CN112101686A - Crews and routes plan compiling method based on feasible label connection network - Google Patents
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Abstract
The invention provides a crews-and-deals traffic-route planning method based on a feasible label switching network, which comprises the steps of obtaining the feasible label switching network through merging calculation according to a feasible path, and obtaining a planning model through integrating calculation according to the feasible label switching network and a preset rule; and (4) carrying out iterative solution on the planning model by using a Lagrange relaxation algorithm to obtain an optimal solution, namely an intersection plan. The invention can greatly reduce the occupied scale of the computer memory required by calculation, thereby obtaining the result in a short time, and is particularly suitable for large-scale traffic planning; the lower bound value and the upper bound value obtained by the Lagrange relaxation algorithm are converged to the optimal values, the difference between the upper bound value and the lower bound value is small, the solving quality is high, and a high-quality riding traffic road plan can be compiled for a railway system; various crew rules are comprehensively considered, the operation is closer to reality, and the feasibility and the authenticity of the crew traffic plan are ensured.
Description
Technical Field
The invention relates to a crews traffic route planning method based on a feasible label connection network, belonging to the technical field of computer data processing.
Background
The railway-ride route planning problem is generally abstracted as a set coverage/partitioning problem with additional constraints. The three most common solutions for solving the large-scale set coverage/partitioning model are a combination of a branch pricing algorithm, a Lagrangian relaxation algorithm, a heuristic algorithm and a relaxation algorithm. Regardless of the solution method employed, efforts are being made to explore more efficient strategies to improve the quality and efficiency of the solution, such as strategies to reduce network size, more efficient branching/pruning strategies, and cross-routing strategies.
Besides the set covering/dividing model, the railway passenger traffic route plan can be modeled into a multi-commodity flow model and a network flow model based on a time-space network, and a heuristic algorithm is adopted for solving. Some scholars propose a network flow model of a railway service traffic plan with an 'attendance rate', and directly solve a small-scale problem through CPLEX. Meanwhile, in order to avoid the symmetry of the network flow model, effective constraint is added to improve the linear relaxation boundary of the integer problem, so that the solving process is accelerated.
Decomposition is a common method to solve the problem of railway crew cut planning because of its inherent complex constraints.
The inventors of the present application found that:
(1) the existing crew rules considered in research contain fewer rules, for example, the rules lack the rules for taking meals by crew groups, so that various rules which need to be met in actual conditions cannot be completely described, and the complexity is greatly increased and the calculation scale is increased easily due to the fact that the number of the rules is simply added;
(2) the existing accurate solving methods in research are only suitable for solving small-scale crew traffic route plans, once the scale becomes huge, the solving methods easily cause the overflow of a computer memory, and the solving time also becomes slow.
Disclosure of Invention
In order to solve the technical problems, the invention provides a crewmember traffic route planning method based on a feasible label switching network, which can greatly reduce the occupied scale of a computer memory required by calculation, thereby obtaining a result in a short time and being particularly suitable for large traffic route planning.
The invention is realized by the following technical scheme.
The invention provides a crews-and-deals traffic-route planning method based on a feasible label switching network, which comprises the steps of obtaining the feasible label switching network through merging calculation according to a feasible path, and obtaining a planning model through integrating calculation according to the feasible label switching network and a preset rule; and (4) carrying out iterative solution on the planning model by using a Lagrange relaxation algorithm to obtain an optimal solution, namely an intersection plan.
The iterative solution of the planning model by using the Lagrange relaxation algorithm comprises the following steps:
conversion: introducing a Lagrange multiplier, and relaxing coupling constraint on the planning model to obtain a dual model of the planning model;
solving the following bound solution: and solving the lower bound solution of the dual model to obtain the optimal solution of the corresponding planning model.
The method for solving the lower bound solution of the dual model comprises the following steps:
a. solving a solution: solving a lower bound solution of the dual model based on a mode of solving the tree structure data;
b. and (3) judging: judging whether the lower bound solution obtained by solving is feasible, if so, directly ending and taking the lower bound solution as an optimal solution, otherwise, executing the step c;
c. adding iteration: adding the lower bound solution to the dual model;
d. and (3) solving an upper bound: computing an upper bound solution using the set coverage model;
e. updating the multiplier: and (c) updating the Lagrange multiplier according to the lower bound solution and the upper bound solution, correspondingly updating the dual model, and then returning to the step a.
