CN112508459A - Railway locomotive turnover method based on improved genetic algorithm - Google Patents
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Abstract
The invention discloses a railway locomotive turnover method based on an improved genetic algorithm, which comprises the steps of S10 establishing a locomotive turnover model, adopting a GA genetic algorithm to solve the S20 model, judging the advantages and disadvantages of individuals according to the size of a population fitness value, evolving an improved population by using selection operation, cross operation and variation operation until the population fitness value is converged to be stable, generating an optimal individual, namely an optimal solution, S30 solving and verifying, and S40 outputting a locomotive turnover diagram as a locomotive turnover scheme of a designated section on a railway line. The invention carries out modeling aiming at the problem that double machines do not form pairs, designs and improves the specific problems of selection, intersection and variation of the genetic algorithm for modeling solution, can realize the rapid solution of the locomotive turnover scheme by a computer, reduces the complexity of the algorithm, is beneficial to the implementation of the rapid and automatic editing of the locomotive turnover diagram by the computer of the railway bureau, is beneficial to the simplification of the software architecture of the computer editing of the locomotive turnover diagram and has certain promotion effect on the implementation of intelligent office of the locomotive section of the railway bureau.
Description
Technical Field
The invention relates to a railway locomotive turnover technology, in particular to a railway locomotive turnover method based on an improved genetic algorithm.
Background
The problem of partial double-machine traction of a fixed section on a heavy-duty railway line is a problem which needs to be explored urgently in the field, namely how to effectively adopt a mode of combining single-machine traction and double-machine traction in the fixed section which is served by a locomotive service section, and improve the operation benefit of the locomotive on the heavy-duty railway. If only single machine traction is adopted in a fixed railway section, only part of the requirements of the train can be met, and the requirements of traction of part of heavy-load trains can not be met, if the double-machine traction is adopted completely, the waste of locomotive transport capacity is caused. In order to optimize the locomotive turnover scheme, the mode of combining single machines and double machines is adopted in the fixed section, so that the limitation of independent adoption of the single machines and the double machines can be broken, the locomotive turnover time can be shortened, and the number of locomotives in use can be reduced. The railway freight line fixed section adopts a single-machine and double-machine combined mode to generate better economic benefits for the operation of the railway international freight class.
Disclosure of Invention
In view of the above problems in the prior art, the present invention provides a railroad locomotive turnaround method based on an improved genetic algorithm.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a railway locomotive turnover method based on an improved genetic algorithm comprises the following steps:
s10, establishing a locomotive turnover model based on the conditions of single-machine or/and double-machine traction trains between the basic station and the return station of the designated section on the railway line;
s20, solving the established locomotive turnover model by adopting a GA genetic algorithm, judging the quality of an individual according to the size of the population fitness value, and evolving and improving the population by adopting selection operation, cross operation and variation operation until the population fitness value is converged to be stable to generate an optimal individual, namely an optimal solution;
s30, verifying the optimal solution obtained by solving;
and S40, automatically editing the result of the verification meeting the requirements into a locomotive turnover diagram output by the computer, and using the locomotive turnover diagram output as a locomotive turnover scheme of the designated section on the railway line.
Specifically, the locomotive turnaround model established in step S10 is:
s.t.：
wherein, the above formula (2) represents the uniqueness that 1 locomotive in the A-Z direction assignsA train in the Z-A direction;
the above formula (3) represents the uniqueness of assigningA train in the Z-A direction to 2 locomotives in the A-Z direction;
the above formula (4) represents the uniqueness of attaching the Z-A direction train to 1 locomotive in the A-Z direction;
the above formula (5) represents the uniqueness of the 2 locomotives attached to the Z-A direction train in the A-Z direction;
the above formula (6) represents the uniqueness of assigning the trains in the A-Z direction to 1 locomotive in the Z-A direction;
the above formula (7) represents the uniqueness of attaching 2 locomotives in the Z-A direction toA train in the A-Z direction;
the above formula (8) represents the uniqueness of attaching 2 locomotives in the Z-A direction toA train in the A-Z direction;
the above formula (9) represents the uniqueness thatA single-machine traction train in the Z-A direction is dragged by one locomotive in the A-Z direction;
the above formula (10) shows that the double-locomotive traction train in the Z-A direction is drawn by two locomotives in the A-Z direction to be unique;
in the AZ section designated on the railway line, A is a basic station, Z is a return station, and the number of trains running in the A-Z direction is N1The number of trains running in the Z-A direction is N2，N1>N2With M in the A-Z direction1Train is single-machine traction with M2The train isA double-machine traction with M in Z-A direction3Train is single-machine traction with M4The train is drawn by two machines, the number of the attached locomotives is not more than two,
are all set variables.
