source, it transforms into a mercenary bee.

[0121] (2) Hired bees collect honey and record relevant information about the nectar source, while simultaneously searching for new nectar sources of better quality near the original source. After collecting honey, the hired bees return to the hive and share the nectar source information they carried by performing a swing dance, recruiting other bees to mine the nectar.

[0122] (3) The follower bees waiting for work in the hive select a nectar source to collect nectar based on the information provided by the hired bees, while searching for new and better nectar sources in the vicinity of the nectar source.

[0123] (4) When the nectar source is exhausted, the hired bees abandon the nectar source and become scout bees to find new nectar sources.

[0124] Under this honey-collecting mechanism, bees complete the entire honey-collecting process through communication and cooperation. Based on this process, the basic flow of the artificial bee colony algorithm can be divided into the initialization phase, the hired bee phase, the follower bee phase, and the scout bee phase. The initialization phase is responsible for setting various parameters of the algorithm and generating initial solutions. The hired bee and follower bee phases perform searches and greedy selections within the solution space, while the scout bee phase replaces solutions that have not been improved multiple times. See also Figure 2 The specific steps for S3 are as follows:

[0125] S31, Encoding and evaluation of the solution;

[0126] A honey source represents a feasible solution to the problem, and the quality of the honey source represents the fitness value of the solution. In this invention, the solution to the vehicle routing problem consists of the travel paths of all vehicles. This invention uses natural number encoding to represent the solution to the problem. See also Figure 3 Suppose there are 6 customers who need delivery services and the distribution center has 3 vehicles. In this case, the solution to the problem can be found using... Figure 3 The sequence is used to represent the problem. The value 0 represents a distribution center, and non-zero numbers represent customer IDs served by the vehicles. The sequence between two 0s represents the delivery route of one vehicle; the delivery routes of three vehicles constitute a complete solution. Therefore, vehicle 1 follows the route 0-1-3-0, vehicle 2 follows the route 0-2-4-0, and vehicle 3 follows the route 0-5-6-0. According to the encoding rules, the dimension of each solution is Dim = N + K + 1, where N represents the number of customers and K represents the number of vehicles.

[0127] Because the search for solutions is random, the algorithm is likely to generate infeasible solutions. To maintain population diversity, this invention allows for the existence of infeasible solutions. Therefore, the objective function value cannot be directly used to evaluate the solution. This invention chooses to use the formula shown below as the evaluation function, which adds a penalty cost for exceeding the vehicle capacity to the original objective function.

[0128]

[0129] S32, Initialization Phase Design;

[0130] The algorithm parameters are initialized, including population size CS, number of hired bees and follower bees SN, maximum number of iterations MaxCycle, number of consecutive iterations without improvement trail, and number of consecutive iterations without improvement threshold Limit, and an initial population is generated. The number of hired bees and follower bees each constitute half of the population size.

[0131] In generating the initial population, both the quality and feasibility of individuals must be considered. The quality of individuals affects the convergence speed of the algorithm, while each individual must satisfy the constraint that the sum of customer demands does not exceed the vehicle capacity. This invention employs a simple insertion heuristic method to generate the initial population, with the specific steps as follows:

[0132] (1) Sequence 2 is obtained by repeatedly randomly swapping a sequence 1 containing all customer points;

[0133] (2) Add a 0 value representing a distribution center to the initial position of an empty sequence 3;

[0134] (3) Demand judgment is performed on customer points in sequence 2 that have not been added to sequence 3. If the sum of demand on the current sub-path is not greater than the vehicle capacity after adding the customer point, the customer point is successfully added; otherwise, the customer point is skipped.

[0135] (4) Proceed sequentially to check and add customer points to sequence 3. If there are no customer points to add, the addition of customer points on the current sub-path ends, and finally 0 value is added.

[0136] (5) Repeat steps (3) and (4) to generate all sub-paths.

[0137] After generating the initial population, the fitness value (fit) of each individual needs to be calculated. The calculation formula is as follows:

[0138]

[0139] In the problem model, the objective is to minimize delivery time. Therefore, the better the individual, the smaller the objective function value. According to the fitness value calculation formula, the smaller the objective function value, the larger the fitness value of the individual, which is consistent with the basic principle of the artificial bee colony algorithm.