In the step d, whether the calculated upper bound solution meets the precision requirement is judged, if the difference gap between the upper bound solution and the lower bound solution of the current iteration meets the precision requirement, the judgment is yes, the process is directly finished, and the upper bound solution is used as the optimal solution.
In the step a, the lower bound solution is solved by calculating the cost value by adopting a tree structure traversal method, and taking the feasible path solution with the minimum cost value as the lower bound solution.
And e, updating the Lagrange multiplier by using a sub-gradient algorithm.
The feasible path is generated in a shortest path searching mode; the feasible path generation rule also comprises working time on duty, transfer time, continuous driving time, rest time, outer-segment duty-staying time, a road-crossing period and meal rest time; the merging calculation is to summarize the multiple feasible paths and delete the feasible paths in which there is a time and space conflict.
The preset rules comprise decision variables, parameter variables, objective functions and constraint conditions; the integration calculation is to parameterize the cost value of the feasible label connection network, and to establish a simultaneous equation set by taking a preset rule as a constraint condition.
The parameter variables comprise a node set, a path arc set, the number of available task groups, a task section and a section task set.
The planning model is obtained by adopting a network flow method to integrate and calculate.
The invention has the beneficial effects that: the occupied scale of the computer memory required by calculation can be greatly reduced, so that the result can be obtained in a short time, and the method is particularly suitable for large-scale traffic planning; the lower bound value and the upper bound value obtained by the Lagrange relaxation algorithm are converged to the optimal values, the difference between the upper bound value and the lower bound value is small, the solving quality is high, and a high-quality riding traffic road plan can be compiled for a railway system; various crew rules are comprehensively considered, the operation is closer to reality, and the feasibility and the authenticity of the crew traffic plan are ensured.
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FIG. 1 is a schematic flow diagram of one embodiment of the present invention;
fig. 2 is a flow chart diagram of the iterative solution process of fig. 1.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
The invention provides a crews-and-deals traffic-route planning method based on a feasible label switching network, which comprises the steps of obtaining the feasible label switching network through merging calculation according to a feasible path, and obtaining a planning model through integrating calculation according to the feasible label switching network and a preset rule; and (4) carrying out iterative solution on the planning model by using a Lagrange relaxation algorithm to obtain an optimal solution, namely an intersection plan.
Therefore, iterative solution is carried out by using a Lagrange relaxation algorithm, on one hand, overlarge-scale calculation is avoided for a single time, so that the memory occupation in the calculation process is reduced, on the other hand, the optimal solution can be effectively approached through the iterative process, and the calculation result quality is high.
Specifically, the action is a specific way of solving by using a lagrangian relaxation algorithm, and the iterative solution of the planning model by using the lagrangian relaxation algorithm includes the following steps:
conversion: introducing a Lagrange multiplier, and relaxing coupling constraint on the planning model to obtain a dual model of the planning model;
solving the following bound solution: and solving the lower bound solution of the dual model to obtain the optimal solution of the corresponding planning model.
Further, as a specific way of iteration, solving the lower bound solution of the dual model includes the following steps:
a. solving a solution: solving a lower bound solution of the dual model based on a mode of solving the tree structure data;
b. and (3) judging: judging whether the lower bound solution obtained by solving is feasible, if so, directly ending and taking the lower bound solution as an optimal solution, otherwise, executing the step c;
c. adding iteration: adding the lower bound solution to the dual model;
d. and (3) solving an upper bound: computing an upper bound solution using the set coverage model;
e. updating the multiplier: and (c) updating the Lagrange multiplier according to the lower bound solution and the upper bound solution, correspondingly updating the dual model, and then returning to the step a.
One possible way to determine whether the solved lower bound solution is feasible is to perform a feasibility check, that is, determine whether the lower bound solution covers all tasks in the preset rule, and if so, it is feasible.
Preferably, as a preferred scheme for avoiding excessive unnecessary iteration processes to reduce unnecessary computation loss, in step d, it is determined whether the calculated upper bound solution meets the accuracy requirement, and if the difference gap between the upper bound solution and the lower bound solution of the current iteration meets the accuracy requirement, it is determined that the difference gap meets the accuracy requirement, and the upper bound solution is directly ended and taken as the optimal solution.
Specifically, because the data structure of the planning model obtained step by step from the feasible path has the characteristic of a typical tree structure, in the step a, the lower bound solution is solved by calculating the cost value by adopting a tree structure traversal method, and the feasible path solution with the minimum cost value is taken as the lower bound solution.
Preferably, as an optimal way of iteration, in step e, the lagrangian multiplier is updated by using a sub-gradient algorithm.
