CN109784530A - The power supply zone optimal setting method of road is floated based on middling speed magnetic - Google Patents
The power supply zone optimal setting method of road is floated based on middling speed magnetic Download PDFInfo
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Abstract
The present invention provides a kind of power supply zone optimal setting methods that road is floated based on middling speed magnetic, comprising: determines section number, siding-to-siding block length and the maximum stator segment number of middling speed magnetic flotation line road；The power supply zone plan of establishment is generated using genetic algorithm；Utilization ability computation model calculates the road under every kind of power supply zone plan of establishment；Update iteration is optimized to the road under every kind of power supply zone plan of establishment using Lagrangian Relaxation Algorithm, is judged using the maximum power supply zone plan of establishment of handling capacity as power supply zone scheme.The present invention floats the influence of road by analysis power supply zone to middling speed magnetic, construct the power supply zone optimal setting method that road is floated based on middling speed magnetic, it solves the problems, such as the power supply zone optimal setting to improve road as target, improves the adaptability of middling speed magnetic flotation line road power supply zone.
Description
Technical field
The present invention relates to magnetic floating traffic field more particularly to a kind of power supply zones that road is floated based on middling speed magnetic
Optimal setting method.
Background technique
Currently, the research floated about magnetic is concentrated mainly on tractive power supply system and train operation in magnetic floating traffic field
Control etc., the research of the power supply zone plan of establishment towards road is less, in the prior art about power supply
The research of subregion setting is mainly from the angle of tractive power supply system, not from the point of view of improving road,
However power supply zone is the minimum unit occupied in middle speed magnetic suspension train operational process, generates biggish shadow to road
It rings.Therefore, it for the transport capacity resource for more reasonably arranging middling speed magnetic floating, needs from the angle of road is improved to power supply
Research is unfolded in the optimal setting of subregion.
Summary of the invention
The present invention provides the power supply zone optimal setting methods that road is floated based on middling speed magnetic, reasonably to pacify
Arrange the floating transport capacity resource of middling speed magnetic.
To achieve the goals above, this invention takes following technical solutions.
The present invention provides a kind of power supply zone optimal setting methods that road is floated based on middling speed magnetic, including such as
Lower step:
S1 determines section number, siding-to-siding block length and the maximum stator segment number of middling speed magnetic flotation line road.
S2 is generated according to section number, siding-to-siding block length and maximum stator segment number on the route using genetic algorithm
The power supply zone plan of establishment.
For S3 according to the power supply zone plan of establishment, Utilization ability computation model calculates every kind of power supply zone plan of establishment
Under road.
S4 optimizes the road under every kind of power supply zone plan of establishment using Lagrangian Relaxation Algorithm
Iteration is updated, judges whether the road under the power supply zone plan of establishment is greater than maximum evolutionary generation, if more than then
It is otherwise back to the maximum power supply zone plan of establishment of handling capacity as the power supply zone scheme of middling speed magnetic flotation line road
Step S2.
Further, it according to section number, siding-to-siding block length and maximum stator segment number on the route, is calculated using heredity
Method generates the power supply zone plan of establishment, comprising:
According to section number, siding-to-siding block length and maximum stator segment number, restricted model variable on the route；
According to the restricted model variable, the stator segment combination in each section in section is connected as one
Individual encodes each individual using binary coding, forms initial population；
It is optimized using each individual of the fitness function to the initial population；
Individual each of after the optimization is carried out by selection operator, crossover operator and mutation operator further excellent
Change, produces population of new generation, as the power supply zone plan of establishment.
Further, according to the power supply zone plan of establishment, Utilization ability computation model calculates every kind of power supply zone
Road under the plan of establishment, including converting the power supply zone plan of establishment generated using genetic algorithm to
Node, segmental arc, arc set on route, and the route under every kind of power supply zone plan of establishment is calculated according to capacity calculation model and is led to
Cross ability.
It further, further include virtual arc in capacity calculation model, the virtual arc is used to be greater than line when train quantity
When the ability of Lu Suoneng carrying, when train can not be run from start node to Zhongdao node by Actual path, from virtual arc
Pass through.
Further, using Lagrangian Relaxation Algorithm to the road under every kind of power supply zone plan of establishment into
Row optimization updates iteration, comprising:
Capacity consistency in ability computation model is added in objective function as penalty term, and identical change is carried out to it
It changes and decomposes；
The shortest path of train operation is found out using the dynamic programming algorithm strategy of recursion forward；
Lagrange multiplier is updated using Subgradient Algorithm；
Using Lagranging heuristic algorithm, the Lagrange multiplier in the Lagrange relaxation problem result acquired is made
For heuristic information, and the operation order of speed magnetic suspension train in each column on route is planned again, acquires feasible solution.
