CN110750938B - Train energy-saving optimization method based on immune evolution particle swarm shuffled frog leaping algorithm - Google Patents
Train energy-saving optimization method based on immune evolution particle swarm shuffled frog leaping algorithm Download PDFInfo
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Abstract
The invention discloses an energy-saving optimization method for a train based on an immune evolution particle swarm shuffled frog leaping algorithm. The method comprises the following steps: firstly, establishing a multi-train energy consumption and time optimization target model by setting train parameters and line parameters; then, the working condition switching points of all vehicles are used as optimization variables, and a shuffled frog leaping algorithm is adopted to search the working condition switching points of the multiple vehicles; then, maintaining an external file by adopting a self-adaptive grid method to obtain an optimal operation strategy and a multi-vehicle speed and energy consumption curve; and finally, selecting the punctual and most energy-saving train operation strategy according to the existing train schedule to obtain the corresponding speed curve and energy consumption curve. The invention improves the precision of the timing energy-saving optimization of the train, optimizes the running condition of the train from the aspects of stop time, departure interval, speed and the like, has obvious energy-saving speed optimization effect and improves the punctuality of the train running.
Description
Technical Field
The invention belongs to the technical field of train operation control, and particularly relates to an energy-saving optimization method for a train based on an immune evolution particle swarm shuffled frog-leaping algorithm.
Background
With the acceleration of economic construction pace in China, the requirements of people on passenger transport and freight transport are continuously improved. Urban rail transit is one of the most important traffic operation modes in China, is convenient for people to go out, and also drives rapid development of national economy. Due to the characteristics of frequent operation and large traffic volume of urban rail transit, the power consumption of the train is very large, so that the method has great significance for optimizing the energy-saving speed of the operation of the urban rail transit train.
In the iterative process, the existing shuffled frog-leaping algorithm can effectively utilize feedback information to perform heuristic search, has enough flexibility and robustness, but also has the defects of prematurity and poor local optimization capability in application, and the worst frog only learns the optimal frog, so that the spatial position of the worst individual can be greatly changed before and after updating. The problem of premature convergence of an algorithm is solved by introducing attraction and rejection factors into a mixed frog-leaping algorithm [ J ] for solving a complex function optimization problem in document 1 (Zhaopong army, Liu Sanyang, ZHAO open-jun, et al, 2009,26(7): 2435-2437.); document 2(Elbeltag E, Hegazy T, Grierson D.A modified smoothed free front-adapting optimization algorithm: applications to project management [ J ]. Structure and information Engineering,2007,3(1):53-60.) improves the optimization accuracy of the algorithm by adding a search acceleration mechanism; document 3 (improvement study of Weilixin, Zhenghuihong, Kinghongqing, et al, shuffled frog leaping algorithm [ J ]. control engineering, 2016,23(2): 167-. Although the updating strategy can enlarge the search range of the solution space, the global optimal solution is easy to skip, the local optimal solution is trapped, and the effective search in the feasible region is not facilitated, so that the optimization effect is not obvious, and the convergence speed is low.
Disclosure of Invention
The invention aims to provide an immune evolution particle swarm shuffled frog leaping algorithm-based train energy-saving optimization method which is high in optimization precision, low in energy consumption and strong in applicability.
The technical solution for realizing the purpose of the invention is as follows: an immune evolution particle swarm shuffled frog leaping algorithm-based train energy-saving optimization method comprises the following steps:
step 1: determining basic parameters of a train line interval to be optimized, wherein the basic parameters comprise train parameters, line parameters and operation parameters;
step 2: setting an optimization target and a constraint condition of train operation, and constructing a train energy consumption multi-target optimization model according to train operation conditions and train operation condition turning points;
and step 3: solving a train energy consumption multi-target optimization model by using an immune evolution particle swarm shuffled frog leaping algorithm and taking turning points of running working conditions of each train as optimization variables to obtain a plurality of groups of non-inferior solutions about traction energy consumption and running time;
and 4, step 4: after the non-inferior solution is automatically stored in the external archive, the external archive is maintained by using a self-adaptive grid method, so that the distribution of particles in the external archive can be expanded in the updating process of the external archive;
and 5: and selecting a group of solutions with the minimum energy consumption from the multiple groups of non-inferior solutions of the optimization result, and drawing the speed and energy consumption curve of the group of trains.
