ISSN 1068-3712, Russian Electrical Engineering, 2017, Vol. 88, No. 12, pp. 839–841. © Allerton Press, Inc., 2017.
Original Russian Text © V.G. Sidorenko, Chzho Min Aung, V.M. Alekseev, E.N. Rozenberg, V.I. Umanskii, 2017, published in Elektrotekhnika, 2017, No. 12, pp. 73–76.
Planning Electric-Rolling-Stock Maintenance in Conditions
of Limited Resources
V. G. Sidorenko
*, Chzho Min Aung
, V. M. Alekseev
, E. N. Rozenberg
, and V. I. Umanskii
Russian University of Transport, Moscow, 127994 Russia
National Research University Higher School of Economics, Moscow, Russia
OAO All Russian Scientific Research Institute of Railway Transport, Moscow, Russia
Received November 14, 2017
Abstract⎯Planning electric-rolling-stock (ERS) maintenance in conditions of limited resources can be car-
ried out based on the following criteria of efficiency of construction of the cycle diagram of the electric rolling
stock: meeting the requirements of the railway-traffic safety provided by adjusting the planned movement
time of the electric rolling stock for the purpose of not allowing an excessive lapse of time between the main-
tenance over that permissible and uniformity of maintenance. The solution of the set problem using the graph
theory allows obtaining the whole set of the permissible values of maintenance and selecting a value that, on
the one hand, corresponds to the planned train time schedule (PTTS) and, on the other hand, differs mini-
mally from the optimal with respect to the selected criterion. This takes a significant amount of time. The
problem can be quickly solved using a genetic algorithm. The introduction of a new criterion—total excess
time lapse between maintenance works over the permissible interval—allows obtaining the solution with any
initial data, which is not always achievable when using the uniform-maintenance criterion. The crossover and
permutation algorithm implemented within the genetic algorithm is adapted taking into account considering
the peculiarities of the agents engaged in solving the problem that has been set out. We have studied the pos-
sibility of using various types of crossover and permutation to construct the cycle diagrams and inf luence of
the parameters of the genetic algorithm on the results. The obtained analytical results are tested for the con-
ditions of the Moscow subway.
Keywords: electric rolling stock, optimization, planning, maintenance, combinatorics, graph theory, genetic
The organization of maintenance of electric rolling
stock in subways is characterized by limited resources:
⎯a tight schedule of operation of the electric roll-
ing stock, with full use of the total available rolling
stock during rush hour;
⎯limited possibilities of extending the depot areas
within very large cities due to the high value of the land
and density of development;
⎯limited possibilities of using the field check sta-
tions (CSs) located on the station tracks due to the use
of these tracks for adjustment operations (turns and
⎯the distribution of check stations and routes
A large number of works have been devoted to
planning the maintenance of electric rolling stock.
These works consider this problem as a
⎯classical mathematical problem of allocation;
⎯mathematical problem solved using the graph
theory and Bellman’s optimality principle ;
⎯mathematical problem solved using the genetic
⎯a mathematical problem of control of the car-
riage processes, these being arrangement of operation
and maintenance of the electric rolling stock of the
railways in the conditions of the time constraints in
given the existence of multiple competitive companies
 or as a problem of arranging monitoring of mainte-
nance [3, 4].
The use of the graph theory to solve the problem of
planning of the maintenance of electric rolling stock
also turned out to be efficient in solving other prob-
lems of control automation of train traffic .
Genetic algorithms (GAs)  have also become
widely used to solve the problem of control automa-
tion of transport systems.
In [1, 6], maintenance-uniformity criterion R
determined by one of two methods.