Further, restricted model variable specifically includes:
The maximum quantity for the stator segment being laid in the c of sectionWith the quantity n for the power supply zone being arranged in the c of sectioncBy
Constraint is as shown in following formula (1) and (2):
The length of i-th of power supply zone inside sectionAs shown in following formula (3):
Shown in the length of section c such as following formula (4):
The length of power supply zoneThe length range constraint of satisfaction is as shown in following formula (5):
Wherein, lcFor the length of section c, lξFor stator segment length,For the maximum quantity of the power supply zone of section c,Maximum quantity for the stator segment being laid in the c of section, ncQuantity (round numbers) for the power supply zone being arranged in the c of section,The length of i-th of power supply zone of section c,Indicate the minimum allowable value of power supply zone length；Indicate power supply zone
The maximum permissible value of length.
Further, it is optimized using each individual of the fitness function to the initial population, including under
The fitness function of formula (6) optimizes each individual of initial population:
Wherein, f indicates that the train run on route, F are the set of all trains, and (i, j) indicates the segmental arc on route, Ef
Indicate the set for all segmental arcs that train f may pass through on the line,Indicate that the Generalized cost of one power supply zone of setting is opposite
In the weight coefficient of train total run time, ncIndicate the number of power supply zone in the c of section, wqIndicate one confession of setting in section
The Generalized cost of electric subregion.
Further, individual each of after the optimization is further optimized by selection operator, including is adopted
The selection of the subregion plan of establishment is powered with the roulette method of following formula (7):
In formula, piIt is F for the power supply zone plan of establishment i probability being selectediFor the fitness of power supply zone plan of establishment i
Value, N are the number of the power supply zone plan of establishment in population.
As seen from the above technical solution provided by the invention, of the invention that road is floated based on middling speed magnetic
Power supply zone optimal setting method is floated the influence of road to middling speed magnetic by analysis power supply zone, especially powered
Influence of the partition length to section tracking interval constructs the power supply zone optimal setting side that road is floated based on middling speed magnetic
Method solves the problems, such as the power supply zone optimal setting to improve road as target, improves middling speed magnetic flotation line road
The adaptability of power supply zone.
The additional aspect of the present invention and advantage will be set forth in part in the description, these will become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, required use in being described below to embodiment
Attached drawing be briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, for this
For the those of ordinary skill of field, without creative efforts, it can also be obtained according to these attached drawings others
Attached drawing.
Fig. 1 is that a kind of power supply zone optimization for floating road based on middling speed magnetic that the embodiment of the present invention 1 provides is set
Set the method flow diagram of method；
Fig. 2 is that a kind of power supply zone optimization for floating road based on middling speed magnetic that the embodiment of the present invention 1 provides is set
Set the process flow diagram of method；
Fig. 3 is influence of the power supply zone length that provides of the embodiment of the present invention 1 to section tracking interval；
Fig. 4 is the coding mode exemplary diagram that the embodiment of the present invention 1 provides；
Fig. 5 is the individual UVR exposure exemplary diagram that the embodiment of the present invention 1 provides；
Fig. 6 is that the initial population that the embodiment of the present invention 1 provides generates exemplary diagram；
Fig. 7 is the multiple point crossover schematic diagram that the embodiment of the present invention 1 provides；
Fig. 8 is the multiple spot variation schematic diagram that the embodiment of the present invention 1 provides；
Fig. 9 is the extensive example wire topologies figure that the embodiment of the present invention 2 provides；
Figure 10 is the genetic algorithm iteration result figure that the embodiment of the present invention 2 provides；
The power supply zone quantity and road comparison diagram that Figure 11 embodiment of the present invention 2 provides.
Specific embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the accompanying drawings, wherein from beginning
Same or similar element or element with the same or similar functions are indicated to same or similar label eventually.Below by ginseng
The embodiment for examining attached drawing description is exemplary, and for explaining only the invention, and is not construed as limiting the claims.
Those skilled in the art of the present technique are appreciated that unless expressly stated, singular " one " used herein, " one
It is a ", " described " and "the" may also comprise plural form.It is to be further understood that being arranged used in specification of the invention
Diction " comprising " refer to that there are the feature, integer, step, operation, element and/or component, but it is not excluded that in the presence of or addition
Other one or more features, integer, step, operation, element, component and/or their group.It should be understood that when we claim member
Part is " connected " or when " coupled " to another element, it can be directly connected or coupled to other elements, or there may also be
Intermediary element.In addition, " connection " used herein or " coupling " may include being wirelessly connected or coupling.Wording used herein
"and/or" includes one or more associated any cells for listing item and all combinations.
Those skilled in the art of the present technique are appreciated that unless otherwise defined, all terms used herein (including technology art
Language and scientific term) there is meaning identical with the general understanding of those of ordinary skill in fields of the present invention.Should also
Understand, those terms such as defined in the general dictionary, which should be understood that, to be had and the meaning in the context of the prior art
The consistent meaning of justice, and unless defined as here, it will not be explained in an idealized or overly formal meaning.
