CN105139685B - A kind of road network evacuation planning method based on maximum flow rate heat source - Google Patents

Abstract

It is in being applied to simulate oriented road network structure, it is characterized in that following steps are carried out the invention discloses a kind of road network evacuation planning method based on maximum flow rate heat source：1st, construct super source node and be associated with oriented road network structure；2 road network evacuation planning parameters are defined；The Path selection of 3 evacuation plannings.The present invention has considered the evacuation time in required evacuation path and has evacuated the aspect influence of capacity two, in the hope of in each Path selection, the evacuation path that most capacity are evacuated in most short evacuation time can be always selected, so as to improve the evacuation efficiency of the road network evacuation planning.

Description

A kind of road network evacuation planning method based on maximum flow rate heat source

Technical field

The invention belongs to path planning, information processing, Geomatics field, and it is related to the application of graph theory, specifically Say it is a kind of road network evacuation planning method based on maximum flow rate heat source.

Background technology

Today's society, the metropolitan density of population is increasing, and the situation of urban traffic blocking is also increasingly protruded, this Outward, can the densification of urban population bring the problem that evacuate harm reduction influence in time when Disaster Event occurs, because This, road network evacuates problem and is increasingly becoming people's problem urgently to be resolved hurrily.The path planning of science how is carried out to refer to Lead and control to treat the action path of population in Evacuation area, will with as big as possible evacuation efficiency and evacuation time as small as possible The region specified is transferred to the masses'safety of devastated, with important real Research Significance.

For such case, such issues that there has been proposed a variety of algorithm models to solve, such as traditional linear gauge Draw and the method such as analog simulation.Later, also occur in that a kind of method of entitled heuritic approach in academia solve it is this kind of dredge The problem of dissipating.One time, a variety of similar heuritic approaches like surging clouds went out, and such as greedy algorithm recalls algorithm, adverse current algorithm Etc. emerge in an endless stream.Several years ago, Lu Qingsong professors propose a kind of heuritic approach of CCRP on the basis of MRCCP algorithms Thought, the heat source for always allowing evacuation path short every time in the case where capacity is evacuated in limitation is evacuated, in practice it has proved that, Efficiency of the efficiency of CCRP than MRCCP improves.Later, have scholar CCRP basis on, it is proposed that it is various Modified hydrothermal process, has plenty of path-first algorithm long, some proposition intelligence off-load algorithms.However, these algorithm ideas are generated Evacuation path always because the resource of residual capacity on path can not be made full use of, extend evacuate every time Path selection when Between and evacuation time, therefore total evacuation time is inevitably influenced whether, so as to the evacuation for causing road network evacuation planning is imitated Rate is low.

The content of the invention

The present invention is to overcome the deficiencies in the prior art part, it is proposed that a kind of road network based on maximum flow rate heat source is dredged Planing method is dissipated, the evacuation time in required evacuation path has been considered and has been evacuated the aspect influence of capacity two, in the hope of on each road When footpath selects, the evacuation path that most capacity are evacuated in most short evacuation time can be always selected, so as to improve the road network The evacuation efficiency of evacuation planning.

The present invention is adopted the following technical scheme that to solve above technical problem：

A kind of road network evacuation planning method based on maximum flow rate heat source of the present invention, is to be applied to simulate oriented road network In structure G (V, E), in the oriented road network structure G (V, E) of simulation, V represents set of node, and has V={ V_s,V_z,V_d}；V_sTable Show source node set, V_zRepresent set of intermediate nodes；V_dRepresent destination node collection；And have：V_s={ V₁,V₂,…,V_i,…,V_a}；V_iRepresent The source node set V_sIn i-th source node, and V_i={ V_i,cap,V_i,occ, V_i,capRepresent the source node set V_sIn i-th source Node V_iThe current capacity of node, V_i,occRepresent the source node set V_sIn i-th source node V_iInitial capacity to be evacuated, 1≤ i≤a；V_z={ V_a+1,…,V_j,…,V_b, V_jRepresent the set of intermediate nodes V_zIn j-th intermediate node, and V_j={ V_j,cap, V_j,capRepresent the set of intermediate nodes V_zIn j-th intermediate node V_jThe current capacity of node, a+1≤j≤b；V_d={ V_b+1,…, V_k,…,V_c, V_kRepresent the destination node collection V_dIn k-th destination node, and V_k={ V_k,cap,V_k,occ, V_k,capRepresent described Destination node collection V_dIn k-th destination node V_kThe current capacity of node, V_k,occRepresent the destination node collection V_dIn k-th mesh Node V_kAccommodated evacuation capacity, b+1≤k≤c；E represents side collection, and has E={ e₁,e₂,…,e_h,…,e_H, e_hRepresent It is described the h articles in collection E while, it is assumed that the h articles side e_hIt is by n-th in the set of node V_hIndividual nodeSet out to its phase Even n-th_h' individual nodeTerminate generated side, and haveRepresent the h articles side e_h's Current capacity,Represent and pass through the h articles side e_hTransit time；It is characterized in, the road network evacuation planning method is by such as Lower step is carried out：

Step 1, the super source node V of construction₀And be associated with the oriented road network structure G (V, E)：

Step 1.1, the super source node V of structure₀, and haveRepresent the super source node V₀ Evacuation capacity；

Step 1.2, by the super source node V₀Respectively with the source node set V_sIn each source node be connected so that Generation a bars side, is designated as Represent the super source node V₀With the source node set V_sIn I source node V_iBe connected generated side, and has： Represent the super source node V₀With it is described Source node set V_sIn i-th source node V_iBe connected generated sideCurrent capacity,Represent and saved by the super source Point^V ₀With the source node set V_sIn i-th source node V_iBe connected generated sideTransit time；

Step 1.3, by the source node set V_sIn i-th source node V_iInitial capacity V to be evacuated_i,occIt is assigned toAnd makeRealize the super source node V₀With the source node set V_sIn i-th source node V_iAssociation； So as to realize the super source node V₀With the association of the oriented road network structure G (V, E) of simulation；

Step 2, the definition of road network evacuation planning parameter：

Step 2.1, the definition of path planning parameter：

The definition moment is t, and for recording the time course of the evacuation planning, initializes t=0；

It is G (V, E) ' to define the oriented road network structure of the traversal path with time dimension, and evacuates shortest path for solving；

The path cost vector for defining t is D_t, and have D_t={ D_t,b+1,D_t,b+2,…,D_t,k,…,D_t,c, D_t,kRepresent The path cost vector D_tIn k-th component, and for storing t from the super source node V₀To the purpose section Point set V_dIn k-th destination node V_kThe minimum time cost for being spent；

The Path selection queue vector for defining t is Path_t, and have Path_t={ P_t,b+1,P_t,b+2,…,P_t,k,…, P_t,c}；P_t,kRepresent the Path selection queue vector Path_tIn k-th component, and for storing t from described super Source node V₀To the destination node collection V_dIn k-th destination node V_kThe minimum time cost D for being spent_t,kCorresponding road Footpath, and it is designated as shortest path；

The path flow rate vector for defining t is Rate_t, and have Rate_t={ R_t,b+1,R_t,b+2,…,R_t,k,…,R_t,c}, R_t,kRepresent the path flow rate vector Rate_tIn k-th component, and for storing Path selection queue vector described in t Path_tIn k-th component P_t,kThe ratio of the current capacity of the maximum of upper receiving and transit time, i.e., from the super source node V₀ To the destination node collection V_dIn k-th destination node V_kShortest path P_t,kFlow rate；

Define the path flow rate vector Rate of t_tMiddle largest component is maximum flow rate R_t,max；

T is defined by the Path selection queue vector Path_tIn maximum flow rate R_t,maxCorresponding shortest path, It is maximum flow rate path, is designated as P_t,max；

Define path output queue collection and be combined into OutPut_Path, and initialize the path output queue set OutPut_ Path is sky；

Step 2.2, road network state parameter are defined and initialized：

Defining the current capacity nodes collection of t isFor all nodes in representing the set of node V in the surplus of t Remaining current capacity, and have Represent m-th node V in the set of node V_mIn the surplus of t Remaining current capacity；

As t=0, initializationV_m,capRepresent m-th node V in the set of node V_mCurrent appearance Amount, so as to obtain the current capacity nodes collection at t=0 moment

Define residual capacity time expanding node to integrate is V_cap, by the current capacity nodes collection at t=0 momentIt is stored in described Residual capacity time expanding node collection V_capIn；

Merge it is described while collection E and while collection E_V0In all sides, constitute side complete or collected works E_union；

