Optimization of a train speed profile based on the expected accident damage criterion

A. V. Borisov^ab, A. N. Ignatov^c, V. A. Borisov<sup>c

a</sup> Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^b Moscow Center for Fundamental and Applied Mathematics, M. V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
^c Moscow Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125933, Russian Federation

Abstract: The paper focuses on designing a freight train speed profile that minimizes the expected damage from various types of railway accidents. Total losses include both damage to a considered train and potential harm to trains on adjacent tracks. The probability functions for all accident types are parameterized by the route's topology and profile, i. e., its local slope and curvature. These probability functions, along with those describing the average financial loss per derailed car, treat train speed as a control variable. The speed profile is a solution to the constrained mathematical programming problem. It is represented as a piecewise constant function, remaining constant over each segment of the route with uniform slope or curvature. This profile satisfies both instantaneous geometric and integral time constraints. Since a piecewise constant speed profile looks physically unrealistic, the paper also proposes a method for transforming it into a profile with uniformly accelerated transitions. A numerical example is provided to illustrate how different loss functions and time constraints affect the choice of an optimal speed profile.

Keywords: piecewise constant control, speed profile, expected damage, nonlinear optimization.

Received: 29.05.2025
Accepted: 15.08.2025

DOI: 10.14357/19922264250304