Further, the train parameters and the line parameters in the step 1 are as follows:
the train parameters comprise the type of the train, the marshalling mode, the load grade, the Thevis equation coefficient, a traction characteristic curve, a braking characteristic curve, the maximum acceleration, the maximum speed and the auxiliary system characteristic;
the line parameters comprise a speed limit section start-stop kilometer post and a corresponding speed limit, a curve section start-stop kilometer post and a corresponding curvature, and a ramp start-stop kilometer post and a corresponding gradient.
Further, in the step 2, the optimization target of train operation, the constraint condition of train operation and the train operation condition are as follows:
the optimization target of train operation comprises a traction energy consumption optimization target and an operation time optimization target;
the constraint conditions of the train operation comprise train speed constraint, parking precision constraint, comfort constraint, departure interval constraint and station-stopping time constraint;
the train operation working conditions comprise a traction working condition, a cruise working condition, an idle working condition and a braking working condition.
Further, the optimization target and the constraint condition of train operation are set in the step 2, and a train energy consumption multi-target optimization model is established according to the train operation condition and the train operation condition turning point, and the method specifically comprises the following steps:
step 2.1, setting a traction energy consumption optimization target and a running time optimization target:
optimal target f for traction energy consumption E Comprises the following steps:
wherein m represents the number of overlapping sections,
represents the actual traction energy consumption in the ith intervalDosage;
runtime optimization goal f T Comprises the following steps:
wherein n represents the number of stations in the power supply section, T running Denotes the inter-station running time, T stop Indicating the time of station stop, T normal Indicating a schedule specified run time;
step 2.2, setting departure interval constraint conditions and departure interval constraint conditions:
the departure interval constraint conditions are as follows:
wherein L represents the train length, S safe Representing the safe braking distance of the train, and v representing the running speed of the train;
so that the departure interval T of the train h Should be greater than or equal to the minimum departure interval T of the train hmin Namely:
T h ≥T hmin (4)
time of stopping T stop The constraint conditions are as follows:
T stopl ≤T stop ≤T stopu (5)
wherein T is stopl ,T stopu Respectively representing the upper limit and the lower limit of the station stopping time;
and 2.3, constructing a train energy consumption multi-objective optimization model according to the train operation working conditions.
Further, the immune evolution particle swarm shuffled frog-leaping algorithm is used in the step 3, the turning points of the running working conditions of each train are used as optimization variables, the train energy consumption multi-objective optimization model is solved, and multiple groups of non-inferior solutions about traction energy consumption and running time are obtained, wherein the method specifically comprises the following steps:
step 3.1: setting a frog-leaping scale P, a group number M, a frog number N in the group, a maximum iteration number T in the group, an individual random movement maximum step length D and a global maximum iteration number T, IEA dynamic adjustment coefficient A required by the algorithm;
step 3.2: randomly generating an initial frog group with the scale of P in a solution space, and calculating the fitness value of each individual;
step 3.3: dividing solution groups into groups according to the size of the fitness value, and recording the worst solution, the optimal solution and the global optimal solution in each group;
step 3.4: carrying out immune evolution updating on the optimal solution of the population, if the fitness value of the new solution is greater than that of the old solution after immune evolution operation, replacing the old solution with the new solution, and otherwise, keeping the old solution unchanged;
the immune evolution update formula is as follows:
wherein the content of the first and second substances,
and
new and old values of the optimal individual in the group are respectively obtained; n (0,1) is a random number following a standard normal distribution; sigma 0 Is the standard deviation corresponding to the initial solution population; a is a standard differential state adjustment coefficient; t is the current evolution algebra; t is a total evolution algebra;
step 3.5: carrying out local and global depth search on the worst solution in each group, if the fitness value of the new solution is larger than that of the old solution, replacing the old solution with the new solution, otherwise, keeping the old solution unchanged, sequencing the N individuals of the group according to the fitness value, and re-determining the optimal solution in the group k
Worst solution for group k
And global maximumOptimal solution
Repeating the step 3.5 until the repetition times reach the set maximum iteration times T in the population;
the formula of the depth search is as follows:
in the formula (I), the compound is shown in the specification,
i.e. the worst individual within the population
Tracking new globally optimal individuals after immune evolution iteration
Location update of (2); wherein
Representing the new value of the worst solution in population k,
representing the oldest value of the worst solution in population k, rand (0,1) is a random number between (0,1),
represents the best solution in the population k,
a new value representing a global optimal solution;
step 3.6: calculating the fitness value of each individual in the group, and mixing the frog group according to the fitness value; if the optimal solution of the iteration reaches the set precision requirement or the iteration times reach the global maximum iteration times T, stopping the algorithm; otherwise, the step 3.3 is carried out.
