This work aims at optimizing a public transportation network and its maintenance. In particular it focuses on determining routes for replacement services and adjusting headways in case of scheduled shutdowns of subway lines. A simulation-based two-layer optimization approach is proposed to solve the problem.
Firstly, a genetic algorithm is used to generate transportation network solutions, consisting of routes for new bus lines and headways for all lines. The solutions are then evaluated by a discrete event simulation model that particularly simulates the passenger flow.
The transportation network and maintenance optimization research is based on the recent case of the renewal Vienna’s oldest subway line. For that purpose, large segments of the line are successively closed for several months.
Since many passengers are affected by subway shutdowns, appropriate measures need to be planned to limit the negative effects. These measures include the establishment of replacement services via new bus lines and headway adjustments (within certain bounds) of the existing lines. Headways need to be adapted to account for any changes in the passenger flow due to the disruption.
The objective is to minimize the mean travel time of passengers that use the public transport and are directly affected by the disruption.
Transportation network optimization model
The transportation network considered in the discrete event simulation model consists of subway, tram, bus, and train lines. The fleet size is known and used as a constraint. To establish replacement services during maintenance, the bus fleet needs to be larger than usual.
The features of the transport network optimization model are as such:
- The creation of passengers is driven by a time-dependent Poisson process.
- Passenger transfer times and vehicle turning maneuver times are triangular distributed.
- The vehicle travel times are direction-dependent (log-normal distribution for subways, triangular for all other means of transportation).
To reduce the scale of the simulation model, only subway passengers that are affected by the disruption are simulated. Passengers are assumed to be affected by the disruption if their original shortest path in the undisrupted network cannot be traversed anymore.
The approach that combines the generic algorithm and transport network optimization model reduces the average travel time of the passenger affected by 5% (west and center instance) to 9% (north instance). One of the replacement lines in all three instances covered the section disrupted during maintenance and reached beyond to improve connectivity.
Additional replacement lines further improved the solution quality by reaching out in other directions and creating additional connections to important crossing stations.