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Optimizing Train Driving to Minimize the Electricity Cost of an Entire Railway Traffic Mesh using Evolutionary Algorithms

Eduardo Pilo de la Fuente, Sudip K. Mazumder, Maria Antonia Simon

arXiv:2609.05493v1cs.NEphysics.app-ph

TL;DR

Railway operation must account for power exchanges across the traffic mesh, not only each train’s energy use. The paper combines train simulation, mesh-level cost calculation, and evolutionary search; in its study cases, the electricity bill fell by around 14% and the power-dependent term by 32%.

  • Problem

    Train operation must be designed around power flows, since power exchanges and capacity constraints depend on the full traffic mesh rather than an individual train.

    Source: §I · p. 1

  • Method

    The procedure simulates train movement, builds the traffic mesh and its electricity cost, then uses an evolutionary algorithm to search for lower-cost driving patterns.

    Source: A. Overview · p. 3

  • Results

    Around 14% reductions in the total electricity bill and 32% in the power-dependent term were achieved in the study cases.

    Source: §V · p. 9

  • Takeaways & Limitations

    The procedure targets both energy-consumption and power-capacity costs and can be applied to complex periodic traffic meshes with multiple services and train types.

    Source: §V · p. 9

Abstract

from arXiv · show

This paper presents a procedure to optimize the way trains are driven, which pursues, in addition to fulfilling operational constraints such as admissible speeds or journey durations, the minimization of the cost related to supplying electrical energy to the trains, including the cost of the energy consumption and the cost of the power capacity utilization. This procedure combines: (i) a traffic model that merges the energy and power footprint of each rail service part of the traffic mesh, and (ii) an evolutionary computation framework that enables searching for the optimal way to drive the trains to achieve an optimal traffic mesh. This procedure is applied to a 450 km long section of the high-speed line from Madrid to Barcelona (Spain).

I. INTRODUCTION

Railway operation must be designed around power exchanges among trains, not only individual energy use. The introduction motivates mesh-level optimization, then reviews approaches to coordinating train operation and regenerative energy.

I. INTRODUCTION

  • Energy-focused optimization can overlook power-capacity costs and limits, which depend on the combined traffic mesh rather than an individual train.The cited limitation includes maximum power a substation can handle.Source: §I · p. 1
  • Train-operation design affects when and where power flows, and the paper aims to optimize energy and power exchanges to improve power-supply performance.Electrical interconnection and regenerative braking enable energy to flow between trains or to the grid.Source: §I · p. 1

II. OPTIMIZATION OF RAILWAY OPERATION

  • Railway-operation research spans single-train driving and multi-train coordination, including synchronization that can use regenerative energy to reduce power peaks.The review distinguishes changing how trains are driven from synchronizing their acceleration and braking.Source: A. Mass Rail Transit (MRT) and Subway… · pp. 1–2

A. Mass Rail Transit (MRT) and Subway systems

  • A multi-phase dynamic-programming method for metro eco-driving optimizes a following train to absorb regenerative energy and a preceding train to generate it during the follower’s acceleration.Source: A. Mass Rail Transit (MRT) and Subway… · p. 2
  • MRT and subway approaches coordinate train timing or speed profiles to increase regenerative-energy use and smooth substation demand.Examples include coordinating dwell times [8], using genetic algorithms to manage dwell times [2], and synchronizing braking with acceleration [3],, [5], [6].Source: A. Mass Rail Transit (MRT) and Subway… · p. 2

B. High-Speed Railways

High-speed-rail optimization work described here focuses mainly on energy efficiency and punctuality, while the reviewed methods use varied driving controls and optimization techniques.

B. High-Speed Railways

  • High-speed AC substations are normally reversible, making train synchronization less impactful for energy saving than in the described urban-rail setting.Source: B. High-Speed Railways · p. 2
  • A genetic algorithm paired with a high-fidelity simulator produced driver guiding commands and measured average energy savings of 18% to 23% on Madrid–Barcelona.Source: B. High-Speed Railways · p. 2
  • Other reviewed strategies use discrete control gears with checkpoint constraints and KKT conditions, or PPO to balance punctuality and traction-energy consumption.Source: B. High-Speed Railways · p. 2
  • Additional work applies NSGA-II to cruising-coasting trajectories and minimizes EMU net energy under battery limits during catenary outages.Source: B. High-Speed Railways · p. 2
  • High-speed-rail operation is described as focusing almost exclusively on energy efficiency and punctuality, rather than reducing substation power peaks.Source: B. High-Speed Railways · p. 2

C. Heavy Freight Rail Systems

Heavy-freight studies address extreme power demand and, in the reviewed examples, coordinate multiple trains to manage regenerative energy and power-system loads.