[0140] S33, Employed Bee Phase Design;

[0141] The hired bee phase borrows the idea of ​​breadth-first search, focusing on extensive searching within the search space to expand the solution search space. To highlight the role of this search strategy, this invention divides search operators into two categories: the first category of operators causes significant differences between individuals before and after updates, and the second category of operators causes minimal differences. For each individual in the population, the hired bee phase uses the first category of operators to perform a neighborhood search. The first category of operators mainly involves changes in customer points between sub-paths or crossover changes between different individuals. These operators cause significant differences between individuals before and after iterations, thus enabling the hired bee phase to achieve extensive searching within the search space. The first category of operators consists of four operators: swap, insertion, reversal, and crossover operators. For specific operations, see [link to documentation]. Figure 4 The algorithm consists of four sub-paths: (a) swap, (b) insertion, (c) reversal, and (d) crossover. The swap operator randomly selects one to three customer points within different sub-paths for swapping. The insertion operator randomly selects one to three customer points within one sub-path and inserts them into another sub-path. The reversal operator randomly selects a range of customer points and then reverses their order. The crossover operator borrows from the selection and crossover operations of genetic algorithms. During iteration, it first retains the sub-path whose total demand is closest to the vehicle capacity, then randomly selects another individual from the population, removes some duplicate customer points, and finally merges the two to generate a new individual.

[0142] S34, designed to follow the bee's stage;

[0143] The follower bee phase borrows the idea of ​​depth-first search, focusing on in-depth exploration of the search space to accelerate the algorithm's convergence speed. The follower bee phase first selects an individual and then uses a second type of operator to perform a neighborhood search. This second type of operator mainly handles changes to client points within a sub-path. These operators are similar to the swap, insertion, and reversal operators in the hired bee phase. However, in swap and insertion operations, only one client point is selected, and all three operator operations are restricted to a single sub-path of the individual, resulting in minimal differences between the individual before and after iteration. Furthermore, in this phase, after each iteration using the three operators, if the individual improves, the search in this phase is repeated; otherwise, the next phase begins. Because the degree of individual mutation is small, these operators can be effectively combined with the depth-first search strategy to accelerate the algorithm's convergence speed. Simultaneously, because the operator mutation operation is simple, the addition of the depth-first search strategy does not significantly reduce the algorithm's search speed.

[0144] The selection method used is roulette wheel selection. The basic idea of ​​roulette wheel selection is that the probability of each individual being selected is directly proportional to its fitness value; that is, the higher the fitness value, the higher the probability of being selected for the next iteration. Therefore, when selecting individuals, the fitness value of each individual in the population is first calculated, and then the selection probability of each individual is calculated based on the fitness value. For individual x... i The formula for calculating the probability of selection is as follows:

[0145]

[0146] Then, the cumulative probability of each individual can be obtained from the selection probability of each individual, which is the sum of the selection probabilities of all individuals ranked before that individual, as shown in the following formula:

[0147]

[0148] Finally, a random number m is generated within the interval [0,1]. If q(x) i-1 ) <m<q(x i If ), then individual i is selected.

[0149] S35, reconnaissance bee phase design;

[0150] During the mercenary and follower bee phases, the fitness values ​​of new individuals and original individuals are compared. If the new individual has a lower fitness value, the original individual has not been improved, and its trail value is incremented by one for the number of consecutive times it has not been improved. Otherwise, the new individual replaces the original individual, and the trail value is reset to zero. In the scout bee phase, the algorithm first identifies the individual with the highest trail value in the population and then compares that individual's trail value with a threshold. If the trail value is greater than the threshold, a new individual is generated to replace the original one, following the initial solution generation method. This replacement mechanism not only maintains population diversity but also improves the algorithm's ability to escape local optima.

[0151] The technical effects of the present invention will be intuitively explained in the following content, which is mainly divided into two parts: performance verification of the improved artificial bee colony algorithm and calculation and analysis of the vehicle path model. These two parts correspond to Embodiment 1 and Embodiment 2, respectively.

