CN107368920B - Energy-saving optimization method for multi-train operation in off-peak hours - Google Patents
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Abstract
The invention discloses an energy-saving optimization method for multi-train operation in off-peak hours. The method comprises the following steps: firstly, setting line data, train data, operation data and basic parameters of a genetic algorithm for the operation of a plurality of trains in an off-peak period; secondly, constructing a running energy consumption calculation model of a plurality of trains in the off-peak period; then, establishing a multi-train optimization model in the off-peak time period by taking the compression value of the station stopping time as an optimization variable, taking an energy-saving index and an on-time index as optimization targets and taking the unidirectional total running time and the variation range of the station stopping time as constraint conditions; then solving the optimization model by using a Pareto multi-objective genetic algorithm to obtain a group of Pareto non-dominated solution sets; and finally, solving the optimized interval running time and each station stop time by extracting the global optimal solution so as to obtain an optimized schedule and complete the solving of the multi-train energy-saving optimization model in the non-peak time period. The invention reduces the energy consumption of multiple trains in off-peak hours and improves the accuracy of train operation time.
Description
Technical Field
The invention belongs to the technical field of train operation control, and particularly relates to a non-peak time period multi-train operation energy-saving optimization method.
Background
In recent years, with the rapid development of socioeconomic and the continuous promotion of urbanization progress in China, urban subways are developed quite rapidly, and therefore the energy consumption of urban rail transit is increased. On the basis of meeting the requirement of the train on-point operation, the energy utilization rate is more effectively improved, the operation cost is reduced, and the method has great significance for the development of railway industry in China.
The train energy-saving operation control is a typical multi-objective multi-constraint optimization control problem, and an accurate mathematical model is difficult to establish to describe the train operation process. The traditional mathematical methods, such as a numerical analysis method, an optimal control theory and the like, are difficult to obtain an accurate solution of a model, only an approximate solution of the model can be obtained even if an iteration method is adopted, and the local optimization is easy to fall into. The method for processing the energy-saving multi-target multi-constraint optimization problem of the train at present mainly comprises the steps of weighting a plurality of optimization targets and converting the multi-target into a single target for optimization, however, the method needs to rely on a large amount of experience accumulation on weighting coefficients, local optimization is easy to cause, only one group of solutions can be obtained, and the optimization speed is slow.
Disclosure of Invention
The invention aims to provide an energy-saving optimization method for multi-train operation in the off-peak time period, which is high in convergence speed and accuracy.
The technical solution for realizing the purpose of the invention is as follows: an energy-saving optimization method for multi-train operation in off-peak hours comprises the following steps:
step 4, solving a multi-train energy-saving optimization model in the off-peak period based on a Pareto multi-objective genetic algorithm to obtain a group of non-dominated solution sets;
and 5, extracting the optimal solution to obtain an optimized schedule, and completing the solution of the multi-train energy-saving optimization model in the non-peak time period.
Further, the line data in step 1 includes a ramp start-stop kilometer post and a corresponding gradient i, a curve segment start-stop kilometer post and a corresponding curvature C, and a speed limit segment start-stop kilometer post and a corresponding speed limit VT(ii) a The train data comprises the marshalling mode, the length L, the load level AW, Thevis equation coefficients (a, b, c) and the maximum acceleration a of the trainmaxMaximum velocity vmaxA traction characteristic curve F (v) and a braking characteristic curve B (v); the basic parameters of the Pareto multi-target genetic algorithm comprise a selection operator, a cross operator, a mutation operator, a maximum evolution algebra, a population size and a fitness function.
Further, the step 2 of constructing the multi-train energy consumption calculation model in the off-peak period specifically includes the following steps:
step 2.1, calculating the traction energy consumption of the train in different areas according to the working condition turning points of the train running section, and obtaining the gradient i and the curvature C of the train in the current simulation step length according to the kilometer post S (t) from the previous simulation step length of the train to the current simulation step length;
step 2.2, calculating the traction force F (v), the braking force B (v) and the resistance parameter f of the train in the current simulation step length according to the speed v (t) and the energy consumption E (t) of the train in the previous simulation step length;
and 2.3, calculating the acceleration a (t) and the traction power P (t) of the train at the current time t according to the working condition and stress analysis of the train, and further calculating the speed v (t + delta t), the kilometer sign S (t + delta t), the traction power P (t + delta t) and the traction energy consumption E (t + delta t) in the next simulation step, wherein the delta t is the simulation step time.