In order to facilitate understanding of embodiments of the present invention, it is done by taking several specific embodiments as an example below in conjunction with attached drawing further
Explanation, and each embodiment does not constitute the restriction to the embodiment of the present invention.
The method of the power supply zone optimal setting method that road is floated based on middling speed magnetic of the invention, it is intended to improve
The adaptability of middling speed magnetic flotation line road power supply zone.
Embodiment 1
Fig. 1 is that a kind of power supply zone optimization for floating road based on middling speed magnetic that the embodiment of the present invention 1 provides is set
Set the method flow diagram of method；Fig. 2 is a kind of power supply that road is floated based on middling speed magnetic that the embodiment of the present invention 1 provides
The process flow diagram of partition zone optimizing setting method, referring to Figures 1 and 2, this method comprises the following steps:
S1 determines section number, siding-to-siding block length and the maximum stator segment number of middling speed magnetic flotation line road；
S2 is generated according to section number, siding-to-siding block length and maximum stator segment number on the route using genetic algorithm
The power supply zone plan of establishment；
For S3 according to the power supply zone plan of establishment, Utilization ability computation model calculates every kind of power supply zone plan of establishment
Under road；
S4 optimizes the road under every kind of power supply zone plan of establishment using Lagrangian Relaxation Algorithm
Iteration is updated, judges whether the road under the power supply zone plan of establishment is greater than maximum evolutionary generation, if more than then
It is otherwise back to the maximum power supply zone plan of establishment of handling capacity as the power supply zone scheme of middling speed magnetic flotation line road
Step S2.
Wherein, power supply zone is the minimum unit of train occupation in middling speed magnetic floating system, and a power supply zone is led by one
Draw electric transforming unit control, a power supply zone can be equivalent to one group of shorter stator segment.
Middling speed magnetic floats road and refers in the middling speed maglev vehicle for setting type and certain organization of driving's method
Under the premise of, middling speed magnetic flotation line road is in certain direction, the maximum quantity for the standard train that can pass through within the unit time, it is preferable that
Unit time is the period that train can be run in one day.
The influence that power supply zone floats road to middling speed magnetic is mainly reflected in power supply zone length and tracks section
In the influence at interval.The block section in power supply zone and wheel rail system for the angle of train operation, in magnetic floating system
Similar, i.e., a power supply zone can only run a train in the same time.Therefore, train is when section is run, tracking interval
It is influenced by power supply zone length.
Schematically, Fig. 3 is influence of the power supply zone length that provides of the embodiment of the present invention 1 to section tracking interval.Ginseng
According to Fig. 3, power supply zone is 2. shorter in (a), (b) in power supply zone it is 2. longer, the length of power supply zone 1. is identical.The train that moves ahead is equal
Power supply zone 2. in operation (positioned at power supply zone 2. with boundary 3.) and do not leave because a power supply zone can only have
One train operation, so the target tracking point of following train is A (away from the intersection of power supply zone 1. and 2. certain peace at this time
Full protection distance ls), because 2. the train that moves ahead also does not leave power supply zone, following train will guarantee in power supply zone
1. inside Brake stop at any time.Therefore, the tracking distance in (a) between two trains is lr+lb+ls+le+ll, wherein lrIndicate tracking
The distance that train is run within the reaction time, lbIndicate the braking distance of following train, leIndicate forward train away from power supply zone 1.
2. intersection distance, llIndicate the train vehicle commander that moves ahead, (b) in tracking distance between two trains be lr+lb+ls+le′+
ll.Since 2. length is different for power supply zone, leWith le′Length it is different, therefore, in the case where (a) and (b), the section of train
Tracking interval is different, and (a) is less than (b).
Further, it according to section number, siding-to-siding block length and maximum stator segment number on route, is generated using genetic algorithm
The power supply zone plan of establishment, comprising:
(1) restricted model variable:
1) for section c, inside the maximum quantity of power supply zone can be setWith can be laid in the c of section
The maximum quantity of stator segmentIdentical, i.e., a power supply zone is only made of a stator segment, and the length of the stator segment is
Minimum value (the stator segment maximum quantity that can be laid with), therefore the maximum quantity phase of the maximum quantity of power supply zone and stator segment
It together, is the length l of section ccDivided by stator segment length lξ(stator segment length depends on line slope, speed and acceleration), section
The quantity n for the power supply zone that can be set in cc(round numbers) suffers restraints as shown in following formula (1) and (2).
The length of i-th of power supply zone inside the c of sectionAs shown in following formula (3):
Wherein, lξFor stator segment length,For the stator segment number for forming the power supply zone.
The sum of length of each power supply zone is the length of section c in the c of section, as shown in following formula (4).