Further, the step 4 of maintaining the external archive by using the adaptive grid method specifically includes:
step 4.1: determining the grid boundary: setting n targets in the multi-target optimization problem, the n targets need 2n grid boundaries, and the upper and lower boundaries of the kth target are ub k And lb k Wherein k is 1,2, …, n; k represents the dimension of grid division, and n represents the number of targets contained in the optimization problem;
step 4.2: determining hypercube boundaries: if the division number of each dimension of the grid is set to d, the grid of each dimension is divided into d hypercubes, and the hypercubes are represented as k i K 1,2, … n, i 1,2, … d, hypercube boundary:
rub k,i ＝[ib k +(i/d)×(ub k -lb k )]×(range k /d) (8)
rlb k,i ＝[ib k +((i-1)/d)×(ub k -lb k )]×(range k /d) (9)
wherein, range k ＝max(x k |x∈Archive)-min(x k | x ∈ Archive), k ═ 1,2, … r, Archive stands for external Archive after Archive update, range k A domain width representing a kth dimension target; ub k Represents the upper boundary, lb, of the kth target k Represents the lower boundary of the kth target, rub k,i Representing cube k i Rlb k,i Representing cube k i After the division number of each dimension is d, only one boundary needs to be determined, because the cube has three boundaries, and the upper and lower boundaries of the plane dimension are determined, the ib is k Represents the boundary of the ith cube in the kth target, i represents the ith hypercube;
step 4.3: positioning the particles: in the grid, each particle is positioned according to the boundaries and individual coordinates of all hypercubes, and the position of the particle is set to x ═ x (x 1 ,x 2 ,…,x n ) If the particle satisfies x k ≥rlb k,i And x k ≤rub k,i Then particle x k In the hypercubek i In the area; wherein, rub k,i Representing cube k i Rlb k,i Representing cube k i A lower boundary of (a);
step 4.4: when the number of particles in the external archive exceeds the upper limit value, a grid in the network with the maximum density value is selected by roulette, and then a particle is randomly selected from the grid and deleted from the external archive.
Compared with the prior art, the invention has the remarkable advantages that: (1) by setting departure interval time and train stop time as constraint conditions and taking train traction energy consumption and running time as optimization targets, the immune evolution updating formula can give consideration to the search of areas outside solution space near the optimal individuals of the group, so that immature convergence can be effectively avoided, and the energy-saving optimization precision of the train under the timing condition is improved; (2) by adopting the immune evolution particle swarm shuffled frog-leaping algorithm, the search range of the learning space is expanded, and the search range cannot be trapped into local optimum, so that the train operation condition is optimized in the aspects of station stopping time, departure interval, speed and the like, the global optimum solution is easier to find, and the energy-saving speed optimization effect is obvious; (3) the depth search formula can enable the worst individual in the group to carry out global and local depth search in the solution space, and ensure that the worst solution can not evolve to the optimal solution of the same group only in the updating process, so the train operation punctuality is improved on the basis of keeping the original departure interval and stop time.
Drawings
Fig. 1 is a schematic flow diagram of a train energy-saving optimization method based on an immune evolution particle swarm shuffled frog-leaping algorithm.
Fig. 2 is a non-inferior solution distribution diagram of traction energy consumption obtained after an immune evolution particle swarm shuffled frog-leaping algorithm is iterated for 100 times in the embodiment of the invention.