Further, based on the above, the present invention can be applied to various traffic planning, but since the present invention is mainly applied to the planning of the railway service traffic plan, the feasible path is generated by the shortest path search method.
In order to ensure that various rules required to be met in the actual situation are described as completely as possible, the feasible path generation rules further comprise work time on duty, transfer time, continuous driving time, rest time, outer-segment duty-staying time, a road-passing period and meal rest time; the merging calculation is that the multiple feasible paths are summarized, and the feasible paths with time and space conflicts are deleted.
Furthermore, the preset rules used in the generation process of the planning model comprise decision variables, parameter variables, objective functions and constraint conditions; the integration calculation is to parameterize the cost value of the feasible label connection network, and to establish a simultaneous equation set by taking a preset rule as a constraint condition.
Specifically, the parameter variables include a node set, a path arc set, the number of available task groups, a task section, and a section task set.
As an optimal scheme of a planning model generation mode, the planning model is obtained by adopting a network flow method for integrated calculation.
Example 1
By adopting the scheme, the railway passenger traffic route plan is compiled, and the following steps are specifically adopted:
step1, considering the feasible label connection network establishment of the duty rule;
step2, establishing a crew traffic planning model based on the feasible label switching network;
and 3, solving a riding traffic route planning model based on a Lagrange relaxation algorithm.
Specifically, the method comprises the following steps:
step1, establishing a feasible label connection network considering the crew rules. The generation process is as follows:
step1, initializing, and establishing a connection network G according to the crew section setts=(Vts,Ats) Set of nodes VtsCarrying out topological sorting, and setting the mark number of the virtual starting point as wo(0)= {0,0,0,0,0,0}, go to Step2;
step2 traversing V according to topological ordertsFor ∀ i ∈ VtsGo to Step 3; if VtsWhen the traversal is finished, turning to Step 7;
step3 for node i, it is labeled as WiThe same reference numbers in the same list are merged, and the W is traversediFor ∀ wi(m)∈WiGo to Step 4; if W isiWhen the traversal is finished, turning to Step2;
step4 for reference number wi(m)Traversing the outgoing arc of node i, ∀ (i, j) ∈ AtsGo to Step5, if yesCompleting the arc-out traversal of the point i, and turning to Step 3;
step5 for reference number wi(m)And recurrently obtaining the label w of the arc (i, j) terminal j according to the label attribute calculation methodj(n)The mark w is judged according to the duty rulej(n)If the operation is feasible, go to Step6;
step6 if the label wj(n)It is possible to add it to the set W of labels at the end j of the arc (i, j)jPerforming the following steps; if the reference sign wj(n)If not, the operation is abandoned. Go to Step 4;
step7, ending, obtaining feasible label connecting network Gts=(Vts,Ats)。
And 2, establishing a crew traffic planning model based on the feasible label switching network.
And inputting known condition data, and constructing a crew traffic route planning model based on the feasible label switching network, wherein the crew traffic route planning model comprises decision variables, parameter variables, objective functions and constraint conditions. Wherein the parameter variables include:
point set V in feasible label connectivity networktsArc set AtsNumber of available crew groups P, crew sector (task) set L.
And 3, solving a riding traffic route planning model based on a Lagrange relaxation algorithm.
The Lagrange relaxation method is suitable for large-scale crew planning and can ensure the quality of the solution. And obtaining a lower bound of the optimal solution by a Lagrange relaxation method, and designing an aggregate coverage model to obtain an upper bound. And designing and updating a sub-gradient algorithm of the Lagrange multiplier, so that the Lagrange relaxation algorithm reduces the upper bound and improves the lower bound in iteration to approach the optimal solution.
(1) Lagrange duality problem
Introducing a Lagrange multiplier rho (l) relaxation coupling constraint (9) and giving a dual model thereof:
………… (2)
st. constraints (10) - (12)
Lagrange relaxation provides a lower bound for the original problem, and the Lagrange multiplier is adjusted through a sub-gradient algorithm, so that the lower bound solution can be continuously improved and converged to the optimal solution.