Further, the off-peak multi-train optimization model in step 3 is specifically as follows:
ldi≤g2(x)＝dn≤udi (4)
in the formula f1(x) The target function related to the energy-saving index is F (t), B (t) is respectively the traction force and the braking force of the standard train at the time t; eta is the regenerative braking energy rate of the adjacent trains; e0(i) The originally planned energy consumption value of the train in the interval i; t is t0,tfRespectively as the train running time and the train ending time; k and K-1 are the number of stations and the number of train running sections respectively; f. of2(x) For an objective function related to the punctual index, Δ diThe station stopping time compression value is the station stopping time compression value of the station i; t isiPlanning the running time for station i; g1(x) As constraints relating to the total run time, g2(x) As constraints relating to the time of station stopping,/diAnd udiRespectively, a minimum stop time and a maximum stop time.
Further, the Pareto multi-objective genetic algorithm based on the step 4 is used for solving a multi-column vehicle energy-saving optimization model in the off-peak period to obtain a group of non-dominated solution sets, which are specifically as follows:
step 4.1, population initialization: initializing a population P, wherein the size of the population is N, and each individual in the population corresponds to a group of stop time compression value matrixes xi＝[Δd1,Δd2,...Δdj,...,ΔdK]K represents the number of stations, and the time schedule takes seconds as the minimum unit, so integer coding is adopted;
step 4.2, energy saving index f1(x) Punctual fingerMark f2(x) And (3) calculating a fitness value: firstly, according to the station-stopping time compression value matrix delta d corresponding to each individual in the populationiCalculating the punctual index f corresponding to each individual in the population2(x) The adaptability value and the new running time and station-stopping time of each interval; then substituting the new operation time into the single-train timing energy-saving optimization model to calculate the total traction energy consumption of the one-way whole-course multi-train operation in the off-peak time period and calculate the energy-saving index f1(x)；
4.3, carrying out non-dominated sorting on the individuals in the population, and calculating the crowdedness of the individuals: firstly, the energy-saving index f of each individual in the population1(x) Punctual index f2(x) The fitness value is subjected to non-dominant sorting, and the sorting number i of each individual in the population is determinedrankThen, carrying out crowding degree calculation on each individual in the non-dominant layer, and determining the non-dominant order relation in the population and the crowding degree of the individual;
and 4.4, selecting elite individuals by using a tournament method to generate offspring populations: randomly selecting individuals from the population P by using a tournament method to perform crossing and variation operations according to the non-dominant sequence relationship and the crowdedness of the individuals in the population P to generate a progeny population Q;
step 4.5, generating a new generation parent population: from the second generation, firstly merging the parent population P and the child population Q to form a new population R, wherein the size of the population is 2N, secondly, carrying out non-dominant sequencing and determining i of each individual in the populationrankCalculating the crowding degree of each individual in the non-dominant layer, selecting the individuals according to the non-dominant order relation and the crowding degree of the individuals to form a next generation parent population P, and keeping the population number of the population as N;
and 4.6, circulating the steps 4.2-4.5 until the maximum iteration number is reached, stopping genetic operation and storing to obtain a Pareto optimal non-dominated solution set.
Further, the step 5 extracts an optimal solution, so as to obtain an optimized schedule, and complete the solution of the multi-train energy-saving optimization model in the non-peak time period, specifically: by extracting a global optimal solution, selecting the most appropriate stop time compression matrix as the global optimal solution according to the established energy-saving and punctual relative importance in a Pareto non-dominated solution set, and solving the optimized interval running time and stop time of each station, so as to obtain an optimized timetable and complete the solution of a non-peak time period multi-train energy-saving optimization model.
Compared with the prior art, the invention has the following remarkable advantages: (1) the train timing energy-saving operation method based on the Pareto multi-target genetic algorithm is not easy to fall into local optimization in the searching process, the evolution result is not limited to a single-value solution, and the method is very suitable for solving a complex multi-target problem; (2) the complex phenomenon is expressed through selection, intersection and variation operations, the adaptive value function is fully utilized without other prior knowledge, the convergence speed is high, and the accuracy is high.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
Fig. 1 is a schematic flow chart of the energy-saving method for multi-train operation in the off-peak period of the present invention.
