Vehicle path problem planning method and system with time window based on time-varying road network

Abstract

The invention provides a time-varying road network-based vehicle path problem planning method and system with a time window. The method comprises the following steps of obtaining client point distribution information and road network historical time-varying information; the method comprises the following steps: determining a road speed time dependence function and road section congestion coefficients and driving time in different time periods based on road network historical data; constructing a time-varying road network-based vehicle path problem mathematical model with a time window; solving the established model by adopting an improved ant colony algorithm to obtain an optimal distribution scheme; and dispatching the vehicle to run according to the optimal distribution scheme. According to the method, the influence of the time-varying road network on urban logistics distribution is considered, the distribution route is reasonably planned, the total distribution cost is reduced, and economization, efficiency and greenization of urban logistics distribution are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of logistics distribution, and particularly to a method and system for planning vehicle routing problems with time windows based on a time-varying road network. Background Art

[0002] With the acceleration of urbanization and the dynamic changes in the traffic network, the vehicle routing problem with time windows under a time-varying road network has become increasingly prominent. This problem involves how to optimize vehicle delivery routes under changing traffic conditions and time constraints to reduce logistics costs, minimize resource waste, and improve delivery efficiency. This is of great significance for addressing urban traffic congestion and enhancing the quality of logistics services.

[0003] A time-varying road network is a complex traffic system in which key indicators such as the traffic state, speed, and congestion level of roads change continuously over time. Such changes may be affected by various factors such as traffic flow, weather conditions, traffic accidents, and road construction. In a time-varying road network, the vehicle driving speed on the same road section may vary significantly at different time periods.

[0004] In the field of modern logistics, the vehicle routing problem with time windows based on a time-varying road network (TDVRPTW) is a key optimization problem. It involves how to plan the delivery routes and times of vehicles in a dynamic traffic network to meet the specific time window requirements of customers, which is an urgent problem to be solved. Summary of the Invention

[0005] Aiming at the deficiencies in the prior art, the present invention provides a method and system for planning vehicle routing problems with time windows based on a time-varying road network. Considering the characteristics of the time-varying road network, the time windows of customer services, and the carbon emissions during the vehicle delivery process, a TDVRPTW optimization model that is more in line with practical applications is constructed with the goal of minimizing the total delivery cost, which can more objectively and accurately reflect the operation of the real logistics system and achieve the economicization, efficiency, and greening of urban logistics distribution.

[0006] The present invention achieves the above technical objectives through the following technical means.

[0007] A method for planning vehicle routing problems with time windows based on a time-varying road network includes the following steps:

[0008] Obtain customer point delivery information and historical time-varying information of the road network;

[0009] Based on the historical data of the road network, determine the road speed time-dependent function, the congestion coefficient and driving time of road sections in different time periods:

[0010] Construct a mathematical model for vehicle routing problems with time windows based on a time-varying road network;

[0011] The established model is solved using an improved ant colony algorithm to obtain the optimal distribution plan;

[0012] Dispatch the vehicles to travel according to the optimal distribution plan.

[0013] Furthermore, obtain the distribution information of customer points and the historical time-varying information of the road network, specifically including:

[0014] Obtain the road information, historical traffic data, and traffic flow data within the research area;

[0015] Obtain the distribution information of customer points to be served within the research area, including geographical location, service time window, and demand;

[0016] Obtain the continuously dynamic change information of vehicle driving speed, including: obtain the historical data of vehicle driving speed;

[0017] Determine the basic vehicle driving speed information according to the all-day change trend of vehicle driving speed.

[0018] Furthermore, based on the historical data of the road network, determine the road speed time-dependent function, specifically:

[0019] Divide a day into M equal time periods, each time period has a length of Δt, and the vehicle driving speed on the same road section is different in different time periods. [(m - 1)Δt, mΔt] represents the m-th equal time period;

[0020] Based on the influence of the road basic conditions on the vehicle driving speed, divide the roads into 7 categories according to the standard: Class I expressway, Class II expressway, Class I arterial road, Class II arterial road, Class III arterial road, sub-arterial road, and public branch road, and are successively referred to as the h-th (h ∈ 1, 2... 7) level roads. The vehicle driving speeds on different level roads are different;

[0021] Calculate the average driving speed v of the vehicle on the h-th level road in the m-th time period [(m - 1)Δt, mΔt] mh , and determine the speed time-dependent function of vehicle driving speed related to road level and driving time period:

[0022]

[0023] In the formula, v 1h is the average driving speed of the vehicle on the h-th level road in the first time period; v Mh is the average driving speed of the vehicle on the h-th level road at the M-th time.

