The grid based approach, a fast local evaluation technique for line planning

Line planning is one of the important steps in the public transit planning process. It is a difficult combinatorial problem with an enormous search space. For networks from practice, which are typically large and have more complex constraints, it takes an unreasonable amount of time to find good solutions with the current methods. When the objective is to minimize passenger travel time, most of the calculation time is spent on solving the passenger routing sub-problem. This paper proposes a local evaluation technique to significantly speed up this most critical component. A change is assumed to have its biggest impact on passengers already travelling close to the change. This idea is implemented by putting a grid over the network and only re-evaluating the part of the network around the change, while still taking into account all passengers. This results in a smaller computation time for each passenger routing, with only a limited loss of quality, and it allows more iterations. On a number of benchmark instances, the results obtained by the grid approach are compared to the same algorithm without any local evaluation. The grid approach is significantly faster and allows to perform 5–20 times more evaluations per second, while having a minimal loss of quality per evaluation. When the available calculation time is limited, the grid based approach obtains the best solutions. On the larger benchmark instances, the grid based approach can use more complex neighborhoods resulting in even better solutions. The method is very flexible and can be integrated in many line planning algorithms and probably even in algorithms for other network problems.