(2) Lower bound algorithm
Because the feasible label connection network has the characteristic of a tree structure, the following bound solution can be obtained through the following algorithm:
step1: and (5) initializing. Set p = 1. For all L ∈ L, (i, j) ∈ Al tsAnd phii=φjSet tt = lij=ttij-ρk (l)。∀i∈Vts，∀wi(m)∈WiIs provided with Ci(m)Is given by reference numeral wi(m)To virtual origin reference wo(0)Cost of, initial Ci(m)=0，wi(m)Is preceded by a numeral per (w)i(m))= wo(0)，Co(0)=0，per(wo(0))=null。
Step 2：∀i∈Vts，(i,j)∈Ats，wi(m)∈WiIf the reference number wj(n)From wi(m)Are recurrently obtained, and C(j(n)≥Ci(m)+ttijThen order Cj(n)=Ci(m)+ttij，per(wj(n))= wj(m)。
Step3: definition set Wtmp={wi(m)│wi(m)∈Wi，(i,j)∈Ad ts}. In the set WtmpIn, find the label ζ of the minimum costoBacktracking to the virtual origin label and setting the corresponding path as the traffic d executed by the crew group pp. Then, set Wtmp=Wtmp\ ζo。
Step4: if all tasks are executedd1,…,dpCovering, then dp+1,…, d|p|Setting a stopping intersection, and finishing the algorithm; if P = | P | or WtmpIf = Φ, the algorithm ends. Otherwise, set p = p +1, and then go to Step 3.
Carrying out feasibility inspection on the obtained lower bound solution, wherein the specific method is to judge whether the lower bound solution meets the constraint (9), namely, if the crew traffic route set obtained by the lower bound algorithm can cover all the crew tasks, the lower bound solution is feasible and the algorithm is finished; otherwise, a feasible crew traffic route set is obtained according to a lower bound solution design algorithm.
(3) Updating lagrange multipliers
In the iterative process, the value of ρ needs to be continuously updated using the following sub-gradient method:
…………（3）
wherein sigmakThe length of the k-th iteration is indicated, and the following rule must be satisfied for dynamic transformation in the search process:
(4) solving the upper bound
Taking the riding traffic routes generated in all iterative processes when the Lagrange relaxation model is solved as alternative traffic routes, the upper bound can be calculated by solving a set coverage problem. Definition of alphas tAnd (4) indicating whether the passenger traffic routes S cover the task l or not, wherein S is an alternative traffic route set. The set coverage model is as follows:
specifically, a way to consider a more complete crew rule, the feasible label switched network establishment process is analyzed as follows:
(1) initial connection network
1) Establishing a node
For any of the crew section tasks ∀ L ∈ L, the crew section arrival and departure nodes are established. For arriving/departing node i0Setting a node i0Four attributes (t)0,s0,φ0,θ0) And respectively showing the arrival/departure time of the node, the arrival/departure station of the node, the index of the corresponding service section task and the belonging motor train cross-road index. Node i0Dd (maximum duration of bus) copies, for each copy point ik(k =0,1, …, Dd) with tk=t0+1440*k，sk=s0，φk=φ0，θk=θ0The set of arrival/departure nodes of the crew section is denoted as Vl ts。
For each of the crew bases, a virtual starting point o and a virtual ending point d are established, the attributes of o including the station s where the crew base is locatedoAnd a crossing start time toAttributes of =0, d include the station s of the attendant basedAnd end of road td=1440 × Dd. The set of all virtual starting points is denoted as Vo tsThe set of virtual endpoints is denoted as Vd tsThe node set is marked as VtsAnd has a relation Vts=Vo ts∪Vl ts∪Vd ts。
2) Establishing an arc
Establishing a task arc (i, j) for a starting node i and an arriving node j of the same crew section task, wherein the arc length is tj-ti. The set of task arcs is denoted Al ts。
For ∀ i ∈ Vl tsIf i is the departure node, and si=soEstablishing a run-out arc (o, i) with an arc length ttocGreater than Td for a given onemaxThe integer of (maximum working time of crew in one day) represents the duty cost of executing the intersection, and the arc set of taking out is marked as Ao ts. If i is an arriving node, and si=sdEstablishing a receding arc (i, d) with an arc length ttij=0, and the set of rounded off arcs is denoted Ad ts。
For ∀ i, j ∈ Vl tsIf i is an arrival node and j is a departure node, si=sjAnd t isj>tiEstablishing a continuous arc with a length tj-ti. Define A respectivelyg ts、Aon tsRepresenting a non-night-crossing continuing arc set and a night-crossing continuing arc set.