Defining the current capacity side collection of t is, for representing the side complete or collected works E_unionIn each bar side in the surplus of t Remaining current capacity, and haveAnd R=H+a；Represent the side complete or collected works E_unionIn r Residue current capacity of the bar side in t, it is assumed that the r articles current capacity of the residue on sideIt is by the set of node V and described Super source node V₀In n-th_rIndividual node V_nrSet out to coupled n-th_r' individual nodeTerminate generated side in t The current capacity of residue, and have

During t=0 moment, by the side complete or collected works E_unionIn from n-th_rIndividual node V_nrSet out to coupled n-th_r' individual section PointTerminate the current capacity on generated sideIt is assigned toSo as to obtain the current capacity at t=0 moment Side collection

Define residual capacity time extension side to integrate is E_cap, by the current capacity side collection at t=0 momentIt is stored in described surplus Covolume amount time extension side collection E_capIn；

Step 3, the Path selection of evacuation planning：

Step 3.1, in t, carry out path planning parameter reset operation：

Step 3.1.1, parameter reset：

The path cost vector D of t is set_t={ D_t,b+1,D_t,b+2,…,D_t,k,…,D_t,cIn each component value be just It is infinitely great；The Path selection queue vector Path of t is set_t={ P_t,b+1,P_t,b+2,…,P_t,k,…,P_t,cIn each vector value It is sky；The path flow rate vector Rate of t is set_t={ R_t,b+1,R_t,b+2,…,R_t,k,…,R_t,cIn each component value be It is empty；The maximum flow rate R of t is set_t,max=0；The maximum flow rate path P of t is set_t,maxIt is sky；

Oriented road network structure G (V, the E) ' reset of step 3.1.2, the traversal path with time dimension：

The oriented road network structure G (V, E) is assigned to G (V, E) '；

According to the residual capacity time expanding node collection V_capMiddle remaining current capacity is corresponding to 0 node acquisition Time dimension, and judge that in the node that the middle remaining current capacity of G (V, E) ' is 0 be invalid on corresponding time dimension；

Collection E in side is extended according to the residual capacity time_capMiddle remaining current capacity is the time corresponding to 0 side acquisition Dimension, and judge that on the side that the middle remaining current capacity of G (V, E) ' is 0 be invalid on corresponding time dimension；So as to obtain The oriented road network structure G (V, E) of traversal path with time dimension '；

Step 3.2, according to oriented road network structure G (V, the E) ' interior joint of the traversal path with time dimension and side whether For invalid, travel through the oriented road network structure G (V, E) of the traversal path with time dimension ' in from the super source node V₀Arrive The destination node collection V_dIn k-th destination node V_kThe all paths passed through；

Choose and reach k-th destination node V_kThe minimum path of time cost is spent in all paths passed through as the K destination node V_kShortest path and be stored in the Path selection queue vector Path of t respectively_tK-th component P_t,kIn； So as to by the destination node collection V_dThe shortest path of middle all purposes node is stored in the Path selection queue vector respectively Path_tIn corresponding component；

Step 3.3, by t Path selection queue vector Path_tIn k-th component P_t,kThe time cost for being spent is deposited Enter the path cost vector D_tK-th component D_t,kIn, so as to by the destination node collection V_dMiddle all purposes node is most Short path spends time cost to be stored in the path cost vector D respectively_tIn corresponding component；

Step 3.4, acquisition t Path selection queue vector Path_tIn k-th component P_t,kRepresented shortest path On allow current maximum to evacuate capacity F_Pt,k；So as to obtain in t from the super source node^V ₀To the destination node collection V_dMaximum evacuation capacity set { F on the shortest path of middle all purposes node_Pt,b+1,F_Pt,b+2,…,F_Pt,k,…,F_Pt,c}；

Step 3.4.1, acquisition t Path selection queue vector Path_tIn k-th component P_t,kRepresented shortest path Footpath, is designated asAnd haveN_t,kIt is most short described in representing Path P_t,kIn remove super source node V₀Outer passed through node total number；Represent the shortest path P_t,kMiddle passed through n_t,kIndividual node, 1≤n_t,k≤N_t,k；

Step 3.4.2, obtain the shortest path P using formula (1)_t,kIt is middle by the 0th nodeAnd pass through N-th_t,kIndividual nodeArrival timeSo as to obtain the shortest path P_t,kThe arrival time of middle passed through node Collection

In formula (1),Represent in the side complete or collected works E_unionIn, by the shortest path P_t,kIn from n-th_t,k-1 Individual nodeSet out to coupled n-th_t,kIndividual nodeTerminate the transit time on generated side；

Step 3.4.3, renewal road network state parameter：

Step 3.4.3.1, according to the shortest path P_t,kIt is middle by n-th_t,kIndividual nodeArrival time Inquire about the residual capacity time expanding node collection V_capIn whether include arrival timeCurrent capacity nodes collection If not including, makeFor empty and be stored in the residual capacity time expanding node collection V_capIn；Otherwise, maintainNo Become；

Inquire about the current capacity nodes collectionIn whether include described n-th_t,kIndividual nodeIn arrival time When the current node capacity of residueIf comprising maintainingIt is constant；Otherwise, by the shortest path P_t,k It is middle by n-th_t,kIndividual nodeThe current capacity of corresponding node in the set of node VIt is assigned toWillIt is stored in the current capacity nodes collectionIn；So as to realize the remaining current node CapacityIt is stored in the residual capacity time expanding node collection V_capIn；

Step 3.4.3.2, step 3.4.3.1 is repeated, so as to obtain the shortest path P_t,kMiddle passed through node Remaining node capacity in respective arrival time dimension, and it is sequentially stored into the residual capacity time expanding node collection V_capIn；

Step 3.4.3.3, according to the shortest path P_t,kIt is middle to pass through from n-th_t,k- 1 nodeSet out to its Connected n-th_t,kIndividual nodeTerminate the arrival time on generated sideInquire about the residual capacity time extension side Collection E_capIn whether include arrival timeWhen current capacity side collectionIf not including, orderFor empty and be stored in The residual capacity time extension side collection E_capIn；Otherwise, maintainIt is constant；

Inquire about the current capacity side collectionIn whether include the shortest path P_t,kIn from n-th_t,k- 1 nodeSet out to coupled n-th_t,kIndividual nodeTerminate generated side in arrival timeWhen the current side of residue CapacityIf comprising maintainingIt is constant；Otherwise, by the side complete or collected works E_unionIn by described Shortest path P_t,kIn from n-th_t,k- 1 nodeSet out to coupled n-th_t,kIndividual nodeTerminate generated side Current capacityIt is assigned toWillIt is stored in the current capacity side collectionIn, so as to realize the remaining current edge capacityIt is stored in the residual capacity time extension side collection E_capIn；

Step 3.4.3.4, step 3.4.3.3 is repeated, so as to obtain the shortest path P_t,kMiddle passed through side exists Remaining edge capacity in respective arrival time dimension, and it is sequentially stored into the residual capacity time extension side collection E_capIn；

Step 3.4.4, the Path selection queue vector Path is obtained according to formula (2)_tIn k-th component P_t,kInstitute's generation Current maximum evacuation capacity is allowed on the shortest path of table

In formula (2),Represent the shortest path P_t,kOn n-th_t,kIndividual nodeIn arrival timeWhen The current capacity of residue；Represent from the shortest path P_t,kOn n-th_t,k- 1 nodeSet out to Coupled n-th_t,kIndividual nodeTerminate generated side in arrival timeWhen the current capacity of residue；

Step 3.5, t is obtained using formula (3) from the super source node V₀To the destination node collection V_dIn k-th Destination node V_kShortest path flow rate R_t,k, so as to obtain t from the super source node V₀To the destination node collection V_dThe flow rate vector of the shortest path of middle all purposes nodeAnd obtain the t Path flow rate vector Rate_tMiddle maximum flow rate R_t,max：

Step 3.6, judge R_t,max=0 and V_0,capWhether=0 set up, if all setting up, performs step 3.10；

If only R_t,max=0 sets up, then it represents that t Path selection queue vector Path_tIt is invalid, and can not in t Evacuated again, the value of t+1 is assigned to t, and return to step 3.1 recalculates evacuation planning path；