2) length of any power supply zoneIt is both needed to meet certain length range constraint.In middling speed magnetic floating system, power supply
Subregion is the minimum unit occupied in train travelling process, therefore, the length of power supply zoneIt needs at least to want to accommodate
The length of one train, and since power supply zone is made of stator segment, therefore the length of power supply zone is at least more than stator segment
Nominal length, in formula (5)Indicate the minimum allowable value of power supply zone length；In addition, due to any power supply zone be both needed to by
Traction power set is powered it, therefore the length of power supply zoneMeet the power supply length range of traction power set
Constraint,It is traction power set for electrical length, the length of any power supply zoneCertain length range need to be met about
Shown in beam such as following formula (5).
(2) according to the restricted model variable, the stator segment combination in each section in section is connected into work
For an individual, each individual is encoded using binary coding, forms initial population.
Schematically, by stator segment combination (the i.e. power supply zone length in each section in m section on route
With the set-up mode of quantity) it connects as an individual (i.e. one solution).Individual UVR exposure uses binary coding, per each and every one
Body is a binary string, is made of the m section (i.e. the part m) on route, and each section uses X binary codings
(value of X is determined by the maximum stator number of segment in each section), constitutes a base for each node homologue of stator segment
Cause, Fig. 4 are the coding mode exemplary diagram that the embodiment of the present invention 1 provides, specifically as shown in figure 4, the stator segment number in a section
It is 11, since two nodes form a stator segment, which is made of 12 nodes (i.e. 12 genes).Two adjacent
1 gene of being encoded to constitute a power supply zone, the difference of two Position Numbers being encoded to where 1 gene indicates composition one
The stator segment number of a power supply zone, Fig. 5 are the individual UVR exposure exemplary diagram that the embodiment of the present invention 1 provides, specific as shown in Figure 5.
The coding in all sections is connected to the coding for forming an individual.
According to above-mentioned coding mode, according to the stator segment number in section each on route, individual each section the (the 1st is successively determined
To m-th of section) binary coding digit.Each section for individual is, it is specified that first and last binary coding
It is 1, remaining position is randomly generated 0 or 1, that is, forms an individual.Fig. 6 is that the initial population that the embodiment of the present invention 1 provides is raw
At exemplary diagram, as shown in fig. 6, continuing to be created as described above different individuals, that is, initial population is formed.
(3) each individual of the initial population is optimized using fitness function.
When being optimized with genetic algorithm to power supply zone length in section each on route and the quantity plan of establishment, each
Individual is a kind of power supply zone Combination Design scheme, needs to measure the superiority and inferiority of each individual by fitness function, with guidance
The direction that algorithm solves.Fitness function f (X) definition is as shown in formula (6):
In formula, f indicates that the train run on route, F are the set of all trains, and (i, j) indicates the segmental arc on route (i.e.
Power supply zone), EfIndicate the set for all segmental arcs that train f may pass through on the line,It indicates that a power supply zone is arranged
Weight coefficient of the Generalized cost relative to train total run time, ncIndicate the number of power supply zone in the c of section, wqIndicate section
The Generalized cost of one power supply zone of interior setting.
Further, the solution target of power supply zone plan of establishment optimization problem is that road and power supply zone are built
It is set as that this two is optimal, the overall travel time minimum of all trains of the maximum target of road is in the present invention come table
Show, therefore the solution target of power supply zone plan of establishment optimization problem is the overall travel time minimum and power supply point of all trains
The construction cost in area is minimum.
(4) each individual after the optimization is intersected and is made a variation by genetic operator, produce a new generation kind
Group.
1) selection operator
The purpose of selection and is protected to select preferably scheme relatively from all possible power supply zone plan of establishment
Stay the parent as next iteration searching process.Preferably, the subregion plan of establishment is powered using roulette method
Selection, power supply zone plan of establishment i selected probability are as follows:
In formula, FiFor the fitness value of power supply zone plan of establishment i, N is the number of the power supply zone plan of establishment in population.
2) crossover operator
Crossover operator simulates the genetic recombination during biological evolution, and the gene between different outstanding parent individualities is handed over
It changes, to generate new individual.Preferably, crossover operator is carried out using multiple point crossover mode, Fig. 7 is that the embodiment of the present invention 1 mentions
The multiple point crossover schematic diagram of confession, detailed process are as shown in Figure 7.
3) mutation operator
The effect of mutation operator is to improve the diversity of population, increases the plan of establishment of power supply zone, prevents algorithm from asking
Solution falls into local optimum or Premature Convergence.Preferably, mutation operator is carried out using multiple spot variation mode, Fig. 8 is that the present invention is implemented
The multiple spot variation schematic diagram that example 1 provides, detailed process are as shown in Figure 8.