FIG. 3 is a graph of the energy-saving speed optimization of the three vehicles in the embodiment of the invention.
FIG. 4 is a graph of optimized speed profile regenerative braking energy utilization in an embodiment of the present invention.
Detailed Description
The invention is further described in detail below with reference to the drawings and specific embodiments.
With reference to fig. 1, the train energy-saving optimization method based on the immune evolution particle swarm shuffled frog-leaping algorithm comprises the following steps:
step 1: determining basic parameters of a train line interval to be optimized, wherein the basic parameters comprise train parameters, line parameters and operation parameters;
further, the train parameters comprise the type of the train, the marshalling mode, the load level, the davis equation coefficient, a traction characteristic curve, a braking characteristic curve, the maximum acceleration, the maximum speed and the auxiliary system characteristic;
the line parameters comprise a speed limit section starting and stopping kilometer post and a corresponding speed limit, a curve section starting and stopping kilometer post and a corresponding curvature, and a ramp starting and stopping kilometer post and a corresponding gradient.
Step 2: setting an optimization target and constraint conditions of train operation, and constructing a train energy consumption multi-target optimization model according to train operation conditions and train operation condition turning points;
further, the optimization objectives of train operation comprise a traction energy consumption optimization objective and an operation time optimization objective;
the constraint conditions of the train operation comprise train speed constraint, parking precision constraint, comfort constraint, departure interval constraint and station-stopping time constraint;
the train operation working conditions comprise a traction working condition, a cruise working condition, an idle working condition and a brake working condition.
Further, an optimization target and constraint conditions of train operation are set, and a train timing energy-saving optimization model is constructed according to train operation conditions, specifically as follows:
step 2.1, setting a traction energy consumption optimization target and a running time optimization target:
(1) tractive effort optimization objective
When the speed curve of the train is optimized, because the running energy consumption between the train stations is uncertain, the maximum utilization of the regenerative braking energy does not represent the minimum running energy consumption of the whole train, when the optimized variable is the speed curve of the train,the utilization amount of the regenerative braking energy of the train needs to be considered, the integral running energy consumption of the train in the power supply interval is calculated, and a traction energy consumption optimization target f is set E Comprises the following steps:
wherein m represents the number of overlapping sections,
representing the actual traction energy consumption utilization amount in the ith interval;
(2) runtime optimization objective
After the stop time, departure interval and the train speed curve are re-optimized, the train still needs to meet the schedule requirement of normal operation, so the total operation time in the train power supply interval is taken as an optimization target to ensure that the train operation time meets the requirement of a specified schedule, and an operation time optimization target f is set T Comprises the following steps:
wherein n represents the number of stations in the power supply section, T running Indicating the run time between stations, T stop Indicating the time of station stop, T normal Indicating a schedule specified run time;
step 2.2, setting departure interval constraint conditions and departure interval constraint conditions:
(1) departure space constraint
The departure interval refers to the departure time interval between two adjacent cars at the starting station. In order to ensure the running safety of the train, the departure interval needs to meet the minimum departure interval constraint of the train, and the minimum departure interval of the train needs to comprehensively consider factors such as the minimum safety distance between trains, the stop time and the transportation capacity requirement. The method for calculating the departure interval constraint condition, namely the minimum departure interval of the adjacent trains, comprises the following steps:
wherein L represents the train length, S safe Representing the safe braking distance of the train, and v representing the running speed of the train;
so that the departure interval T of the train h Should be greater than or equal to the minimum departure interval T of the train hmin Namely:
T h ≥T hmin (4)
(2) time of station stop constraint
In order to ensure that the train can run at the accurate point between each station, the running time between each station needs to be restrained, and the station stopping time T stop The constraint conditions are as follows:
T stopl ≤T stop ≤T stopu (5)
wherein T is stopl ,T stopu Respectively representing the upper limit and the lower limit of the station stopping time;
and 2.3, constructing a train energy consumption multi-objective optimization model according to the train operation working conditions.