[0152] Example 1;

[0153] To verify the performance of the improved artificial bee colony algorithm (DBABC) proposed in this invention, a comparative experiment was conducted using the original artificial bee colony algorithm (OABC) and an improved artificial bee colony algorithm (MABC) proposed in existing literature. OABC uses three operators: exchange, insertion, and reversal; MABC uses four operators: exchange, insertion, reversal, and crossover. Furthermore, neither of these two bee colony algorithms differentiates between or within subpaths. Regarding parameter settings, this paper sets the parameters of all three bee colony algorithms to CS = 20 and Limit = SN * Dim, thus ensuring fairness in the performance comparison.

[0154] First, this embodiment selects the E-n51-k5 test set of the classic CVRP standard test set to compare the optimal and average values ​​obtained by the three algorithms in 20 runs to evaluate the algorithm performance. The convergence speed of the algorithm is described in [reference needed]. Figure 5 The results show that the DBABC proposed in this invention significantly outperforms the other two bee colony algorithms in terms of convergence speed and stability. From the perspective of operators, although DBABC's search performance may not be as good as MABC in the follower bee stage, DBABC combines a depth-first search strategy, which significantly accelerates the algorithm's convergence speed.

[0155] Meanwhile, this embodiment selected two CVRP standard test sets (set A and set B) to further evaluate the overall performance of DBABC. As shown in Table 1, the bolded values ​​represent the best results obtained by the three algorithms. From the numerical experimental results, the DBABC designed in this invention has significant advantages in terms of solution quality and stability. This is because the design of the follower bee and scout bee search strategy further balances the algorithm's ability in terms of search breadth and search depth, thereby enhancing the algorithm's local search and global search capabilities.

[0156] Table 1

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[0160] Example 2

[0161] This embodiment uses the A-group dataset from the standard test set CVRP for simulation experiments, ensuring that customer points and distribution centers in this set of examples are distributed on coordinate axes ranging from 0 to 100 km. The fatigue index λ is set to 0.05, the driver's continuous delivery time is set to no more than 4 hours, and the driver's initial delivery speed is 55 km / h. To investigate the difference between the optimal delivery scheme before and after considering the impact of driver fatigue, this embodiment uses an improved artificial bee colony algorithm to solve for the imbalance in vehicle routes, total delivery time, and driver workload under two different experimental scenarios. The imbalance is represented by the average difference in driver delivery time.

[0162] Table 2

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[0165] The experimental results are shown in Table 2. Compared with the delivery plan that does not consider the impact of driver fatigue, the total delivery time increases by an average of approximately 10.72% after considering the impact of fatigue, while the unevenness of driver delivery time decreases by an average of 11.53%. In high-intensity working environments, the impact of fatigue is objectively present. Because driver delivery efficiency tends to decline during the delivery process, companies may set delivery time requirements that are difficult for drivers to meet when developing delivery plans. For example, in example A-n38-k5, due to fatigue, the driver actually needs 14.12 hours to complete the delivery task. If the impact of fatigue is ignored, the driver is required to complete the delivery within 13.27 hours. At the same time, the unevenness of driver workload in example A-n38-k5 decreases from 54.55% to 38.63%, meaning that in the optimal path after the impact of fatigue, the driver workload is more evenly distributed. It is worth noting that when the impact of fatigue is small, order allocation is not affected. However, the degree of fatigue's impact on each driver is inconsistent, leading to a greater unevenness in delivery time.

[0166] To better illustrate the impact of driver fatigue on the optimal delivery route, this section will continue to use example A-n38-k5 for detailed explanation. See [link / reference] Figure 6 Comparing the vehicle routes of the two optimal delivery plans reveals significant differences, primarily due to the varying degrees of consideration given to fatigue during delivery. On one hand, fatigue limits restrict drivers' continuous delivery time, thus limiting the number of customers on a route. On the other hand, if a driver's continuous delivery time is excessively long, their delivery efficiency may be significantly lower than that of other drivers. To minimize total delivery time, optimizing the delivery plan tends to allocate customers to drivers with higher delivery efficiency.