Wherein, genetic algorithm be using the biological evolution process in nature as background, by during biological evolution breeding,
The concepts such as selection, hybridization, variation and competition are introduced into algorithm, and carry out effective search to parameter space using randomized technique
Evolution algorithm has very strong global optimization search capability.Algorithm first with some form (compiles variable coding before search
Variable after code is known as chromosome), different chromosome constitutes a group.After initial population generates, someways comment
Estimate its adaptive value out to be intersected by genetic operator and made a variation according to the principle of the survival of the fittest and the survival of the fittest, produce new
Generation population.The last reign of a dynasty optimum individual finally searched is by decoding, the as optimal solution or satisfactory solution of problem.In basic genetic
In algorithm, selection, intersection and variation constitute the genetic manipulation of genetic algorithm, parameter coding, the setting of initial population, fitness
Design, genetic manipulation design, the control parameter of function set five elements and constitute the core content of genetic algorithm.Preferably,
In this algorithm, individual is expressed using binary coded form, is given birth at random on the basis of meeting the constraint condition of model variable
At initial population.
Further, capacity calculation model is the model constructed to calculate the floating road of middling speed magnetic, model
Essence is route map of train drawing problem, i.e. combinatorial optimization problem of the train in limited time-space distribution.The basic principle is that
Actual track is abstracted by physical space network using node, segmental arc, the form of arc set (path), and by introducing cumulative flow
The continuous time axis that variable runs train in segmental arc it is discrete be multiple equal periods, establish train operation " when it is m-
Space " network inputs certain train number, can be run in " time-space " network and the train number that does not clash i.e.
For the handling capacity on the route.In addition, being different from traditional train combinatorial optimization problem.Preferably, the present invention is in a model
Introduce the concept of " virtual arc ", the effect of virtual arc be when train quantity is greater than the ability that route can carry, train without
Method is run from start node to Zhongdao node by Actual path, but can be passed through from virtual arc, therefore to a certain extent
Reduce the solution difficulty of model.
Preferably, according to the power supply zone plan of establishment, Utilization ability computation model calculates every kind of power supply zone plan of establishment
Under road, including converting node, segmental arc, arc set on route for the power supply zone plan of establishment,
And the road under every kind of power supply zone plan of establishment is calculated according to capacity calculation model.Capacity calculation model it is specific
Shown in content such as following formula (8)~(23).
The meaning of all letters is respectively as shown in following table 1- table 3 in above-mentioned formula (8)~(23).
The symbolism statement that table 1 is gathered
The symbolism of 2 parameter of table is stated
The symbolism of 3 decision variable of table is stated
Wherein, objective function Z1, indicate that the total run time of all trains on the line is minimum；Constraint condition (9)~
(11) train is respectively indicated in start node, the mobile equilibrium of intermediate node and Zhongdao node, and (12) indicate physical network and space-time
Mappings constraint between network, (13) and (14) indicate that train constrains at the earliest time of departure of start node, and (15) indicate column
For vehicle in adjacent segmental arc out of and into constraining constantly, (16)~(18) indicate runing time constraint of the train in segmental arc,
(19) dwell time constraint is indicated, (20) indicate that segmental arc occupies mappings constraint, and (21) indicate capacity consistency, and (22) and (23) indicate
Accumulation flow variables constrain substantially.
Wherein, the point in physical network is the endpoint of middling speed magnetic flotation line road power supply zone, and segmental arc is a power supply point
The line segment of two endpoints composition in area.
The power supply zone plan of establishment refers to the quantity and each confession for the power supply zone being arranged in the section of middling speed magnetic flotation line road
The length of electric subregion.
Further, the road under every kind of power supply zone plan of establishment is carried out with Lagrangian Relaxation Algorithm
Optimization updates iteration, comprising:
By solving Lagrange relaxation problem, the Optimal Boundary of former problem is obtained first, then update by continuous iteration
The mode of Lagrange multiplier makes the solution of relaxation problem gradually approach the optimal solution of former problem.It should be noted that Lagrangian
Relaxed algorithm is that the Complex Constraints in former problem relax, and is added in objective function using the Complex Constraints as penalty term,
To make the constraint condition of former problem be simplified.Pass through below to Lagrangian Relaxation Algorithm solution middling speed magnetic flotation line road
The solution procedure of capacity calculation model is introduced.
(1) Lagrange relaxation problem
It is added to capacity consistency as penalty term in objective function, and identical transformation and decomposition is carried out to it: described
Middling speed magnetic float in road computation model, the constraint for restricting model solution efficiency is capacity consistency, i.e. formula (21).It should
Constraint causes middling speed magnetic to float the interaction in road calculating process between train, considerably increases the solution of model
Therefore scale by formula (21) relaxation, and is added in objective function as penalty term.
In formula, ρI, j, tFor the Lagrange multiplier of formula (21), indicate that train occupies resource caused by (i, j) in moment t
Expense.Identical transformation is carried out to above formula (24), obtains following formula (25).
In Lagrange relaxation problem, target function type (25) can be decomposed into 1 constant term and all train LRfIt
With, as shown in (26) under formula, wherein LRfConsist of two parts, a part is the Saving in time costs of all trains, and another part is column
Vehicle occupies the sum of the Lagrange multiplier of driving resource.