FIG. 2 is a flow chart of solving the multi-train energy-saving optimization model in the non-peak time period.
FIG. 3 is a non-dominated optimal solution set diagram of a multi-objective Pareto frontier in the present invention.
FIG. 4 is a global optimal solution energy index change diagram selected by each generation of the Pareto multi-target genetic algorithm in the invention.
FIG. 5 is a global optimal solution time index variation diagram selected by each generation of the Pareto multi-target genetic algorithm in the invention.
Fig. 6 is a drawing energy consumption diagram of each train in each section after optimization.
Fig. 7 is an optimized train operation diagram.
Detailed Description
With reference to fig. 1, the energy-saving optimization method for multi-train operation in off-peak hours of the present invention includes the following steps:
step 4, solving a multi-train energy-saving optimization model in the off-peak period based on a Pareto multi-objective genetic algorithm to obtain a group of non-dominated solution sets;
and 5, extracting the optimal solution to obtain an optimized schedule, and completing the solution of the multi-train energy-saving optimization model in the non-peak time period.
Further, the line data in step 1 includes a ramp start-stop kilometer post and a corresponding gradient i, a curve segment start-stop kilometer post and a corresponding curvature C, and a speed limit segment start-stop kilometer post and a corresponding speed limit VT(ii) a The train data comprises the marshalling mode, the length L, the load level AW, Thevis equation coefficients (a, b, c) and the maximum acceleration a of the trainmaxMaximum velocity vmaxA traction characteristic curve F (v) and a braking characteristic curve B (v); the basic parameters of the Pareto multi-target genetic algorithm comprise a selection operator, a cross operator, a mutation operator, a maximum evolution algebra, a population size and a fitness function.
Further, the step 2 of constructing the multi-train energy consumption calculation model in the off-peak period specifically includes the following steps:
step 2.1, calculating the traction energy consumption of the train in different areas according to the working condition turning points of the train running section, and obtaining the gradient i and the curvature C of the train in the current simulation step length according to the kilometer post S (t) from the previous simulation step length of the train to the current simulation step length;
step 2.2, calculating the traction force F (v), the braking force B (v) and the resistance parameter f of the train in the current simulation step length according to the speed v (t) and the energy consumption E (t) of the train in the previous simulation step length;
and 2.3, calculating the acceleration a (t) and the traction power P (t) of the train at the current time t according to the working condition and stress analysis of the train, and further calculating the speed v (t + delta t), the kilometer sign S (t + delta t), the traction power P (t + delta t) and the traction energy consumption E (t + delta t) in the next simulation step, wherein the delta t is the simulation step time.
Further, the off-peak multi-train optimization model in step 3 is specifically as follows:
ldi≤g2(x)＝dn≤udi (4)
in the formula f1(x) The target function related to the energy-saving index is F (t), B (t) is respectively the traction force and the braking force of the standard train at the time t; eta is the regenerative braking energy rate of the adjacent trains; e0(i) The originally planned energy consumption value of the train in the interval i; t is t0,tfRespectively as the train running time and the train ending time; k and K-1 are the number of stations and the number of train running sections respectively; f. of2(x) For an objective function related to the punctual index, Δ diThe station stopping time compression value is the station stopping time compression value of the station i; t isiPlanning the running time for station i; g1(x) As constraints relating to the total run time, g2(x) As constraints relating to the time of station stopping,/diAnd udiRespectively, a minimum stop time and a maximum stop time.