Specifically, the setting variables in step S10 are:
Further, the solving process using the GA genetic algorithm in step S20 includes:
s21, coding the locomotive turnover model by a multi-parameter cascade coding method, wherein the coding is carried out by 1-N1+M2The internal natural numbers are randomly arranged as 1 chromosome, and N is used2The data are respectively different schemes, wherein, 1 to N1+M2The internal natural numbers respectively represent the train numbers of the trains in sequence in the A-Z direction, and the different schemes comprise a traction scheme, a double-machine scheme, a single-machine hanging scheme and a double-machine hanging scheme;
s22, using the objective function f (x) ═ z (x) as the fitness function;
s23, selection operation: by adopting a selection method combining an optimal storage strategy and steady-state replication, in a new population, a plurality of optimal individuals are reserved, do not participate in crossover and variation operation, and are directly replicated to the next generation, and the individual with the minimum current fitness is the most optimal individual;
s24, intersection operation: adopting uniform two-point crossing, and exchanging genes on each gene locus of two paired individuals with the same crossing probability to form a new individual;
s25, mutation operation: by adopting a linkage uniform variation method, the phenomenon that the variation position is repeated with an original certain gene position in a chromosome string to generate illegal solution due to the uniform variation of a single gene position is avoided.
Specifically, the specific process of the selection operation is as follows:
s23a survival number of individuals in next generation population
S23b, getting
Determining the survival number of the corresponding individual in the next generation population
(ii) individuals;
s23c, sorting the individuals according to the fitness, and sequentially taking the first
The individual is the best solution, does not participate in crossover and mutation, and is copied into the next generation population as M individuals in the next generation population.
Specifically, the specific process of the intersection operation is as follows:
for parent P, with cross probability PcRandomly generating a mask word W equal to the length of the individual code string1w2w3....wlWherein l is the length of the individual code string, in order to avoid the repeated assignment of the locomotive, two mutation sites are randomly generated in the W site of the mask word, so that the gene sites between the mutation sites are inverted to form a new chromosome, wherein,
if w i0 means that the corresponding bit in the parent P is not an ectopic bit,
if w i1 indicates that the corresponding position in the parent P is a mutation position.
Specifically, the mutation operation is performed as follows:
for a given parent P, with a probability of dissimilarity PmTaking a random number k from a corresponding range of values1As the variation point, take the random number k as its k1Finding out the position corresponding to the number k in the original chromosome gene string, and changing the value of the position into the value of k in the original chromosome gene string1The corresponding value.
Further, the specific operation procedure in step S20 is as follows:
step 1: initializing a population size N, pm，pcIteration times M;
step 2: generating M 21 to N1+M2The natural numbers in the system are randomly arranged by a random function to serve as an initial locomotive assignment scheme;
step 3: taking out stepIn the range of 1 to N1+M2Natural numbers not present in it, last N2Randomly inserting bits in the unit bits, wherein the value of the uninserted bits is 0 as a double-machine scheme;
step 4: taking 1 to N in the previous step1+M2Natural numbers not present in it, the last two N2Randomly inserting bits in the units as a locomotive attaching scheme, wherein the value of the non-inserted bit is 0;
step 5: calculating a value of fitness f (x);
step 6: selecting and operating;
step 7: judging whether the cross operation is satisfied: if yes, go to Step 8; otherwise, go to Step 7;
step 8: performing cross operation;
step 9: repeatedly executing the steps of Step3 and Step 4;
step 10: judging whether the mutation operation is satisfied: if yes, go to Step 11; otherwise, go to Step 10;
step 11: performing mutation operation;
step 12: repeatedly executing the steps of Step3 and Step 4;
step 13: generating p (t + 1);
step 14: calculating m as m + 1;
step 15: and (3) judging: if M is less than M, M is equal to M +1, the Step is turned to Step4, and if M is greater than or equal to M, the operation is finished, and the current transportation result is output.
Specifically, in step S30, solution verification is performed by using C + + software based on the known train operation table of the designated section on the railway line.