(2) method for solving of the subproblem based on Dynamic Programming
The shortest path of train operation is found out using the dynamic programming algorithm strategy of recursion forward: by Lagrange relaxation
Problem is converted into multistage decision problem, and finds out the most short of train operation using the dynamic programming algorithm strategy of recursion forward
Path.Involved symbol is as shown in table 4 below in dynamic programming algorithm.
The statement of related symbol in 4 dynamic programming algorithm of table
Shown in state transition equation such as formula (27) in dynamic programming algorithm, that is, be used to calculate+1 stage of kth most
Excellent target function value ok+1, wherein ΔK, k+1Resource expense corresponding to train occupation power supply zone driving resource in formula (21).
(27) obtain the optimal objective function value of each state of each stage according to the following formula.
ok+1=min { ok+ΔK, k+1} (27)
Details are provided below for the solution of dynamic programming algorithm:
Step I: basis input
1) line information: station, section, power supply zone (mainly segmental arc information)；
2) train operation essential information: train number, train terminus, train can operating path (including actual arcs and virtual
Arc) etc..
Step II: initialization
Initial road network VE is created, start node (o is setf, σf) minimum " expense " of any intermediate node (j, t ') is arrived as o
(j, t ')=+ ∞,T=1 ..., T, o (of, σf)=0.
Step III: label is updated
According to above- mentioned information, dynamic programming algorithm carries out following tag update step:
Step IV: shortest path is obtained
1) node (j is found by dynamic programming algorithm*, t '*), and as start node to just in the node of operation
The shortest optimal node in path at (j, t ')；
2) when node (j, t ') is not the Zhongdao node of road network, node (j, t ') is added in road network, and update section
Data at point (i, t)；
3) reversely recall the shortest path that node (j, t ') arrives node (i, t)；
4) algorithm terminates.
Step V: output
Shortest path of the output start node to Zhongdao node.
(3) Lagrange multiplier update method
Lagrange multiplier is updated using Subgradient Algorithm: it should be noted that the basic thought of Subgradient Algorithm is
Keep the lower bound of linear programming problem as big as possible, and gradually approach optimal solution according to certain ascent direction, using subgradient
Algorithm is shown come the following formula of more new-standard cement (28) for updating Lagrange multiplier:
In formula, q is current the number of iterations, αq=1/ (q+1).
Subgradient Algorithm is the decline side for determining gradient to the occupancy situation of driving resource according to train in iterative process
To realize the update to Lagrange multiplier.By continuously adjusting Lagrange multiplier and each train to path
Selection, and then realize the reasonable distribution to driving resource.
(4) Lagranging heuristic algorithm
After Lagrangian Relaxation Algorithm, the Complex Constraints in former problem are relaxed, so that the feasible zone of former solution
It is extended, in fact it could happen that the case where obtained solution is infeasible solution.Therefore it needs efficiently to obtain by certain method feasible
Solution.Preferably, the present invention will use Lagranging heuristic algorithm, the glug in the Lagrange relaxation problem result acquired
Bright day multiplier planned again as heuristic information, and to the operation order of speed magnetic suspension train in each column on route, into
And acquire feasible solution.Specific step is as follows:
Step I: initialization
The number of iterations is initialized, q=1 is enabled；
Dividing value in initialization, the floor value that Lagrangian Relaxation Algorithm is obtained is as the initial value of current upper, it may be assumed that
Step II: the optimal solution of current upper is sought
1) sequence run on the line according to the height of train priority planning train, the priority of train is by LRPfValue
Size determine, LRPfCalculation method such as following formula (29) shown in:
LRP in formula (29)fValue it is bigger, illustrate that conflict when train f is run on the line is more serious, can be adjusted
Range is smaller, LRPfValue it is smaller then on the contrary.Preferably, the present invention is according to LRPfValue sequence from big to small successively to train into
Professional etiquette is drawn.
2) according to train priority ranking as a result, successively acquiring train operation with dynamic programming algorithm to train f
Shortest path；
3) if the train inputted can not be planned that the train can select within the defined ability utilization scope period
Pass through from virtual arc.
Step III: the upper bound is updated
1) comparison current upper value and dividing value in a upper the number of iterations, utilize formulaOn current
Dividing value is updated；
2) formula is utilizedCalculate the interval between bound；
3) the number of iterations is updated using formula q=q+1.
It should be noted that during being solved with Lagranging heuristic algorithm, the step of most critical be determine it is every
The drawing sequence of train, the LRP of every train is successively calculated by formula (29)fValue determines that it, by the sequence of drawing, and is used
Solving the shortest path algorithm identical with Lagrange relaxation subproblem solves the shortest path of train, during solution,
If there is train due to the conflict of route up train resource is more serious can not drawing, then train can select to pass through from virtual arc,
Runing time only at this time due to train on virtual arc is longer, and the target function value of original function can be made to increase.
