CN117094629A - Dangerous goods full-load distribution path optimization and vehicle dispatching method - Google Patents

Abstract

The invention belongs to the technical field of distribution path planning, and discloses a method for optimizing the full-load distribution path of dangerous goods and vehicle dispatching. The method includes establishing a model of the number of vehicles, the total cost and total risk of vehicle travel, and distribution time, and establishing a mathematical model for vehicle path optimization. P1. Establish a vehicle dispatch model P2 and perform a two-stage solution (including path optimization solution method and vehicle dispatch optimization solution method). By solving the model P1, the present invention can obtain the arrival from the distribution center to each demand point and the return to the distribution center after the distribution is completed. Based on the vehicle driving route, the vehicle scheduling problem can be transformed into a VRP problem with a time window. By solving the P2 model, the vehicle scheduling optimization plan can be obtained. By optimizing driving routes and scientifically dispatching vehicles, the present invention can minimize transportation costs and transportation risks in the transportation process, while allocating the least number of vehicles and ensuring fairness in the amount of vehicle transportation tasks.

Description

A method for optimizing the delivery route and dispatching vehicles for fully loaded dangerous goods

Technical Field

The present invention relates to the technical field of distribution route planning, and in particular to a method for optimizing the distribution route of fully loaded dangerous goods and dispatching vehicles.

Background Art

The fully loaded vehicle scheduling problem was proposed by Ball, Bodin, Golden and others in 1983. It refers to the need for multiple fully loaded vehicles to perform between the distribution center and the demand point. This problem is also called the multiple transportation scheduling problem. In the process of dangerous goods transportation, if the demand at the task point is not less than the capacity of the transportation vehicle, there may be more than one vehicle to perform each transportation task. In order to complete the distribution task, the vehicle needs to run fully loaded. For example, the transportation problem of oil products at gas stations. The storage tank capacity of gas stations is usually ^30-120m3 , while the common tanker tank capacity is ^3-30m3. A gas station needs multiple tankers to transport fully loaded to meet the requirements.

The optimization of the transportation route of fully loaded vehicles for dangerous goods is a multi-objective optimization problem. There may be multiple non-dominated routes between the distribution center and the demand point. It is necessary to select the corresponding route to arrange vehicle transportation according to risk preference. After selecting the transportation route, fewer vehicles are required to participate in the distribution task by dispatching the transportation vehicles, that is, each vehicle needs to undertake as many transportation tasks as possible, that is, the idle time in the process from the beginning of the entire transportation task to the completion of all tasks is minimized. Only by optimizing the driving route and scientifically dispatching vehicles can the transportation cost and total risk of completing all transportation tasks be minimized, while the number of vehicles allocated is minimized and the fairness of vehicle transportation tasks is guaranteed. Therefore, how to optimize the route and how to optimize vehicle scheduling are technical problems that need to be solved.

Summary of the invention

The purpose of the present invention is to solve the technical problems in the prior art of dangerous goods full-load distribution, and to provide a dangerous goods full-load distribution path optimization and vehicle scheduling method.

In order to achieve the above object, the present invention adopts the following technical solutions:

A method for optimizing the distribution path and dispatching vehicles for a fully loaded dangerous goods distribution, characterized in that it comprises the following steps:

Step 1) Establish a model for the number of vehicles, total cost and total risk of vehicle travel, and delivery time;

1.1) Let the demand at the demand point d be q _d , the core load of each vehicle be g, and let q _d ≥ g, that is, a vehicle can only complete all or part of a task. The number of vehicles required to complete the delivery task at the task point d is a _d , then The total number of vehicles required to complete the delivery task of all demand points is Σ _d a _d ;

1.2) There are two cases where the transportation cost of transporting dangerous goods by transport vehicles on road section (i, j) is: The cost of empty driving is Then the transportation cost c ¹ _od from distribution center o to demand point d is the sum of the transportation costs of the sections passed, that is:

variable Indicates that the road segment (i, j) ∈ E is on the path from the distribution center o to the demand point d, otherwise

When the empty vehicle returns, the path is the path with the minimum cost from the demand point d to the distribution center o. If we say that the delivery task of demand point d is completed, the transportation cost is