[0024] Furthermore, based on the historical data of the road network, determine the congestion coefficient of road sections in different time periods, specifically:

[0025] Based on the speed-time dependence function, the driving speed of vehicles in the m time period on section (i, j) can be determined according to the road level of the section and the time period, denoted as Section (i, j) can represent the section between customer i and customer j;

[0026] Calculate the congestion coefficient of section (i, j) in different time periods based on the road network traffic conditions:

[0027]

[0028] v h is the free flow speed of the road at level h; is the speed of the vehicle traveling from customer i to customer j within [(m - 1)Δt, mΔt]; when , the section is regarded as congested, when , the section is regarded as normal, when , the section is regarded as unobstructed;

[0029] Assume that the departure time of vehicle k from customer i is T ik +t ik , T ik +t ik within [(m - 1)Δt, mΔt], where T ik is the arrival time of vehicle k at customer i, and t ik is the service duration of vehicle k at customer i;

[0030] If the delivery vehicle arrives at customer j within the m time period, the travel time where L ij is the length of section (i, j), is the driving speed of the vehicle on section (i, j) within the time period [(m - 1)Δt, mΔt];

[0031] If the delivery vehicle travels across r time periods, the distance traveled within the mth time period is The distance that still needs to be traveled on section (i, j) after the mth time period is Then the distance traveled within the m + rth time period is The travel time from customer i to customer j is where is the travel time of the vehicle on section (i, j) within the m + rth time period, is the driving speed of the vehicle on section (i, j) within the time period [(m + r - 1)Δt, (m + r)Δt].

[0032] Furthermore, construct a mathematical model for the vehicle routing problem with time windows based on the time-varying road network, specifically as follows:

[0033] The objective function is determined with the aim of minimizing the sum of vehicle dispatching cost, vehicle transportation cost, carbon emission cost, and time window penalty cost as follows:

[0034]

[0035] where K represents the set of vehicles; all customer sets are V = V c ∪V0, where V c is the set of all customer points, and V0 = {0} represents the distribution center; the decision variable indicates whether vehicle k arrives at customer j from customer i in the m-th time period, 1 for yes and 0 for no; the decision variable indicates whether vehicle k arrives at customer j from the distribution center in the m-th time period, 1 for yes and 0 for no; the unit vehicle dispatching cost is c1, the unit time transportation cost is c2, the unit carbon emission cost is c3, and the carbon emission coefficient is e; represents the travel time of vehicle k from customer i to customer j in the m-th time period; [ET j , LT j is the service time window of customer j, ET j is the earliest acceptable service time of customer j, LT j is the latest acceptable service time of customer j, T jk is the time when vehicle k arrives at customer j; ET j is the earliest acceptable service time of customer j; the early arrival penalty cost per unit time is c4; the late arrival penalty cost per unit time is c5;

[0036]

[0037] where: is the fuel consumption from point i to point j in the m-th time period; λ is the fuel calorific value; C is the engine friction coefficient; Z is the engine speed; P is the engine displacement; is the transmission coefficient; g is the gravitational constant; δ is the air resistance coefficient; m0 is the vehicle unladen weight; Q ijk is the load on the section where vehicle k travels from customer i to customer j, is the distance traveled by the vehicle on section (i, j) in the m-th time period;

[0038] Based on the constraint conditions of vehicle in-out balance constraint, vehicle loading balance constraint, vehicle capacity constraint, working time constraint, and congestion constraint, the model is constructed as follows:

[0039]

[0040] 0 ≤ Q ijk ≤ Q

[0041]

[0042] Among them, Q is the maximum load of the vehicle, and d j is the delivery demand of customer j, and p j is the pick-up demand of customer j, and p i is the pick-up demand of customer i, and T s is the start time of distribution at the distribution center, and T f is the closing time of the distribution center; decision variables represents whether vehicle k arrives at the distribution center from customer j in the m-th time period. If it is, it is 1; if not, it is 0; Q 0jk is the load on the section where vehicle k travels from the distribution center to customer j; Q i0k is the load on the section where vehicle k travels from customer i to the distribution center; Q jik is the load on the section where vehicle k travels from customer j to customer i; α is the lower limit of the congestion level.

[0043] Furthermore, an improved ant colony algorithm is used to solve the established model to obtain the optimal distribution plan, which is specifically as follows:

[0044] Initialization settings: Set the number of ants N, the maximum number of iterations T max , the pheromone evaporation factor ρ, the number of vehicles K, the service time window [ET j , LT j for each customer, and initialize the pheromone on each path;

[0045] Determine the rule for dynamically updating pheromone: Use an adaptive mechanism to adjust the pheromone and the weight of the heuristic function, make the pheromone weight increase non-linearly with the increase of the iteration number t, and make the weight of the heuristic function decrease non-linearly with the increase of the iteration number t. Construct the weight θ1(t) of the pheromone factor in the t-th iteration and the weight θ2(t) of the expected heuristic factor in the t-th iteration as follows:

[0046]

[0047] θ2(t) = 6 - 2e -t

[0048] Customer node selection: Place N ants at the distribution center, let n = 1, and unVisit n be the set of customer points not visited by ant n, and the taboo list congestion coefficient factor α ij The calculation formula is:

[0049]

[0050] The probability that ant n selects customer j from customer i in the t-th iteration is:

[0051]

[0052] where τ ij is the pheromone factor; η ij is the expected heuristic factor, α ij is the congestion coefficient factor; θ1(t) is the weight of the pheromone factor, θ2(t) is the weight of the expected heuristic factor, and θ3 is the weight of the congestion coefficient factor;

[0053] Construct the initial delivery route of the ant: Each time a path is selected, check whether the path meets the constraint conditions; if not, reselect the path; if it meets the conditions, update the set of customers to be visited unVisit n of ant n and the taboo list tatu n ; if no more customers can be added to the current route due to not meeting the constraint conditions, the ant immediately returns to the distribution center, completes this delivery route, and starts constructing a new delivery route from the distribution center again to continue serving the remaining unvisited customers; repeat the construction process until the set of customers to be visited Finally, obtain the initial delivery route route n of ant n; when ant n has visited all customers, set n = n + 1 and continue to construct the initial delivery route of the next ant until n > N to obtain the initial path planning results route of all ants regarding the customers;

[0054] Cost calculation and local search: In each iteration, the following steps are specifically included:

[0055] Calculate the total delivery cost in the current iteration;

[0056] Record the optimal total delivery cost and the optimal path in the current iteration;

[0057] Compare with the currently known optimal solution, and update the optimal solution if it is better;

[0058] Perform local search optimization, and the specific method is as follows:

[0059] Randomly select two non - consecutive points in the path and try to reverse this path segment;

[0060] Check whether the reversed path still meets the load and time window constraints;

[0061] If it meets the constraints and the total delivery cost is reduced, accept the reversed path;

[0062] Update the optimal total delivery cost and the optimal route;

[0063] Pheromone update: The elite ant strategy is adopted to strengthen the pheromone of the historical optimal path. The pheromone update strategy is as follows:

[0064]

[0065] Among them, τ ij (t) is the pheromone level on the road section (i, j) at the t-th iteration; ρ is the pheromone evaporation rate, 0 ≤ ρ < 1; the elite ant is the ant with the minimum objective value in the current iteration; is the pheromone increment of ant n on the road section (i, j) at the t-th iteration; ε is the pheromone weight of the elite ant; is the pheromone increment of the elite ant on the road section (i, j) at the t-th iteration; G is a constant; cost n is the total distribution cost of ant n, the total distribution cost of the elite ant ;

[0066] Judgment of the algorithm termination condition: If the iteration number is not reached, then t = t + 1, and the dynamic update rule of pheromone is re-determined; otherwise, the algorithm ends and the optimal distribution plan is output.

[0067] A system for a vehicle routing problem planning method with time windows based on a time-varying road network includes a data preprocessing module I, a data preprocessing module II, a path planning module, and a vehicle scheduling module;

[0068] The data preprocessing module I is used to connect to the road network data system, analyze the historical data of road conditions, and determine the road grades, vehicle driving speeds, and congestion level information of each road section;

[0069] The data preprocessing module II receives the distribution information of customers from the user side;

[0070] The path planning module is connected to the data preprocessing module I and the data preprocessing module II, and is used to perform path planning on the received customer points; the path planning module inputs the path planning into the vehicle scheduling module, which is used to schedule multiple distribution vehicles to execute the distribution plan.

[0071] Furthermore, the path planning module is provided with a model construction unit, an algorithm solving unit, and a distribution plan generation unit; the model construction unit is used to construct the vehicle routing problem model with time windows based on the time-varying road network; the algorithm solving unit uses the improved ant colony algorithm to solve the model; the distribution plan generation unit is used to generate the distribution plan.

[0072] The beneficial effects of the present invention are as follows:

[0073] The vehicle routing problem planning method and system with time windows based on a time-varying road network according to the present invention studies the time-varying characteristics of the road network in the real scenario, takes into account the differences in vehicle driving speeds and congestion levels on different grades of roads, reasonably plans the distribution routes, avoids the impact of road condition changes on the distribution efficiency and accuracy, and at the same time considers the carbon emissions during the vehicle distribution process, and can maximize the economicization, efficiency and greening of urban logistics distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. The drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, it is obvious that other drawings can also be obtained based on these drawings.

[0075] Figure 1 It is a schematic flow chart of the vehicle routing problem planning method with time windows based on a time-varying road network according to the present invention.

[0076] Figure 2 It is an algorithm flow chart of the improved ant colony algorithm according to the present invention.