[0167] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing urban logistics vehicle routes considering driver dynamic efficiency, characterized in that, Includes the following steps: S1, determine the relationship between driver fatigue and performance; S2, Establish a vehicle routing optimization model; S3, Solve the established model described above; S1, determining the relationship between driver fatigue and performance, specifically includes the following steps: S11, introduce the fatigue curve model; S12, Analyze the relationship between driver fatigue and performance; S2, establishing a vehicle routing optimization model, specifically includes the following steps: S21, Define the problem objectives and constraints; S22, Determine the symbolic representation of parameters and variables; S23, Establish a mathematical model; The fatigue curve model introduced here adopts a classic fatigue curve model from the field of ergonomics, and its specific function expression is as follows: ； in, Let t represent the driver's fatigue level. This is the fatigue index, representing the rate at which fatigue accumulates. In the analysis of the relationship between driver fatigue and performance, the fatigue curve model is transformed to determine the driver delivery speed function under the influence of fatigue, as shown in the formula: ； in, Let t be the driver's delivery speed. The initial velocity; As can be seen from the driver delivery speed function, the driver's delivery speed changes non-linearly. Therefore, the relationship between delivery speed and distance is expressed as follows: ； in, Let be the distance between node i and node j. and These are the times when they arrive at node i and node j, respectively; The time taken by the driver to travel from node i to node j is calculated. The formula is: ； The symbolic representation of the determined parameters and variables includes the following parameters and their descriptions: Urban logistics and distribution network ; Node set, Where 0 represents a distribution center. For nodes; An arc set is composed of paths between nodes. ; Vehicle assembly, In this system, there is a one-to-one correspondence between vehicles and drivers; The distance between node i and node j; Maximum capacity of the vehicle; The demand for node i; The travel time of the vehicle from node i to node j; The time it takes for the vehicle to arrive at node i; The longest continuous delivery time allowed by the driver; A 0-1 variable, which is 1 when vehicle k travels from node i to node j, and 0 otherwise; A 0-1 variable, which is 1 when vehicle k visits node i, and 0 otherwise; The establishment of the mathematical model includes, based on the problem objective, constraints, and symbolic representation, establishing a mathematical model for vehicle routing optimization: （1）； （2）； （3）； （4）； （5）； （6）； （7）； （8）； （9）； （10）； （11）； Equation (1) is the objective function, representing minimizing the total delivery time; Equation (2) indicates that each node can only be served by one vehicle; Equation (3) indicates that if vehicle k provides services to node j, it must visit node j; Equation (4) indicates that if vehicle k provides services to node i, it must leave node i after the service is completed; Equation (5) indicates that all vehicles start from the distribution center, must return to the distribution center after serving all nodes on the path, and each vehicle travels along only one delivery route; Equation (6) indicates that the sum of the demands of all nodes on each delivery path cannot exceed the maximum capacity of the vehicle; Equation (7) indicates that the number of vehicles used cannot exceed the number of vehicles owned by the distribution center; Equation (8) indicates the time relationship between vehicles arriving at two nodes in succession; Equation (9) indicates that the delivery time of each vehicle does not exceed the allowed continuous delivery time; Equations (10) and (11) are constraints on the values ​​of decision variables.

2. The urban logistics vehicle route optimization method considering driver dynamic efficiency according to claim 1, characterized in that, S3, solving the established model, specifically includes the following steps: S31, Encoding and evaluation of the solution; S32, Initialization Phase Design; S33, Employed Bee Phase Design; S34, designed to follow the bee's stage; S35, reconnaissance bee phase design.

3. The urban logistics vehicle route optimization method considering driver dynamic efficiency according to claim 1, characterized in that, In defining the problem objectives and constraints, the problem is described as follows: A distribution center has several vehicles that provide logistics delivery services to multiple nodes, where the location and demand of the nodes are known; each node can only be served by one vehicle and only once, and the number of vehicles dispatched cannot exceed the number of vehicles owned by the distribution center; each vehicle has a capacity limit, so the sum of the node demands on each delivery route cannot exceed the maximum capacity of the vehicle; each vehicle departs from the distribution center and must return to the distribution center after serving all nodes on the route. Assuming that driver fatigue is not present at the initial moment, but fatigue accumulates over time, the driver's performance changes due to the effects of fatigue during delivery; in addition, the driver's continuous delivery time is limited to a preset time.

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