1.3) The risk of transporting dangerous goods on road section (i, j) is r _ij , and the total risk of transporting from distribution center o to demand point d is:

1.4) Assume that the driving time of the vehicle on the road section (i, j) is The average loading time of a vehicle is Δt ¹ , the unloading time is Δt ² , and the driving time of a vehicle from distribution center o to demand point d is

The travel time of a vehicle from demand point d to distribution center o is

The total time it takes for a vehicle to depart from distribution center o, complete the delivery task at demand point d and return to the distribution center is:

Assume that the vehicle departs from the distribution center at The time to complete the demand point d and return to the distribution center is

1.5) Assume that the earliest time for a vehicle to depart from the distribution center and the latest time window for its return to the distribution center are [b _d , _ed ], then

The time when the vehicle arrives at the demand point d must meet the following conditions:

The time when the vehicle departs from distribution center o The following conditions must be met:

At the same time, the time window [b ₀ ,e ₀ ] of the distribution center must also be met, that is

Step 2), establish a vehicle path optimization mathematical model P1;

The P1 model is:

min f＝(f ₁ ,f ₂ ) (10)

s.t.

in:

Formula (10) represents the minimization objective vector composed of two objective functions;

Formula (11) is the expression of transportation cost function;

Formula (12) is the expression of transportation risk function;

Formula (13) ensures that a complete transportation path is formed from the distribution center o to the demand node d;

Formula (14) is the decision variable;

N represents the set of n nodes, and E represents the set of road segments between nodes;

Step 3) Establish the vehicle scheduling model P2, let _xijk ( _xijk ∈[0,1]) be whether vehicle k will perform task j after completing task i, if yes, _xijk = 1, otherwise _xijk = 0; _yik ( _yik ∈[0,1]) be whether task i is performed by vehicle k, if yes, _yik = 1, otherwise _yik = 0; for task i, if i∈J _d, its time window is The service duration is Δt _0d ;

The P2 model is:

s.t.

Where: Formula (15) represents the objective function, In the function Represents the minimum number of vehicles, M is an integer, ensuring the priority of the vehicle number target, It means that when the number of vehicles is the same, the standard deviation of the running time of all vehicles is the smallest to ensure that the intensity of the transportation task undertaken by each vehicle is fair. Formulas (16)-(19) ensure that each vehicle can only perform one operation at the same time and execute them in sequence. Each operation is completed by only one vehicle. Formula (20) represents the time when vehicle k arrives at node j. Formula (21) ensures that the time when it arrives at node j must meet the time window constraint. Formulas (22) and (23) are the time window requirements for the earliest departure and latest return time of the vehicle. Formulas (24) and (25) are decision variables. K is the vehicle set and C is the distribution node set.

Step 4), perform two-stage solution;

4.1) P1 model, i.e., path optimization solution method: In the first stage, the pulse algorithm is used to obtain the Pareto solution of all paths from the distribution center to each demand node; in the second stage, the Pareto path from the distribution center to each demand node obtained in the first stage is encoded and solved using the NSGA-II algorithm;

4.2) P2 model, i.e., vehicle scheduling optimization solution method:

First, initialize the demand information;

Second, the pulse algorithm is used to find the Pareto path from distribution center o to demand node d;

Third, the Pareto path between distribution center o and all demand nodes is obtained by using the NSGA-II multi-objective optimization method;

Fourth, the decision maker chooses one of the path options based on risk preferences;

Fifth, the UMDA-based VRP solving method is used to obtain the vehicle scheduling schedule under the path plan, that is, the vehicle scheduling plan.

Furthermore, the paths from the first-stage distribution center to each demand node in step 4.1) are Represents the Pareto path set from the distribution center node o to the demand node d. 3. A method for optimizing the path and dispatching vehicles for the full-load distribution of dangerous goods according to claim 1, characterized in that: in the second stage NSGA-II algorithm in step 4.1), according to the encoding method, fitness function and population update strategy.

Furthermore, the encoding method is individual encoding, using natural number encoding, the encoding length is m, and the format is n ₁ , n ₂ ...n _m , where: The i-th value in the code is n _i , which means that the distribution center o is connected to the demand node d _i by the Transport routes.