[0077] Figure 3 It is a schematic diagram of the vehicle routing problem planning system with time windows based on a time-varying road network according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0078] The following will describe in detail the embodiments of the present invention. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present invention and should not be construed as a limitation of the present invention.

[0079] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "axial", "radial", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise specifically defined.

[0080] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected with", "fixed", etc. should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0081] As Figure 1 shown, the vehicle routing problem planning method with time windows based on a time-varying road network according to the present invention includes the following:

[0082] S01: Obtain customer point information and road network historical time-varying information, specifically as follows:

[0083] Obtain road information, historical traffic data, and traffic flow data within the research area;

[0084] Obtain the delivery information of the customer points to be served within the research area, including geographical location, service time window, and demand;

[0085] Obtain the continuous dynamic change information of the vehicle driving speed, including: obtaining the historical data of the vehicle driving speed;

[0086] Determine the basic vehicle driving speed information according to the all-day change trend of the vehicle driving speed.

[0087] S02: Based on the road network historical data, determine the road speed time-dependent function, specifically as follows:

[0088] Considering the impact of the time-varying road network, a day is divided into M equal time periods, each with a length of Δt. The vehicle driving speed on the same road section is different in different time periods, and [(m - 1)Δt, mΔt] represents the m-th equal time period.

[0089] Based on the impact of road basic conditions on vehicle driving speed, according to the national standard of "Urban Comprehensive Transportation System Planning Standard", roads are divided into 7 categories: Class I expressway, Class II expressway, Class I arterial road, Class II arterial road, Class III arterial road, sub-arterial road, and public branch road, which are successively referred to as roads of the h-th (h ∈ 1, 2... 7) level. The vehicle driving speeds on different level roads are different.

[0090] Based on the analysis of the vehicle driving speeds of the same level roads in each time period obtained from the data collection system, calculate the average driving speed v of the vehicle on the h-th level road in the m-th time period [(m - 1)Δt, mΔt] mh , and determine the speed-time dependence function of vehicle driving speed with respect to road level and driving time period:

[0091]

[0092] In the formula, v 1h is the average driving speed of the vehicle on the h-th level road in the first time period; v Mh is the average driving speed of the vehicle on the h-th level road at the M-th time;

[0093] Based on the speed-time dependence function, the driving speed of the vehicle on the road section (i, j) in the m-th time period can be determined by the road level and the time period of the road section, denoted as The road section (i, j) can represent the road section between customer i and customer j.

[0094] The driving time of the vehicle is affected by the speed. Assume that the departure time of vehicle k from customer i is T ik +t ik , T ik +t ik is within [(m - 1)Δt, mΔt], where T ik is the arrival time of vehicle k at customer i, and t ik is the service duration of vehicle k at customer i; there are two possibilities for the vehicle to travel from customer i to customer j, either across time periods or not. If the delivery vehicle arrives at customer j within the m-th time period and does not need to travel across time periods, then the driving time where L ij is the length of the road section (i, j), is the driving speed of the vehicle on the road section (i, j) during the time period [(m - 1)Δt, mΔt]; if the delivery vehicle needs to drive across time periods, assuming the delivery vehicle drives across r time periods, the distance traveled within the m-th time period is The distance that needs to be continued to drive on the road section (i, j) after the m-th time period is Then the distance traveled within the (m + r)-th time period is The driving time for the vehicle to travel from customer i to customer j is where is the driving time of the vehicle on the road section (i, j) within the (m + r)-th time period, is the driving speed of the vehicle on the road section (i, j) during the time period [(m + r - 1)Δt, (m + r)Δt];

[0095] Calculate the congestion coefficient of the road section (i, j) in different time periods based on the road network traffic conditions:

[0096]

[0097] v h is the free flow speed of the road of level h, that is, the highest speed at which the vehicle can drive stably without congestion; is the speed of the vehicle traveling from customer i to customer j within [(m - 1)Δt, mΔt]. When , the road section is regarded as congested. When , the road section is regarded as normal. When , the road section is regarded as unobstructed.

[0098] S03: Construct a mathematical model for the vehicle routing problem with time windows based on the time-varying road network:

[0099] Specifically, with the goal of minimizing the sum of vehicle dispatch costs, vehicle transportation costs, carbon emission costs, and time window penalty costs, the objective function is determined as follows:

[0100]

[0101] where K represents the set of vehicles; the set of all customers is V = V c ∪V0, where V c is the set of all customer points, and V0 = {0} represents the distribution center; the decision variable represents whether vehicle k reaches customer j from customer i during the m-th time period. If it is, it is 1; if not, it is 0; the decision variable represents whether vehicle k reaches customer j from the distribution center during the m-th time period. If it is, it is 1; if not, it is 0; the unit vehicle dispatch cost is c1, the unit time transportation cost is c2, the unit carbon emission cost is c3, and the carbon emission coefficient is e; Denote the travel time of the vehicle from customer i to customer j in the m-th time period; [ET j ,LT j is the service time window of customer j, ET j is the earliest acceptable service time of customer j, LT j is the latest acceptable service time of customer j, T jk is the time when vehicle k arrives at customer j; ET j is the earliest acceptable service time of customer j; Penalty costs will be incurred if the vehicle arrives at the customer earlier or later than the time window. The penalty cost per unit time for arriving early is c4, and the penalty cost per unit time for arriving late is c5.