And step 3: the method comprises the steps of solving a train energy consumption multi-objective optimization model by using an immune evolution particle swarm shuffled frog-leaping algorithm and taking turning points of running working conditions of each train as optimization variables to obtain multiple groups of non-inferior solutions about traction energy consumption and running time, as shown in fig. 2, the method specifically comprises the following steps:
the train operation condition turning points comprise a cruise point, an idle point and a braking point;
step 3.1: setting parameters such as a frog leap scale P, a group number M, a frog number N in the group, a maximum iteration number T in the group, an individual random movement maximum step length D, a global maximum iteration number T, IEA dynamic adjustment coefficient A and the like required by the algorithm;
step 3.2: randomly generating an initial frog group with the scale of P in a solution space, and calculating the fitness value of each individual;
step 3.3: dividing solution groups into groups according to the size of the fitness value, and recording the worst solution, the optimal solution and the global optimal solution in each group;
step 3.4: optimal solution to population
Carrying out immune evolution updating according to the formula (6), and if the fitness value of the new solution after immune evolution operation is larger than that of the old solution, using the new solution
Substitute old solution
Otherwise, keeping the old solution unchanged;
the immune evolution update formula is as follows:
wherein, the first and the second end of the pipe are connected with each other,
and
new and old values of the optimal individual in the group are respectively obtained; n (0,1) is a random number following a standard normal distribution; sigma 0 Is the standard deviation corresponding to the initial solution population; a is a standard differential state adjustment coefficient; t is the current evolution algebra; t is a total evolution algebra;
in the initial stage of evolution, the formula (6) can give consideration to the search of the region outside the solution space near the optimal individual of the group, so that the group keeps better diversity, the exploration capability is enhanced, and the immature convergence is effectively avoided; in the later stage of evolution, along with the continuous enhancement of local searching capability, the algorithm approaches to a global optimal solution with higher precision;
step 3.5: old value of worst solution to population k
A deep search is performed both locally and globally using equation (7), if the new value of the worst solution for group k
Is greater than the old solution
Replacing the old solution with the new solution, otherwise keeping the old solution unchanged; then sorting the N individuals of the population according to the fitness value, and re-determining the optimal solution in the population k
Worst solution in group k
And global optimal solution
Repeating the step 3.5 until the repetition times reach the set maximum iteration times T in the population;
the formula of the depth search is as follows:
in the formula (I), the compound is shown in the specification,
i.e. the worst individual within the population
Tracking new globally optimal individuals after immune evolution iteration
Location update of (2); wherein
The new value representing the worst solution in population k,
in the representative group kThe worst-solution old value of rand (0,1) is a random number between (0,1),
represents the best solution in the population k,
a new value representing a global optimal solution;
the formula (7) can make the worst individual in the group perform global and local deep search in the solution space, and enhance the mining capability;
step 3.6: calculating the fitness value of each individual in the group, and mixing the frog group according to the fitness value; if the optimal solution of the iteration reaches the set precision requirement or the global maximum iteration time T, stopping the algorithm; otherwise, the step 3.3 is carried out.
And 4, step 4: after the non-inferior solution is automatically stored in the external archive, the external archive is maintained by using a self-adaptive grid method, so that the distribution of particles in the external archive can be expanded in the updating process of the external archive, and the method is as follows;
step 4.1: determining the grid boundary: determining a target space domain corresponding to particles in an external archive by the positions of grids, wherein if a multi-objective optimization problem contains n targets, the n targets need 2n grid boundaries; the upper and lower boundaries of the kth target are ub k And lb k Wherein k is 1,2, …, n; k represents the dimension of grid division, and n represents the number of targets contained in the optimization problem;
and 4.2: determining hypercube boundaries: if the division number of each dimension of the grid is set to d, the grid of each dimension is divided into d hypercubes, and the hypercubes are represented as k i K 1,2, … n, i 1,2, … d, hypercube boundary:
rub k,i ＝[ib k +(i/d)×(ub k -lb k )]×(range k /d) (8)
rlb k,i ＝[ib k +((i-1)/d)×(ub k -lb k )]×(range k /d) (9)
wherein the range k ＝max(x k |x∈Archive)-min(x k | x ∈ Archive), k ═ 1,2, … r, Archive stands for external Archive after Archive update, range k A domain width representing a kth dimension target; ub k Represents the upper boundary, lb, of the kth target k Represents the lower boundary of the kth target, rub k,i Representative cube k i Rlb k,i Representing cube k i After the division number of each dimension is d, only one boundary needs to be determined, because the cube has three boundaries, and the upper and lower boundaries of the plane dimension are determined, the ib is k Represents the boundary of the ith cube in the kth target, i represents the ith hypercube;
step 4.3: positioning the particles: in the grid, each particle is located according to the boundaries and individual coordinates of all hypercubes, and the position of the particle is set to x ═ x (x) 1 ,x 2 ,…,x n ) If the particle satisfies x k ≥rlb k,i And x k ≤rub k,i Then particle x k In hypercube k i In the region; wherein rub k,i Representing cube k i Rlb k,i Representing cube k i The lower boundary of (2).