Furthermore, the fitness function uses [c_value, r_value] = f(indi) to represent the fitness of individual indi, where c_value and r_value are the cost and risk of transportation according to the path selection plan in individual indi, respectively.

Furthermore, in the population update strategy, the population obtains new individuals through crossover, and the crossover operation adopts the integer crossover method; first, two individuals are randomly selected from the population, two positions pos1 and pos2 (pos1＜pos2) are randomly generated, and the positions pos1 to pos2 of the two individuals are swapped to generate two new individuals;

The mutation operation uses integer mutation method to get a new individual. An individual is randomly selected and two positions pos1 and pos2 (pos1 < pos2) are randomly generated. The selected individual pos1 to pos2 are compared one by one. Perform the difference operation and take the absolute value to generate a new individual.

Compared with the prior art, the present invention has the following beneficial effects:

By solving model P1, the present invention can obtain the vehicle driving routes from the distribution center to each demand point and return to the distribution center after delivery. After selecting the vehicle driving route according to risk preference, how the decision maker should determine the vehicle dispatch plan is still a problem that needs to be solved. When the number of dispatchable vehicles is limited, the number of dispatched vehicles is an optimization goal that needs to be considered.

When the decision maker selects a certain route plan based on risk preference, in order to achieve the goal of fewer vehicles participating in the distribution task, each vehicle needs to undertake as many transportation tasks as possible, that is, the idle time in the process of starting the entire transportation task and completing all tasks is minimized. The present invention converts the vehicle scheduling problem into a VRP problem with a time window, and by solving the P2 model, a vehicle scheduling optimization solution can be obtained.

The present invention arranges vehicle transportation plans, optimizes routes, and optimizes vehicle dispatching plans, so that the transportation cost and transportation risk of the transportation process can be minimized, while the number of vehicles allocated is minimized and the fairness of vehicle transportation tasks is guaranteed.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 shows the vehicle departure and arrival timeline.

FIG. 2 is a timeline of vehicle departure and arrival after adjusting the operation time according to the present invention.

Figure 3 is a schematic diagram of the transformation of job scheduling into a VRP problem.

Figure 4 is a schematic diagram of the total cost and total risk after the paths between the distribution center and each demand node are connected.

Figure 5 shows the individual encoding method in the NSGA-II algorithm.

Figure 6 Flowchart for solving the scheduling problem of a single-model hazardous goods transport vehicle.

FIG. 7 is a diagram of a small-scale test network in an embodiment of the present invention.

FIG8 is a Pareto solution for path selection of the present invention.

Fig. 9 Comparison between the two-stage algorithm (TSA) and the general NSGA-II algorithm (GGA).

DETAILED DESCRIPTION

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

In this delivery process, in order to simplify the operation process, the following assumptions are made:

(1) When a hazardous goods transport vehicle is fully loaded, its risk is only related to the risk of the driving section and has nothing to do with the vehicle load and vehicle condition. In other words, the risk is calculated based on the risk measurement value of the driving section.

(2) When a hazardous goods transport vehicle is empty, its risk value is 0, that is, when the vehicle returns to the distribution center after unloading hazardous goods at the demand point, it chooses a route with the lowest cost (shortest distance or shortest time).

Step 1) Establish a model for the number of vehicles, total cost and total risk of vehicle travel, and delivery time;

1.1) Assume that m demand points need to be completed There are dangerous goods distribution tasks, the demand for each task is q ₁ ,q ₂ ,…,q _m , the distribution time window of demand point d is [b _d , _ed ], there are several paths P _od between distribution center o and demand point d, the demand at demand point d is q _d , the core load of each vehicle is g, and q _d ≥g, that is, a vehicle can only complete all or part of a task. The number of vehicles required to complete the distribution task at task point d is a _d , then a _d ＝q _d /g. When q _d /g is an integer, a _d ＝q _d /g; when q _d /g is not an integer, The total number of vehicles required to complete the delivery task of all demand points is ∑ _d a _d . The number of vehicles required is a constant when the demand of the demand point is known. Although the total number of vehicles is a constant, the same vehicle can participate in the delivery tasks of multiple demand points if the time window conditions are met. The total number of dispatched vehicles and the departure and arrival times of vehicles are studied in vehicle scheduling optimization.