[0102] The carbon emission cost is determined by the fuel consumption. Considering the influence of the driving speed, the fuel consumption calculation formula is as follows:

[0103]

[0104] Where: F ij m is the fuel consumption from point i to point j in the m-th time period; λ is the fuel calorific value; C is the engine friction coefficient; Z is the engine speed; P is the engine displacement; is the transmission coefficient; g is the gravitational constant; δ is the air resistance coefficient; m0 is the vehicle's unladen weight; Q ijk is the load on the section where vehicle k travels from customer i to customer j, is the distance traveled by the vehicle on the section (i, j) in the m-th time period;

[0105] Based on constraints such as vehicle in-out balance constraint, vehicle loading capacity balance constraint, vehicle capacity constraint, working time constraint, congestion constraint, etc., the model is constructed as follows:

[0106]

[0107] 0 ≤ Q ijk ≤ Q

[0108]

[0109] Where Q is the maximum load of the vehicle, d j is the delivery demand of customer j, p j is the pick-up demand of customer j, p i is the pick-up demand of customer i, T s is the start time of distribution at the distribution center, T f is the closing time of the distribution center; Decision variable indicates whether vehicle k arrives at the distribution center from customer j in the m-th time period. If it is, it is 1; if not, it is 0; Q 0jkThe load on the section where vehicle k travels from the distribution center to customer j; Q i0k The load on the section where vehicle k travels from customer i to the distribution center; Q jik The load on the section where vehicle k travels from customer j to customer i; α lower limit of congestion level

[0110] S04: Solve the established model using the improved ant colony algorithm to obtain the optimal distribution plan:

[0111] Use methods such as dynamically adjusting pheromone and elite ant strategy to improve the solving efficiency of the ant colony algorithm. At the same time, introduce a local search algorithm and combine it with the ant colony algorithm to optimize the solving results. The steps are as Figure 2 shown. The specific algorithm steps are described as follows:

[0112] S041: Initialization. Set the number of ants N, the maximum number of iterations T max , the pheromone evaporation factor ρ, the number of vehicles K, and the service time window [ET j , LT j for each customer. Initialize the pheromone on each path.

[0113] S042: Determine the rule for dynamically updating pheromone. Use an adaptive mechanism to adjust the pheromone and the weight of the heuristic function, making the pheromone weight increase non-linearly with the increase of the iteration number t, and the weight of the heuristic function decrease non-linearly with the increase of the iteration number t. Construct the weight θ1(t) of the pheromone factor in the t-th iteration and the weight θ2(t) of the expected heuristic factor in the t-th iteration as follows:

[0114]

[0115] θ2(t) = 6 - 2e -t

[0116] S043: Customer node selection. Place N ants at the distribution center, let n = 1, and unVisit n be the set of customer points not visited by ant n, and introduce a congestion coefficient to improve the state transition rule, with the congestion coefficient factor α The calculation formula is: ij Calculate as follows:

[0117]

[0118] The probability that ant n selects customer j from customer i in the t-th iteration is:

[0119]

[0120] Among them, τ ij is the pheromone factor; ηij is the expected heuristic factor, α ij is the congestion coefficient factor; θ1(t) is the weight of the pheromone factor, θ2(t) is the weight of the expected heuristic factor, and θ3 is the weight of the congestion coefficient factor;

[0121] Each time a path is selected, check whether the path meets the constraint conditions. If not, reselect the path. If it meets the conditions, update the set of unvisited customer points unVisit of ant n n and the taboo list tatu n 。If no more customers can be added to the current route due to not meeting the constraint conditions, the ant immediately returns to the distribution center to complete this distribution route. Start constructing a new distribution route from the distribution center again and continue to serve the remaining unvisited customers. Repeat the above construction process until the set of unvisited customers Finally, obtain the initial distribution route route of ant n n 。When ant n has visited all customers, set n = n + 1 and continue to construct the initial distribution route of the next ant until n > N. Finally, obtain the initial path planning results route of all ants regarding the customers.

