A short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm

Abstract

The present invention discloses a short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm, comprising: (1) establishing a three-dimensional vehicle / pedestrian-time-space network according to the evacuation starting point, evacuation end point, departure time window and arrival time window of the evacuees; (2) defining binary decision variables and establishing a multi-passenger multi-driver network flow model; (3) assigning a difficult constraint to a Lagrangian multiplier, and relaxing it into an objective function to obtain a new Lagrangian relaxation function. Solve the Lagrangian dual problem with the Lagrangian multiplier as a variable; (4) update the Lagrangian multiplier using a subgradient method; (5) construct a new vehicle / pedestrian-time-space network, solve a new vehicle path problem model, and simultaneously update the search step size and the number of iterations; (6) if the number of iterations does not meet the requirements at this time, iterate (3)-(5) until the condition is met and the cycle ends. The present invention can complete the evacuation of more people with as little cost as possible.

Description

Technical Field

[0001] The invention belongs to the technical field of path planning, and in particular relates to a short-term early warning evacuation path planning method based on a Lagrangian relaxation algorithm. Background Art

[0002] Natural disasters include floods, wind and hail, drought, typhoons, earthquakes, geological disasters, low temperatures and freezing, and snowstorms. In recent years, the economic losses caused by disasters have increased significantly. In order to reduce the direct or potential danger to life caused by disasters, it is necessary to evacuate the population from the disaster-stricken areas to safe places on a large scale. Such extreme events require the evacuation of a large number of people from the disaster-stricken areas in a short period of time or without any warning. The preparation time for the predictability of disaster occurrence directly affects the issuance of evacuation notices. The evacuation problem can be divided into short-term warning evacuation and no warning evacuation. Evacuation of short-term warning disasters, such as typhoons or floods, usually issues warnings 24 to 72 hours in advance, so that evacuees and emergency management agencies can be more prepared for evacuation. In the preparation of short-term warning evacuation plans, the lack of private cars and lack of fuel are two major problems in emergency evacuation.

[0003] If passengers can be allowed to walk from the starting point to the boarding point or from the alighting point to the destination on the basis of carpooling evacuation, the flexibility of passengers can be fully utilized to reduce the detours that drivers must take to serve passengers, thereby shortening the evacuation time as much as possible. However, in actual disaster evacuations, it is difficult to determine feasible boarding or alighting points for passengers without cars in advance. Therefore, studying the problem of short-term warning carpooling evacuation that allows passengers to walk has a high practical application value for successfully completing the evacuation of short-term warning disasters. Summary of the invention

[0004] Technical problem to be solved: In view of the problems existing in the prior art, the present invention proposes a short-term early warning evacuation path planning method based on the Lagrangian relaxation algorithm, which introduces the walking of people evacuated without a car into the carpooling evacuation, so as to complete the evacuation of more people with the least possible cost.

[0005] Technical solution:

[0006] A short-term warning evacuation path planning method based on Lagrangian relaxation algorithm, the short-term warning evacuation path planning method is used to introduce the walking information of people evacuating without cars into carpooling evacuation, so as to solve the short-term warning carpooling evacuation problem under the condition that passengers are allowed to walk;

[0007] The short-term early warning evacuation path planning method comprises the following steps:

[0008] S1, according to the evacuation starting point, evacuation destination, departure time window, arrival time window and vehicle capacity of the evacuees with vehicles, add virtual nodes and virtual road sections corresponding to the starting and ending points of all evacuees in the traffic network, determine the reachable nodes of the evacuees without vehicles and the feasible paths of the evacuees with vehicles, and establish a three-dimensional vehicle / pedestrian-time-space network; the three-dimensional vehicle / pedestrian-time-space network includes a three-dimensional vehicle / pedestrian-time-space node set, a vehicle / pedestrian-time-space arc set connected between vehicle / pedestrian-time-space nodes constructed according to feasible rules, and the use cost of each vehicle / pedestrian-time-space arc;

[0009] S2, defines the binary decision variables Where p∈P, set P is the set of all evacuees; (v,u,i,j,t,s)∈Φ, y(p,v,u,i,j,t,s)∈{0,1}, Φ is the set of feasible arcs; taking minimizing the total route cost of evacuees without cars as the objective function, a multi-passenger and multi-driver network flow model is established; if y(p,v,u,i,j,t,s) is equal to 1, then evacuee p reaches node i at time t by way v, and reaches node j at time s by way u; way v and way u include two ways: taking a vehicle and walking;

[0010] S3, assign the hard constraint to the Lagrange multiplier, relax it into the objective function to obtain a new Lagrange relaxation function, and solve the Lagrange dual problem with the Lagrange multiplier as a variable;

[0011] S4, update the Lagrange multiplier using the subgradient method;

[0012] S5, using the updated Lagrange multipliers to construct a new vehicle / pedestrian-time-space network, solving the new vehicle routing problem model, and updating the search step size and number of iterations;

[0013] S6, repeating steps S3 to S5 until the number of iterations reaches a preset iteration number threshold, and then ending the loop.