1.2) There are two cases where the transportation cost of transporting dangerous goods by transport vehicles on road section (i, j) is: The cost of empty driving is Then the transportation cost c ¹ _od from distribution center o to demand point d is the sum of the transportation costs of the sections passed, that is:

variable Indicates that the road segment (i, j) ∈ E is on the path from the distribution center o to the demand point d, otherwise

When the empty vehicle returns, the path is the path with the minimum cost from the demand point d to the distribution center o. It means that its value can be obtained by using the shortest path solving algorithm. Then the delivery task of demand point d is completed, and the transportation cost is

1.3) The risk of transporting dangerous goods on road section (i, j) is r _ij , and the total risk of transporting from distribution center o to demand point d is:

1.4) Assume that the driving time of the vehicle on the road section (i, j) is The average loading time of a vehicle is Δt ¹ , the unloading time is Δt ² , and the driving time of a vehicle from distribution center o to demand point d is

The travel time of a vehicle from demand point d to distribution center o is

The total time it takes for a vehicle to depart from distribution center o, complete the delivery task at demand point d and return to the distribution center is:

Assume that the vehicle departs from the distribution center at The time to complete the demand point d and return to the distribution center is

1.5) Assume that the earliest time for a vehicle to depart from the distribution center and the latest time window for its return to the distribution center are [b _d , _ed ], then

The time when the vehicle arrives at the demand point d must meet the following conditions:

The time when the vehicle departs from distribution center o The following conditions must be met:

At the same time, the time window [b ₀ ,e ₀ ] of the distribution center must also be met, that is

Step 2), establish a vehicle path optimization mathematical model P1;

P1:

minf＝(f ₁ ,f ₂ ) (10)

s.t.

in:

Formula (10) represents the minimization objective vector composed of two objective functions;

Formula (11) is the expression of transportation cost function;

Formula (12) is the expression of transportation risk function;

Formula (13) ensures that a complete transportation path is formed from the distribution center o to the demand node d;

Formula (14) is the decision variable;

N represents the set of n nodes, and E represents the set of road segments between nodes.

By solving model P1, we can obtain the vehicle routes from the distribution center to each demand point and back to the distribution center after delivery. After selecting the vehicle route according to risk preference, how decision makers should determine the vehicle dispatch plan is still a problem that needs to be solved. When the number of dispatchable vehicles is limited, the number of dispatched vehicles is an optimization goal that needs to be considered.

When the decision maker selects a route plan based on risk preference, in order to achieve the goal of having fewer vehicles involved in the delivery task, each vehicle needs to take on as many transportation tasks as possible, that is, the idle time in the process from the beginning of the entire transportation task to the completion of all tasks is minimized.

For the convenience of analysis, each delivery task of each demand point is decomposed into several jobs, that is, one delivery of each vehicle is one job. For any job, the task must be completed within the range of the earliest start time to the latest end time. As shown in Figure 1, all tasks of the distribution center can be represented in a timeline. As can be seen from the figure, in order to minimize the number of vehicles used in the entire delivery cycle, the jobs (dark blocks) projected onto the total timeline should not overlap as much as possible, because the dark blocks overlap on the timeline, and their corresponding jobs must be assigned different vehicles. Therefore, the optimization goal for the minimum number of vehicles can be regarded as sliding the dark blocks on the timelines of each task so that the jobs projected onto the total timeline are as non-overlapping as possible, so as to achieve the minimum use of vehicles.

Figure 2 shows the operation timeline after adjusting the start time of some operations. Judging from the overlap of operations on the total timeline in the figure, all current delivery tasks only require two vehicles, achieving the goal of optimizing the number of vehicles. This method provides an idea for optimizing vehicle scheduling, that is, by adjusting the operation start time under the premise that the operation process meets the time window requirements, the optimization goal of the number of vehicles can be achieved. However, the scheduling result in Figure 2 is not the best result for the balance of tasks undertaken by vehicles (the first vehicle completes 8 operations, while the second vehicle only completes 1 operation). Therefore, the balance of vehicle operation distribution must also be considered in the process of optimizing operation scheduling.