Further, the Pareto multi-objective genetic algorithm based on step 4 is used to solve the multi-column vehicle energy-saving optimization model in the off-peak period to obtain a group of non-dominated solution sets, which is specifically as follows in combination with fig. 2:
step 4.1, population initialization: initializing a population P, wherein the size of the population is N, and each individual in the population corresponds to a group of stop time compression value matrixes xi＝[Δd1,Δd2,...Δdj,...,ΔdK]K represents the number of stations, and the time schedule takes seconds as the minimum unit, so integer coding is adopted;
step 4.2, energy saving index f1(x) Punctual index f2(x) And (3) calculating a fitness value: firstly, according to the station-stopping time compression value matrix delta d corresponding to each individual in the populationiCalculating the punctual index f corresponding to each individual in the population2(x) The adaptability value and the new running time and station-stopping time of each interval; then substituting the new operation time into the single-train timing energy-saving optimization model to calculate the total traction energy consumption of the one-way whole-course multi-train operation in the off-peak time period and calculate the energy-saving index f1(x)；
4.3, carrying out non-dominated sorting on the individuals in the population, and calculating the crowdedness of the individuals: firstly, the energy-saving index f of each individual in the population1(x) Punctual index f2(x) The fitness value is subjected to non-dominant sorting, and the sorting number i of each individual in the population is determinedrankThen, carrying out crowding degree calculation on each individual in the non-dominant layer, and determining the non-dominant order relation in the population and the crowding degree of the individual;
and 4.4, selecting elite individuals by using a tournament method to generate offspring populations: randomly selecting individuals from the population P by using a tournament method to perform crossing and variation operations according to the non-dominant sequence relationship and the crowdedness of the individuals in the population P to generate a progeny population Q;
step 4.5, generating a new generation parent population: from the second generation, firstly merging the parent population P and the child population Q to form a new population R, wherein the size of the population is 2N, secondly, carrying out non-dominant sequencing and determining i of each individual in the populationrankCalculating the crowding degree of each individual in the non-dominant layer, selecting the individuals according to the non-dominant order relation and the crowding degree of the individuals to form a next generation parent population P, and keeping the population number of the population as N;
and 4.6, circulating the steps 4.2-4.5 until the maximum iteration number is reached, stopping genetic operation and storing to obtain a Pareto optimal non-dominated solution set.
Further, the step 5 extracts an optimal solution, so as to obtain an optimized schedule, and complete the solution of the multi-train energy-saving optimization model in the non-peak time period, specifically: by extracting a global optimal solution, selecting the most appropriate stop time compression matrix as the global optimal solution according to the established energy-saving and punctual relative importance in a Pareto non-dominated solution set, and solving the optimized interval running time and stop time of each station, so as to obtain an optimized timetable and complete the solution of a non-peak time period multi-train energy-saving optimization model.
Example 1
With reference to fig. 1 to 7, in the energy-saving optimization method for multi-train operation in the off-peak time of the embodiment, simulation analysis is performed on data from the south station of guangzhou to the south station of university at the seven-gauge line of guangzhou subway (in the uplink direction), and the set simulation off-peak time is as follows: the number of the initial planned unit hour departure pairs from 6:00 to 7:00, is 6, and the number of the unit hour departure pairs in the upward direction is 6. As shown in fig. 1, the method comprises the following steps:
step 1: setting train operation basic data and Pareto algorithm parameters, including line data, train data, operation data and basic parameters of a genetic algorithm for off-peak multi-train operation, wherein: the line data comprises a ramp starting and stopping kilometer post and a corresponding gradient i, a curve section starting and stopping kilometer post and a corresponding curvature C, and a speed limit section starting and stopping kilometer post and a corresponding speed limit VTB, carrying out the following steps of; train data including the train's formation, length L, load level AW, Thevis equation coefficients (a, b, c), maximum acceleration amaxMaximum velocity vmaxA traction characteristic curve F (v) and a braking characteristic curve B (v); basic parameters of the Pareto multi-target genetic algorithm comprise a selection operator, a crossover operator, a mutation operator, a maximum evolution algebra, a population size and a fitness function;
step 2: constructing a multi-train energy consumption calculation model in the off-peak period, specifically, calculating the traction energy consumption of the train in different intervals according to the working condition turning points of the train running section, and firstly, obtaining the gradient i and the curvature C of the train corresponding to the simulation step length according to the kilometer post S (t) from the previous simulation step length of the train to the current simulation step length; secondly, according to the speed v (t) and the energy consumption E (t) of the train in the previous simulation step length, the traction force F (v), the braking force B (v) and the resistance parameter f of the train in the current simulation step length are obtained; finally, according to the working condition and stress analysis of the train, calculating the acceleration a (t) and the traction power P (t) of the train at the current time t, and further calculating the speed v (t + delta t), the kilometer sign S (t + delta t), the traction power P (t + delta t) and the traction energy consumption E (t + delta t) in the next simulation step length, wherein delta t is the simulation step length time;