[0014] Furthermore, in step S1, the process of adding virtual nodes and virtual road sections corresponding to the starting and ending points of all evacuees in the traffic network and determining the reachable nodes for evacuees without vehicles and the feasible paths for evacuees with vehicles includes the following steps:

[0015] A11, for the starting point o of the evacuee p p , add the corresponding virtual starting point o′ p and road section (o p ,o′ p ), road section (o p ,o′ p ) cost is 0; for the destination d of the evacuee pp , add the corresponding virtual starting point d′ p and road section (d p ,d′ p ), road section (d p ,d′ p ) cost is 0;

[0016] A12, starting point for evacuation without car pr , if from o pr If the shortest walking distance to the actual node i in the network is less than or equal to 600 meters, then node o pr and node i is added to the set of feasible boarding points H for the evacuee pr without a car pr , and add the shortest path to the walking path set Walk of the car-free evacuee pr pr ; where pr∈PR, the set PR is the set of all evacuees without a car; for the destination d of the evacuee pr without a car pr , if from the actual node i to d in the network pr If the shortest walking distance is less than or equal to 600 meters, node d pr and node i is added to the set of feasible drop-off points X for the car-free evacuee pr pr , and add the shortest path to the walking path set Walk of the car-free evacuee pr pr ; The shortest road distance adopts the actual road network distance;

[0017] A13, for the evacuation personnel pd by car, calculate the starting point o of pd pd To the end point pd The shortest path pd , the length is l pd , where pd∈PD, the set PD is the set of all people evacuated by car;

[0018] A14, for the evacuees with cars pd and the evacuees without cars pr, if the actual node i∈H pr And the actual node j∈X in the network pr , then calculate the starting point o of the evacuated personnel pd from the vehicle pd Start, pass through nodes i and j to reach the end point d pd The shortest path path, the shortest path length is recorded as l pr ; if l pr ≤3×l pd , change the path path pd and path path is added to the set of feasible paths for evacuating people pd by car pd .

[0019] Furthermore, in step S1, the process of constructing the three-dimensional vehicle / pedestrian-time-space node set includes the following steps:

[0020] B11, virtual starting point o′ for the evacuated personnel pd by car pd , and its corresponding vehicle-time-space node is (v pd ,o′ pd ,a pd ), where v pd is the vehicle status of the evacuee pd, a pd is the earliest departure time of the evacuee pd with a car; the virtual destination d′ of the evacuee pd with a car pd , and its corresponding vehicle-time-space node is (v pd ,d′ pd ,b′ pd ), where b′ pd is the latest arrival time of the evacuees pd by car;

[0021] B12, virtual starting point o′ for the evacuee pr without a car pr , and its corresponding vehicle / pedestrian-time-space node is (0,o′ pr ,a pr ), where a pr is the earliest departure time of the evacuee pr with a car; the virtual destination d′ of the evacuee pr without a car pr , and its corresponding vehicle / pedestrian-time-space node is (0,d′ pr ,b′ pr ), where b′ pr is the latest arrival time of the evacuees pr without a car;

[0022] B13, for the set Feasible pd For each feasible time of each node i on each path in, add the vehicle / walking-time space node (v pd ,i,t), where t is the vehicle v pd The time of arrival at node i;

[0023] B14, for the collection Walk pr For each feasible time of each node i on each path in, add the vehicle / walking-time space node as (w pr ,i,t), where w pr represents the walking state of the car-free evacuee pr, and t is the time when the car-free evacuee pr arrives at the node i on foot;

[0024] B15, add all vehicle / pedestrian-time and space nodes obtained in the above steps B11-B14 to the feasible node set Ω; add the vehicle / pedestrian-time and space nodes obtained in the above steps B11-B12 to the virtual node set Ω 0 ; Add the vehicle / walking-time-space nodes obtained in the above steps B13-B14 to the actual node set Ω * .