Through the above analysis, each job can only be performed by one vehicle. After completing one job, the vehicle will move on to the next job. If each job is regarded as a node on a two-dimensional plane, all demand points are arranged according to the node number, and then each job in the delivery task is numbered accordingly, such as the job of the delivery task to demand point d ₁ is D ₂ 's homework is D ₃ 's homework is By analogy, J = J _d1 ∪ _{J d2} ∪ ... ∪ _{J dm} represents the set of all jobs. The vehicle scheduling problem can be transformed into a VRP problem with a time window (as shown in Figure 3), and its objective function is the minimum number of vehicles. For job i, if i∈J _d, its time window is The service time is Δt _0d . Since the node represents the operation information, it does not contain the demand information and can be regarded as 0. There is no capacity constraint for the transport vehicle.

Step 3) Establish the vehicle scheduling model P2, let _xijk ( _xijk ∈[0,1]) be whether vehicle k will perform task j after completing task i, if yes, _xijk = 1, otherwise _xijk = 0; _yik ( _yik ∈[0,1]) be whether task i is performed by vehicle k, if yes, _yik = 1, otherwise _yik = 0; for task i, if i∈J _d, its time window is The service duration is Δt _0d ;

The P2 model is:

s.t.

Where: Formula (15) represents the objective function, In the function Represents the minimum number of vehicles, M is an integer, ensuring the priority of the vehicle number target, It means that when the number of vehicles is the same, the standard deviation of the running time of all vehicles is the smallest to ensure that the intensity of the transportation task undertaken by each vehicle is fair. Formulas (16)-(19) ensure that each vehicle can only perform one operation at the same time and execute them in sequence. Each operation is completed by only one vehicle. Formula (20) represents the time when vehicle k arrives at node j. Formula (21) ensures that the time when it arrives at node j must meet the time window constraint. Formulas (22) and (23) are the time window requirements for the earliest departure and latest return time of the vehicle. Formulas (24) and (25) are decision variables. K is the vehicle set and C is the distribution node set.

Step 4), perform two-stage solution;

4.1) Model P1 is the path optimization solution method: In the first stage, the pulse algorithm is used to obtain the Pareto solution of all paths from the distribution center to each demand node. Directly using NSGA-II requires that all paths between nodes be included in the calculation. When the network scale is large, it is difficult for the evolutionary algorithm to obtain the optimal solution. You can consider excluding some paths that cannot become the optimal solution. The optimization goal of model P1 is to obtain the Pareto solution set of the total cost and total risk from the distribution center to all demand nodes. If this calculation process is regarded as connecting the paths from the distribution center to each demand node, then the cost and risk of transportation on the connected paths are calculated (Figure 4). represents the cost and risk of the path from the distribution center to the demand node d, They represent the cost and risk after returning from the demand node d to the distribution center. Assume is a solution in the Pareto solution set. If (c _d , r _d )＜(c′ _d , r′ _d ) (＜ indicates dominance), then will not appear in the Pareto solution set. This conclusion can be easily proved by contradiction if is a solution in the Pareto solution set, then at least or One of the two conditions, namely c′ _d ≤c _d or r′ _d ≤r _d, must hold, which contradicts (c _d ,r _d )＜(c′ _d ,r′ _d ).

From the above analysis, we can know that to obtain the Pareto solution set of model P1, we can first find the Pareto solution of the path from the distribution center to each demand node. Only this part of the path may appear in the Pareto path set of the model. In the second stage, the Pareto path from the distribution center to each demand node obtained in the first stage will be encoded and solved using the NSGA-II algorithm. The paths from the distribution center to each demand node in the first stage are Represents the Pareto path set from the distribution center node o to the demand node d. The two-stage method does not need to consider other paths except the Pareto path in the second stage calculation. Compared with directly using the NSGA-II algorithm to solve, the amount of calculation can be greatly reduced. Under the same population size and number of iterations, the chance of obtaining the optimal solution is significantly increased.

The encoding method is individual encoding, using natural number encoding, the encoding length is m, the format is n ₁ , n ₂ ...n _m ,

in: The i-th value in the code is n _i , which means that the distribution center o is connected to the demand node d _i by the For example, if the number of Pareto paths from distribution center 0 to demand nodes d ₁ -d ₄ is 2, 3, 5, and 4 respectively, then the code [1, 4, 3, 5] means that in this individual, the first path in the Pareto path set from distribution center to d ₁ is selected, the first path in the Pareto path set from distribution center to d ₂ is selected, the third path in the Pareto path set from distribution center to d ₃ is selected, and the first path in the Pareto path set from distribution center to d ₄ is selected for transportation.

