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Optimization Models for Energy-efficient Railway Timetables
Shuvomoy Das GuptaSystems Control GroupDepartment of Electrical & Computer EngineeringUniversity of Toronto
Outline
• Background• Literature review• Creating a feasible railway timetable• A robust mixed integer optimization model (ACC 2015)• A two-stage linear optimization model (Transportation Research Part B, accepted)• Concluding remarks
Time
Speed
Accelerating
Coasting
Speed Holding
Braking
Power
Time
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--
-
Energy Produced
Regenerative Braking Energy
EnergyConsumed
How a train moves
Platform i
Platform j
Temporal representation of the phases of train t around platform i
• Our goal is to maximize the overlapping time between the acceleration phase of
with the braking phase of
braking
accelerating
accelerating
braking
braking
accelerating
dwelling
dwelling
dwelling
Notation:
accelerating
braking
dwelling
accelerating
braking
dwelling
accelerating
braking
dwelling
accelerating
braking
dwelling
accelerating
braking
dwelling
braking
accelerating
accelerating
braking
braking
accelerating
dwelling
dwelling
dwelling
braking
accelerating
dwelling
braking
accelerating
dwelling
= The temporally closest train of t to the right
= The temporally closest train of t to the left
= The temporally closest train of t =
or
=
accelerating
braking
dwelling
braking
accelerating
dwelling
(exclusively)
Train
Platform
Braking
Dwelling
Accelerating
Time
Speed
= Duration of braking phase of train t during arrival at platform i
= Duration of accelerating phase of train t during departure from platform i
Known:
Unknown:
= Start time of the braking phase of train t during arrival at platform i
= End time of the accelerating phase of train t during departure from platform i
}
Decision Variables
Train
Relevant event times of a train around a platform
}
Uncertain
Power
Time
Characterization of suitable train pairs
Power
Time