If all invalid, then it represents that moment Path selection queue vector Path_tEffectively, and from the Path selection queue to Amount Path_tIt is middle by maximum flow rate R_t,maxCorresponding shortest path is selected, and is stored in the maximum flow rate path P_t,max, and be designated asAnd the maximum flow rate path P_t,maxIt is middle through celebrating a festival The arrival time collection of point is designated asAnd have Represent the maximum flow rate path P_t,maxIn remove super source node V₀Outer passed through node total number,Represent described Maximum flow rate path P_t,maxMiddle passed throughIndividual node,Remember the maximum flow rate path P_t,max Corresponding maximum capacity of evacuating is F_t,max；By the maximum flow rate path P_t,maxIn remove the super source node V₀Outer pathway institute The node of process is stored in the path output queue set OutPut_Path, and records maximum capacity and each node evacuated Arrival time；And perform step 3.7；

Step 3.7, using formula (4) respectively to the maximum flow rate path P_t,maxThe residue on middle passed through node and side is led to Row capacity is modified, and modified values are newly stored into the residual capacity time expanding node collection V_capDuring with the residual capacity Between extend side collection E_capIn, so as to realize the residual capacity time expanding node collection V_capSide is extended with the residual capacity time Collection E_capRenewal；

In formula (4),Represent the maximum flow rate path P_t,maxOnIt is individual NodeSet out to coupledIndividual nodeTerminate generated side in arrival timeWhen The current capacity of residue；Represent the maximum flow rate path P_t,maxOnIndividual nodeArrive Up to the timeWhen the current capacity of residue；

Step 3.8, obtain the super source node V using formula (5)₀In the current capacity V of the residue of t_0,cap：V_{0, cop}= V_{0, cap}-F_{T, max} (5)

Step 3.9, judge V_0,capWhether=0 set up, if so, then perform step 3.10；Otherwise, step 3.1 is performed；

Step 3.10, the evacuation planning terminate, and the path output queue collection in maximum flow rate path is stored described in acquisition Close the final result of OutPut_Path.

Compared with the prior art, beneficial effects of the present invention are embodied in：

1st, the present invention is on the basis of existing CCRP heuritic approaches thought, has bypassed selection evacuation path most long and most Short evacuation path, the concept of addition time dimension carrys out the state of Dynamic Maintenance network structure, reduces the selection of effective shortest path Difficulty；Using the measure of path flow rate, evacuation capacity and dredging that evacuation path is spent on path are evacuated in comprehensive utilization The time of dissipating, with the practicality for evacuating the flow rate in path to evaluate the evacuation path, strive for that maximum can be realized at each moment Evacuation capacity；

2nd, the present invention adds time dimension dynamically to maintain most in the shortest path from source node to destination node is chosen Short path collection, when destination node is chosen, preferential to reject invalid node under correspondence time dimension, road is reduced on invalid side Footpath cost.When all traversal paths are completed, an optimal shortest path collection just can be obtained, it is achieved thereby that path cost Minimum effect；

3rd, the present invention is on the basis of shortest path, using required shortest path evacuation capacity at a time and Spend time taking proportionate relationship, i.e. flow rate value to judge the average evacuation capacity of this shortest path, choose wherein flow rate value maximum Shortest path as the evacuation path at the moment, realize the maximum effect of the average passenger distributing volume in path；

4th, the evacuation path selected by the present invention is the evacuation capacity in foundation path and spends time taking proportionate relationship, therefore road The dense degree of web frame is big not as its influence to existing evacuation planning algorithm to result influence degree of the invention, Therefore the present invention has more preferable adaptability and stability.

Brief description of the drawings

Fig. 1 is road net model figure of the present invention；

Fig. 2 is the road net model figure containing super source node of present invention construction；

Fig. 3 is flow chart of the method for the present invention.

Specific embodiment

In the present embodiment, a kind of road network evacuation planning method based on maximum flow rate heat source, is to be applied to simulation to have In to road network structure G (V, E), in oriented road network structure G (V, E) is simulated, V represents set of node, and has V={ V_s,V_z,V_d, structure Make result as shown in Figure 1；V_sRepresent source node set, V_zRepresent set of intermediate nodes；V_dRepresent destination node collection；And have：V_s={ V₁, V₂,…,V_i,…,V_a}；V_iRepresent source node set V_sIn i-th source node, and V_i={ V_i,cap,V_i,occ, V_i,capRepresent source node Collection V_sIn i-th source node V_iThe current capacity of node, V_i,occRepresent source node set V_sIn i-th source node V_iInitial wait to dredge Dissipate capacity, 1≤i≤a, road network evacuation in, source node set represent be there is accident and population than comparatively dense place, such as The places such as office block, supermarket, school；What set of intermediate nodes was represented is the cross junction run into during evacuation, is turned round Place etc.；What destination node collection was represented is the last accumulation point of Evacuation during road network is evacuated, such as square, bomb shelter etc.； These places are modeled as corresponding node in the present invention；As shown in figure 1, source node V₂={ 50,15 }, wherein 50 represent Source node V₂The current capacity of node be 50, the current capacity for describing normal node；15 represent source node V₂Initial wait to dredge It is 15 to dissipate capacity, represents and is evacuating at first, and how many capacity the node needs to be evacuated；Current capacity is dredged with initial Scattered capacity can be with equal, it is also possible to unequal；V_z={ V_a+1,…,V_j,…,V_b, V_jRepresent set of intermediate nodes V_zIn in the middle of j-th Node, and V_j={ V_j,cap, V_j,capRepresent set of intermediate nodes V_zIn j-th intermediate node V_jThe current capacity of node, a+1≤j ≤ b, as shown in figure 1, intermediate node V₄={ 8 }, wherein 8 represent intermediate node V₄The current capacity of node be 8；V_d= {V_b+1,…,V_k,…,V_c, V_kRepresent destination node collection V_dIn k-th destination node, and V_k={ V_k,cap,V_k,occ, V_k,capRepresent Destination node collection V_dIn k-th destination node V_kThe current capacity of node, V_k,occRepresent destination node collection V_dIn k-th section of mesh Point V_kAccommodated evacuation capacity, b+1≤k≤c, as shown in figure 1, destination node V₁₃={ 200,200 }, wherein first 200 Represent destination node V₁₃Current capacity；Represent destination node V for second 200₁₃The evacuation capacity that can be accommodated, i.e., in road network The capacity evacuated and come from source node can be received in evacuation；V is set under usual state_k,occWith V_k,capIt is equal；E represents side collection, And have E={ e₁,e₂,…,e_h,…,e_H, e_hWhen representing the h articles in collection E, it is assumed that the h articles side e_hIt is by n-th in set of node V_h Individual node V_nhSet out to coupled n-th_h' individual nodeTerminate generated side, n_hAnd n_h' node is represented respectivelyWith NodeNode serial number in set of node V, and have Represent the h articles side e_hIt is current Capacity,Represent and pass through the h articles side e_hTransit time；

As shown in figure 1, by intermediate node V₈Set out to intermediate node V₁₁The current capacity on the side of composition isBy Intermediate node V₈Set out to intermediate node V₁₁The transit time on the side of composition isAs shown in figure 1, describing single file The road network structure in road；Invention can also be used to describe the road network structure of two-way traffic, for example, can utilizeWithRepresent respectively by intermediate node V₈Set out to intermediate node V₁₁The side of end and by intermediate node V₁₁Set out to centre Node V₈The current capacity on the side of end, both can with it is equal can also be unequal；Specific situation can be according in real world Depending on road network True Data；

In the present embodiment, a kind of road network evacuation planning method based on maximum flow rate heat source is to enter according to the following procedure OK：

Step 1, the super source node V of construction₀And be associated with oriented road network structure G (V, E)：Construction result such as Fig. 2 institutes Show；

Step 1.1, the super source node V of structure₀, and have Represent super source node V₀Dredge Capacity is dissipated, as shown in Fig. 2 according to source node V₁, V₂And V₃Initial capacity sum to be evacuated, obtain V₀={ 30 }, 30 represent structure The super source node V for making₀Evacuation capacity be 30；

Step 1.2, by super source node V₀Respectively with source node set V_sIn each source node be connected, so as to generate a bars Side, is designated ase_i' represent super source node^V ₀With source node set V_sIn i-th source node V_iIt is connected The side for being generated, and have：And have： Represent super source node^V ₀With source node set V_sIn i-th Source node V_iBe connected generated side e_i' current capacity,Represent and pass through super source node V₀With source node set V_sIn i-th Individual source node V_iBe connected generated side e_i' transit time；

Step 1.3, by source node set V_sIn i-th source node V_iInitial capacity to be evacuatedIt is assigned toAnd makeRealize super source node V₀With source node set V_sIn i-th source node V_iAssociation；So as to realize super source node V₀ With the association for simulating oriented road network structure G (V, E), as shown in Fig. 2 super source node V₀With source node V₂The side e of phase adhesion₂'= { 15,0 }, wherein 15 represent side e₂' the current capacity in sideIt is 15；0 represents by side e₂' the time cost for being spentIt is 0；