The fitness function uses [c_value, r_value] = f(indi) to represent the fitness of individual indi, where c_value and r_value are the cost and risk of transportation according to the path selection plan of individual indi.

In the population update strategy, the population obtains new individuals through crossover, and the crossover operation adopts the integer crossover method; first, two individuals are randomly selected from the population, and two positions pos1 and pos2 (pos1 < pos2) are randomly generated. The positions pos1 to pos2 of the two individuals are swapped to generate two new individuals; the mutation operation adopts the integer mutation method to obtain new individuals, randomly select an individual, and randomly generate two positions pos1 and pos2 (pos1 < pos2), and the positions pos1 to pos2 of the selected individuals are swapped one by one with the positions pos1 to pos2 of the selected individuals. Perform the difference operation and take the absolute value to generate a new individual.

After analysis, model P2 can be transformed into a VRP problem with the goal of achieving fairness in the number of vehicles and the intensity of transportation tasks undertaken by each vehicle. Except that the objective function needs to be changed from transportation distance and number of vehicles to number of vehicles and fairness of transportation tasks, the other calculation steps can be completely solved by the VRPHTW solution method based on the distribution estimation algorithm.

4.2) P2 model, namely the vehicle scheduling optimization solution method:

First, initialize the demand information d=1;

Second, the pulse algorithm is used to find the Pareto path from the distribution center o to the demand node d, d = d + 1;

Third, if d is greater than m, the NSGA-II-based multi-objective optimization method is used to find the Pareto path between the distribution center o and all demand nodes.

Fourth, decision makers choose one of the path options based on risk preferences.

Fifth, the UMDA-based VRP solving method is used to obtain the vehicle scheduling schedule under the path plan, that is, the vehicle scheduling plan.

Example:

Test the transportation network. In Figure 7, node 0 is the distribution center, and nodes 1, 2, 4, 7, and 8 are demand points. The distance and risk of each section in the network are shown in Table 1, and the demand and time window of each demand point are shown in Table 2. The nuclear load of the transport vehicle is g = 13.5m ³ , the average loading time is Δt ¹ = 0.75h, the unloading time is Δt ² = 0.75h, the average vehicle speed is 45km/h, the full-load transportation cost is 50 yuan/km, and the empty-car transportation cost is 10 yuan/km. By arranging the vehicle transportation plan, the transportation process can achieve the minimum transportation cost and transportation risk.

Table 1 Length of each road section and the risk of transport vehicles driving on the road section

Table 2 shows the demand and the time window for accepting unloading of all demand nodes. It is a hard time window and must arrive within the specified time. If it arrives earlier than the earliest start time, it needs to wait. The earliest time for a vehicle to depart from the distribution center and the latest time to return to the distribution center are 08:00 and 20:00 respectively.

Table 2 Demand points and time windows

After step 4.1, the Pareto shortest path (departure path) and the shortest distance path (return path) from the distribution center to each demand point can be obtained (see Table 3).

Table 3 Optional paths returned from the distribution center to each demand point

After obtaining the Pareto path set from the distribution center to each demand node, the improved NSGA-II algorithm is used to obtain the Pareto solution of the total transportation cost and total risk from the distribution center to all demand nodes (Figure 8 shows the distribution of Pareto solutions, and Table 4 shows the path selection plan after decoding the corresponding individuals of the Pareto solution).

Table 4 Path selection scheme (Pareto solution, scheme 1 to scheme 14)

After a transportation plan is selected, the vehicle scheduling schedule under the path plan can be obtained by using the above model P2 solution method for the path in the plan. The vehicle scheduling plan under path plan 1 in Table 4 (Table 5) is selected. There are 17 delivery tasks in total, which require 5 vehicles to perform. The node column represents the delivery node where the transport vehicle arrives. The timetable includes the start of loading, the departure of the vehicle from the distribution center, the start of unloading at the demand node, the return to the distribution center after unloading, and the arrival of the distribution center.