Compared with the prior art, the invention has the following beneficial effects:
the invention carries out modeling aiming at the problem that double machines do not form pairs, designs and improves the specific problems of selection, intersection and variation of the genetic algorithm for modeling solution, can realize the rapid solution of the locomotive turnover scheme by a computer, reduces the complexity of the algorithm, is beneficial to the implementation of the rapid and automatic editing of the locomotive turnover diagram by the computer of the railway bureau, is beneficial to the simplification of the software architecture of the computer editing of the locomotive turnover diagram and has certain promotion effect on the implementation of intelligent office of the locomotive section of the railway bureau.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention.
FIG. 2 is a schematic diagram of a chromosome arrangement of a selection operation according to an embodiment of the present invention.
FIG. 3 is a diagram illustrating a cross operation process according to an embodiment of the present invention.
FIG. 4 is a schematic diagram illustrating a variant operation according to an embodiment of the present invention.
FIG. 5 is a graph of locomotive turnaround at the output of an embodiment of the present invention.
Detailed Description
The present invention is further illustrated by the following figures and examples, which include, but are not limited to, the following examples.
Examples
As shown in FIG. 1, the railway locomotive turnaround method based on the improved genetic algorithm comprises the following steps:
s10, establishing a locomotive turnover model based on the conditions of single-machine or/and double-machine traction trains between the basic station and the return station of the designated section on the railway line.
Setting in AZ section designated on railway line, A is basic station, Z is retracing station, its running time table is known, and partial trains are drawn by two machines, and the number of running trains in A-Z direction is N1The number of trains running in the Z-A direction is N2，N1>N2With M in the A-Z direction1Train is single-machine traction with M2The train isA double-machine traction with M in Z-A direction3Train is single-machine traction with M4The train is drawn by two machines, the number of the attached locomotives is not more than two,
are all set variables.
The locomotive turnover model is as follows:
s.t.：
wherein, the above formula (2) represents the uniqueness that 1 locomotive in the A-Z direction assignsA train in the Z-A direction;
the above formula (3) represents the uniqueness of assigningA train in the Z-A direction to 2 locomotives in the A-Z direction;
the above formula (4) represents the uniqueness of attaching the Z-A direction train to 1 locomotive in the A-Z direction;
the above formula (5) represents the uniqueness of the 2 locomotives attached to the Z-A direction train in the A-Z direction;
the above formula (6) represents the uniqueness of assigning the trains in the A-Z direction to 1 locomotive in the Z-A direction;
the above formula (7) represents the uniqueness of attaching 2 locomotives in the Z-A direction toA train in the A-Z direction;
the above formula (8) represents the uniqueness of attaching 2 locomotives in the Z-A direction toA train in the A-Z direction;
the above formula (9) represents the uniqueness thatA single-machine traction train in the Z-A direction is dragged by one locomotive in the A-Z direction;
the above formula (10) shows the uniqueness that the double-locomotive traction train in the Z-A direction is dragged by two locomotives in the A-Z direction.
S20, solving the established locomotive turnaround model by adopting a GA genetic algorithm, judging the quality of the individual according to the size of the population fitness value, and evolving the improved population by adopting selection operation, cross operation and variation operation until the population fitness value is converged to be stable to generate the optimal individual, namely obtaining the optimal solution.
The specific process is as follows:
s21, the number of trains running in the A-Z direction is N1And M is2The train is drawn by two machines. The number of trains running in the Z-A direction is N2(N1>N2) And M4The train is drawn by two machines. Therefore, at the Z station, M must be made5(M5＝N1-N2-M4) The locomotives are attached to the running trains in the Z-A direction (the number of the attached locomotives is not more than two). The multi-parameter cascade coding method is used for coding the locomotive turnover model, and the coding is carried out by 1-N1+M2The internal natural numbers are randomly arranged as 1 chromosome, and N is used2The data are respectively different schemes, wherein, 1 to N1+M2The internal natural numbers respectively represent the train numbers of the trains in sequence in the A-Z direction, and the different schemes comprise a traction scheme, a double-machine scheme, a single-machine hanging scheme and a double-machine hanging scheme. The specific encoding method is shown in fig. 2, and the meanings thereof respectively represent:
the locomotive pulling the 6 th train in the A-Z direction is assigned to pull the 1 st train in the Z-A direction, i.e., 6 → 1;
the locomotive of train 2 in the traction A-Z direction is assigned to traction train 2 in the Z-A direction, i.e., 2 → 2;
A locomotive of the 3 rd train in the tractionA-Z direction is assigned to traction the 1 st train in the Z-A direction as the 2 nd locomotive, i.e., 3 → 1 (double locomotive);
A locomotive of the 1 st train in the tractionA-Z direction is assigned to traction the 2 nd train in the Z-A direction asA 2 nd locomotive, i.e., 1 → 2 (double locomotive);
the locomotive of the 1 st train in the tractionA-Z direction is assigned asA hitched locomotive the 1 st train in the hitched Z-A direction, i.e. 1 → 1 (stand-alone hitching);
the locomotive of the 6 th train in the tractionA-Z direction is assigned asA hitched locomotive the 2 nd train in the hitched Z-A direction, i.e. 6 → 2 (stand-alone hitching);
A locomotive towing the 2 nd train in theA-Z direction is assigned asA 2 nd attached locomotive to attach the 1 st train in the Z-A direction, i.e., 2 → 1 (double-locomotive attached);
the locomotive of the train in the traction A-Z direction is not doubly attached to the 2 nd train in the Z-A direction, namely the 2 nd train in the Z-A direction is not doubly attached to the locomotive.
