The price of symmetric line plans in the Parametric City.

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. We prove that the symmetry gap is 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. • Optimal line plans in an entirely symmetric city model are not symmetric by default. • Line planning on an idealized infrastructure model to represent generic cities. • Analytical examination of the deviation from the optimum by symmetry assumption. • While infinitely large in practice, the symmetry gap is provably small in practice. • Development of an approximation algorithm utilizing the symmetric structure. [ABSTRACT FROM AUTHOR]