Step 4.4: when the number of particles in the external archive exceeds the upper limit value, a grid in the network with the maximum density value is selected by roulette, and then a particle is randomly selected from the grid and deleted from the external archive.
And 5: and selecting a group of solutions with the minimum energy consumption from the multiple groups of non-inferior solutions of the optimization result, and drawing the speed and energy consumption curve of the group of trains.
The invention is described in further detail below with reference to the figures and the embodiments.
Example 1
In this embodiment, the actual data of a certain subway line in China is used for simulation research, and verification analysis is performed on the basis of the actual line data and schedule data of the subway line by taking the first power supply interval of the uplink line as an example. Tables 1-4 list some line data and schedule data from south Guangzhou station to Xietun station.
Table 1 distance from south station of guangzhou to xietun station
Table 2 Guangzhou south station to Xietun station line slope chart
Table 3 table of radius of curvature of line from south station to xu village station of Guangzhou
TABLE 4 southern station to xu-village station part of the timetable data
The optimized train operation results are shown in table 5.
TABLE 5 optimization results of three-vehicle speed regulation curve
As shown in fig. 3, after the train speed curve is optimized, the regenerative braking energy utilization during the operation in the power supply section is divided into four sections, and the regenerative braking energy utilization is shown in fig. 4.
(1) When the descending train brakes at the southern Guangzhou station, the ascending train is dragged and started from the southern Guangzhou station, the overlapping interval is [276s,285.9s ], and the regenerative braking energy of the ascending train using the descending train 1 is 2.86 kW.h within 9.9s of overlapping time;
(2) when the descending train 2 starts from the Xicun to the stone wall station, the train enters the coasting working condition in advance at 337s, and when the train runs to 352.6s, the descending train 2 is dragged and accelerated again by the braking energy of the ascending train due to the fact that the ascending train enters the braking working condition from the Guangzhou south station to the stone wall station; the overlapping interval of the regenerative braking energy of the section is [352.6s,360.5s ], the overlapping time is 7.9s, and the utilization amount of the regenerative braking energy is 2.64 kW.h;
(3) the method comprises the following steps that an ascending train enters an idle running working condition in advance at 407.7s in the running process from the stone wall to the Xicun station, the train is in a descending ramp and runs at a low acceleration, when the train runs to 441s, the descending train 2 is in a braking working condition from the Xicun to the stone wall station, the ascending train enters a traction working condition again, the overlapping interval of regenerative braking energy utilization is [444.1s,449.6s ], the overlapping time is 5.5s, and the regenerative braking energy utilization is 1.66 kW.h;
(4) when the descending train 2 runs from the stone wall to the southern Guangzhou station, the train accelerates to 503.2s, the speed reaches 59.03km/h, the train directly enters the coasting working condition, the cruising working condition is cancelled, when the train runs to 522.2s, the descending train 2 is dragged and accelerated again because the ascending train enters the braking working condition, the regenerative braking energy utilization interval of the train is [522.5s,531.2s ], the overlapping time is 8.7s, and the regenerative braking energy utilization amount is 2.58 kW.h.