A virtual arc (o, d) is established between a virtual starting point (o) and a virtual ending point (d) associated with the same crew base, indicating that the crew member stays in the crew base without performing any crew section, and the arc length ttodIs one greater than 0 and much less than TdmaxThe integer of (a), represents the cost of the stay at the crew base. Each virtual arc is a hand-off that does not contain any crew segments, referred to as a parking hand-off. The set of virtual arcs is denoted as Aod tsAnd has a relation Aod ts ⊂Ao ts , Aod ts ⊂Ad ts。
The arc set is denoted Ats=Ao ts∪Al ts^∪Ag ts∪Aon ts∪Ad ts。
(2) The crew rules are described. The following crew rules are given to ensure that the crew traffic is feasible:
1) working time on duty: the cumulative working time (including driving, resting, transferring) Td in one day must not exceed the maximum working time Tdmax。
2) Transfer time: when the crew member continuously acts as the crew section for the different motor train unit to cross, the interval Tt between the ending time of the first crew section and the starting time of the next crew section is not less than the minimum transfer time Ttmin。
3) Continuous driving time: the crew member continuously executes the crew sector (including the shift time but not the rest time), and the continuous driving time To should not exceed the maximum continuous driving time Tomax。
4) Rest time: after the crew sections are performed continuously, the crew must have a break time for a short break (or meal). Rest time Tr can not be less than minimum rest time Trmin。
5) The outer period duty-off time: when the crew member needs to rest at night at the crew transfer station, the rest time should be at least the minimum night rest time Tsmin。
6) The road crossing period is as follows: the crew must return to their affiliated crew base within Dd days, which means that the interval Tp between the start and end of the crew traffic must not exceed Dd 1440.
7) The rest time of the meal: the crew must be within a specified time window [ ML ]min,MLmax]And [ MS ]min,MSmax]The meals are respectively eaten. The dining time Te cannot be shorter than the minimum dining time TeminFurthermore, having a meal rest at least on duty Tea bAfter hours, start before Te of ride-backb fThe hour is over.
(3) Feasible label switched network
In the relay network, pairs ∀ i ∈ VtsRecording related riding information in the form of labels, the set of labels at the point being denoted as Wi={wi(1),wi(2),…,wi(m)}. For reference number wi(m)∈WiDefine 5 attributes wi(m)=(Tdi(m),Toi(m),Tci(m),Tpi(m),Mbi(m)) The meaning and calculation method of each attribute are as follows:
Tdi(m)integrating time for bus segmentThe length (including the time of taking out and taking back, intermitting and having a meal) is used for judging whether the crew group needs to take back or rest in the outer shift, and the length is cleared when the crew group (the outer shift) finishes taking back. Tdi(m)Calculated from its preamble label. Suppose wj(n)Is wi(m)Means that there is an arc from node j to i, ttji=ti-tj. If j is the crew base, Tdi(m)=0, the passenger traffic route starts. Td if arc (j, i) is a night-crossing arci(m)And =0, the crew section ends and the crew takes a rest overnight. In other cases: tdi(m)=Tdj(n)+ttji。
Toi(m)The duration of continuous driving for the passenger traffic section is calculated from its preamble designation. And Tdi(m)Similarly, if j is the crew base, or arc (j, i) is an overnight arc, then Toi(m)And = 0. Toi (m) =0 if there is a break or meal on arc (j, i), and the continuous crew procedure ends. In other cases, Toi(m)=Toj(n)+ttji。
Tci(m)The duration of the continuous interruption (waiting) for the passenger traffic is calculated from its preamble. If arc (j, i) is the working arc, Tci(m)And = 0. In other cases, Tci(m)=Tcj(n)+ttji。
Tpi(m)The cumulative length of the bus is calculated from the preamble number. If arc (j, i) is a night-crossing arc, Tpi(m)=Tpj(n)+ttji. In the remaining cases, with Tdi(m)The same is true.
Mbi (m) represents the meal status for lunch and dinner. For determining whether each crew member has lunch or dinner within a given time window. If the accumulated continuous driving time is not less than the minimum working time before meal rest, the accumulated interruption (waiting) time is not less than the minimum time for meal, and the moment of the current task meets the meal time requirement, i.e. Toi(m)≥Tea b,Tci(m)≥TeminAnd t isi-MLmin≥Temin(or t)i-MSmin≥Temin)，Then lunch (or dinner) is needed and three values of 0,1, 2 for the meal status are defined, representing three meal statuses before lunch, after lunch-before dinner and after dinner, respectively.
And marking the nodes in the connecting network according to the crew rules and the marking attribute calculation method.
Specifically, the crew road planning model is represented as a plurality of functions and/or constraints, namely:
model (model)
Wherein the symbols are as follows:
the objective function (8) minimizes the sum of all the length of the passenger traffic. The constraints (9) ensure that each crew section is executed by at least one crew group. The constraint (10) is a flow conservation constraint. Constraints (11) ensure that crew members perform routing tasks or stop.