C. Heavy Freight Rail Systems

  • Heavy freight rail’s extreme power demand can make voltage stability a concern and distinguish its optimization strategies.Source: C. Heavy Freight Rail Systems · p. 2
  • The train-track-power model coordinates freight trajectories so accelerating trains absorb braking energy in the same supply section, turning random loads into planned loads.Source: C. Heavy Freight Rail Systems · p. 2
  • A large-scale adaptive algorithm, LA-MOCSO, is used to coordinate multiple trains’ speed profiles and allocate regenerative energy on long-distance freight routes.Source: C. Heavy Freight Rail Systems · p. 2

D. Billing Optimization

The section frames electricity billing as a railway-operation optimization problem and outlines a pipeline from individual train simulation to evolutionary search over traffic meshes. Its single-train model computes movement and electrical power under track and operating constraints.

D. Billing Optimization

  • A commuter-rail billing study optimizes contracted power capacity using Spanish tariffs, failure rates, traffic density, and pseudo-static simulation to reduce the total bill.Source: D. Billing Optimization · p. 3

A. Overview

  • The proposed pipeline simulates each train, generates the traffic mesh, calculates total electricity cost, and uses an evolutionary algorithm to search for cheaper train movements.The electricity cost includes consumed energy and power-capacity utilization.Source: A. Overview · p. 3, Figure 1 · p. 3

B. Single Train Simulation

  • The single-train module integrates Newton’s second law for a service with an origin, destination, and intermediate stops, balancing traction against weight, curve, and running-resistance forces.The rotating inertial mass coefficient is typically between 1.05 and 1.15.Source: B. Single Train Simulation · p. 3
  • The reference MTD modes are acceleration, cruising, and braking; optimized driving may also use coasting, while speed and acceleration limits constrain train movement.Electrical power is calculated from traction force at each time step, with conversion efficiencies and auxiliary power included.Source: B. Single Train Simulation · pp. 3–4, Figure 3 · p. 3, Figure 4 · p. 4

C. Traffic Mesh Construction

The traffic model builds an overall mesh by superimposing periodic meshes, one for each train service. Each service mesh is made from time-shifted copies of a single-train simulation.

C. Traffic Mesh Construction

  • The overall traffic mesh superimposes periodic meshes, one for each train service.The model supports meshes formed from periodic meshes defined by stops, train type, service start time, and service period.Source: C. Traffic Mesh Construction · p. 4, Figure 5 · p. 4
  • Each service mesh is constructed by copying and time-shifting its single-train simulation.The shifts follow that service’s starting time and period.Source: C. Traffic Mesh Construction · p. 4
  • A service mesh is parameterized by its list of stops, train type, starting time, and period.These parameters define the periodic meshes that can be combined into the overall traffic mesh.Source: Figure 5 · p. 4, C. Traffic Mesh Construction · p. 4

D. Optimization

The optimization searches for train-driving plans that reduce electricity costs while respecting the allowed time margin. It evaluates combined traffic using power-capacity, energy, and delay terms, and varies several driving controls.

D. Optimization

  • The procedure uses the Evolutionary Computation Framework, evaluating candidate solutions with the traffic simulation.Both the framework and simulation are implemented in C++.Source: D. Optimization · p. 4
  • The search minimizes electricity cost for each service without exceeding its maximum admissible time margin.The reference is each service’s MTD operation, with flexibility in journey duration used to pursue lower costs.Source: D. Optimization · p. 4
  • The objective combines contracted-power cost, energy cost, and a penalty for exceeding the allowed service duration.The power and energy terms are computed by electrical zone from supplied substation power; the delay term uses service overrun.Source: D. Optimization · p. 4
  • Candidate driving plans combine speed, traction-force, and acceleration reductions with added coasting sections.These actions are applied in optimization sections where they can affect energy and power consumption.Source: D. Optimization · p. 4

D.1 Maximum speed optimization

The procedure parameterizes four driving changes in track-specific sections: reducing maximum speed, traction force, and acceleration, and adding coasting before speed reductions.