The utilization rate of the regenerative braking energy of the train is improved by adjusting and optimizing the speed curve, the original departure interval and stop time are kept, the utilization efficiency of the regenerative braking energy of the train is improved, and the optimization effect is better. By adjusting the speed curve, the running energy consumption of the train is reduced by 10.07 kW.h, and the energy-saving effect is remarkable.
Claims (4)
1. An immune evolution particle swarm shuffled frog leaping algorithm-based train energy-saving optimization method is characterized by comprising the following steps of:
step 1: determining basic parameters of a train line interval to be optimized, wherein the basic parameters comprise train parameters, line parameters and operation parameters;
step 2: setting an optimization target and a constraint condition of train operation, and constructing a train energy consumption multi-target optimization model according to train operation conditions and train operation condition turning points, wherein the optimization target and the constraint condition are as follows:
step 2.1, setting a traction energy consumption optimization target and a running time optimization target:
optimal target f for traction energy consumption E Comprises the following steps:
wherein m represents the number of overlapping sections,
representing the actual traction energy consumption utilization amount in the ith interval;
run-time optimization goal f T Comprises the following steps:
wherein n represents the number of stations in the power supply section, T running Denotes the inter-station running time, T stop Indicating the time of station stop, T normal Indicating a schedule specified run time;
step 2.2, setting departure interval constraint conditions and departure interval constraint conditions:
the departure interval constraint conditions are as follows:
wherein L represents the train length, S safe Representing the safe braking distance of the train, and v representing the running speed of the train;
so that the departure interval T of the train h Should be greater than or equal to the minimum departure interval T of the train hmin Namely:
T h ≥T hmin (4)
time of stopping T stop The constraint conditions are as follows:
T stopl ≤T stop ≤T stopu (5)
wherein T is stopl ,T stopu Respectively representing the upper limit and the lower limit of the station stopping time;
2.3, constructing a train energy consumption multi-objective optimization model according to the train operation working condition;
and step 3: solving a train energy consumption multi-target optimization model by using an immune evolution particle swarm shuffled frog leaping algorithm and taking turning points of running working conditions of each train as optimization variables to obtain a plurality of groups of non-inferior solutions about traction energy consumption and running time;
and 4, step 4: after the non-inferior solution is automatically stored in the external archive, the external archive is maintained by using a self-adaptive grid method, so that the distribution of particles in the external archive can be expanded in the updating process of the external archive;
the external archive is maintained by using the adaptive grid method, which specifically comprises the following steps:
step 4.1: determining the grid boundary: setting n targets in the multi-target optimization problem, the n targets need 2n grid boundaries, and the upper and lower boundaries of the kth target are ub k And lb k Wherein k is 1,2, …, n; k represents the dimension of grid division, and n represents the number of targets contained in the optimization problem;
step 4.2: determining hypercube boundaries: if the division number of each dimension of the grid is set as d, the grid of each dimension is divided into d hypercubes, and the hypercube is represented as k i K 1,2, … n, i 1,2, … d, hypercube boundary:
rub k,i ＝[ib k +(i/d)×(ub k -lb k )]×(range k /d) (8)
rlb k,i ＝[ib k +((i-1)/d)×(ub k -lb k )]×(range k /d) (9)
wherein, range k ＝max(x k |x∈Archive)-min(x k | x ∈ Archive), k ═ 1,2, … r, Archive stands for external Archive after Archive update, range k A domain width representing a k-th dimension of the object; ub k Represents the upper boundary, lb, of the kth target k Represents the lower boundary of the kth target, rub k,i Representative cube k i Rlb k,i Representing cube k i After the division number of each dimension is d, only one boundary needs to be determined, because the cube has three boundaries, and the upper and lower boundaries of the plane dimension are determined, the ib is k Representing the boundary of the ith cube in the kth target, i representing the ith hypercube;
step 4.3: positioning the particles: in the grid, each particle is positioned according to the boundaries and individual coordinates of all hypercubes, and the position of the particle is set to x ═ x (x 1 ,x 2 ,…,x n ) If the particle satisfies x k ≥rlb k,i And x k ≤rub k,i Then particle x k In hypercube k i In the region; wherein, rub k,i Representative cube k i Rlb k,i Representing cube k i A lower boundary of (a);
step 4.4: when the number of particles in the external archive exceeds the upper limit value, selecting a grid in the network with the maximum density value by adopting a roulette mode, then randomly selecting a particle from the grid and deleting the particle from the external archive;
and 5: and selecting one solution with the minimum energy consumption from the multiple groups of non-inferior solutions of the optimization result, and drawing the speed and energy consumption curve of the train.
