A multi-objective vehicle path planning method with soft time windows

Abstract

The present invention is aimed at the problem of multi-objective path planning, and discloses a multi-objective vehicle path planning method with a soft time window, which belongs to the field of intelligent transportation. The method first reads the vehicle path data set and constructs a road network topology map; sets the path length and the number of compatible passengers as the target, solves all non-dominated solutions in the initial population, and adds a soft time window to update the current optimal solution; uses a 0-1 random number to judge the state transition probability and adds a penalty value to globally update the passenger flow method, and selects the optimal solution set that meets the constraint conditions. The present invention provides an effective and stable multi-objective vehicle path planning method with a soft time window, which helps to explore a path that makes the path length shorter, the number of compatible passengers more, and the transportation time as short as possible while meeting the constraint conditions, and has good application prospects.

Description

Technical Field

[0001] The invention belongs to the field of intelligent transportation, and specifically relates to a multi-objective vehicle path planning problem. A multi-objective vehicle path planning method with a soft time window is proposed. Background Art

[0002] Vehicle path planning plays a very important role in urban transportation. At present, the path transportation cost accounts for a large proportion of the cost of the urban transportation system. Reasonable path planning is one of the important methods to improve the current situation of urban transportation. In vehicle path planning, it is necessary to combine the actual road conditions and comprehensively consider the optimal solution of multiple objectives. Therefore, it is of great practical significance to study the multi-objective vehicle path planning method.

[0003] The vehicle routing problem is the core problem to be solved in route planning. Vehicle routing problem: Given the vehicle distribution center, customer point location and cargo demand, the vehicle departs from the distribution center, transports passengers from the starting point to the destination, and finally returns to the distribution center. At the same time, each customer can only be transported by one vehicle and the cargo volume demand of the customer point is guaranteed. A reasonable operation plan is determined, and the optimal solution of multiple objectives is obtained under multiple constraints (including the shortest path, the largest number of compatible passengers, the lowest transportation cost, etc.).

[0004] The multi-objective vehicle path planning method with soft time windows is highly practical and easy to implement, and is widely used. Unlike the vehicle path planning method with hard time windows, the soft time window constraint sets a flexible time, allowing waiting time and delay time caused by failure to arrive according to the time window constraint, which has obvious practicality. In addition, the soft time window method can effectively improve the scalability and practicality of the model and improve the overall service quality. The present invention will introduce a multi-objective vehicle path planning method with soft time windows. Summary of the invention

[0005] A multi-objective vehicle routing method with soft time windows is to use a real trajectory data set, design a soft delivery time window that is more in line with the actual situation, reasonably regulate the time constraints of the vehicle, comprehensively achieve multiple goals, and improve the accuracy of the solution. In the process of multi-objective vehicle routing planning using soft time windows, the goal is to minimize the length of the resulting path, maximize the number of compatible passengers, and minimize the waiting time and delay time caused by not arriving according to the customer point time window constraints.

[0006] The present invention is a multi-objective vehicle path planning method with a soft time window. Figure 1 As shown, the method is characterized by the following steps:

[0007] Step 1: Get the trajectory data set and use N = {0, 1, ..., i, ..., m} to represent the distribution center and customer points, where i∈N, 0≤i≤m, and i = 0 represents the distribution center, i = 1, ..., m represents m customer points, and use (x i ,y i ) represents the coordinates of the distribution center and the customer point. At the distribution center, a maximum of M vehicles with the same model and a maximum load capacity of R are used to complete the delivery task of all customer points. i Represents the demand for goods at the i-th customer point and satisfies maxc i ≤R, represents the maximum number of compatible passengers on a single path and ensures that C ≤ R, using [E i ,L i ] as the time window between the distribution center and the customer point, where E i represents the earliest time to serve customer point i, L i Indicates the latest time to serve customer point i. First, the optimal point set is used to generate the initial path set PT with a customer scale of S, where the possible values ​​of S are 25, 50 and 100. The road network topology is constructed based on the coordinates of the distribution center and customer points, the cargo demand, the time window information and the maximum compatible number of passengers of the vehicle.