[0122] S044: Cost calculation and local search. In each iteration, perform the following steps:

[0123] Calculate the total distribution cost in the current iteration;

[0124] Record the optimal total distribution cost and the optimal path in the current iteration;

[0125] Compare with the currently known optimal solution. If it is better, update the optimal solution;

[0126] Perform local search optimization. The specific method is as follows:

[0127] Randomly select two non - consecutive points on the path and try to reverse this path segment;

[0128] Check whether the reversed path still meets the load and time - window constraints;

[0129] If it meets the constraints and the total distribution cost decreases, accept the reversed path;

[0130] Update the optimal total distribution cost and the optimal route.

[0131] S045: Pheromone update. Adopt the elite ant strategy to strengthen the pheromone of the historical optimal path. The pheromone update strategy is:

[0132]

[0133] Among them, τij τ(t) is the pheromone level on the road section (i, j) at the t-th iteration; ρ is the pheromone evaporation rate, 0 ≤ ρ < 1; the elite ant is the ant with the minimum objective value in the current iteration; Δτ(t)n is the pheromone increment of ant n on the road section (i, j) at the t-th iteration; ε is the pheromone weight of the elite ant; is the elite ant at the t-th iteration on the pheromone increment on the road section (i, j); G is a constant; cost n is the total distribution cost of ant n, the elite ant 's total distribution cost.

[0134] S046: Judgment of the algorithm end condition. If the number of iterations is not reached, then t = t + 1, go to S042; otherwise, the algorithm ends and the optimal distribution plan is output.

[0135] S05: The scheduling vehicle travels according to the optimal distribution plan: Specifically, the scheduling and distribution vehicle travels according to the optimal distribution plan to serve each customer point in turn.

[0136] As Figure 3 shown, the system of the vehicle routing problem planning method with time windows based on the time-varying road network described in the present invention includes a data preprocessing module I, a data preprocessing module II, a path planning module, and a vehicle scheduling module;

[0137] The data preprocessing module I is used to connect to the road network data system and determine information conditions such as the road grade, vehicle driving speed time-dependent function, and congestion level of each road section based on the obtained historical data of the time-varying road network; the data preprocessing module II receives the distribution information of the customers at the user end, including the customer point demand, customer service time window, customer geographical coordinates, etc.;

[0138] The path planning module receives the data processed by the data preprocessing modules I and II, and then performs distribution path planning for all customer points to be served; the path planning module inputs the determined optimal distribution path plan into the vehicle scheduling module for scheduling multiple distribution vehicles to execute the distribution plan;

[0139] The path planning module is provided with a model construction unit, an algorithm solving unit, and a distribution plan generation unit; the model construction unit is used to construct the vehicle routing problem model with time windows based on the time-varying road network; the algorithm solving unit uses the improved ant colony algorithm to solve the model; the distribution plan generation unit is used to generate the distribution plan.

[0140] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0141] The series of detailed descriptions listed above are only specific descriptions of the feasible embodiments of the present invention, and they are not intended to limit the protection scope of the present invention. Any equivalent embodiments or modifications made without departing from the spirit of the art of the present invention should be included in the protection scope of the present invention.

Claims

1. A vehicle routing problem planning method with time windows based on a time-varying road network, characterized in that, The steps are as follows: Obtain the delivery information of customer points and the historical time-varying information of the road network; Based on the historical road network data, determine the road speed time-dependent function and the congestion coefficients and travel times of road segments in different time periods: Construct a mathematical model of the vehicle routing problem with time windows based on the time-varying road network; Use an improved ant colony algorithm to solve the established model to obtain the optimal delivery plan; Dispatch vehicles to travel according to the optimal delivery plan.

2. The vehicle routing problem planning method with time windows based on a time-varying road network according to claim 1, wherein Obtain the delivery information of customer points and the historical time-varying information of the road network, specifically including: Obtain the road information, historical traffic data, and traffic flow data in the research area; Obtain the delivery information of customer points to be served in the research area, including geographical location, service time window, and demand; Obtain the continuous dynamic change information of vehicle driving speed, including: obtain the historical data of vehicle driving speed; Determine the basic vehicle driving speed information according to the all-day change trend of vehicle driving speed.

3. The vehicle routing problem planning method with time windows based on a time-varying road network according to claim 1, characterized in that Based on the historical road network data, determine the road speed time-dependent function, specifically: Divide a day into M equal time periods, each time period has a length of Δt, and the driving speed of the vehicle on the same road segment is different in different time periods. [(m - 1)Δt, mΔt] represents the mth equal time period; Based on the influence of the road basic conditions on the vehicle driving speed, divide the roads into 7 categories according to the standard: Class I expressway, Class II expressway, Class I arterial road, Class II arterial road, Class III arterial road, secondary arterial road, and public branch road, and are successively referred to as roads of the hth (h ∈ 1, 2... 7) level. The driving speeds of vehicles on different level roads are different; Calculate the average driving speed \(v\) of the vehicle on the \(h\)-level road in the time period \(m\) \([(m - 1)\Delta t,m\Delta t]\). mh Determine the speed-time dependence function of the vehicle's driving speed with respect to the road level and the driving time period: where, v 1h is the average driving speed of the vehicle on the road of level h in the first time period; v Mh is the average driving speed of the vehicle on the road of level h at the M-th time.