and step 3: the compression value of the station stopping time is used as an optimization variable, the energy-saving index and the on-time index are used as optimization targets, the unidirectional total running time and the variation range of the station stopping time are used as constraint conditions, a multi-train optimization model in the off-peak time period is established, and the station stopping time and the interval running time in the off-peak time period are reasonably optimized. The optimization model is as follows:
ldi≤g2(x)＝dn≤udi (4)
in the formula f1(x) The target function related to the energy-saving index is F (t), B (t) are respectively the traction force and the braking force of the train at a certain time scale; eta is the regenerative braking energy rate of the adjacent trains; e0(i) The originally planned energy consumption value of the train in the interval i; t is t0,tfRespectively the running time and the ending time of the train; k and K-1 are the number of stations and the number of train running sections respectively; f. of2(x) For an objective function related to the punctual index, Δ diThe station stopping time compression value is the station stopping time compression value of the station i; t isiPlanning the running time for station i; g1(x) As constraints relating to the total run time, g2(x) As constraints relating to the stop times, respectively the minimum stopTime and maximum station-stop time values;
and 4, step 4: solving a multi-column vehicle energy-saving optimization model in the off-peak period based on a Pareto multi-objective genetic algorithm to obtain a group of non-dominated solution sets, and combining with the graph 2, the method specifically comprises the following steps:
(1) and (5) initializing a population. Initializing a population P, wherein the size of the population is N. Each individual in the population corresponds to a group of stop time compression value matrixes xi＝[Δd1,Δd2,...Δdj,...,ΔdK]And K represents the number of stations. The time schedule takes seconds as the minimum unit, so integer coding is adopted;
(2) energy saving index f1(x) Punctual index f2(x) And calculating a fitness value. Firstly, according to the station-stopping time compression value matrix delta d corresponding to each individual in the populationiCalculating the punctual index f corresponding to each individual in the population2(x) The adaptability value and the new running time and station-stopping time of each interval; then substituting the new operation time into the single-train timing energy-saving optimization model to calculate the total traction energy consumption of the one-way whole-course multi-train operation in the off-peak time period and calculate the energy-saving index f1(x)；
(3) And (4) carrying out non-dominant sorting on the individuals in the population, and calculating the crowdedness of the individuals. Firstly, the energy-saving index f of each individual in the population1(x) Punctual index f2(x) The fitness values are subjected to non-dominant sorting to determine i of each individual in the populationrankThen carrying out crowding degree calculation on each individual in the non-dominant layer, and determining the non-dominant order relation in the population and the crowding degree of the individual;
(4) elite individuals are selected by the tournament method to produce offspring populations. Randomly selecting individuals from the population P by using a tournament method to perform crossing and variation operations according to the non-dominant sequence relationship and the crowdedness of the individuals in the population P to generate a progeny population Q;
(5) and generating a new generation of parent population. From the second generation, firstly merging the parent population P and the child population Q to form a new population R, wherein the size of the population is 2N, secondly, carrying out non-dominant sequencing and determining i of each individual in the populationrankValue, then congestion degree for each individual in non-dominant layerCalculating, selecting proper individuals according to the non-dominant order relation and the crowding degree of the individuals to form a next generation parent population P, and keeping the population number of the population as N;
(6) and generating a new offspring population through selection, crossing and mutation operations of the genetic algorithm, and so on until an ending condition is met, stopping the genetic operation, and storing a non-dominated solution set of the Pareto frontier.
And 5: and extracting a global optimal solution, selecting the most appropriate stop time compression matrix as the global optimal solution according to the established energy-saving and punctual relative importance in a Pareto non-dominated solution set, and solving the optimized interval running time and stop time of each station so as to obtain an optimized time schedule and complete the solution of the multi-train energy-saving optimization model in the non-peak time period.
According to the method in the step 1, the Guangzhou subway line seven is a subway line opened at the end of the 2016 year of the Guangzhou subway, the south station of the Guangzhou in the first period of the seven is the southwest station of the Guangzhou and the south station of the southeast to university, the seven lines are all underground lines with the total length of 17.5 kilometers, the train purchased by the seven lines is a B-type electric locomotive provided by south vehicles in China, the vehicles adopt a marshalling mode of 4-motor-2-trailer, and each motor car compartment is provided with 4 traction motors and 16 traction motors in total. The overall length of the vehicle is 118.32 m. The total mass of the train includes both the mass of the cars and the mass of the passengers. According to the passenger carrying quantity, the load grade of the train is divided into: AW0 (no load), AW1 (seat load), AW2 (rated load), AW3 (overload load) four levels. The related parameters of the genetic algorithm are that the population size is 100, the maximum iteration times is 30 times, the selection rate is 0.9, the cross ratio is 0.8, and the mutation rate is 0.005.