Step 2, the definition of road network evacuation planning parameter：

Step 2.1, the definition of path planning parameter：

The definition moment is t, and for recording the time course of evacuation planning, initializes t=0；

The oriented road network structure G (V, E) of traversal path of the definition with time dimension ', and evacuate shortest path for solving；

The path cost vector for defining t is D_t, and have D_t={ D_t,b+1,D_t,b+2,…,D_t,k,…,D_t,c, D_t,kRepresent Path cost vector D_tIn k-th component, and for storing t from super source node^V ₀To destination node collection V_dIn k-th Destination node V_kThe minimum time cost for being spent；

The Path selection queue vector for defining t is Path_t, and have Path_t={ P_t,b+1,P_t,b+2,…,P_t,k,…, P_t,c}；P_t,kRepresent Path selection queue vector Path_tIn k-th component, and for storing t from super source node V₀Arrive Destination node collection V_dIn k-th destination node V_kThe minimum time cost D for being spent_t,kCorresponding path, and it is designated as shortest path Footpath；

The path flow rate vector for defining t is Rate_t, and have Rate_t={ R_t,b+1,R_t,b+2,…,R_t,k,…,R_t,c}, R_t,kRepresent path flow rate vector Rate_tIn k-th component, and for storing t Path selection queue vector Path_tIn K-th component P_t,kThe ratio of the current capacity of the maximum of upper receiving and transit time, i.e., from super source node V₀To destination node collection V_dIn k-th destination node V_kShortest path P_t,kFlow rate；

Define the path flow rate vector Rate of t_tMiddle largest component is maximum flow rate R_t,max；

T is defined by Path selection queue vector Path_tIn maximum flow rate R_t,maxCorresponding shortest path, is most Big flow rate path, is designated as P_t,max；

Define path output queue collection and be combined into OutPut_Path, and initialization path output queue set OutPut_Path It is sky；

Step 2.2, road network state parameter are defined and initialized：

Defining the current capacity nodes collection of t isLead in the residue of t for all nodes in representing set of node V Row capacity, and have Represent m-th node V in set of node V_mPassed through in the residue of t and held Amount；

As t=0, initializationV_m,capRepresent m-th node V in set of node V_mCurrent capacity, from And obtain the current capacity nodes collection at t=0 moment

Define residual capacity time expanding node to integrate is V_cap, by the current capacity nodes collection at t=0 momentIt is stored in residue Capacity time expanding node collection V_capIn；

Merge side collection E and by super source node V₀Respectively with source node set V_sIn each source node be connected so as to generation Side collectionIn all sides, constitute side complete or collected works E_union；

Defining the current capacity side collection of t isFor representing side complete or collected works E_unionIn each bar side t residue lead to Row capacity, and haveAnd R=H+a；Represent side complete or collected works E_unionIn the r articles side in t The current capacity of the residue at moment, it is assumed that the r articles current capacity of the residue on sideIt is by set of node V and super source node V₀In n_rIndividual node V_nrSet out to coupled n-th_r' individual nodeTerminate residue current capacity of the generated side in t, and Haven_rAnd n_r' node V is represented respectively_nrAnd nodeIn set of node V and super source node V₀In node Numbering；

When the t=0 moment, by side complete or collected works E_unionIn from n-th_rIndividual node V_nrSet out to coupled n-th_r' individual node Terminate the current capacity on generated sideIt is assigned toSo as to obtain the current capacity side collection at t=0 moment

Define residual capacity time extension side to integrate is E_cap, by the current capacity side collection at t=0 momentIt is stored in remaining appearance Amount time extension side collection E_capIn；

Step 3, the Path selection of evacuation planning：The flow chart of the bright middle routing resource of we is as shown in Figure 3：

Step 3.1, in moment t, carry out path planning parameter reset operation：

Performing step 3.1 can carry out the calculating in evacuation planning path to step 3.6；For mutually lower possible in the same time There is a plurality of evacuation path, i.e., may have under synchronization it is multiple solve, it is necessary to successive ignition performs step 3.1 to step 3.6, Therefore need to reset parameters described below before calculating every time, it is ensured that the railway network planning under current iteration number of times under current time The validity of parameter, and calculate effective maximum flow rate path under current road network structure state；So as to guarantee in synchronization Under obtain a plurality of different evacuation path to greatest extent；

Step 3.1.1, parameter reset：

The path cost vector D of t is set_t={ D_t,b+1,D_t,b+2,…,D_t,k,…,D_t,cIn each component value be just It is infinitely great；The Path selection queue vector Path of t is set_t={ P_t,b+1,P_t,b+2,…,P_t,k,…,P_t,cIn each vector value It is sky；The path flow rate vector Rate of t is set_t={ R_t,b+1,R_t,b+2,…,R_t,k,…,R_t,cIn each component value be It is empty；The maximum flow rate R of t is set_t,max=0；The maximum flow rate path P of t is set_t,maxIt is sky；

Oriented road network structure G (V, the E) ' reset of step 3.1.2, the traversal path with time dimension：

Oriented road network structure G (V, E) is assigned to G (V, E) '；

According to residual capacity time expanding node collection V_capMiddle remaining current capacity is the time corresponding to 0 node acquisition Dimension, and judge that in the node that the middle remaining current capacity of G (V, E) ' is 0 be invalid on corresponding time dimension；

Collection E in side is extended according to the residual capacity time_capMiddle remaining current capacity is the time dimension corresponding to 0 side acquisition, And judge that on the side that the middle remaining current capacity of G (V, E) ' is 0 be invalid on corresponding time dimension；So as to obtain the band time The oriented road network structure G (V, E) of traversal path of dimension '；

For example, traversal path road network structure G (V, E) with time dimension ' in, it is assumed that from node V₅Set out to node V₈Knot The side of beam moment t=5 residual capacity be 0, then by traversal path road network structure G (V, E) ' in this side set at the t=5 moment It is invalid edges；

Whether step 3.2, it is nothing according to oriented road network structure G (V, the E) ' interior joint of the traversal path with time dimension and side Effect, the traversal traversal path with time dimension oriented road network structure G (V, E) ' in from super source node V₀To destination node collection V_dIn K-th destination node V_kThe all paths passed through；

Choose and reach k-th destination node V_kThe minimum path of time cost is spent in all paths passed through as the K destination node V_kShortest path and be stored in moment t Path selection queue vector Path respectively_tIn k-th component P_t,kIn； So as to by destination node collection V_dThe shortest path of middle all purposes node is stored in Path selection queue vector Path respectively_tAccordingly In component；

Traditional shortest path first mainly has dijkstra's algorithm, A^*Algorithm etc., adds time dimension to obtain most Short path；In the present invention, by taking dijkstra's algorithm as an example, using a kind of improved dijkstra's algorithm：Using most rickle Method optimizes the selection in Dijkstra to destination node；Assuming that set of node has been selected in the presence of one, in this has selected set of node, Using minimum heaping method, from the oriented road network structure G (V, E) of the traversal path with time dimension ' in choose super source node V₀ The minimum node of time cost is spent as transition node, further according to residual capacity time expanding node collection V_capAnd residual capacity Time extension side collection E_capQuery Result, judge the effective of all sides with the destination node as starting point and corresponding terminal Property, if invalid, it is invalid that the side is set to；If effectively, the information of corresponding terminal is added having selected in set of node, carry out The searching operation of next node, until having traveled through all nodes, then can obtain the shortest path from source node to destination node Footpath；As illustrated in fig. 2, it is assumed that step 3 is performed first in moment t=0, from super source node V₀To destination node V₁₃Path be Example, obtains its shortest path P_0,13={ V₀,V₁,V₅,V₈,V₁₁,V₁₃}；

Step 3.3, by t Path selection queue vector Path_tIn k-th component P_t,kThe time cost for being spent is deposited Enter path cost vector D_tIn k-th component D_t,kIn, so as to by destination node collection V_dThe shortest path of middle all purposes node Spent time cost is stored in path cost vector D respectively_tIn corresponding component；For example, the t=0 moment from super source node to Destination node V₁₃Shortest path P_0,13={ V₀,V₁,V₅,V₈,V₁₁,V₁₃Spend time cost for path side transit time Sum, is deposited into path cost vector D_0,13In, D_0,13=0+1+1+3+1=6；