[0025] Furthermore, in step B13, for the set Feasible pd For each node i of each path in, if i is the starting point o of the car evacuating personnel pd pd , then a pd ≤t≤b pd , where a pd is the earliest departure time of pd, b pd is the latest departure time of pd; if i is the destination d of the evacuated person pd by car pd , then a′ pd ≤t≤b′ pd , where a′ pd is the latest arrival time of pd, b′ pd is the latest departure time of pd; if i is neither the starting point o of the evacuee pd pd , nor is it the end point pd , then a pd ≤t≤b′ pd ;

[0026] In step B14, for the set Walk pr For each node i of each path in , if i is the starting point o of the vehicle-free evacuation personnel pr pr , then a pr ≤t≤b pr , where a pr is the earliest departure time of pr, b pr is the latest departure time of pr; if i is the destination d of the evacuee pr without a car pr , then a′ pr ≤t≤b′ pr . Where a′ pr is the latest arrival time of pr, b′ pr is the latest departure time of pr; if i is neither the starting point o of the car-free evacuee pr nor the starting point o of the car-free evacuee pr pr , nor is it the end point pr , then a pr ≤t≤b′ pr .

[0027] Furthermore, in step S1, the process of constructing the vehicle / pedestrian-time-space arc set includes the following steps:

[0028] For the feasible node set Ω and the virtual node set Ω 0 and the actual node set Ω * Analyze all vehicle / pedestrian-time-space nodes in:

[0029] If (v pd ,i,t)∈Ω * And (v pd ,j,s)∈Ω * , and the road segment from node i to node j exists in the traffic network and satisfies t(i,j)≤(st)≤t(i,j)+15, then (v pd ,v pd ,i,j,t,s) is added to the feasible arc set Φ, where t(i,j) is the cost of passing the road segment (i,j);

[0030] If (w pr ,i,t)∈Ω * And (w pr ,j,s)∈Ω * , and the road segment from node i to node j is in the traffic network and satisfies (st) = T(i,j), then (w pr ,w pr ,i,j,t,s) are added to the feasible arc set Φ and the actual arc set Φ * , where T(i,j) is the cost of walking through the road segment (i,j);

[0031] If (v pd ,i,t)∈Ω * And (w pr ,i,s)∈Ω * , and satisfy 0≤(st)≤15, then (v pd ,w pr ,i,j,t,s) are added to the feasible arc set Φ and the actual arc set Φ * ;

[0032] If (w pr ,i,t)∈Ω * And (v pd ,i,s)∈Ω * , and satisfy 0≤(st)≤15, then (w pr ,v pd ,i,i,s,t) are added to the feasible arc set Φ and the actual arc set Φ * ;

[0033] If (v pd,o′ pd ,a pd )∈Ω 0 And (v pd ,o pd ,t)∈Ω * , then add (v pd ,v pd ,o′ pd ,o pd ,a pd ,t) to the feasible arc set Φ and the virtual arc set Φ 0 ;

[0034] If (v pd ,d′ pd ,b′ pd )∈Ω 0 And (v pd ,d pd ,t)∈Ω * , then add (v pd ,v pd ,d pd ,d′ pd ,t,b′ pd ) to the feasible arc set Φ and the virtual arc set Φ 0 ;

[0035] If (0,o′ pr ,a pr )∈Ω 0 , and (v pd ,o pr ,t)∈Ω * ,(w pr ,o pr ,t)∈Ω * , then add (0,v pd ,o′ pr ,o pr ,a pr ,t) and (0,w pr ,o′ pr ,o pr ,a pr ,t) to the feasible arc set Φ and the virtual arc set Φ 0 ;

[0036] If (0,d′ pr ,b′ pr )∈Ω 0 , and (v pd ,d pr ,t)∈Ω * ,(w pr ,d pr ,t)∈Ω * , then add (v pd,0,d pr ,d′ pr ,t,b′ pr ) and (w pr ,0,d pr ,d′ pr ,t,b′ pr ) to the feasible arc set Φ and the virtual arc set Φ 0 ;

[0037] for Set (0,0,o′ pr ,d′ pr ,a pr ,b′ pr ) is added to the feasible arc set Φ and the virtual arc set Φ 0 .

[0038] Furthermore, the process of defining the usage cost of each vehicle / walking-time-space arc includes the following steps:

[0039] for Define the usage cost of arc (v,u,i,j,t,s) = st; for If node i is the virtual starting point o′ p , then define the usage cost of arc (v,u,i,j,t,s) = 0; for If node j is a virtual endpoint d′ p , then the usage cost c(v,u,i,j,t,s) of the virtual starting point definition arc (v,u,i,j,t,s) = 0.

[0040] Furthermore, in step S2, the multi-passenger and multi-driver network flow model established is:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] Initialize λ in(v,i,t) ,λ out(v,i,t) and λ pr are all 0, k=0, ZR * =10000,θ 0 =1.