Table 5 Vehicle dispatching schedule with minimum total transportation cost (Scheme 1)

Table 6 shows the vehicle scheduling scheme under the condition of selecting scheme 14. There are still 17 delivery tasks, but 6 vehicles are required to execute them. It can be seen that the number of vehicles required and the number of demand nodes served by each vehicle are different when different path schemes are selected. However, after calculation, it can be found that under the same path selection scheme, the scheduling scheme is not unique, but the number of vehicles used and the standard deviation of the running time of each vehicle are the same. This is because when the demand time windows of two different demand nodes overlap a large part, the order of transportation tasks between these nodes does not violate the time window constraint, which is also consistent with the actual situation in transportation.

Table 6 Vehicle dispatch schedule with minimum total transport risk (Scheme 14)

Verification example:

In order to verify the effectiveness of the method of the present invention, in addition to the two-stage algorithm (TSA) proposed in the paper, a general NSGA-II algorithm (GGA) is designed for the path planning problem. Different from the two-stage algorithm, the general NSGA-II algorithm adopts a priority-based encoding method PriorityBased Encoding, and its encoding length is |N|*m, while in the two-stage algorithm of the present invention, the encoding length is m.

The parameters of the two algorithms are set as follows: the population size is 100, and the number of iterations is 50 generations. Figure 9 (a) to (d) are the Pareto optimal frontiers obtained after iterations of 5, 10, 20 and 50 generations, respectively. By comparison, it can be found that when iterating to the 10th generation, the TSA algorithm can obtain the final solution, while when iterating to the 50th generation, the GGA algorithm still has not obtained the optimal solution. However, this is only for a network with 9 nodes. For large-scale networks, this gap will become larger. The two-stage algorithm designed for path planning in the present invention has a coding length that has no direct relationship with the network scale. Therefore, for large-scale networks, the algorithm is still effective. In the second stage, the problem scale of VRPTW is only related to the number of demand nodes, but has nothing to do with the scale of the transportation network. Therefore, the vehicle scheduling method of the present invention has high efficiency, whether it is a small-scale or large-scale transportation network.

Claims (6)