Step 3.4, acquisition t Path selection queue vector Path_tIn k-th component P_t,kRepresented shortest path On allow current maximum to evacuate capacitySo as to obtain in t from super source node^V ₀To destination node collection V_dIn own Maximum evacuation capacity set { F on the shortest path of destination node_Pt,b+1,F_Pt,b+2,…,F_Pt,k,…,F_Pt,c}；

Step 3.4.1, acquisition t Path selection queue vector Path_tIn k-th component P_t,kRepresented shortest path Footpath, is designated asAnd haveN_t,kRepresent shortest path P_t,kIn remove super source node V₀Outer passed through node total number；Represent shortest path P_t,kMiddle passed through n-th_t,kIndividual section Point, 1≤n_t,k≤N_t,k；For example, the t=0 moment is from super source node V₀To destination node V₁₃Shortest path P_0,13={ V₀,V₁,V₅, V₈,V₁₁,V₁₃, except super source node V₀Outer is 5 by node, then N_0,13=5；

Step 3.4.2, obtain shortest path P using formula (1)_t,kIt is middle by the 0th nodeAnd for passing through n_t,kIndividual nodeArrival timeSo as to obtain shortest path P_t,kThe arrival time collection of middle passed through node

In formula (1),Represent in side complete or collected works E_unionIn, i.e. side collection E and super source node V₀Respectively with source node Collection V_sIn the connected side collection E of each source node_V0In, by shortest path P_t,kIn from n-th_t,k- 1 nodeSet out to its Connected n-th_t,kIndividual nodeTerminate the transit time on generated side；For example, moment t=0 is from super source node V₀To mesh Node V₁₃Shortest path P_0,13={ V₀,V₁,V₅,V₈,V₁₁,V₁₃, shortest path P_0,13In all nodes arrival time collection It is { 0,0,1,2,5,6 }；

Step 3.4.3, renewal road network state parameter：

Step 3.4.3.1, according to shortest path P_t,kIt is middle by n-th_t,kIndividual nodeArrival timeInquiry Residual capacity time expanding node collection V_capIn whether include arrival timeCurrent capacity nodes collectionIf not wrapping Contain, then makeFor empty and be stored in residual capacity time expanding node collection V_capIn；Otherwise, maintainIt is constant；

The current capacity nodes collection of inquiryIn whether include n-th_t,kIndividual nodeIn arrival timeWhen residue Current node capacityIf comprising maintainingIt is constant；Otherwise, by shortest path P_t,kIt is middle by n_t,kIndividual nodeThe current capacity of corresponding node in set of node VIt is assigned toWillDeposit Enter current capacity nodes collectionIn；So as to realize the current node capacity of residueIt is stored in the expansion of residual capacity time Exhibition set of node V_capIn；

Step 3.4.3.2, step 3.4.3.1 is repeated, so as to obtain shortest path P_t,kMiddle passed through node is each Remaining node capacity from arrival time dimension, and it is sequentially stored into residual capacity time expanding node collection V_capIn；

For example, it is assumed that performing step 3 first in moment t=0, current road network structure G (V, E) ' all nodes and side have Effect, it is known that moment t=0 from super source node V is obtained by step 3.2 and step 3.4.2 respectively₀To destination node V₁₃Shortest path Footpath P_0,13={ V₀,V₁,V₅,V₈,V₁₁,V₁₃And P_0,13In all nodes arrival time collection { 0,0,1,2,5,6 }, then source section Point V₁Arrival time t=0 residual capacity from step 2.2Expanded by the residual capacity time Exhibition set of node V_capThe current capacity nodes collection at middle t=0 momentComprising then performing shortest path P_0,13={ V₀,V₁,V₅, V₈,V₁₁,V₁₃In next process node V₅Operation；But such as V₅In arrival time t=1, the residual capacity time expands Exhibition set of node V_capIn not comprising current capacity nodes collectionThen makeFor empty and be stored in V_capIn；IfIn not comprising Moment t=1 node V₅The current node capacity of residueThen makeAnd willIt is stored in In, realize byIt is stored in V_capIn；It is similar to successively, obtains intermediate node V₈In the residual capacity of arrival time t=2Intermediate node V₁₁In the residual capacity of arrival time t=5Destination node V₁₃ In the residual capacity of arrival time t=6Successively by these nodes in its arrival time dimension The current capacity nodes that remaining node capacity is stored in corresponding time dimension are concentrated, so as to realize holding the current node of these nodes Amount is stored in V_capIn；

Step 3.4.3.3, according to shortest path P_t,kIt is middle to pass through from n-th_t,k- 1 nodeSet out to coupled N-th_t,kIndividual nodeTerminate the arrival time on generated sideInquiry residual capacity time extension side collection E_capIn be It is no comprising arrival timeWhen current capacity side collectionIf not including, orderFor empty and be stored in residual capacity Time extension side collection E_capIn；Otherwise, maintainIt is constant；

The current capacity side collection of inquiryIn whether include shortest path P_t,kIn from n-th_t,k- 1 nodeSet out To coupled n-th_t,kIndividual nodeTerminate generated side in arrival timeWhen the current edge capacity of residueIf comprising maintainingIt is constant；Otherwise, by side complete or collected works E_unionIn by shortest path P_t,k In from n-th_t,k- 1 nodeSet out to coupled n-th_t,kIndividual nodeTerminate the current capacity on generated sideIt is assigned toWillIt is stored in current capacity side collectionIn, thus realize by The current edge capacity of residueIt is stored in residual capacity time extension side collection E_capIn；

Step 3.4.3.4, step 3.4.3.3 is repeated, so as to obtain shortest path P_t,kMiddle passed through side is respective Remaining edge capacity in arrival time dimension, and it is sequentially stored into residual capacity time extension side collection E_capIn；

For example, shortest path P in above-mentioned example_0,13={ V₀,V₁,V₅,V₈,V₁₁,V₁₃Each bar side residual capacity calculate such as Under：For example by super source node V₀Set out to source node V₁End side arrival time t=0 residual capacityBy Step 2.2 understandsBy residual capacity time extension side collection E_capThe current capacity side collection at middle t=0 momentIncluded in, then perform shortest path P_0,13In next process side operation；By source node V₁Set out in the middle of extension Node V₅Terminate residual capacity of the generated side in arrival time t=0WithIt is similar, held by residue Amount time extension side collection E_capThe current capacity side collection E at middle t=0 moment_c ⁽ _a ⁰ _p ⁾Comprising then continuing executing with shortest path P_0,13In The next operation on the side of process；

But for example by extension intermediate node V₅Set out to extension intermediate node V₈The side that is generated of end in arrival time During t=1, it is E to integrate on residual capacity time extension side_capIn not comprising current capacity side collectionThen makeIt is sky, and willIt is stored in E_capIn；If current capacity side collectionIn not comprising remaining current edge capacityThen make And be stored inIn, thus realize byIt is stored in E_capIn；It is similar to successively, by extension intermediate node V₈Set out to extension Intermediate node V₁₁The side that is generated of end arrival time t=2 residual capacityBy extension intermediate node V₁₁Set out to destination node V₁₃The side that is generated of end arrival time t=5 residual capacitySuccessively These are concentrated when the remaining edge capacity in its arrival time dimension is stored in the current capacity of corresponding time dimension, so that real The current edge capacity on these sides is now stored in E_capIn；

Step 3.4.4, Path selection queue vector Path is obtained according to formula (2)_tIn k-th component P_t,kRepresented Current maximum evacuation capacity F is allowed on shortest path_Pt,k：

In formula (1),Represent shortest path P_t,kOn n-th_t,kIndividual nodeIn arrival timeWhen it is surplus Remaining current capacity, by residual capacity time expanding node collection V_capMiddle acquisition；Represent from shortest path P_t,kOn N-th_t,k- 1 nodeSet out to coupled n-th_t,kIndividual nodeTerminate generated side in arrival timeWhen the current capacity of residue, by residual capacity time extension side collection E_capMiddle acquisition；

For example, examples cited in step 3.4.3, it is assumed that perform step 4 first in moment t=0, current oriented road network structure All nodes and side in G (V, E) ' are all effective, obtain V_0,cap=30, shortest path P_0,13={ V₀,V₁,V₅,V₈,V₁₁,V₁₃In Node { V₁,V₅,V₈,V₁₁,V₁₃The current capacity of residue in each corresponding arrival time dimension { 0,1,2,5,6 } is { 50,6,30,18,200 }, the current capacity of residue of each side in each corresponding arrival time dimension { 0,0,1,2,5 } is { 10,5,4,7,6 }, then being obtained using formula (2) allows the current maximum capacity of evacuating to be above this shortest path