According to the method in step 3, the total operation time constraint is set to 1385s, the upper limit value of the station stop time is set to 60s, and the transfer station and the non-transfer station in the lower limit value of the station stop time are set to 30s and 25s respectively.
According to the method in the step 4, energy consumption indexes and punctual index change curves of the selected global optimal solution in each generation of feasible solution sets in the Pareto multi-objective genetic algorithm optimized population are obtained, and are respectively shown in fig. 4 and 5. It is shown that the energy consumption index of the globally optimal solution per generation in 30 generation individuals fluctuates between 12.41kw.h and 12.64kw.h and approaches 12.47kw.h, while the corresponding on-time index fluctuates around 0s and approaches 0 s.
According to the method in step 5, a non-dominated solution distribution map, i.e. a distribution of Pareto fronts, over the fitness space is obtained, as shown in fig. 3. The graph shows that the energy consumption index of the train is approximately in inverse proportion to the punctual index, and the longer the running time between the train stations is, the higher the energy consumption is. However, increasing the same operation time does not reduce the energy consumption by the same amount, which is reflected in a gradual decrease of the trend of the operation time between train stations influencing the energy consumption change.
According to the method in the step 5, a train operation diagram and a traction energy consumption diagram which are optimized from 6:00 to 7:00 are obtained, and are respectively shown in the figure 6 and the figure 7. The stop time of the three stations of the rock wall, the thanksura and the village is the lower limit value of the stop time, so that the stop time is not compressed, and the stop time of the other 6 stations is correspondingly compressed. After optimization, the deviation of the arrival time of the train is 0s, so that the requirement of passengers on waiting time is met. The optimized station-stopping time is 25-60 s, and the station-stopping time constraint range is met. Before and after optimization, the total operation time of the circuit is always kept 1385s unchanged, and the constraint that the total operation time is unchanged is met. The total station-stopping time is reduced from 295s to 247s for 48s, the interval running time is increased from 1090s to 1138s for 48s, and the interval running time accounts for 3.47% of the total running time. The whole-process traction energy consumption of each train is reduced from 206.9025kw.h to 196.2072kw.h, the final traction energy consumption is reduced by 10.6953kw.h, and the optimal proportion of the traction energy consumption reaches 5.17%.
Claims (5)
1. The energy-saving optimization method for the operation of the multiple trains in the off-peak period is characterized by comprising the following steps of:
step 1, setting train operation basic data and Pareto algorithm parameters, wherein the train operation basic data and the Pareto algorithm parameters comprise line data, train data and operation data of off-peak multi-train operation and basic parameters of a Pareto multi-target genetic algorithm;
step 2, constructing a multi-train energy consumption calculation model in the off-peak period;
step 3, establishing a multi-train energy-saving optimization model in a non-peak time period by taking the compression value of the station stopping time as an optimization variable, taking an energy-saving index and an on-time index as optimization targets and taking the unidirectional total running time and the station stopping time variation range as constraint conditions;
step 4, solving a multi-train energy-saving optimization model in the off-peak period based on a Pareto multi-objective genetic algorithm to obtain a group of non-dominated solution sets;
step 5, extracting an optimal solution to obtain an optimized schedule, and completing the solution of the multi-train energy-saving optimization model in the non-peak time period;
the multi-train energy-saving optimization model in the non-peak time period in the step 3 specifically comprises the following steps:
ldi≤g2(x)＝dn≤udi (4)
in the formula f1(x) F (t) is a target function related to the energy-saving index, and the tractive force of the standard train at the time t; e0(i) The originally planned energy consumption value of the train in the interval i; t is t0,tfRespectively as the train running time and the train ending time; k and K-1 are the number of stations and the number of train running sections respectively; f. of2(x) For an objective function related to the punctual index, Δ diThe station stopping time compression value is the station stopping time compression value of the station i; t isiPlanning the running time for station i; g1(x) As constraints relating to the total run time, g2(x) As constraints relating to the time of station stopping,/diAnd udiMinimum and maximum stop times, respectively, v (t) the speed of the train。
2. The method according to claim 1, wherein the route data in step 1 includes a ramp starting and stopping kilometer sign and corresponding gradient i, a curve section starting and stopping kilometer sign and corresponding curvature C, a speed limit section starting and stopping kilometer sign and corresponding speed limit VT(ii) a The train data comprises the marshalling mode, the length L, the load level AW, Thevenir equation coefficients a, b and c and the maximum acceleration a of the trainmaxMaximum velocity vmaxA traction characteristic curve F (v) and a braking characteristic curve B (v); the basic parameters of the Pareto multi-target genetic algorithm comprise a selection operator, a cross operator, a mutation operator, a maximum evolution algebra, a population size and a fitness function.