[0053] Furthermore, in step S3, the hard constraint is assigned to the Lagrange multiplier, and is relaxed into the objective function to obtain a new Lagrange relaxation function. The process of solving the Lagrange dual problem with the Lagrange multiplier as a variable includes the following steps:

[0054] S31, introducing the Lagrange multiplier λ into the multi-passenger and multi-driver network flow model established in step S2 above in(v,i,t) ,λ out(v,i,t) and λ pr , relax the hard constraint to the objective function, and obtain the new Lagrangian relaxation function as follows:

[0055]

[0056] S32, establish a new multi-passenger and multi-driver network flow model as follows:

[0057] z LR =L (13);

[0058] st

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] S33, using the GAMS solver to solve the model in step S32, the obtained solution vector set is

[0067] Further, in step S4, the process of updating the Lagrange multipliers using the subgradient method includes the following steps:

[0068] S41. Calculate the Lagrange multipliers λ in(v,i,t) , λ out(v,i,t) and λ pr subgradients according to the following formula:

[0069]

[0070]

[0071]

[0072] S42. Update the Lagrange multipliers λ in(v,i,t) , λ out(v,i,t) and λ pr using the following formula:

[0073]

[0074]

[0075]

[0076] Further, in step S5, the process of constructing a new vehicle / walking - time - space network using the updated Lagrange multipliers, solving the new vehicle routing problem model, and simultaneously updating the search step size and the number of iterations includes the following steps:

[0077] S51. Create a new set of vehicle / walking - space - time nodes a new set of vehicle / walking - space - time arcs

[0078] S51. For If y(pd, v pd , v pd , i, j, t, s) = 1 and (w pr , i, s) ∈ Ω * , New_Ω * = New_Ω * ∪{(v pd , i, t), (v pd , j, s), (w pr , i, s)};

[0079] For (v pd , i, t) ∈ New_Ω * , (v pd , j, s) ∈ New_Ω * , If (v pd , vpd ,i,j,t,s)∈Ω * , New_Φ * =New_Φ * ∪{(v pd ,v pd ,i,j,t,s)};

[0080] For (v pd ,i,t)∈New_Ω * ,(w pr ,j,s)∈Ω * , if (v pd ,w pr ,i,j,t,s)∈Ω * , New_Φ * =New_Φ * ∪{(v pd ,w pr ,i,j,t,s)};

[0081] For (v pd ,i,t)∈New_Ω * ,(w pr ,j,s)∈Ω * , if (w pr ,v pd ,j,i,s,t)∈Ω * , New_Φ * =New_Φ * ∪{(w pr ,v pd ,j,i,s,t)};

[0082] S52, establish a new vehicle routing problem as follows:

[0083]

[0084] st

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] x(pr,v,u,i,j,t,s)∈{0,1} (34);

[0092] S53, using the GAMS solver to solve the above vehicle routing problem, obtain the solution vector and the optimal value ZR k ;

[0093] If ZR k <ZR * , update the optimal solution according to the following formula:

[0094]

[0095]

[0096] ZR * =ZR k (37);

[0097] S54, y * Substitute (p,v,u,i,j,t,s) into the objective function Z of the original problem to obtain the lower bound solution LB k ;

[0098] S55, update the search step length θ k And the number of iterations k:

[0099]

[0100] k=k+1 (39).

[0101] Beneficial effects:

[0102] The short-term early warning evacuation path planning method based on the Lagrangian relaxation algorithm of the present invention can allow passengers to walk from the starting point to the boarding point or walk from the alighting point to the end point on the basis of carpooling evacuation. By introducing the walking of people evacuating without a car into carpooling evacuation, the flexibility of passengers is fully utilized to reduce the detours that drivers must take to serve passengers, thereby completing the evacuation of more people with the least possible cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 This is a flow chart of a short-term early warning evacuation path planning method based on a Lagrangian relaxation algorithm according to an embodiment of the present invention;

[0104] Figure 2 A three-dimensional vehicle / pedestrian-time-space network structure diagram of an embodiment of the present invention;

[0105] Figure 3 This is a time-space diagram of the solution results of the embodiment of the present invention. DETAILED DESCRIPTION

[0106] The following examples will enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0107] Figure 1 Flow chart of the short-term warning evacuation path planning method based on Lagrangian relaxation algorithm according to an embodiment of the present invention. Figure 1 ,This short-term warning evacuation path planning method is used to introduce the walking information of the evacuees without a car into the carpooling evacuation and solve the short-term warning carpooling evacuation problem when the passengers are allowed to walk;