4. The vehicle routing problem planning method with time windows based on a time-varying road network according to claim 3, wherein Based on the historical road network data, determine the congestion coefficients of road segments in different time periods, specifically: Based on the speed-time dependence function, the driving speed of vehicles in the m time period on the road section (i, j) can be determined according to the road level of the road section and the time period it is in, denoted as The road section (i, j) can represent the road section between customer i and customer j; Calculate the congestion coefficient of road segment (i, j) in different time periods based on the road network traffic conditions: v h is the free flow speed of the h-level road; is the speed at which the vehicle travels from customer i to customer j within [(m - 1)Δt, mΔt]; when the road section is regarded as congested, when the road section is regarded as normal, when the road section is regarded as unobstructed; Suppose the departure time of vehicle k from customer i is T ik +t ik , T ik +t ik Within [(m - 1)Δt, mΔt], where T ik is the arrival time of vehicle k at customer i, and t ik is the service duration of vehicle k at customer i; If the delivery vehicle arrives at customer j within the m-th time period, the travel time where L ij is the length of the road section (i, j), is the driving speed of the vehicle on the road section (i, j) during the time period [(m - 1)Δt, mΔt]; If the delivery vehicle travels across r time periods, the distance traveled in the m-th time period is The remaining distance to be traveled on the section (i, j) after the m-th time period is Then the distance traveled in the (m + r)-th time period is The travel time for customer i to travel to customer j is Where is the travel time of the vehicle on the section (i, j) in the (m + r)-th time period, is the travel speed of the vehicle on the section (i, j) in the time period [(m + r - 1)Δt, (m + r)Δt].

5. The vehicle routing problem planning method with time windows based on a time-varying road network according to claim 3, wherein Construct a mathematical model of the vehicle routing problem with time windows based on the time-varying road network, specifically: Determine the objective function with the goal of minimizing the sum of vehicle dispatch cost, vehicle transportation cost, carbon emission cost, and time window penalty cost as follows: Among them, \(K\) represents the set of vehicles; the set of all customers is \(V = V c \cup V_0\), where \(V c \) is the set of all customer points, and \(V_0=\{0\}\) represents the distribution center; the decision variable indicates whether vehicle \(k\) arrives at customer \(j\) from customer \(i\) in the \(m\)-th time period. If so, it is \(1\), otherwise it is \(0\); the decision variable indicates whether vehicle \(k\) arrives at customer \(j\) from the distribution center in the \(m\)-th time period. If so, it is \(1\), otherwise it is \(0\); the unit vehicle dispatch cost is \(c_1\), the unit time transportation cost is \(c_2\), the unit carbon emission cost is \(c_3\), and the carbon emission coefficient is \(e\); represents the travel time of vehicle \(k\) from customer \(i\) to customer \(j\) in the \(m\)-th time period; \([ET j , LT j \) is the service time window of customer \(j\), \(ET j \) is the earliest acceptable service time of customer \(j\), \(LT j \) is the latest acceptable service time of customer \(j\), \(T jk \) is the time when vehicle \(k\) arrives at customer \(j\); \(ET j \) is the earliest acceptable service time of customer \(j\); the penalty cost per unit time for early arrival is \(c_4\); the penalty cost per unit time for late arrival is \(c_5\); Wherein: is the fuel consumption from point i to point j in the m-th time period; λ is the fuel calorific value; C is the engine friction coefficient; Z is the engine speed; P is the engine displacement; is the transmission coefficient; g is the gravitational constant; δ is the air resistance coefficient; m0 is the unladen weight of the vehicle; Q ijk is the load on the section where vehicle k travels from customer i to customer j, is the distance traveled by the vehicle on the section (i, j) in the m-th time period; Construct the model based on the constraint conditions of vehicle in-out balance constraint, vehicle loading capacity balance constraint, vehicle capacity constraint, working time constraint, and congestion constraint as follows: 0≤Q ijk ≤Q Among them, Q is the maximum load of the vehicle, d j is the delivery demand of customer j, p j is the pick-up demand of customer j, p i is the pick-up demand of customer i, T s is the start time of distribution at the distribution center, T f is the closing time of the distribution center; decision variable indicates whether vehicle k arrives at the distribution center from customer j in the m-th time period, 1 if yes, 0 if no; Q 0jk is the load on the section where vehicle k travels from the distribution center to customer j; Q i0k is the load on the section where vehicle k travels from customer i to the distribution center; Q jik is the load on the section where vehicle k travels from customer j to customer i; α lower limit of congestion level.

