The Price of Symmetric Line Plans in the Parametric City

Abstract

We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. The symmetry gap is provably small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations.

Line Planning in Public Transport: Bypassing Line Pool Generation

“…See [3,24] for further results on the complexity of the problem using terminal stations in path networks representing Istanbul Metrobüs and trees representing the Quito Trolebús. In [18], an integer programming formulation which includes line planning on all lines is presented and applied to small instances while in [17], line planning on all circular lines in a specific class of graphs is considered.…”