Step 3.5, t is obtained using formula (3) from super source node V₀To destination node collection V_dIn k-th destination node V_kShortest path flow rate R_t,k, for example, shortest path P_0,13Flow rate R_0,13=F_P0,13/D_0,13=4/6=0.677；So as to Obtain t from super source node V₀To destination node collection V_dThe flow rate vector Rate of the shortest path of middle all purposes node_t= {R_t,b+1,R_t,b+2,…,R_t,k,…,R_t,c}；And obtain the path flow rate vector Rate of t_tMiddle maximum flow rate R_t,max：

R_t,k=F_Pt,k/D_t,k (3)

Step 3.6, judge R_t,max=0 and V_0,capWhether=0 set up, if all setting up, performs step 3.10；

If only R_t,max=0 sets up, then it represents that t Path selection queue vector Path_tIt is invalid, and can not in t Evacuated again, the value of t+1 is assigned to t, and return to step 3.1 recalculates evacuation planning path；

If all invalid, then it represents that in t Path selection queue vector Path_tEffectively, one can be selected to can perform Evacuation path, and from Path selection queue vector Path_tIt is middle by maximum flow rate R_t,maxCorresponding shortest path is selected, and is stored in Maximum flow rate path P_t,max, and be designated asAnd max-flow Rate path P_t,maxMiddle the arrival time collection by nodeAnd haveN_t,max' represent maximum flow rate path P_t,maxIn remove super source node V₀Outer passed through node is total Number,Represent maximum flow rate path P_t,maxMiddle passed through n-th_t,max' individual node, 1≤n_t,max′≤N_t,max′；Note is maximum Flow rate path P_t,maxCorresponding maximum capacity of evacuating is F_t,max；

As shown in figure 3, obtaining maximum flow rate and corresponding shortest path according to this step；By maximum flow rate path P_t,maxIn Except super source node V₀The node that outer pathway is passed through is stored in path output queue set OutPut_Path, and records maximum The arrival time of capacity and each node is evacuated, for example, in oriented road network structure as shown in Figure 2, it is assumed that this step is obtained first Shortest path P with maximum flow rate_t,maxIt is at the t=0 moment from super source node V₀To destination node V₁₃Shortest path P_0,13={ V₀,V₁,V₅,V₈,V₁₁,V₁₃And path in all nodes corresponding arrival time collection { 0,0,1,2,5,6 }, it is allowed to it is logical Capable maximum capacity of evacuating is F_P0,13=4, as shown in the first row output in table 1, except super source node is not written into, other nodes are adopted Write with the form of "-node (arrival time) ", path planning form is V1 (0)-V5 (1)-V8 (2)-V11 (5)-V13 (6)； The source node of the shortest path is V₁, the destination node of arrival is V₁₃, the maximum capacity of evacuating on path is 4, performs the evacuation The time cost that path is spent is 6；And perform step 3.7；

Step 3.7, using formula (4) respectively to maximum flow rate path P_t,maxThe residue on middle passed through node and side is current to be held Amount is modified, and modified values are newly stored into residual capacity time expanding node collection V_capWith residual capacity time extension side collection E_cap In, so as to realize residual capacity time expanding node collection V_capWith residual capacity time extension side collection E_capIn each component value more Newly；

In formula (4),Represent maximum flow rate path P_t,maxOn n-th_t,max' -1 nodeIt is dealt into coupled n-th_t,max' individual nodeTerminate generated side in arrival timeWhen residue lead to Row capacity；Represent maximum flow rate path P_t,maxOn n-th_t,max' individual nodeIn arrival timeWhen the current capacity of residue；

For example, examples cited in step 3.4.3, obtain first with maximum flow rate path P_0,13={ V₀,V₁,V₅,V₈, V₁₁,V₁₃In, extend intermediate node V₅Initial residual capacity in arrival time t=1Calculated using formula (4) After obtainExtension intermediate node V₈Residual capacity in arrival time t=2Obtained after being calculated using formula (4)Other nodes are right in each institute The residual capacity in arrival time dimension answered calculates acquisition successively；In maximum flow rate path institute by each side each corresponding Arrival time on residual capacity calculate operation it is all similar, by extension intermediate node V₅Set out to extension intermediate node V₈ Terminating residual capacity of the generated side in arrival time t=1 isObtained after being calculated using formula (4)Residual capacity is 0, it is meant that as shown in step 4.1, and the side will be at the t=1 moment It is invalid；Residual capacity of remaining side on the time dimension of corresponding arrival time can successively calculate acquisition；

Therefore, it is sequentially completed residual capacity time expanding node collection V_capWith residual capacity side collection E_capIn each component value Renewal；

Step 3.8, obtain super source node V using formula (5)₀In the current capacity V of the residue of moment t_0,cap, calculating gained is The current available capacity for also needing to evacuate：

V_{0, cap}-V_{0, cap}=F_{T, max} (5)

Step 3.9, judge V_0,capWhether=0 set up, if so, then perform step 3.10；Otherwise, step 3.1 is performed, this Place turns to the calculating that step 3.1 re-executes a new round, the value of t+1 is not assigned into t, it is meant that may be used also under current time t Can there is an evacuation path, what will be performed is the iterative calculation in the maximum flow rate path of a new round under current time t；

Step 3.10, evacuation planning terminate, and acquisition stores the path output queue set OutPut_ in maximum flow rate path The final result of Path；For example, road network structure as shown in Figure 1, its result such as path output queue set OutPut_ of table 1 Shown in Path examples, a plurality of evacuation planning path for ensureing that total number of evacuation total evacuation is finished is outputed, there is permission on path The number and evacuation time of evacuation.

The path output queue set OutPut_Path examples of table 1

Source node	Number of evacuation	Path planning	Evacuation time
					4		6
	1		7
					4		8
	1		8
					2		9
	5		10
					4		7
	1		8
					4		13
	2		10
					1		10
	1		10

More than, preferably a kind of implementation method only of the invention gives the example of oriented uni-direction road grid structure, in addition, This method can apply in the middle of oriented two-way road network structure completely, specific embodiment, and user can be according to real generation The road grid traffic on boundary carries out mathematical modeling and parameter setting, can obtain identical effect.It should be noted that, it is any to be familiar with Those skilled in the art the invention discloses technical scope in, technology according to the present invention scheme and its inventive concept It is subject to equivalent or relevant parameter changes, should be all included within the scope of the present invention.

Claims (1)

1. a kind of road network evacuation planning method based on maximum flow rate heat source, be applied to simulate oriented road network structure G (V, E in), in the oriented road network structure G (V, E) of simulation, V represents set of node, and has V={ V_s,V_z,V_d}；V_sRepresent source node Collection, V_zRepresent set of intermediate nodes；V_dRepresent destination node collection；And have：V_s={ V₁,V₂,…,V_i,…,V_a}；V_iRepresent the source section Point set V_sIn i-th source node, and V_i={ V_i,cap,V_i,occ, V_i,capRepresent the source node set V_sIn i-th source node V_i's Node passes through capacity, V_i,occRepresent the source node set V_sIn i-th source node V_iInitial capacity to be evacuated, 1≤i≤a；V_z ={ V_a+1,…,V_j,…,V_b, V_jRepresent the set of intermediate nodes V_zIn j-th intermediate node, and V_j={ V_j,cap, V_j,capTable Show the set of intermediate nodes V_zIn j-th intermediate node V_jThe current capacity of node, a+1≤j≤b；V_d={ V_b+1,…,V_k,…, V_c, V_kRepresent the destination node collection V_dIn k-th destination node, and V_k={ V_k,cap,V_k,occ, V_k,capRepresent the purpose Set of node V_dIn k-th destination node V_kThe current capacity of node, V_k,occRepresent the destination node collection V_dIn k-th section of mesh Point V_kAccommodated evacuation capacity, b+1≤k≤c；E represents side collection, and has E={ e₁,e₂,…,e_h,…,e_H, e_hRepresent described When the h articles in collection E, it is assumed that the h articles side e_hIt is by n-th in the set of node V_hIndividual nodeSet out to coupled N-th_h' individual nodeTerminate generated side, and have Represent the h articles side e_hIt is current Capacity,Represent and pass through the h articles side e_hTransit time；It is characterized in that, the road network evacuation planning method is by following step Suddenly carry out：

Step 1, the super source node V of construction₀And be associated with the oriented road network structure G (V, E)：

Step 1.1, the super source node V of structure₀, and have V₀={ V_0,cap,Represent the super source node V₀'s Evacuate capacity；