3. The off-peak multi-train operation energy-saving optimization method according to claim 1, wherein the off-peak multi-train energy consumption calculation model is constructed in step 2, and specifically comprises the following steps:
step 2.1, calculating the traction energy consumption of the train in different areas according to the working condition turning points of the train running section, and obtaining the gradient i and the curvature C of the train in the current simulation step length according to the kilometer post S (t) from the previous simulation step length of the train to the current simulation step length;
step 2.2, calculating the traction force F (v), the braking force B (v) and the resistance parameter f of the train in the current simulation step length according to the speed v (t) and the energy consumption E (t) of the train in the previous simulation step length;
and 2.3, calculating the acceleration a (t) and the traction power P (t) of the train at the current time t according to the working condition and stress analysis of the train, and further calculating the speed v (t + delta t), the kilometer sign S (t + delta t), the traction power P (t + delta t) and the traction energy consumption E (t + delta t) in the next simulation step, wherein the delta t is the simulation step time.
4. The off-peak multi-train operation energy-saving optimization method according to claim 1, wherein the Pareto multi-objective genetic algorithm-based solution of the off-peak multi-train energy-saving optimization model in step 4 is used to obtain a set of non-dominated solution sets, which are as follows:
step 4.1, population initialization: initializing a population P, wherein the size of the population is N, and each individual in the population corresponds to a group of stop time compression value matrixes xi＝[Δd1,Δd2,...Δdj,...,ΔdK-1]K represents the number of stations, and the time schedule takes seconds as the minimum unit, so integer coding is adopted;
step 4.2, energy saving index f1(x) Punctual index f2(x) And (3) calculating a fitness value: firstly, according to the station-stopping time compression value matrix delta d corresponding to each individual in the populationiCalculating the punctual index f corresponding to each individual in the population2(x) The adaptability value and the new running time and station-stopping time of each interval; then substituting the new operation time into the single-train energy-saving optimization model to calculate the total traction energy consumption of the one-way whole-course multi-train operation in the off-peak time period and calculate the energy-saving index f1(x)；
4.3, carrying out non-dominated sorting on the individuals in the population, and calculating the crowdedness of the individuals: firstly, the energy-saving index f of each individual in the population1(x) Punctual index f2(x) The fitness value is subjected to non-dominant sorting, and the sorting number i of each individual in the population is determinedrankThen, carrying out crowding degree calculation on each individual in the non-dominant layer, and determining the non-dominant order relation in the population and the crowding degree of the individual;
and 4.4, selecting elite individuals by using a tournament method to generate offspring populations: randomly selecting individuals from the population P by using a tournament method to perform crossing and variation operations according to the non-dominant sequence relationship and the crowdedness of the individuals in the population P to generate a progeny population Q;
step 4.5, generating a new generation parent population: from the second generation, firstly merging the parent population P and the child population Q to form a new population R, wherein the size of the population is 2N, secondly, carrying out non-dominant sequencing and determining i of each individual in the populationrankCalculating the crowdedness of each individual in the non-dominant layer, selecting the individuals according to the non-dominant sequence relation and the crowdedness of the individuals to form a next generation parent population P, and keepingThe population number of individuals is N;
and 4.6, circulating the steps 4.2-4.5 until the maximum iteration number is reached, stopping genetic operation and storing to obtain a Pareto optimal non-dominated solution set.
5. The off-peak multi-train operation energy-saving optimization method according to claim 1, wherein the optimal solution is extracted in step 5, so as to obtain an optimized schedule and complete the solution of the off-peak multi-train energy-saving optimization model, and specifically comprises the following steps: by extracting a global optimal solution, selecting the most appropriate stop time compression matrix as the global optimal solution according to the established energy-saving and punctual relative importance in a Pareto non-dominated solution set, and solving the optimized interval running time and stop time of each station, so as to obtain an optimized timetable and complete the solution of a non-peak time period multi-train energy-saving optimization model.
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