[0108] The short-term early warning evacuation path planning method comprises the following steps:

[0109] S1, according to the evacuation starting point, evacuation end point, departure time window, arrival time window and vehicle capacity of the evacuees with cars, add virtual nodes and virtual road sections corresponding to the starting and ending points of all evacuees in the traffic network, determine the reachable nodes of evacuees without cars and the feasible paths of evacuees with cars, and establish a three-dimensional vehicle / pedestrian-time-space network; the three-dimensional vehicle / pedestrian-time-space network includes a three-dimensional vehicle / pedestrian-time-space node set, a vehicle / pedestrian-time-space arc set connected between vehicle / pedestrian-time-space nodes constructed according to feasible rules, and the use cost of each vehicle / pedestrian-time-space arc.

[0110] S2, defines the binary decision variables Where p∈P, set P is the set of all evacuees; (v,u,i,j,t,s)∈Φ, y(p,v,u,i,j,t,s)∈{0,1}, Φ is the set of feasible arcs; with minimizing the total route cost of non-car evacuees as the objective function, a multi-passenger multi-driver network flow model is established. If y(p,v,u,i,j,t,s) is equal to 1, then evacuee p can reach node j at time s from node i at time t by vehicle / walking mode v at time s by vehicle / walking mode u.

[0111] S3, assign the hard constraint to the Lagrange multiplier, relax it into the objective function to obtain a new Lagrange relaxation function, and solve the Lagrange dual problem with the Lagrange multiplier as a variable.

[0112] S4, update the Lagrange multiplier using the subgradient method.

[0113] S5, uses the updated Lagrange multipliers to construct a new vehicle / pedestrian-time-space network, solves the new vehicle routing problem model, and updates the search step size and number of iterations.

[0114] S6, repeating steps S3 to S5 until the number of iterations reaches a preset iteration number threshold, and then ending the loop.

[0115] (1) According to the evacuation starting point, evacuation end point, departure time window and arrival time window of the evacuees, a three-dimensional vehicle / pedestrian-time-space network is established. Table 1 shows the evacuee information of this example. In this example, the detour tolerance of the vehicle is set to 0, so the vehicle's driving path is the shortest path of the vehicle, that is, 1-2-4-5-8. At the same time, the vehicle capacity is set to 3 and the maximum walking distance is set to 3. The feasible boarding point set for vehicle-free evacuee 1 is {2,4}, and the feasible alighting point set is {5,6}; the feasible boarding point set for vehicle-free evacuee 2 is {3,4}, and the feasible alighting point set is {4,5}.

[0116] Table 1 Evacuation personnel information table of this example

[0117]

[0118] (2) Define binary decision variables Define binary decision variables:

[0119]

[0120] A multi-passenger and multi-driver network flow model is established. The model objective function is to minimize the total route cost, and the constraints include the starting point flow balance constraint, the terminal flow balance constraint, the intermediate node flow balance constraint, the vehicle capacity constraint, and the vehicle use constraint for each evacuee.

[0121] (3) Assign the vehicle capacity constraint and vehicle usage constraint to the Lagrange multiplier λ respectively. in(v,i,t) ,λ out(v,i,t) and λ pr , relax to the objective function to get the new Lagrangian relaxation function L, and solve the Lagrangian dual problem with Lagrangian multipliers as variables. The objective function of the problem is L, and the constraints include the starting flow balance constraint, the terminal flow balance constraint, and the intermediate node flow balance constraint of each evacuee:

[0122]

[0123] (4) Calculate the Lagrange multiplier λ in(v,i,t) ,λ out(v,i,t) and λ pr The subgradient of:

[0124]

[0125]

[0126]

[0127] Update the Lagrange multiplier λ in(v,i,t) ,λ out(v,i,t) and λpr , the calculation formula is as follows:

[0128]

[0129]

[0130]

[0131] (5) Based on the results of step (3), a new vehicle / pedestrian-time-space network is constructed to solve the new vehicle routing problem model. The model variables are The objective function is to minimize the total route cost of car-free evacuation personnel. The constraints include the starting point flow balance constraint, the terminal flow balance constraint, the intermediate node flow balance constraint, the vehicle capacity constraint, and the vehicle use constraint. At the same time, the search step size and the number of iterations are updated:

[0132]

[0133] k=k+1.

[0134] (6) If the number of iterations does not meet the requirement, iterate steps (3) to (5) until the condition is met and the loop ends.