Step 1.2, by the super source node V₀Respectively with the source node set V_sIn each source node be connected, so as to generate a Bar side, is designated ase′_iRepresent the super source node V₀With the source node set V_sIn i-th source Node V_iBe connected generated side, and has： Represent the super source node V₀Saved with the source Point set V_sIn i-th source node V_iBe connected generated side e '_iCurrent capacity,Represent and pass through the super source node V₀ With the source node set V_sIn i-th source node V_iBe connected generated side e '_iTransit time；

Step 1.3, by the source node set V_sIn i-th source node V_iInitial capacity V to be evacuated_i,occIt is assigned toAnd OrderRealize the super source node V₀With the source node set V_sIn i-th source node V_iAssociation；So as to realize The super source node V₀With the association of the oriented road network structure G (V, E) of simulation；

Step 2, the definition of road network evacuation planning parameter：

Step 2.1, the definition of path planning parameter：

The definition moment is t, and for recording the time course of the evacuation planning, initializes t=0；

It is G (V, E) ' to define the oriented road network structure of the traversal path with time dimension, and evacuates shortest path for solving；

The path cost vector for defining t is D_t, and have D_t={ D_t,b+1,D_t,b+2,…,D_t,k,…,D_t,c, D_t,kRepresent described Path cost vector D_tIn k-th component, and for storing t from the super source node V₀To the destination node collection V_dIn k-th destination node V_kThe minimum time cost for being spent；

The Path selection queue vector for defining t is Path_t, and have Path_t={ P_t,b+1,P_t,b+2,…,P_t,k,…,P_t,c}； P_t,kRepresent the Path selection queue vector Path_tIn k-th component, and for storing t from the super source node V₀To the destination node collection V_dIn k-th destination node V_kThe minimum time cost D for being spent_t,kCorresponding path, and remember It is shortest path；

The path flow rate vector for defining t is Rate_t, and have Rate_t={ R_t,b+1,R_t,b+2,…,R_t,k,…,R_t,c},R_t,kTable Show the path flow rate vector Rate_tIn k-th component, and for storing Path selection queue vector Path described in t_t In k-th component P_t,kThe ratio of the current capacity of the maximum of upper receiving and transit time, i.e., from the super source node V₀To institute State destination node collection V_dIn k-th destination node V_kShortest path P_t,kFlow rate；

Define the path flow rate vector Rate of t_tMiddle largest component is maximum flow rate R_t,max；

T is defined by the Path selection queue vector Path_tIn maximum flow rate R_t,maxCorresponding shortest path, is most Big flow rate path, is designated as P_t,max；

Define path output queue collection and be combined into OutPut_Path, and initialize the path output queue set OutPut_Path It is sky；

Step 2.2, road network state parameter are defined and initialized：

Defining the current capacity nodes collection of t isLead in the residue of t for all nodes in representing the set of node V Row capacity, and have Represent m-th node V in the set of node V_mLead in the residue of t Row capacity；

As t=0, initialization Represent m-th node V in the set of node V_mCurrent capacity, from And obtain the current capacity nodes collection at t=0 moment

Define residual capacity time expanding node to integrate is V_cap, by the current capacity nodes collection at t=0 momentIt is stored in the residue Capacity time expanding node collection V_capIn；

Merge side the collection E and Bian JiIn all sides, constitute side complete or collected works E_union；

Defining the current capacity side collection of t isFor representing the side complete or collected works E_unionIn each bar side t residue lead to Row capacity, and haveAnd R=H+a；Represent the side complete or collected works E_unionIn the r articles side In the current capacity of the residue of t, it is assumed that the r articles current capacity of the residue on sideIt is by the set of node V and described super Source node V₀In n-th_rIndividual nodeSet out to coupled n-th_r' individual nodeTerminate generated side in the surplus of t Remaining current capacity, and have

During t=0 moment, by the side complete or collected works E_unionIn from n-th_rIndividual nodeSet out to coupled n-th_r' individual node Terminate the current capacity on generated sideIt is assigned toSo as to obtain the current capacity side collection at t=0 moment

Define residual capacity time extension side to integrate is E_cap, by the current capacity side collection at t=0 momentIt is stored in the residual capacity Time extension side collection E_capIn；

Step 3, the Path selection of evacuation planning：

Step 3.1, in t, carry out path planning parameter reset operation：

Step 3.1.1, parameter reset：

The path cost vector D of t is set_t={ D_t,b+1,D_t,b+2,…,D_t,k,…,D_t,cIn each component value be it is just infinite Greatly；The Path selection queue vector Path of t is set_t={ P_t,b+1,P_t,b+2,…,P_t,k,…,P_t,cIn each vector value be It is empty；The path flow rate vector Rate of t is set_t={ R_t,b+1,R_t,b+2,…,R_t,k,…,R_t,cIn each component value be sky；If Put the maximum flow rate R of t_t,max=0；The maximum flow rate path P of t is set_t,maxIt is sky；

Oriented road network structure G (V, the E) ' reset of step 3.1.2, the traversal path with time dimension：

The oriented road network structure G (V, E) is assigned to G (V, E) '；

According to the residual capacity time expanding node collection V_capMiddle remaining current capacity is the time corresponding to 0 node acquisition Dimension, and judge that in the node that the middle remaining current capacity of G (V, E) ' is 0 be invalid on corresponding time dimension；

Collection E in side is extended according to the residual capacity time_capMiddle remaining current capacity is the time dimension corresponding to 0 side acquisition, And judge that on the side that the middle remaining current capacity of G (V, E) ' is 0 be invalid on corresponding time dimension；So as to obtain the band time The oriented road network structure G (V, E) of traversal path of dimension '；

Whether step 3.2, it is nothing according to oriented road network structure G (V, the E) ' interior joint of the traversal path with time dimension and side Effect, travel through the oriented road network structure G (V, E) of the traversal path with time dimension ' in from the super source node V₀To described Destination node collection V_dIn k-th destination node V_kThe all paths passed through；

Choose and reach k-th destination node V_kThe minimum path of time cost is spent in all paths passed through as k-th mesh Node V_kShortest path and be stored in the Path selection queue vector Path of t respectively_tK-th component P_t,kIn；So as to By the destination node collection V_dThe shortest path of middle all purposes node is stored in the Path selection queue vector Path respectively_tPhase In the component answered；

Step 3.3, by t Path selection queue vector Path_tIn k-th component P_t,kThe time cost for being spent is stored in described Path cost vector D_tK-th component D_t,kIn, so as to by the destination node collection V_dThe shortest path of middle all purposes node Spent time cost is stored in the path cost vector D respectively_tIn corresponding component；

Step 3.4, acquisition t Path selection queue vector Path_tIn k-th component P_t,kAllowed on represented shortest path Current maximum evacuation capacitySo as to obtain in t from the super source node V₀To the destination node collection V_dMiddle institute Maximum evacuation capacity set on the shortest path of purposeful node

Step 3.4.1, acquisition t Path selection queue vector Path_tIn k-th component P_t,kRepresented shortest path, note For $P_{t,k}=\{V_0^{P_{t,k}},V_1^{P_{t,k}},...,V_{n_{t,k}-1}^{P_{t,k}},V_{n_{t,k}}^{P_{t,k}}...,V_{N_{t,k}}^{P_{t,k}}\},$ And have $V_0^{P_{t,k}}=V_0,$ N_t,kRepresent the shortest path P_t,kIn remove super source node V₀Outer passed through node total number；Represent the shortest path P_t,kMiddle passed through n-th_t,kIt is individual Node, 1≤n_t,k≤N_t,k；

Step 3.4.2, obtain the shortest path P using formula (1)_t,kIt is middle by the 0th nodeAnd n-th for passing through_t,k Individual nodeArrival timeSo as to obtain the shortest path P_t,kThe arrival time collection of middle passed through node

$\left\{\begin{array}{cc}{T}_0^{P_{t,k}}=t,& \\ T_{n_{t,k}}^{P_{t,k}}=T_{n_{t,k}-1}^{P_{t,k}}+e_{tra}^{<V_{n_{t,k}-1}^{P_{t,k}},V_{n_{t,k}}^{P_{t,k}}>},& \&ForAll;n_{t,k},1\&le;n_{t,k}\&le;N_{t,k}\end{array}\right.---\left(1\right)$

In formula (1),Represent in the side complete or collected works E_unionIn, by the shortest path P_t,kIn from n-th_t,k- 1 nodeSet out to coupled n-th_t,kIndividual nodeTerminate the transit time on generated side；