D.1 Maximum speed optimization

  • Maximum-speed optimization divides the line into sections that each belong to at most one track maximum-speed section.A [0,1] factor sets a new operational speed limit for each optimization section.Source: §D.1 · p. 4, Figure 6 · p. 4

D.2 Maximum traction force optimization

  • Maximum-traction-force optimization scales the force limit in the same sections used for speed optimization.The [0,1] factor can reduce maximum traction force where doing so improves the objective function, smoothing acceleration.Source: §D.2 · pp. 4–5

D.3 Maximum acceleration optimization

  • To smooth train movement, maximum-acceleration factors are defined within [0,1] for each maximum-speed section on the track; operational acceleration limits are also added to the single-train simulation.Source: §D.3 · p. 5

D.4 Coasting section optimization

  • Coasting sections are introduced for each speed reduction, with each section ending at that reduction.A [0,1] optimization factor sets coasting length relative to a preset maximum distance.Source: §D.4 · p. 5, Figure 7 · p. 5

IV. CASE STUDY

In Case 1, optimized driving reduced total energy cost by 15% relative to MTD operation. The study evaluates periodic Madrid–Lleida services on the high-speed line and also reports energy and power-peak changes by electrical zone.

A. Description of the Madrid-Lleida Section

  • The case study considers a 445 km Madrid–Lleida high-speed section with trains running in both directions every 10 minutes.Services stop in Zaragoza for five minutes and use series 103 trains; the MTD trip durations are 5712 seconds Madrid–Lleida and 5736 seconds Lleida–Madrid, excluding stops.Source: §IV · p. 5, Figure 8 · p. 5, A. Description of the Madrid-Lleida… · p. 5

B. Case 1: Two Energy Price Sections, No Power Capacity Costs

  • 12% and 16% energy-consumption reductions were achieved in electrical zones 1 and 2, respectively.The optimization saved more energy in zone 2, where energy cost was higher.Source: Figure 10 · p. 6
  • In Case 1, although power peaks shaving is not targeted because its assigned cost is zero, energy consumption indirectly reduces maximum power peaks by 6%-25%, depending on the electrical zone.Source: B. Case 1: Two Energy Price Sections,… · p. 6
  • 15% lower total energy cost was achieved against MTD operation by using the available time margin.Table IV reports the objective-function improvements for Case 1.Source: Table IV · p. 6, B. Case 1: Two Energy Price Sections,… · p. 6
  • The study also examines how total cost varies with the time margin.Figure 14 presents this sensitivity analysis for Case 1, without a reported numerical outcome in the supplied text.Source: Figure 13 · p. 7, Figure 14 · p. 7

C. Case 2: Two Power-Capacity Cost Sections, No Energy Costs

In Case 2, the optimization uses the 10-minute time margin to reduce power-capacity costs, despite energy costs being set to zero. It also reduces energy consumption indirectly and prioritizes the electrical zone with the higher maximum-power cost.

C. Case 2: Two Power-Capacity Cost Sections, No Energy Costs

F. Case 3: Two Energy and Power Cost Sections

In Case 3, the optimization reduces both energy consumption and power peaks, with larger reductions in the higher-priced electrical zone. The case uses a 10-minute time margin and reports comparisons with the original MTD operation.

F. Case 3: Two Energy and Power Cost Sections

V. CONCLUSIONS

The paper presents a procedure for optimizing train operations under zone-dependent electricity pricing, accounting for energy consumption and power-capacity utilization. It reports tests on a Madrid–Barcelona high-speed-line section and reductions in the total electricity bill and power-dependent term.

V. CONCLUSIONS

  • The procedure minimizes electricity-supply cost, including energy consumption and power-capacity utilization, using zone-dependent pricing.It is applicable to complex periodic traffic meshes with multiple services and train types.Source: §V · p. 9
  • Around 14% reduction in the total electricity bill and 32% in the power-dependent term were achieved in the study cases.The optimization was tested on a 445 km Madrid–Barcelona high-speed-line section using Siemens S-103 trains and different electrical power and energy scenarios.Source: §V · p. 9
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