[0135] The above contents are further detailed descriptions of the present invention in combination with specific preferred implementation modes. It cannot be determined that the specific implementation of the present invention is limited to these descriptions. For technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm, characterized in that: The short-term warning evacuation path planning method is used to introduce the walking information of people evacuating without cars into carpooling evacuation, solving the short-term warning carpooling evacuation problem when passengers are allowed to walk; The short-term early warning evacuation path planning method The following steps are involved: S1, according to the evacuation starting point, evacuation destination, departure time window, arrival time window and vehicle capacity of the evacuees with vehicles, add virtual nodes and virtual road sections corresponding to the starting and ending points of all evacuees in the traffic network, determine the reachable nodes of the evacuees without vehicles and the feasible paths of the evacuees with vehicles, and establish a three-dimensional vehicle / pedestrian-time-space network; the three-dimensional vehicle / pedestrian-time-space network includes a three-dimensional vehicle / pedestrian-time-space node set, a vehicle / pedestrian-time-space arc set connected between vehicle / pedestrian-time-space nodes constructed according to feasible rules, and the use cost of each vehicle / pedestrian-time-space arc; S2, defines the binary decision variables Where p∈P, set P is the set of all evacuees; (v,u,i,j,t,s)∈Φ, y(p,v,u,i,j,t,s)∈{0,1}, Φ is the set of feasible arcs; taking minimizing the total route cost of evacuees without cars as the objective function, a multi-passenger and multi-driver network flow model is established; if y(p,v,u,i,j,t,s) is equal to 1, then evacuee p reaches node i at time t by way v, and reaches node j at time s by way u; way v and way u include two ways: taking a vehicle and walking; S3, assign the hard constraint to the Lagrange multiplier, relax it into the objective function to obtain a new Lagrange relaxation function, and solve the Lagrange dual problem with the Lagrange multiplier as a variable; S4, update the Lagrange multiplier using the subgradient method; S5, using the updated Lagrange multipliers to construct a new vehicle / pedestrian-time-space network, solving the new vehicle routing problem model, and updating the search step size and number of iterations; S6, repeating steps S3 to S5 until the number of iterations reaches a preset iteration number threshold, and then ending the loop; In step S2, the multi-passenger and multi-driver network flow model established is: Initialize λ in(v,i,t) ,λ out(v,i,t) and λ pr are all 0, k=0, ZR * =10000,θ 0 =1.

2. The short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm according to claim 1 is characterized in that: In step S1, the process of adding virtual nodes and virtual road sections corresponding to the starting and ending points of all evacuees in the traffic network and determining the reachable nodes for evacuees without vehicles and the feasible paths for evacuees with vehicles includes the following steps: A11, for the starting point o of the evacuee p p , add the corresponding virtual starting point o′ p and road section (o p ,o′ p ), road section (o p ,o′ p ) cost is 0; for the destination d of the evacuee p p , add the corresponding virtual starting point d′ p and road section (d p ,d′ p ), road section (d p ,d′ p ) cost is 0; A12, starting point for evacuation without car pr , if from o pr If the shortest walking distance to the actual node i in the network is less than or equal to 600 meters, then node o pr and node i is added to the set of feasible boarding points H for the evacuee pr without a car pr , and add the shortest path to the walking path set Walk of the car-free evacuee pr pr ; where pr∈PR, the set PR is the set of all evacuees without a car; for the destination d of the evacuee pr without a car pr , if from the actual node i to d in the network pr If the shortest walking distance is less than or equal to 600 meters, node d pr and node i is added to the set of feasible drop-off points X for the car-free evacuee pr pr , and add the shortest path to the walking path set Walk of the car-free evacuee pr pr ; The shortest road distance adopts the actual road network distance; A13, for the evacuation personnel pd by car, calculate the starting point o of pd pd To the end point pd The shortest path pd , the length is l pd , where pd∈PD, the set PD is the set of all people evacuated by car; A14, for the evacuees with cars pd and the evacuees without cars pr, if the actual node i∈H pr And the actual node j∈X in the network pr , then calculate the starting point o of the evacuated personnel pd from the car pd Start, pass through nodes i and j to reach the end point d pd The shortest path path, the shortest path length is recorded as l pr ; if l pr ≤3×l pd , change the path path pd and path path is added to the set of feasible paths for evacuating people pd by car pd .