Step 3.4.3, renewal road network state parameter：

Step 3.4.3.1, according to the shortest path P_t,kIt is middle by n-th_t,kIndividual nodeArrival timeInquiry The residual capacity time expanding node collection V_capIn whether include arrival timeCurrent capacity nodes collectionIf no Comprising then makingFor empty and be stored in the residual capacity time expanding node collection V_capIn；Otherwise, maintainIt is constant；

Inquire about the current capacity nodes collectionIn whether include described n-th_t,kIndividual nodeIn arrival timeWhen The current node capacity of residueIf comprising maintainingIt is constant；Otherwise, by the shortest path P_t,kMiddle institute By n-th_t,kIndividual nodeThe current capacity of corresponding node in the set of node VIt is assigned toWillIt is stored in the current capacity nodes collectionIn；So as to realize the remaining current node capacity It is stored in the residual capacity time expanding node collection V_capIn；

Step 3.4.3.2, step 3.4.3.1 is repeated, so as to obtain the shortest path P_t,kMiddle passed through node is each Remaining node capacity from arrival time dimension, and it is sequentially stored into the residual capacity time expanding node collection V_capIn；

Step 3.4.3.3, according to the shortest path P_t,kIt is middle to pass through from n-th_t,k- 1 nodeSet out to coupled N-th_t,kIndividual nodeTerminate the arrival time on generated sideInquire about the residual capacity time extension side collection E_cap In whether include arrival timeWhen current capacity side collectionIf not including, orderFor empty and be stored in described Residual capacity time extension side collection E_capIn；Otherwise, maintainIt is constant；

Inquire about the current capacity side collectionIn whether include the shortest path P_t,kIn from n-th_t,k- 1 node Set out to coupled n-th_t,kIndividual nodeTerminate generated side in arrival timeWhen the current edge capacity of residueIf comprising maintainingIt is constant；Otherwise, by the side complete or collected works E_unionIn by described most short Path P_t,kIn from n-th_t,k- 1 nodeSet out to coupled n-th_t,kIndividual nodeTerminate the logical of generated side Row capacityIt is assigned toWillIt is stored in the current capacity side collectionIn, So as to realize the remaining current edge capacityIt is stored in the residual capacity time extension side collection E_capIn；

Step 3.4.3.4, step 3.4.3.3 is repeated, so as to obtain the shortest path P_t,kMiddle passed through side is respective Remaining edge capacity in arrival time dimension, and it is sequentially stored into the residual capacity time extension side collection E_capIn；

Step 3.4.4, the Path selection queue vector Path is obtained according to formula (2)_tIn k-th component P_t,kIt is representative most Current maximum evacuation capacity is allowed on short path

$F_{P_{t,k}}=\min \left\{\begin{array}{c}{V}_{0,cap}\\ V_{cap}^{(V_{n_{t,k}}^{P_{t,k}},T_{n_{t,k}}^{P_{t,k}})}\\ e_{cap}^{(<V_{n_{t,k}-1}^{P_{t,k}},V_{n_{t,k}}^{P_{t,k}}>,T_{n_{t,k}-1}^{P_{t,k}})}\end{array}\right.---\left(2\right)$

$\begin{array}{cc}s.t.& \&ForAll;n_{t,k},1\&le;n_{t,k}\&le;N_{t,k}\end{array}$

In formula (2),Represent the shortest path P_t,kOn n-th_t,kIndividual nodeIn arrival timeWhen it is surplus Remaining current capacity；Represent from the shortest path P_t,kOn n-th_t,k- 1 nodeSet out to its Connected n-th_t,kIndividual nodeTerminate generated side in arrival timeWhen the current capacity of residue；

Step 3.5, t is obtained using formula (3) from the super source node V₀To the destination node collection V_dIn k-th purpose Node V_kShortest path flow rate R_t,k, so as to obtain t from the super source node V₀To the destination node collection V_dIn The flow rate vector Rate of the shortest path of all purposes node_t={ R_t,b+1,R_t,b+2,…,R_t,k,…,R_t,c}；And obtain the t The path flow rate vector Rate at moment_tMiddle maximum flow rate R_t,max：

$R_{t,k}=F_{P_{t,k}}/D_{t,k}---\left(3\right)$

Step 3.6, judge R_t,max=0 and V_0,capWhether=0 set up, if all setting up, performs step 3.10；

If only R_t,max=0 sets up, then it represents that t Path selection queue vector Path_tIt is invalid, and can not be again in t Evacuated, the value of t+1 is assigned to t, and return to step 3.1 recalculates evacuation planning path；

If all invalid, then it represents that moment Path selection queue vector Path_tEffectively, and from the Path selection queue vector Path_tIt is middle by maximum flow rate R_t,maxCorresponding shortest path is selected, and is stored in the maximum flow rate path P_t,max, and be designated as $P_{t,max}=\{V_0^{\&prime;P_{t,max}},V_1^{\&prime;P_{t,max}},...,V_{n_{t,\max }^{\&prime;}-1}^{\&prime;P_{t,max}},V_{n_{t,\max }^{\&prime;}}^{\&prime;P_{t,max}}...,V_{N_{t,\max }^{\&prime;}}^{\&prime;P_{t,max}}\},$ And the maximum flow rate path P_t,maxIt is middle through celebrating a festival The arrival time collection of point is designated asAnd have $V_0^{\&prime;P_{t,max}}=V_0,$ N′_t,maxRepresent the maximum flow rate path P_t,maxIn remove super source node V₀Outer passed through node total number,Represent described Maximum flow rate path P_t,maxMiddle passed through the n-th '_t,maxIndividual node, 1≤n '_t,max≤N′_t,max；Remember the maximum flow rate path P_t,maxCorresponding maximum capacity of evacuating is F_t,max；By the maximum flow rate path P_t,maxIn remove the super source node V₀Outward The node that path is passed through is stored in the path output queue set OutPut_Path, and records the maximum capacity and each evacuated The arrival time of node；And perform step 3.7；

Step 3.7, using formula (4) respectively to the maximum flow rate path P_t,maxThe residue on middle passed through node and side is current to be held Amount is modified, and modified values are newly stored into the residual capacity time expanding node collection V_capExpand with the residual capacity time Side collection E_capIn, so as to realize the residual capacity time expanding node collection V_capSide collection is extended with the residual capacity time E_capRenewal；

$\left\{\begin{array}{c}{e}_{cap}^{(<V_{n_{t,\max }^{\&prime;}-1}^{\&prime;P_{t,\max }},V_{n_{t,\max }^{\&prime;}}^{\&prime;P_{t,\max }}>,T_{n_{t,\max }^{\&prime;}-1}^{\&prime;P_{t,\max }})}=e_{cap}^{(<V_{n_{t,\max }^{\&prime;}-1}^{\&prime;P_{t,\max }},V_{n_{t,\max }^{\&prime;}}^{\&prime;P_{t,\max }}>,T_{n_{t,\max }^{\&prime;}-1}^{\&prime;P_{t,\max }})}-F_{t,\max }\\ V_{cap}^{(V_{n_{t,\max }^{\&prime;}-1}^{\&prime;P_{t,\max }},V_{n_{t,\max }^{\&prime;}}^{\&prime;P_{t,\max }})}=V_{cap}^{(V_{n_{t,\max }^{\&prime;}}^{\&prime;P_{t,\max }},V_{n_{t,\max }^{\&prime;}}^{\&prime;P_{t,\max }})}-F_{t,\max }\end{array}\right.---\left(4\right)$

$\begin{array}{cc}s.t.& n_{t,\max }^{\&prime;},\&ForAll;1\&le;n_{t,\max }^{\&prime;}\&le;N_{t,\max }^{\&prime;}\end{array}$

In formula (4),Represent the maximum flow rate path P_t,maxOn the n-th '_t,max- 1 nodeSet out to coupled the n-th '_t,maxIndividual nodeTerminate generated side in arrival timeWhen it is surplus Remaining current capacity；Represent the maximum flow rate path P_t,maxOn the n-th '_t,maxIndividual nodeReach TimeWhen the current capacity of residue；

Step 3.8, obtain the super source node V using formula (5)₀In the current capacity V of the residue of t_0,cap：

V_0,cap=V_0,cap-F_t,max (5)

Step 3.9, judge V_0,capWhether=0 set up, if so, then perform step 3.10；Otherwise, step 3.1 is performed；

Step 3.10, the evacuation planning terminate, and the path output queue set in maximum flow rate path is stored described in acquisition The final result of OutPut_Path.