Embodiment 2
The embodiment of the present invention 2 provides the power supply zone optimal setting method example based on road.It is first
First, it is encoded according to the line condition (including station, section etc.) of example, power supply zone setting side is generated by genetic algorithm
Case；Secondly, calculating the road under every kind of power supply zone plan of establishment, and it is updated iteration；Finally, until target
Function convergence selects the maximum power supply zone plan of establishment of road.
(1) example route introduction
Fig. 9 is the extensive example wire topologies figure that the embodiment of the present invention 2 provides, referring to Fig. 9, middling speed magnetic float meter
Route is two-wire circuit, overall length 90km, completely sets 5 stations altogether, completely shares 4 sections, the length in each section and can
The maximum number difference for setting subsegment is as shown in table 5.According to the floating examination of the middling speed magnetic of middle vehicle Tangshan rolling stock Co., Ltd design
The actual conditions for testing line, taking the length of each stator segment is 500m.Choosing the middle speed magnetic suspension train that desin speed is 200km/h is
The run the period of research object, train takes 06:00-23:00.
5 line basis data of table
The embodiment of the present invention only optimizes the power supply zone plan of establishment in section, therefore the power supply inside station point
Section length and quantity are all provided with as definite value, and (do not analyze using the starting station of train down direction and terminal station as node consideration
Train internal power supply zone quantity and length AT STATION, when train leaves the last one segmental arc in section 4, i.e. expression train
Into terminus).
(2) genetic algorithm iteration result
Figure 10 is the genetic algorithm iteration result figure that provides of the embodiment of the present invention 2, referring to Fig.1 0, with the increasing of the number of iterations
Add, the target function value of model gradually becomes smaller.When iteration is to the 60th time, model starts to restrain, i.e., the 60th iteration acquires
Solution is the last solution of model, and the final goal functional value of model is 4220min.
(3) the power supply zone plan of establishment and corresponding road solving result
The iteration result for occurring the be mutated the 1st, 10 and 60 time in genetic algorithm iterative process is chosen, finds its correspondence respectively
The power supply zone plan of establishment and the power supply zone plan of establishment under road solving result, table 6- table 8 distinguish
Indicate the 1st, the 10 and 60 corresponding power supply zone plan of establishment of genetic algorithm iteration result, Figure 11 embodiment of the present invention 2 mentions
The power supply zone quantity and road comparison diagram of confession, referring to Fig.1 1 and table 6- table 8.
The 1st iteration of table 6
The 10th iteration of table 7
The 60th iteration of table 8
It can obtain from the data in upper table 6- table 8, power when power supply zone number is the 11, the 10th and 60 time when the 1st iteration
Subregion number is respectively 31 and 36.Gradually excellent with target, the number of power supply zone gradually increases, and (the driving of each power supply zone
Resource) length gradually shorten.When model is restrained, the final power supply zone plan of establishment such as table 5, from the power supply in each section point
From the point of view of the distribution of the quantity and length in area, the characteristics of presenting, substantially conforms to the power supply zone of section both ends (entering the station and outbound place)
Length is shorter, and the power supply zone inside section is longer because train enter the station it is lower with the speed of service at outbound place, in section
The speed of service in portion is higher, and is actually consistent, and also demonstrates the applicability of method proposed by the invention.
The power supply zone quantity and road comparison diagram that Figure 11 embodiment of the present invention 2 provides, referring to Fig.1 1, wherein
The handling capacity of route is 81 trains when the 1st iteration, and the 10th iteration is 135 trains, and the 60th iteration is 158 trains, by
This is as it can be seen that the influence of different power supply zone set-up mode to road is very big, wherein from the 1st iteration to
10 iteration, road improve 66.7%, and the 10th time to the 60th time iteration, road improves
17.0%.
Genetic algorithm, which is demonstrated, by the solving result of Figure 11 solves the power supply point based on the floating road of middling speed magnetic
The validity of area's optimal setting scheme, by constantly iteration, can acquire, which can improve the power supply zone of road, is set
Scheme is set, and the amplitude that road improves is obvious.
Those skilled in the art will be understood that the application type of above-mentioned optimal setting method is only for example, other it is existing or
The optimal setting method being likely to occur from now on is such as applicable to the embodiment of the present invention, should also be included in the scope of the present invention with
It is interior, and be incorporated herein by reference.
In conclusion the power supply zone optimal setting method based on road of the embodiment of the present invention, by from
It improves road angle to set out, the limitation that conventional method only considers from traction power supply angle is overcome, so that practicability
Enhancing；From the optimal setting of stator segment angle analysis power supply zone, more meet the actual conditions on middling speed magnetic flotation line road；Consider something lost
The combination of propagation algorithm and Lagrangian Relaxation Algorithm improves the efficiency of calculating and the reliability of calculated result.