3. The short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm according to claim 1 is characterized in that: In step S1, the process of constructing the three-dimensional vehicle / pedestrian-time-space node set includes the following steps: B11, virtual starting point o′ for the evacuated personnel pd by car pd , and its corresponding vehicle-time-space node is (v pd ,o′ pd ,a pd ), where v pd is the vehicle status of the evacuee pd, a pd is the earliest departure time of the evacuee pd with a car; the virtual destination d′ of the evacuee pd with a car pd , and its corresponding vehicle-time-space node is (v pd ,d′ pd ,b′ pd ), where b′ pd is the latest arrival time of the evacuees pd by car; B12, virtual starting point o′ for the evacuee pr without a car pr , and its corresponding vehicle / pedestrian-time-space node is (0,o′ pr ,a pr ), where a pr is the earliest departure time of the evacuee pr with a car; the virtual destination d′ of the evacuee pr without a car pr , and its corresponding vehicle / pedestrian-time-space node is (0,d′ pr ,b′ pr ), where b′ pr is the latest arrival time of the evacuees pr without a car; B13, for the set Feasible pd For each feasible time of each node i on each path in, add the vehicle / walking-time space node (v pd ,i,t), where t is the vehicle v pd The time of arrival at node i; B14, for the collection Walk pr For each feasible time of each node i on each path in, add the vehicle / walking-time space node as (w pr ,i,t), where w p r represents the walking state of the car-free evacuee pr, and t is the time when the car-free evacuee pr arrives at the node i on foot; B15, add all vehicle / pedestrian-time and space nodes obtained in the above steps B11-B14 to the feasible node set Ω; add the vehicle / pedestrian-time and space nodes obtained in the above steps B11-B12 to the virtual node set Ω 0 ; Add the vehicle / walking-time-space nodes obtained in the above steps B13-B14 to the actual node set Ω * .

4. The short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm according to claim 3 is characterized in that: In step B13, for the set Feasible pd For each node i of each path in, if i is the starting point o of the car evacuating personnel pd pd , then a pd ≤t≤b pd , where a pd is the earliest departure time of pd, b pd is the latest departure time of pd; If i is the destination d of the evacuated person pd by car pd , then a′ pd ≤t≤b′ pd , where a′ pd is the latest arrival time of pd, b′ pd is the latest departure time of pd; If i is neither the starting point o of the evacuee with car pd nor the evacuee with car pd pd , nor is it the end point pd , then a pd ≤t≤b′ pd ; In step B14, for the set Walk pr For each node i of each path in , if i is the starting point o of the vehicle-free evacuation personnel pr pr , then a pr ≤t≤b pr , where a pr is the earliest departure time of pr, b pr is the latest departure time of pr; if i is the destination d of the evacuee pr without a car pr , then a′ pr ≤t≤b′ pr ; where a′ pr is the latest arrival time of pr, b′ pr is the latest departure time of pr; if i is neither the starting point o of the car-free evacuee pr nor the starting point o of the car-free evacuee pr pr , nor is it the end point pr , then a pr ≤t≤b′ pr .

5. The short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm according to claim 3 is characterized in that: In step S1, the process of constructing the vehicle / pedestrian-time-space arc set includes the following steps: For the feasible node set Ω and the virtual node set Ω 0 and the actual node set Ω * Analyze all vehicle / pedestrian-time-space nodes in: If (v pd ,i,t)∈Ω * And (v pd ,j,s)∈Ω * , and the road segment from node i to node j exists in the traffic network and satisfies t(i,j)≤(st)≤t(i,j)+15, then (v pd ,v pd ,i,j,t,s) is added to the feasible arc set Φ, where t(i,j) is the cost of passing the road segment (i,j); If (w pr ,i,t)∈Ω * And (w pr ,j,s)∈Ω * , and the road segment from node i to node j is in the traffic network and satisfies (st) = T(i,j), then (w pr ,w pr ,i,j,t,s) are added to the feasible arc set Φ and the actual arc set Φ * , where T(i,j) is the cost of walking through the road segment (i,j); If (v pd ,i,t)∈Ω * And (w pr ,i,s)∈Ω * , and satisfy 0≤(st)≤15, then (v pd ,w pr ,i,j,t,s) are added to the feasible arc set Φ and the actual arc set Φ * ; If (w pr ,i,t)∈Ω * And (v ppd ,i,s)∈Ω * , and satisfy 0≤(st)≤15, then (w pr ,v pd ,i,i,s,t) are added to the feasible arc set Φ and the actual arc set Φ * ; If (v pd ,o′ pd ,a pd )∈Ω 0 And (v pd ,o pd ,t)∈Ω * , then add (v pd ,v pd ,o′ pd ,o pd ,a pd ,t) to the feasible arc set Φ and the virtual arc set Φ 0 ; If (v pd ,d′ pd ,b′ pd )∈Ω 0 And (v pd ,d pd ,t)∈Ω * , then add (v pd ,v pd ,d pd ,d′ pd ,t,b′ pd 0 to the feasible arc set Φ and the virtual arc set Φ 0 ; If (0,o′ pr ,a pr )∈Ω 0 , and (v pd ,o pr ,t0∈Ω * ,(w pr ,o pr ,t0∈Ω * , then add (0,v pd ,o′ pr ,o pr ,a pr ,t) and (0,w pr ,o′ pr ,o pr ,a pr ,t) to the feasible arc set Φ and the virtual arc set Φ 0 ; If (0,d′ pr ,b′ pr )∈Ω 0 , and (v pd ,d pr ,t)∈Ω * ,(w pr ,d pr ,t)∈Ω * , then add (v pd ,0,d pr ,d′ pr ,t,b′ pr ) and (w pr ,0,d pr ,d′ pr ,t,b′ pr ) to the feasible arc set Φ and the virtual arc set Φ 0 ; for Set (0,0,o′ pr ,d′ pr ,a pr ,b′ pr ) is added to the feasible arc set Φ and the virtual arc set Φ 0 .

