The purpose of the project is to see how optimising train driving strategy can help save energy in railway operations.

1. Train Trajectory Optimisation for
Energy Saving
-- BEng Final Year Project
-- Yeziwei Wang (Maggie)
-- Supervisor: Prof. Clive Roberts

2. Background and Purpose
Current Problems
 Increasing energy prices
 Increasingly urgent environmental concerns
 The development of automatic train
operation
 Driving Strategy is a relatively easy way to
save energy compared to improve vehicle or
railway design
Project Purpose
 Develop genetic algorithm to find the
optimal train trajectory compromising
between journey time and energy
consumption.
 Case study on a commercial train line with
three different rolling stock.

3. Trajectory/ Train Operation Strategy
Consuming energy
No energy Consumption
Acceleration Cruising Coasting Braking
Max speed
Coasting
speed

4. No coasting control
Train Trajectory Power Graph
Consuming energy No energy Consumption

5. Coasting speed at 144km/h
Train Trajectory Power Graph
Consuming energy No energy Consumption

6. Single Train Simulator (STS)
ST
S
Vehicle: mass,
max speed etc.
Route: station,
gradient etc.
Coasting
control: coasting
speed
Simulation Results:
journey time,
velocity profile,
Energy
consumption etc.
Brute force
Best
Train
Trajectory
Genetic
Algorithm

7. Algorithms
Brute Force: Calculate all the combination of
coasting and max speed to find the optimal
trajectory.
Genetic Algorithm: Search the best
combination of coasting and max speed to
find the optimal trajectory
First Generation
Fitness Function (STS)
Rank the population
according to fitness
result
Create new
generation
Output Final
Result
Reach
generation
limit?
Yes
No
Coasting speed
Max speed
STS
All
Coasting
Speed?
All max
Speed?
Output Final
Result
Yes
Yes
No
No

8. Genetic Algorithm Implementation
Initialisation
 Initialisation includes: variable numbers,
variable constraints, iterations, population
size, routes and vehicles.
 Initialise the programme, so that in the
following testing stage, there is no need to
change the code to tune the parameters of
the algorithm.

9. Genetic Algorithm
 The first generation is randomly generated from the
variable limits
 In this case, coasting speed from range 54km/h
~198km/h; max speed from 110km/h ~ 190km/h
First Generation First Generation
Fitness Function (STS)
Rank the population
according to fitness
result
Create new
generation
Output Final
Result
Reach
generation
limit?
Yes
No

10. Genetic Algorithm
Fitness Function
 Two input variables: journey time and energy consumption.
 A general fitness function to observe the result from
considering only one factor.
 For each vehicle, the fitness function constrains the journey
time to the corresponding timetable time
First Generation
Fitness Function (STS)
Rank the population
according to fitness
result
Create new
generation
Output Final
Result
Reach
generation
limit?
Yes
No

11. Genetic Algorithm
 Combine two variables (coasting velocity and max
speed), journey data (journey time and energy) and
fitness result into a matrix
 Sort the matrix according to fitness result and as a
result, all the other data are also in the right place
Ranking
First Generation
Fitness Function (STS)
Rank the population
according to fitness
result
Create new
generation
Output Final
Result
Reach
generation
limit?
Yes
No

12. Genetic Algorithm
First Generation
Fitness Function (STS)
Rank the population
according to fitness
result
Create new
generation
Output Final
Result
Reach
generation
limit?
Yes
No
1. Elite Children
2. Crossover
3. Mutation
4. New children
New Generation
Pass on
Cross over
Mutation
Mutation
Replace

13. My GA Output
 The Convergence curve of the process
shows the performance of the
algorithm, which plots the best
individual in each generation.
 The table of the final result shows the
fitness function ranking and the
corresponding simulation data
First Generation
Fitness Function (STS)
Rank the population
according to fitness
result
Create new
generation
Output Final
Result
Reach
generation
limit?
Yes
No

14. Case Study
Railway Line: Euston – MK - Rugby Vehicle
 Virgin – Pendolino
 Virgin – Voyager
 London Midlands – Class350
 These three vehicles are the ones that are
currently running on this railway line.