1. A method for optimizing the distribution path and dispatching vehicles for a fully loaded dangerous goods distribution, characterized in that it comprises the following steps: Step 1) Establish a model for the number of vehicles, total cost and total risk of vehicle travel, and delivery time; 1.1) Assume that the demand at the demand point d is q _d , the core load of each vehicle is g, and q _d ≥ g. The number of vehicles required to complete the delivery task at the task point d is a _d . Then The total number of vehicles required to complete the delivery task of all demand points is Σ _d a _d ; 1.2) There are two cases where the transportation cost of transporting dangerous goods by transport vehicles on road section (i, j) is: The cost of empty driving is Then the transportation cost c ¹ _od from distribution center o to demand point d is the sum of the transportation costs of the sections passed, that is: variable Indicates that the road segment (i, j) ∈ E is on the path from the distribution center o to the demand point d, otherwise When the empty vehicle returns, the path is the path with the minimum cost from the demand point d to the distribution center o. If we say that the delivery task of demand point d is completed, the transportation cost is 1.3) The risk of transporting dangerous goods on road section (i, j) is r _ij , and the total risk of transporting from distribution center o to demand point d is: 1.4) Assume that the driving time of the vehicle on the road section (i, j) is The average loading time of a vehicle is Δt ¹ , the unloading time is Δt ² , and the driving time of a vehicle from distribution center o to demand point d is The travel time of a vehicle from demand point d to distribution center o is The total time it takes for a vehicle to depart from distribution center o, complete the delivery task at demand point d and return to the distribution center is: Assume that the vehicle departs from the distribution center at The time to complete the demand point d and return to the distribution center is 1.5) Assume that the earliest time for a vehicle to depart from the distribution center and the latest time window for its return to the distribution center are [b _d , _ed ], then The time when the vehicle arrives at the demand point d must meet the following conditions: The time when the vehicle departs from distribution center o The following conditions must be met: At the same time, the time window [b ₀ ,e ₀ ] of the distribution center must also be met, that is Step 2), establish a vehicle path optimization mathematical model P1; The P2 model is: minf＝(f ₁ ,f ₂ ) (10) s.t. in: Formula (10) represents the minimization objective vector composed of two objective functions; Formula (11) is the expression of transportation cost function; Formula (12) is the expression of transportation risk function; Formula (13) ensures that a complete transportation path is formed from the distribution center o to the demand node d; Formula (14) is the decision variable; N represents the set of n nodes, and E represents the set of road segments between nodes; Step 3), establish the vehicle scheduling model P2, let _xijk ( _xijk ∈[0,1]) be whether vehicle k performs task j after completing task i, if yes, _xijk = 1, otherwise _xijk = 0; _yik ( _yik ∈[0,1]) be whether task i is performed by vehicle k, if yes, _yik = 1, otherwise _yik = 0; for task i, if i∈J _d , its time window is The service duration is Δt _0d ; The P2 model is: s.t. Where: Formula (15) represents the objective function, In the function Represents the minimum number of vehicles, M is an integer, ensuring the priority of the vehicle number target, It means that when the number of vehicles is the same, the standard deviation of the running time of all vehicles is the smallest to ensure that the intensity of the transportation task undertaken by each vehicle is fair. Formulas (16)-(19) ensure that each vehicle can only perform one operation at the same time, and execute them in sequence. Each operation is completed by only one vehicle. Formula (20) represents the time when vehicle k arrives at node j; Formula (21) ensures that the time of arrival at node j must meet the time window constraint; Formulas (22) and (23) are the time window requirements for the earliest departure and latest return time of the vehicle. Formulas (24) and (25) are decision variables; K is the vehicle set, and C is the distribution node set; Step 4), perform two-stage solution; 4.1) P1 model, i.e., path optimization solution method: In the first stage, the pulse algorithm is used to obtain the Pareto solution of all paths from the distribution center to each demand node; in the second stage, the Pareto paths from the distribution center to each demand node obtained in the first stage are encoded and solved using the NSGA-II algorithm; 4.2) P2 model, i.e., vehicle scheduling optimization solution method: First, initialize the demand information; Second, the pulse algorithm is used to find the Pareto path from distribution center o to demand node d; Third, the Pareto path between distribution center o and all demand nodes is obtained by using the NSGA-II multi-objective optimization method; Fourth, the decision maker chooses one of the path options based on risk preferences; Fifth, the UMDA-based VRP solving method is used to obtain the vehicle scheduling schedule under the path plan, that is, the vehicle scheduling plan. 2. A method for optimizing the route and dispatching vehicles for the distribution of fully loaded dangerous goods according to claim 1, characterized in that: the routes from the distribution center to each demand node in the first stage in step 4.1) are respectively Represents the Pareto path set from distribution center node o to demand node d. 3. A method for optimizing the route and dispatching vehicles for fully loaded dangerous goods distribution according to claim 1, characterized in that: in the step 4.1), in the second stage NSGA-II algorithm, the encoding method, fitness function and population update strategy are used. 4. A method for optimizing the route and dispatching vehicles for full-load distribution of dangerous goods according to claim 3, characterized in that: the coding method is individual coding, using natural number coding, the coding length is m, the format is n ₁ , n ₂ ...n _m , in: The i-th value in the code is n _i , which means that the distribution center o is connected to the demand node d _i by the Transport routes. 5. A method for optimizing the path and dispatching vehicles for full-load distribution of dangerous goods according to claim 3, characterized in that: the fitness function uses [c_value, r_value] = f(indi) to represent the fitness of individual indi, where c_value and r_value are the cost and risk of transportation according to the path selection plan of individual indi, respectively. 6. A method for optimizing the route and dispatching vehicles for full-load distribution of dangerous goods according to claim 3, characterized in that: in the population update strategy, the population obtains new individuals by crossover, and the crossover operation adopts the integer crossover method; firstly, two individuals are randomly selected from the population, two positions pos1 and pos2 are randomly generated, and pos1 < pos2, and the positions pos1 to pos2 of the two individuals are interchanged to generate two new individuals; The mutation operation uses integer mutation method to get a new individual. Randomly select an individual and randomly generate two positions pos1 and pos2, and pos1 < pos2. The selected individual pos1 to pos2 are compared one by one. Perform the difference operation and take the absolute value to generate a new individual.