6. The short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm according to claim 5 is characterized in that: The process of defining the usage cost of each vehicle / pedestrian-time-space arc includes the following steps: for Define the usage cost of arc (v,u,i,j,t,s) = st; for If node i is the virtual starting point o′ p , then define the usage cost of arc (v,u,i,j,t,s) = 0; for If node j is a virtual endpoint d′ p , then the usage cost c(v,u,i,j,t,s) of the virtual starting point definition arc (v,u,i,j,t,s) = 0.

7. The short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm according to claim 1, characterized in that: In step S3, the hard constraint is assigned to the Lagrange multiplier and relaxed into the objective function to obtain a new Lagrange relaxation function. The process of solving the Lagrange dual problem with the Lagrange multiplier as a variable includes the following steps: S31, introducing the Lagrange multiplier λ into the multi-passenger and multi-driver network flow model established in step S2 above in(v,i,t) ,λ out(v,i,t) and λ pr , relax the hard constraint to the objective function, and obtain the new Lagrangian relaxation function as follows: S32, establish a new multi-passenger and multi-driver network flow model as follows: z LR =L (13); st S33, using the GAMS solver to solve the model in step S32, the obtained solution vector set is 8. The short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm according to claim 7, characterized in that: In step S4, the process of updating the Lagrange multiplier using the subgradient method includes the following steps: S41, calculate the Lagrange multiplier λ according to the following formula in(v,i,t) ,λ out(v,i,t) and λ pr The subgradient of: S42, update the Lagrange multiplier λ using the following formula in(v,i,t) ,λ out(v,i,t) and λ pr :

9. The short-term early warning evacuation path planning method based on Lagrangian relaxation algorithm according to claim 7, characterized in that: Step S5, using the updated Lagrange multiplier to construct a new vehicle / pedestrian-time-space network, solving a new vehicle routing problem model, and updating the search step size and the number of iterations, includes the following steps: S51, create a new vehicle / pedestrian-time and space node set New Vehicle / Pedestrian-Spacetime Arc Collection S51, for If y(pd, v pd , v pd , i, j, t, s) = 1 and (w pr , i, s) ∈ Ω * , New_Ω * = New_Ω * ∪{(v pd , i, t), (v pd , j, s), (w pr , i, s)}; For (v pd ,i,t)∈New_Ω * ,(v pd ,j,s)∈New_Ω * , if (v pd ,v pd ,i,j,t,s)∈Ω * , New_Φ * =New_Φ * ∪[(v pd ,v pd ,i,j,t,s)}; For (v pd ,i,t)∈New_Ω * ,(w pr ,j,s)∈Ω * , if (v pd ,w pr ,i,j,t,s)∈Ω * , New_Φ * =New_Φ * ∪{(v pd ,w pr ,i,j,t,s)}; For (v pd ,i,t)∈New_Ω * ,(w pr ,j,s)∈Ω * , if (w pr ,v pd ,j,i,s,t)∈Ω * , New_Φ * =New_Φ * ∪{(w pr ,v pd ,j,i,s,t)}; S52, establish a new vehicle routing problem as follows: S53, using the GAMS solver to solve the above vehicle routing problem, obtain the solution vector and the optimal value ZR k ; If ZR k <ZR * , update the optimal solution according to the following formula: ZR * =ZR k (37); S54, y * Substitute (p,v,u,i,j,t,s) into the objective function Z of the original problem to obtain the lower bound solution LB k ; S55, update the search step length θ k And the number of iterations k: k=k+1 (39).

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