[0008] Step 2: Use the path length of the solution and the number of compatible passengers on the path as the objective functions f1 and f2, where the domain of f1 is the shortest distance from the start point to the end point of a single path in the road network, and the domain of f2 is R, and their ranges are all real numbers. When the value of f1 is smaller and the value of f2 is larger, it means that the current solution is better. For different solutions T1 and T2 that meet the constraints, and T1, T2∈PT, solve all non-dominated solution individuals in PT that satisfy the Pareto dominance relationship of f1(T1)>f1(T2) and f2(T1)>f2(T2), or f1(T1)<f1(T2) and f2(T1)<f2(T2), and save all the non-dominated solutions obtained in the external non-dominated solution set PT_set to build a multi-objective vehicle routing problem model;

[0009] Step 3: Set a soft time window based on the multi-objective vehicle routing problem model, that is, the waiting time and delay time caused by not arriving according to the customer point time window constraint are used as the objective functions f3 and f4, where the domain of f3 and f4 is PT and the range is a real number. At this time, the values ​​of f3 and f4 are required to be as small as possible, and the time for the vehicle to return to the distribution center is guaranteed not to exceed the time window constraint, so that the current solution is better. For different solutions that meet the soft time window constraint, solve the non-dominated solution according to the Pareto dominance relationship and save all the non-dominated solutions obtained in the external non-dominated solution set PT_set. Set the customer scale to S, the fixed parameter α, the adjustment parameters θ, β, w1, w2 and the maximum number of iterations, set the number of iterations j = 1, and start iteration;

[0010] Step 4: At the jth iteration, randomly select a solution from the non-dominated solution set PT_set to select the next state, accumulate and calculate the state transition probability, and determine whether the state transition probability is greater than the current accumulated probability by generating a 0-1 random number. Select the next desirable customer point and calculate the state transition probability according to formula (1).

[0011]

[0012] where τ uv is the flow of people on edge (u,v), η uv is a heuristic value, J k (u) is the set of customers that vehicle k does not serve when it is at point u, t u is the time when the vehicle arrives at customer point u, [E u ,L u ] is the time window of customer point u, and the target is considered comprehensively through parameters w1 and w2, where w1+w2=1, θ and β parameters are used to balance the heuristic value and traffic flow. The larger the value, the greater the proportion. The function of is to calculate the state transition probability, where the part composed of passenger flow and heuristic value points to the edge with the shortest path and the largest number of compatible passengers, and the part of calculating time window and overall time points to the edge that meets the time window constraint;

[0013] Step 5: At the jth iteration, randomly select a solution from the non-dominated solution set PT_set to update the flow of people on the path, that is, update the flow of people using formula (2) and formula (3).

[0014] τ uv =τ uv *(1-α) (2)

[0015]

[0016]

[0017] Formula (3) is determined by the total distance of the optimal vehicle dispatched each time, that is, the current optimal solution, and the penalty value shown in formula (4) is added In this way, super solutions that exceed the global optimal solution are rewarded. At the same time, symmetric processing is adopted in formula (3), that is, when processing the current customer point in the current optimal path, the symmetric customer points in the current optimal path are also processed to reduce the solution time;

[0018] Step 6: Determine the termination condition. The iteration condition is that the current number of iterations is greater than the maximum number of iterations. If the iteration termination condition is met, the external non-dominated solution set is the optimal solution set for the multi-objective vehicle path planning problem with a soft time window. Output the optimal solution set and stop the iteration; otherwise, set the number of iterations j = j + 1 and return to step 3. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The present invention discloses a flow chart of a multi-objective vehicle path planning method with a soft time window. DETAILED DESCRIPTION

[0020] Take the standard test packages C101-25, R101-25, and RC101-25 with a customer scale of 25 in the Solomon benchmark instance as an example, and combine the attached Figure 1 The specific implementation method of a multi-objective vehicle path planning method with a soft time window proposed by the present invention is described.

[0021] Step 1: Get the trajectory data set, use N = {0, 1, ..., i, ..., m} to represent the distribution center and customer points, where i∈N, 0≤i≤m, and i = 0 represents the distribution center, i = 1, ..., m represents m customer points, and use (x i ,y i ) represents the coordinates of the distribution center and the customer point. At the distribution center, a maximum of M vehicles with the same model and a maximum load capacity of R are used to complete the delivery task of all customer points. i Represents the demand for goods at the i-th customer point and satisfies maxc i ≤R, represents the maximum number of compatible passengers on a single path and ensures that C ≤ R, using [E i ,L i ] as the time window between the distribution center and the customer point, where E i represents the earliest time to serve customer point i, L i Indicates the latest time to serve customer point i. First, the optimal point set is used to generate an initial path set PT with a customer scale of 25, and a road network topology is constructed based on the location coordinates of the distribution center and customer points, cargo demand, time window information, and the maximum compatible number of passengers for the vehicle is 200. The customer point information is stored in the form of a data table, as shown in Table 1.

[0022] Table 1 Distribution center and customer point information

[0023]

[0024]

[0025] After obtaining detailed information, calculate the distance d between the distribution center and the i-th customer point and between each customer point io (i≠o; i=0,1,2...,m; o=0,1,2...,m), using the formula Find the straight-line distance between any two points.