S22, using the objective function f (x) ═ z (x) as the fitness function.
S23, selection operation: by adopting a selection method combining an optimal storage strategy and steady-state replication, in a new population, a plurality of optimal individuals are reserved, do not participate in crossover and variation operation, and are directly replicated to the next generation, and the individual with the minimum current fitness is the most optimal individual; the specific operation process is as follows:
s23a survival number of individuals in next generation population
S23b, getting
Determining the survival number of the corresponding individual in the next generation population
(ii) individuals;
s23c, sorting the individuals according to the fitness, and sequentially taking the first
The individual is the best solution, does not participate in crossover and mutation, and is copied into the next generation population as M individuals in the next generation population.
S24, intersection operation: adopting uniform two-point crossing, and exchanging genes on each gene locus of two paired individuals with the same crossing probability to form a new individual; the specific process is shown in fig. 3.
For parent P, with cross probability PcRandomly generating a mask word W equal to the length of the individual code string1w2w3....wlWherein l is the length of the individual code string, in order to avoid the repeated assignment of the locomotive, two mutation sites are randomly generated in the W site of the mask word, so that the gene sites between the mutation sites are inverted to form a new chromosome, wherein,
if w i0 means that the corresponding bit in the parent P is not an ectopic bit,
if w i1 indicates that the corresponding position in the parent P is a mutation position.
S25, mutation operation: by adopting a linkage uniform variation method, the phenomenon that the variation position is repeated with an original certain gene position in a chromosome string to generate illegal solution due to the uniform variation of a single gene position is avoided, and the specific process is shown in figure 4.
For a given parent P, with a probability of dissimilarity PmTaking a random number k from a corresponding range of values1As the variation point, take the random number k as its k1Finding out the position corresponding to the number k in the original chromosome gene string, and changing the value of the position into the value of k in the original chromosome gene string1The corresponding value.
The specific operation process in step S20 is as follows:
step 1: initializing a population size N, pm，pcIteration times M;
step 2: generating M 21 to N1+M2The natural numbers in the system are randomly arranged by a random function to serve as an initial locomotive assignment scheme;
step 3: taking 1 to N in the previous step1+M2Natural numbers not present in it, last N2Randomly inserting bits in the unit bits, wherein the value of the uninserted bits is 0 as a double-machine scheme;
step 4: taking 1 to N in the previous step1+M2Natural numbers not present in it, the last two N2Randomly inserting bits in the units as a locomotive attaching scheme, wherein the value of the non-inserted bit is 0;
step 5: calculating a value of fitness f (x);
step 6: selecting and operating;
step 7: judging whether the cross operation is satisfied: if yes, go to Step 8; otherwise, go to Step 7;
step 8: performing cross operation;
step 9: repeatedly executing the steps of Step3 and Step 4;
step 10: judging whether the mutation operation is satisfied: if yes, go to Step 11; otherwise, go to Step 10;
step 11: performing mutation operation;
step 12: repeatedly executing the steps of Step3 and Step 4;
step 13: generating p (t + 1);
step 14: calculating m as m + 1;
step 15: and (3) judging: if M is less than M, M is equal to M +1, the Step is turned to Step4, and if M is greater than or equal to M, the operation is finished, and the current transportation result is output.
And S30, verifying the solved optimal solution by using C + + software based on the known train operation table of the designated section on the railway line.