Based on the above, the process of solving the planning model of the bus route plan based on the lagrangian relaxation algorithm in the invention can be substantially described as follows: and obtaining a lower bound of the optimal solution by a Lagrange relaxation method, designing a set coverage model to obtain an upper bound, and reducing the upper bound and improving the lower bound by the Lagrange relaxation algorithm in iteration to approach the optimal solution by updating a sub-gradient algorithm of a Lagrange multiplier. That is: the method comprises the steps of describing various riding rules related in the railway riding traffic route plan through a feasible label switching network, converting a feasible riding traffic route generation process into a classic shortest path search problem, constructing a network flow model on the basis of the feasible label switching network, solving a lower bound based on a Lagrange relaxation algorithm and obtaining an upper bound by utilizing a set coverage model so as to solve the problem of large-scale riding traffic route plan compilation.
In summary, the invention provides a method for planning a passenger traffic route based on a feasible label switching network, which can quickly plan a high-quality passenger traffic route under the constraint of comprehensively considering various passenger rules.
Claims (10)
1. A crews and deals with the planning method of the route based on feasible label switching network, characterized by that: the method comprises the following steps:
merging and calculating the feasible paths to obtain a feasible label switching network;
integrating and calculating according to the feasible label connection network and a preset rule to obtain a planning model;
and carrying out iterative solution on the planning model by using a Lagrange relaxation algorithm to obtain a passenger traffic route plan.
2. The method of claim 1, wherein the step of planning the crews based on feasible label connectivity network comprises: the iterative solution of the planning model by using the Lagrange relaxation algorithm comprises the following steps:
conversion: introducing a Lagrange multiplier, and relaxing coupling constraint on the planning model to obtain a dual model of the planning model;
solving the following bound solution: and obtaining the optimal solution of the planning model by solving the lower bound solution of the dual model.
3. The method of claim 2, wherein the step of planning the crews based on feasible label connectivity network comprises: the method for solving the lower bound solution of the dual model comprises the following steps:
a. solving a solution: solving a lower bound solution of the dual model based on a mode of solving the tree structure data;
b. and (3) judging: judging whether the lower bound solution obtained by solving is feasible, if so, directly ending and taking the lower bound solution as an optimal solution, otherwise, executing the step c;
c. adding iteration: adding the lower bound solution to the dual model;
d. and (3) solving an upper bound: calculating the upper bound solution using a set coverage model;
e. updating the multiplier: and updating the Lagrange multiplier according to the lower bound solution and the upper bound solution, and correspondingly updating the dual model.
4. The method of claim 3, wherein the step of planning the crews based on feasible label connectivity network comprises: in the step d, whether the calculated upper bound solution meets the precision requirement is judged, if the difference gap between the upper bound solution and the lower bound solution of the current iteration meets the precision requirement value, the judgment is yes, the process is directly finished, and the upper bound solution is used as the optimal solution.
5. The method of claim 3, wherein the step of planning the crews based on feasible label connectivity network comprises: in the step a, the lower bound solution is solved by calculating the cost value by adopting a tree structure traversal method, and taking the feasible path solution with the minimum cost value as the lower bound solution.
6. The method of claim 3, wherein the step of planning the crews based on feasible label connectivity network comprises: and e, updating the Lagrange multiplier by using a sub-gradient algorithm.
7. The method of claim 1, wherein the step of planning the crews based on feasible label connectivity network comprises: the feasible path is generated in a shortest path searching mode; the feasible path generation rule also comprises working time on duty, transfer time, continuous driving time, rest time, outer-segment duty-staying time, a road-crossing period and meal rest time; the merging calculation is to summarize the multiple feasible paths and delete the feasible paths in which there is a time and space conflict.
8. The method of claim 1, wherein the step of planning the crews based on feasible label connectivity network comprises: the preset rules comprise decision variables, parameter variables, objective functions and constraint conditions; the integration calculation is to parameterize the cost value of the feasible label connection network, and to establish a simultaneous equation set by taking a preset rule as a constraint condition.
9. The method of claim 8, wherein the step of planning the crews based on feasible label connectivity network comprises: the parameter variables comprise a node set, a path arc set, the number of available task groups, a task section and a section task set.
10. The method of claim 1, wherein the step of planning the crews based on feasible label connectivity network comprises: the planning model is obtained by adopting a network flow method to integrate and calculate.
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