[0026] Step 2: Use the path length of the obtained solution and the number of compatible passengers on the path as the objective functions f1 and f2, where the domain of f1 is the shortest distance from the start point to the end point of a single path in the road network, and the domain of f2 is R, and their ranges are all real numbers. When the value of f1 is smaller and the value of f2 is larger, it means that the current solution is better. For different solutions T1 and T2 that meet the constraints, and T1, T2∈PT, solve all non-dominated solution individuals in PT that satisfy the Pareto dominance relationship of f1(T1)>f1(T2) and f2(T1)>f2(T2), or f1(T1)<f1(T2) and f2(T1)<f2(T2), and save all the non-dominated solutions obtained in the external non-dominated solution set PT_set to construct a multi-objective vehicle routing problem model.

[0027] Step 3: Set a soft time window based on the multi-objective vehicle routing problem model, that is, take the waiting time and delay time caused by not arriving according to the customer point time window constraint as the objective functions f3 and f4, where the domain of f3 and f4 is PT and the range is a real number. At this time, the values ​​of f3 and f4 are required to be as small as possible, and the time for the vehicle to return to the distribution center is guaranteed not to exceed the time window constraint, so that the current solution is better. For different solutions that meet the soft time window constraint, solve the non-dominated solution according to the Pareto dominance relationship and save all the non-dominated solutions obtained in the external non-dominated solution set PT_set. Set the customer scale to 25, fixed parameter α=0.05, parameter β=1, θ=5, w1=0.9, w2=0.1 and the maximum number of iterations to 500, set the number of iterations j=1, and start iteration.

[0028] Step 4: At the jth iteration, randomly select a solution from the non-dominated solution set PT_set to select the next state, accumulate and calculate the state transition probability, and determine whether the state transition probability is greater than the current accumulated probability by generating a 0-1 random number. Select the next desirable customer point and calculate the state transition probability according to formula (5).

[0029]

[0030] where τ uv is the flow of people on edge (u,v), η uv is a heuristic value, J k (u) is the set of customers that vehicle k does not serve when it is at point u, t u is the time when the vehicle arrives at customer point u, [E u ,L u ] is the time window of customer point u, and the target is considered comprehensively through parameters w1 and w2, where w1+w2=1, θ and β parameters are used to balance the heuristic value and traffic flow. The larger the value, the greater the proportion. The role of is to calculate the state transition probability, where the part composed of passenger flow and heuristic value points to the edge with a shorter path and the largest number of compatible passengers, and the part of calculating the time window and the overall time points to the edge that meets the time window constraint.

[0031] Step 5: At the jth iteration, randomly select a solution from the non-dominated solution set PT_set to update the pedestrian flow in the path, that is, update the pedestrian flow through formula (6) and formula (7).

[0032] τ uv =τ uv *(1-α) (6)

[0033]

[0034]

[0035] Formula (6) is determined by the total distance of the optimal vehicle dispatched each time, that is, the current optimal solution, and the penalty value shown in formula (7) is added In this way, a super solution that exceeds the global optimal solution is rewarded. At the same time, symmetric processing is adopted in formula (6), that is, when processing the current customer point in the current optimal path, the symmetric customer points in the current optimal path are also processed to reduce the solution time.

[0036] Step 6: Determine the termination condition. The iteration condition is that the current number of iterations is greater than the maximum number of iterations. If the iteration termination condition is met, the external non-dominated solution set is the optimal solution set for the multi-objective vehicle path planning problem with soft time windows. Output the optimal solution set and stop iteration; otherwise, set the number of iterations j = j + 1, and return to step 3. For example, for the three groups of examples of the standard test packages C101-25, R101-25 and RC101-25 with a customer scale of 25 in the Solomon benchmark instance, the same parameters and experimental conditions are set. After 500 iterations, the optimal vehicle path planning obtained by different standard test packages when meeting multiple constraints is shown in Tables 2, 3 and 4, respectively, and the optimal solution under the optimal vehicle path planning condition is described in Table 5.

[0037] Table 2 Optimal solution of vehicle path planning for standard test package C101-25

[0038]

[0039] Table 3 Optimal solution of vehicle path planning for standard test package R101-25

[0040]

[0041] Table 4 Optimal solution of vehicle path planning for standard test package RC101-25

[0042]

[0043] Table 5 Experimental results of different standard test packages

[0044]

[0045] Through the above experimental process, a multi-objective vehicle path planning method with soft time windows can be realized. Multiple experiments are carried out for standard test packages C101-25, R101-25 and RC101-25 with a customer scale of 25 in the Solomon benchmark instance. After 500 iterations of each experiment, it can be seen that the present invention can obtain an optimal solution including a shorter path and more compatible passengers when adding a soft time window, and when the same parameters are set, the vehicle utilization rate is more average, the total length of the path is shorter, and the number of passengers compatible with the path is greater. Therefore, the present invention is stable and effective in solving the multi-objective vehicle path planning problem with soft time windows.