As seen through the above description of the embodiments, those skilled in the art can be understood that the present invention can
It realizes by means of software and necessary general hardware platform.Based on this understanding, technical solution of the present invention essence
On in other words the part that contributes to existing technology can be embodied in the form of software products, the computer software product
It can store in storage medium, such as ROM/RAM, magnetic disk, CD, including some instructions are used so that a computer equipment
(can be personal computer, server or the network equipment etc.) executes the certain of each embodiment or embodiment of the invention
Method described in part.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of protection of the claims
Subject to.
Claims (8)
1. a kind of power supply zone optimal setting method for floating road based on middling speed magnetic, which is characterized in that including as follows
Step:
S1 determines section number, siding-to-siding block length and the maximum stator segment number of middling speed magnetic flotation line road；
S2 is generated using genetic algorithm and is powered according to section number, siding-to-siding block length and maximum stator segment number on the route
The subregion plan of establishment；
According to the power supply zone plan of establishment, Utilization ability computation model calculates under every kind of power supply zone plan of establishment S3
Road；
S4 optimizes update to the road under every kind of power supply zone plan of establishment using Lagrangian Relaxation Algorithm
Iteration, judges whether the road under the power supply zone plan of establishment is greater than maximum evolutionary generation, if more than will then lead to
Otherwise the power supply zone scheme that the maximum power supply zone plan of establishment of ability is crossed as middling speed magnetic flotation line road is back to step
S2。
2. the method according to claim 1, wherein described according to section number, section on the route
Length and maximum stator segment number, generate the power supply zone plan of establishment using genetic algorithm, comprising:
According to section number, siding-to-siding block length and maximum stator segment number, restricted model variable on the route；
According to the restricted model variable, the stator segment combination in each section in section is connected as one by one
Body encodes each individual using binary coding, forms initial population；
It is optimized using each individual of the fitness function to the initial population；
Individual each of after the optimization is further optimized by selection operator, crossover operator and mutation operator,
Produce population of new generation, as the power supply zone plan of establishment.
3. the method according to claim 1, wherein described according to the power supply zone plan of establishment, benefit
The road under every kind of power supply zone plan of establishment is calculated with capacity calculation model, including calculating described using heredity
The power supply zone plan of establishment that method generates is converted into node, segmental arc, arc set on route, and is calculated according to capacity calculation model
Road under every kind of power supply zone plan of establishment.
4. according to the method described in claim 3, it is characterized in that, further include virtual arc in the capacity calculation model, institute
The virtual arc stated is used for when train quantity is greater than the ability that route can carry, and train can not be saved by Actual path from starting
When point operation to Zhongdao node, pass through from virtual arc.
5. the method according to claim 1, wherein the utilization Lagrangian Relaxation Algorithm powers to every kind
Road under the subregion plan of establishment optimizes update iteration, comprising:
Capacity consistency in ability computation model is added in objective function as penalty term, and it is carried out identical transformation and
It decomposes；
The shortest path of train operation is found out using the dynamic programming algorithm strategy of recursion forward；
Lagrange multiplier is updated using Subgradient Algorithm；
Using Lagranging heuristic algorithm, using the Lagrange multiplier in the Lagrange relaxation problem result acquired as opening
Photos and sending messages, and the operation order of speed magnetic suspension train in each column on route is planned again, acquire feasible solution.
6. according to the method described in claim 2, it is characterized in that, the restricted model variable specifically includes:
The maximum quantity for the stator segment being laid in the c of sectionWith the quantity n for the power supply zone being arranged in the c of sectioncIt suffers restraints
As shown in following formula (1) and (2):
The length of i-th of power supply zone inside sectionAs shown in following formula (3):
Shown in the length of section c such as following formula (4):
The length of power supply zoneThe length range constraint of satisfaction is as shown in following formula (5):
Wherein, lcFor the length of section c, lξFor stator segment length,For the maximum quantity of the power supply zone of section c,
Maximum quantity for the stator segment being laid in the c of section, ncQuantity (round numbers) for the power supply zone being arranged in the c of section,Area
Between c i-th of power supply zone length,Indicate the minimum allowable value of power supply zone length；Indicate that power supply zone is long
The maximum permissible value of degree.
7. according to the method described in claim 2, it is characterized in that, it is described using fitness function to the initial population
Each individual optimize, the fitness function including (6) according to the following formula optimizes each individual of initial population:
Wherein, f indicates that the train run on route, F are the set of all trains, and (i, j) indicates the segmental arc on route, EfIt indicates
The set for all segmental arcs that train f may pass through on the line,Indicate setting one power supply zone Generalized cost relative to
The weight coefficient of train total run time, ncIndicate the number of power supply zone in the c of section, wqIndicate one power supply of setting in section
The Generalized cost of subregion.
8. according to the method described in claim 2, it is characterized in that, it is described by selection operator to every after the optimization
Individual is further optimized, and the selection of the subregion plan of establishment is powered including the roulette method using following formula (7):
In formula, piIt is F for the power supply zone plan of establishment i probability being selectediFor the fitness value of power supply zone plan of establishment i, N
For the number of the power supply zone plan of establishment in population.
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