And S40, automatically editing the result of the verification meeting the requirements into a locomotive turnover diagram output by the computer, and using the locomotive turnover diagram output as a locomotive turnover scheme of the designated section on the railway line.
The train operating table shown in table 1 was used as an example data analysis. In an AZ section of a certain line, A is a basic section in locomotive traffic information, Z is a return section, and part in the section is subjected to double-machine traction.
TABLE 1 train operation table
C + + software is used for solving, the turnover time of the locomotive in the section is calculated to be 31455min, and 22 locomotives are needed. The locomotive turnaround chart is automatically edited and output through a computer, as shown in fig. 4, the locomotive connection scheme is as follows:
a station section A: 010 → 021, 004 → 001, 002 → 003, 018 → 007, 016 → 009, 028 → 013, 018 → 015, 022 → 011, 006 → 017, 014 → 019, 026 → 023, 008 → 012, 020 → 003 (double machine), 012 → 011 (double machine), 020 → 017 (double machine 018), → 003 (attached hook), 024 → 003 (attached hook), 028 → 021 (attached hook), 012 → 001 (attached hook).
Z station segment: 021 → 026, 005 → 008, 009 → 014, 013 → 018, 015 → 020, 017 → 024, 001 → 028, 007 → 022, 019 → 004, 011 → 006, 021 → 010, 023 → 012, 003 → 016, 023 → 022, 011 → 008 (duplex), 003 → 018 (duplex), 003 → 020 (duplex), 017 → 006 (duplex), 003 → 012 (duplex).
In conclusion, the invention aims at minimizing the number of the locomotives, establishes a mathematical model of the locomotive turnover, skillfully calculates the optimal traction scheme and the attachment scheme of the locomotive through a genetic algorithm, and calculates and verifies through a calculation example that the locomotive turnover continuing scheme obtained through the mathematical model is beneficial.
The above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, but all changes that can be made by applying the principles of the present invention and performing non-inventive work on the basis of the principles shall fall within the scope of the present invention.
Claims (9)
1. A railway locomotive turnover method based on an improved genetic algorithm is characterized by comprising the following steps:
s10, establishing a locomotive turnover model based on the conditions of single-machine or/and double-machine traction trains between the basic station and the return station of the designated section on the railway line;
s20, solving the established locomotive turnover model by adopting a GA genetic algorithm, judging the quality of an individual according to the size of the population fitness value, and evolving and improving the population by adopting selection operation, cross operation and variation operation until the population fitness value is converged to be stable to generate an optimal individual, namely an optimal solution;
s30, verifying the optimal solution obtained by solving;
and S40, automatically editing the result of the verification meeting the requirements into a locomotive turnover diagram output by the computer, and using the locomotive turnover diagram output as a locomotive turnover scheme of the designated section on the railway line.
2. The improved genetic algorithm based railroad locomotive turnaround method of claim 1, wherein the locomotive turnaround model established in step S10 is:
s.t.：
wherein, the above formula (2) represents the uniqueness that 1 locomotive in the A-Z direction assignsA train in the Z-A direction;
the above formula (3) represents the uniqueness of assigningA train in the Z-A direction to 2 locomotives in the A-Z direction;
the above formula (4) represents the uniqueness of attaching the Z-A direction train to 1 locomotive in the A-Z direction;
the above formula (5) represents the uniqueness of the 2 locomotives attached to the Z-A direction train in the A-Z direction;
the above formula (6) represents the uniqueness of assigning the trains in the A-Z direction to 1 locomotive in the Z-A direction;
the above formula (7) represents the uniqueness of attaching 2 locomotives in the Z-A direction toA train in the A-Z direction;
the above formula (8) represents the uniqueness of attaching 2 locomotives in the Z-A direction toA train in the A-Z direction;
the above formula (9) represents the uniqueness thatA single-machine traction train in the Z-A direction is dragged by one locomotive in the A-Z direction;
the above formula (10) shows that the double-locomotive traction train in the Z-A direction is drawn by two locomotives in the A-Z direction to be unique;
in the AZ section designated on the railway line, A is a basic station, Z is a return station, and the number of trains running in the A-Z direction is N1The number of trains running in the Z-A direction is N2，N1>N2With M in the A-Z direction1Train is single-machine traction with M2The train isA double-machine traction with M in Z-A direction3Train is single-machine traction with M4The train is drawn by two machines, the number of the attached locomotives is not more than two,
are all set variables.