Claims

1. A multi-objective vehicle path planning method with soft time windows, characterized in that: The following steps are involved: Step 1: Get the trajectory data set and use N = {0, 1, ..., i, ..., m} to represent the distribution center and customer points, where i∈N, 0≤i≤m, and i = 0 represents the distribution center, i = 1, ..., m represents m customer points, and use (x i ,y i ) represents the coordinates of the distribution center and the customer point. At the distribution center, a maximum of M vehicles with the same model and a maximum load capacity of R are used to complete the delivery task of all customer points. i Represents the demand for goods at the i-th customer point and satisfies maxc i ≤R, represents the maximum number of compatible passengers on a single path and ensures that C ≤ R, using [E i ,L i ] as the time window between the distribution center and the customer point, where E i represents the earliest time to serve customer point i, L i Indicates the latest time to serve customer point i. First, the optimal point set is used to generate the initial path set PT with a customer scale of S, where the possible values ​​of S are 25, 50 and 100. The road network topology is constructed based on the coordinates of the distribution center and customer points, the cargo demand, the time window information and the maximum compatible number of passengers of the vehicle. Step 2: Use the path length of the solution and the number of compatible passengers on the path as the objective functions f1 and f2, where the domain of f1 is the shortest distance from the start point to the end point of a single path in the road network, and the domain of f2 is R, and their ranges are all real numbers. When the value of f1 is smaller and the value of f2 is larger, it means that the current solution is better. For different solutions T1 and T2 that meet the constraints, and T1, T2∈PT, solve all non-dominated solution individuals in PT that satisfy the Pareto dominance relationship of f1(T1)>f1(T2) and f2(T1)>f2(T2), or f1(T1)<f1(T2) and f2(T1)<f2(T2), and save all the non-dominated solutions obtained in the external non-dominated solution set PT_set to build a multi-objective vehicle routing problem model; Step 3: Set a soft time window based on the multi-objective vehicle routing problem model, that is, the waiting time and delay time caused by not arriving according to the customer point time window constraint are used as the objective functions f3 and f4, where the domain of f3 and f4 is PT and the range is a real number. At this time, the values ​​of f3 and f4 are required to be as small as possible, and the time for the vehicle to return to the distribution center is guaranteed not to exceed the time window constraint, so that the current solution is better. For different solutions that meet the soft time window constraint, solve the non-dominated solution according to the Pareto dominance relationship and save all the non-dominated solutions obtained in the external non-dominated solution set PT_set, set the customer scale S, fixed parameter α, adjustment parameters θ, β, w1, w2 and the maximum number of iterations, set the number of iterations j = 1, and start iteration; Step 4: At the jth iteration, randomly select a solution from the non-dominated solution set PT_set to select the next state, accumulate and calculate the state transition probability, and determine whether the state transition probability is greater than the current accumulated probability by generating a 0-1 random number. Select the next desirable customer point and calculate the state transition probability according to formula (1). where τ uv is the flow of people on edge (u,v), η uv is a heuristic value, J k (u) is the set of customers that vehicle k does not serve when it is at point u, t u is the time when the vehicle arrives at customer point u, [E u ,L u ] is the time window of customer point u, and the target is considered comprehensively through parameters w1 and w2, where w1+w2=1, θ and β parameters are used to balance the heuristic value and traffic flow. The larger the value, the greater the proportion. The function of is to calculate the state transition probability, where the part composed of passenger flow and heuristic value points to the edge with the shortest path and the largest number of compatible passengers, and the part of calculating time window and overall time points to the edge that meets the time window constraint; Step 5: At the jth iteration, randomly select a solution from the non-dominated solution set PT_set to update the flow of people on the path, that is, update the flow of people using formula (2) and formula (3). t uv =t uv *(1-a) (2) Formula (3) is determined by the total distance of the optimal vehicle dispatched each time, that is, the current optimal solution, and the penalty value shown in formula (4) is added In this way, super solutions that exceed the global optimal solution are rewarded. At the same time, symmetric processing is adopted in formula (3), that is, when processing the current customer point in the current optimal path, the symmetric customer points in the current optimal path are also processed to reduce the solution time; Step 6: Determine the termination condition. The iteration condition is that the current number of iterations is greater than the maximum number of iterations. If the iteration termination condition is met, the external non-dominated solution set is the optimal solution set for the multi-objective vehicle path planning problem with a soft time window. Output the optimal solution set and stop the iteration; otherwise, set the number of iterations j = j + 1 and return to step 3.

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