6. The vehicle routing problem planning method with time windows based on a time-varying road network according to claim 1, wherein Use an improved ant colony algorithm to solve the established model to obtain the optimal delivery plan, specifically as follows: Initial settings: Set the number of ants N, the maximum number of iterations T max , the pheromone evaporation factor ρ, the number of vehicles K, the service time window [ET j , LT j , and initialize the pheromone on each path; Determine the rule for dynamically updating pheromone: Use an adaptive mechanism to adjust the pheromone and the weight of the heuristic function, make the pheromone weight increase non-linearly with the increase of the iteration number t, and the weight of the heuristic function decrease non-linearly with the increase of the iteration number t. Construct the weight θ1(t) of the pheromone factor in the tth iteration and the weight θ2(t) of the expected heuristic factor in the tth iteration as follows: θ2(t) = 6 - 2e -t Customer node selection: Place N ants at the distribution center, let n = 1, and unVisit n is the set of customer nodes not visited by ant n, and the taboo list congestion coefficient factor α ij The calculation formula is as follows: The probability that ant n selects customer j from customer i in the t-th iteration is as follows: Among them, τ ij is the pheromone factor; η ij is the expected heuristic factor, α ij is the congestion coefficient factor; θ1(t) is the weight of the pheromone factor, θ2(t) is the weight of the expected heuristic factor, and θ3 is the weight of the congestion coefficient factor; Construct the initial delivery route of the ant: Each time a path is selected, check whether the path meets the constraint conditions; if not, reselect the path; if so, update the set of unvisited customer points unVisit of ant n n and the taboo list tatu n ; If no more customers can be added to the current route because it does not meet the constraint conditions, the ant immediately returns to the distribution center, completes this delivery route, and starts constructing a new delivery route with the distribution center as the starting point again to continue serving the remaining unvisited customers; repeat the construction process until the set of unvisited customers Finally, obtain the initial delivery route route of ant n n ; When ant n has visited all customers, let n = n + 1, and continue to construct the initial delivery route of the next ant until n > N, and obtain the initial path planning results route of all ants regarding the customers; Cost calculation and local search: In each iteration, it specifically includes the following steps: Calculate the total delivery cost in the current iteration; Record the optimal total delivery cost and the optimal path in the current iteration; Compare with the currently known optimal solution. If it is better, update the optimal solution; Perform local search optimization, and the specific method is as follows: Randomly select two discontinuous points on the path and try to reverse this path segment; Check whether the reversed path still satisfies the load and time window constraints; If the constraints are satisfied and the total delivery cost is reduced, accept the reversed path; Update the optimal total delivery cost and the optimal route; Pheromone update: The elite ant strategy is adopted to strengthen the pheromone of the historical optimal path. The pheromone update strategy is as follows: Among them, τ ij (t) is the pheromone level on the road section (i, j) at the t-th iteration; ρ is the pheromone evaporation rate, 0 ≤ ρ < 1; the elite ant is the ant with the minimum objective value in the current iteration; is the pheromone increment of ant n on the road section (i, j) at the t-th iteration; ε is the pheromone weight of the elite ant; is the pheromone increment of the elite ant on the road section (i, j) at the t-th iteration; G is a constant; cost n is the total distribution cost of ant n, the total distribution cost of the elite ant ; Algorithm termination condition determination: If the iteration times have not been reached, then t = t + 1, and the dynamic pheromone update rule is re-determined; otherwise, the algorithm terminates and the optimal delivery plan is output.

7. A system for the planning method of the vehicle routing problem with time windows based on a time-varying road network according to any one of claims 1-6, characterized in that, It includes Data Preprocessing Module Ⅰ, Data Preprocessing Module Ⅱ, Route Planning Module and Vehicle Scheduling Module; The Data Preprocessing Module Ⅰ is used to interface with the road network data system, analyze the historical data of road conditions, and determine the road grades, vehicle driving speeds, and congestion level information of each section; The Data Preprocessing Module Ⅱ receives the delivery information of customers from the user side; The Route Planning Module is connected to the Data Preprocessing Module Ⅰ and the Data Preprocessing Module Ⅱ, and is used to plan the routes for the received customer points; The Route Planning Module inputs the route plan into the Vehicle Scheduling Module, which is used to dispatch multiple delivery vehicles to execute the delivery plan.

8. The system of the vehicle routing problem planning method with time windows based on a time-varying road network according to claim 7, characterized in that, The Route Planning Module is provided with a model construction unit, an algorithm solving unit and a delivery plan generation unit; the model construction unit is used to construct the vehicle routing problem model with time windows based on the time-varying road network; the algorithm solving unit uses the improved ant colony algorithm to solve the model; the delivery plan generation unit is used to generate the delivery plan.

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