3. The improved genetic algorithm based railroad locomotive turnaround method of claim 2, wherein the setting variables in step S10 are:
4. The improved genetic algorithm based railway locomotive turnaround method of claim 3, wherein the solving with the GA genetic algorithm in the step S20 comprises:
s21, coding the locomotive turnover model by a multi-parameter cascade coding method, wherein the coding is carried out by 1-N1+M2The internal natural numbers are randomly arranged as 1 chromosome, and N is used2The data are respectively different schemes, wherein, 1 to N1+M2The internal natural numbers respectively represent the train numbers of the trains in sequence in the A-Z direction, and the different schemes comprise a traction scheme, a double-machine scheme, a single-machine hanging scheme and a double-machine hanging scheme;
s22, using the objective function f (x) ═ z (x) as the fitness function;
s23, selection operation: by adopting a selection method combining an optimal storage strategy and steady-state replication, in a new population, a plurality of optimal individuals are reserved, do not participate in crossover and variation operation, and are directly replicated to the next generation, and the individual with the minimum current fitness is the most optimal individual;
s24, intersection operation: adopting uniform two-point crossing, and exchanging genes on each gene locus of two paired individuals with the same crossing probability to form a new individual;
s25, mutation operation: by adopting a linkage uniform variation method, the phenomenon that the variation position is repeated with an original certain gene position in a chromosome string to generate illegal solution due to the uniform variation of a single gene position is avoided.
5. The improved genetic algorithm based railroad locomotive turnaround method of claim 4, wherein the specific process of the selection operation is as follows:
s23a survival number of individuals in next generation population
S23b, getting
Determining the survival number of the corresponding individual in the next generation population
(ii) individuals;
s23c, sorting the individuals according to the fitness, and sequentially taking the first
The individual is the best solution, does not participate in crossover and mutation, and is copied into the next generation population as M individuals in the next generation population.
6. The improved genetic algorithm based railroad locomotive turnaround method of claim 5, wherein the specific process of the crossing operation is as follows:
for parent P, with cross probability PcRandomly generating a mask word W equal to the length of the individual code string1w2w3....wlWherein l is the length of the individual code string, in order to avoid the repeated assignment of the locomotive, two mutation sites are randomly generated in the W site of the mask word, so that the gene sites between the mutation sites are inverted to form a new chromosome, wherein,
if wi0 means that the corresponding bit in the parent P is not an ectopic bit,
if wi1 indicates that the corresponding position in the parent P is a mutation position.
7. The improved genetic algorithm-based railroad locomotive turnaround method according to claim 6, wherein the mutation operation is performed by the following specific processes:
for a given parent P, with a probability of dissimilarity PmTaking a random number k from a corresponding range of values1As the variation point, take the random number k as its k1Finding out the position corresponding to the number k in the original chromosome gene string, and changing the value of the position into the value of k in the original chromosome gene string1The corresponding value.
8. The improved genetic algorithm based railroad locomotive turnaround method according to claim 7, wherein the specific operation process in the step S20 is as follows:
step 1: initializing a population size N, pm，pcIteration times M;
step 2: generating M21 to N1+M2The natural numbers in the system are randomly arranged by a random function to serve as an initial locomotive assignment scheme;
step 3: taking 1 to N in the previous step1+M2Natural numbers not present in it, last N2Randomly inserting bits in the unit bits, wherein the value of the uninserted bits is 0 as a double-machine scheme;
step 4: taking 1 to N in the previous step1+M2Natural numbers not present in it, the last two N2Randomly inserting bits in the units as a locomotive attaching scheme, wherein the value of the non-inserted bit is 0;
step 5: calculating a value of fitness f (x);
step 6: selecting and operating;
step 7: judging whether the cross operation is satisfied: if yes, go to Step 8; otherwise, go to Step 7;
step 8: performing cross operation;
step 9: repeatedly executing the steps of Step3 and Step 4;
step 10: judging whether the mutation operation is satisfied: if yes, go to Step 11; otherwise, go to Step 10;
step 11: performing mutation operation;
step 12: repeatedly executing the steps of Step3 and Step 4;
step 13: generating p (t + 1);
step 14: calculating m as m + 1;
step 15: and (3) judging: if M is less than M, M is equal to M +1, the Step is turned to Step4, and if M is greater than or equal to M, the operation is finished, and the current transportation result is output.
9. The improved genetic algorithm based railroad locomotive turnaround method of claim 8, wherein in step S30, the solution verification is performed using C + + software based on known train schedules for designated sections on the railroad line.
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