15. Virgin – Pendolino
o Class 390 Pendolino is a type
of electric high-speed train
operated by Virgin Trains
o It is one of the fastest
domestic electric multiple
units operating in Britain
o Its max speed is 225km/h

16. Virgin – Voyager
o The Class221 Super Voyager
is a diesel-electric multiple-
unit express trains
o Currently these trains are
divided between two
operators, Virgin Trains and
Cross Country.
o For the chosen line, the train
is operated by Virgin Trains.
o Its max speed is 200km/h

17. London Midlands - Class350
o The British Rail Class 350 is a
class of electrical multiple unit
on regional express services
o Its max speed is 180 km/h

18. Algorithm Performance
My GA
Pendolino Voyager Class350
Best
Journey
Time
Minimal
Energy
Cost
Best
Journey
Time
Minimal
Energy
Cost
Best
Journey
Time
Minimal
Energy
Cost
Fitness
Result
3217.2 s 875.49
kWh
3174.7 s 423.36
kWh
3220 s 411.82
kWh
Coasting
Speed
(km/h)
190.8 54 194.4 54 190.8 54
Max
Speed
(km/h)
190 110 190 110 190 110
Matlab GA
Pendolino Voyager Class350
Best
Journey
Time
Minimal
Energy
Cost
Best
Journey
Time
Minimal
Energy
Cost
Best
Journey
Time
Minimal
Energy
Cost
Fitness
Result
3217.19 s 875.494
kWh
3174.66 s 423.363
kWh
3220.12 s 411.82
kWh
Coasting
Speed
(km/h)
195.5 54 190 54 190.8 54
Max
Speed
(km/h)
190 110 190 110 190 110

19. Algorithm Comparison
Generation Size: 25
Iteration: 80
 For the same condition above,
both can obtain the optimal
result.
 Both genetic algorithm
converges between 10 to 60
generations.
 Matlab GA toolbox has a better
starting point.

20. Algorithm Performance
My GA
Pendolino Voyager Class350
Best
Journey
Time
Minimal
Energy
Best
Journey
Time
Minimal
Energy
Cost
Best
Journey
Time
Minimal
Energy
Cost
Fitness
Result
3217.2 s 875.49 kWh 3174.7 s 423.36
kWh
3220 s 411.82
kWh
Coasting
Speed
(km/h)
190.8 15 194.4 15 190.8 15
Max Speed
(km/h)
190 110 190 110 190 110
Brute Force
Pendolino Voyager Class350
Best
Journey
Time
Minimal
Energy
Cost
Best
Journey
Time
Minimal
Energy
Cost
Best
Journey
Time
Minimal
Energy
Cost
Fitness
Result
3217.19 s 875.5
kWh
3174.66s 423.36
kWh
3220 s 411.8 kWh
Coasting
Speed
(km/h)
190.8 54 190.8 54 190.8 54
Max
Speed
(km/h)
190 110 190 110 190 110
 The genetic algorithm successfully finds the global optimal.

21. Virgin - Pendolino
 Journey time and energy consumption are equally important (p =
0.5)
 Timetable Time = 63min = 3780s, Energy = 1530.6kWh
 Optimal Journey time is 3778.7s : within1% difference
 Optimal Energy consumption is 1410.8kWh – saving 8.5% energy

22. Virgin - Voyager  Journey time and energy consumption with the same weighting (p
= 0.5)
 Timetable Time = 54min = 3240s, Energy = 1060.7kWh
 Optimal Journey time is 3240.1s : within1% difference
 Optimal Energy consumption is 97.6kWh – saving 10% energy

23. London Midlands
– Class350
 Journey time and energy consumption are equally important (p =
0.5)
 Timetable Time = 57min = 3420s, Energy = 786.2kWh
 Optimal Journey time is 3420.5s : within1% difference
 Optimal Energy consumption is 721.82kWh – saving 8.9% energy

24. Overall Energy Saving
Virgin Trains London Midlands
Pendolino Voyager Class350
Journey time (min) 63 54 57
Energy (kWh) No coasting Coasting No coasting Coasting No coasting Coasting
1530.6 1410.8 1060.7 963.13 786.2 721.8
Energy saving(kWh) 119.8 97.6 64.4
Energy saving% 8.5% 10% 8.9%
Services per year 572 312 3224
Energy cost saving £20,557.68 /year £9,135.36 /year £62,287.68 /year
Total Saving £30,217.2 /year £62,287.68 /year
• 30p per kWh energy cost

25. Conclusions
Driving Strategy
 For one specific railway line, there is one
optimal driving strategy considering only one
factor, time or energy, regardless of the type of
rolling stock.
 When consider two factors having the same
importance, the driving strategy change
accordingly.
 For three different vehicle, changing driving
strategy can save energy while keep the
journey time close to current timetable time or
even save on journey time.
Algorithms
 Brute Force is a very simple but thorough algorithm,
which can definitely obtain the best result.
 However, Brute Force is time consuming and requires
a lot of computing power, which is not suitable for
practical design.
 Genetic Algorithm calculates the optimal in a more
sophisticated and fast manner.
 Its disadvantage is that the result of each time may
not be the same thus the definite optimal may be
missed.
 Using the two algorithm together can overcome the
disadvantages of each algorithm.