2. The train energy-saving optimization method based on the immune evolution particle swarm shuffled frog-leaping algorithm according to claim 1, wherein the train parameters and the line parameters in the step 1 are as follows:
the train parameters comprise the type of the train, the marshalling mode, the load grade, the Thevis equation coefficient, a traction characteristic curve, a braking characteristic curve, the maximum acceleration, the maximum speed and the auxiliary system characteristic;
the line parameters comprise a speed limit section start-stop kilometer post and a corresponding speed limit, a curve section start-stop kilometer post and a corresponding curvature, and a ramp start-stop kilometer post and a corresponding gradient.
3. The train energy-saving optimization method based on the immune evolution particle swarm shuffled frog-leaping algorithm according to claim 1, wherein in the step 2, the optimization target of train operation, the constraint condition of train operation and the train operation condition are as follows:
the optimization target of train operation comprises a traction energy consumption optimization target and an operation time optimization target;
the constraint conditions of the train operation comprise train speed constraint, parking precision constraint, comfort constraint, departure interval constraint and station-stopping time constraint;
the train operation working conditions comprise a traction working condition, a cruise working condition, an idle working condition and a brake working condition.
4. The train energy-saving optimization method based on the immune-evolved particle swarm shuffled frog-leaping algorithm according to claim 1, wherein the immune-evolved particle swarm shuffled frog-leaping algorithm is used in the step 3, each train operation condition turning point is used as an optimization variable, a train energy consumption multi-objective optimization model is solved, and multiple groups of non-inferior solutions about traction energy consumption and operation time are obtained, and the method specifically comprises the following steps:
step 3.1: setting a frog-leaping scale P, a group number M, a frog number N in the group, a maximum iteration number T in the group, an individual random movement maximum step length D and a global maximum iteration number T, IEA dynamic adjustment coefficient A required by the algorithm;
step 3.2: randomly generating an initial frog group with the scale of P in a solution space, and calculating the fitness value of each individual;
step 3.3: dividing the solution groups into groups according to the size of the fitness value, and recording the worst solution, the optimal solution and the global optimal solution in each group;
step 3.4: carrying out immune evolution updating on the optimal solution of the population, if the fitness value of the new solution is greater than that of the old solution after immune evolution operation, replacing the old solution with the new solution, and otherwise, keeping the old solution unchanged;
the immune evolution update formula is as follows:
wherein the content of the first and second substances,
and
new and old values of the optimal individual in the group are respectively obtained; n (0,1) is a random number following a standard normal distribution; sigma 0 Is the standard deviation corresponding to the initial solution population; a is a standard differential state adjustment coefficient; t is the current evolution algebra; t is a total evolutionary algebra;
step 3.5: carrying out local and global depth search on the worst solution in each group, if the fitness value of the new solution is larger than that of the old solution, replacing the old solution with the new solution, otherwise, keeping the old solution unchanged, sequencing the N individuals of the group according to the fitness value, and re-determining the optimal solution in the group k
Worst solution for group k
And global optimal solution
Repeating the step 3.5 until the repetition times reach the set maximum iteration times T in the population;
the depth search formula is:
in the formula (I), the compound is shown in the specification,
i.e. the worst individual within the population
Tracking new globally optimal individuals after immune evolution iteration
Location update of (2); wherein
Representing the new value of the worst solution in population k,
representing the oldest value of the worst solution in population k, rand (0,1) is a random number between (0,1),
represents the best solution in the population k,
a new value representing a global optimal solution;
step 3.6: calculating the fitness value of each individual in the group, and mixing the frog group according to the fitness value; if the optimal solution of the iteration reaches the set precision requirement or the iteration times reach the global maximum iteration times T, stopping the algorithm; otherwise, the step 3.3 is carried out.
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