Recoverable Robustness in Shunting and Timetabling

In practical optimization problems, disturbances to a given instance are unavoidable due to unpredictable events which can occur when the system is running. In order to face these situations, many approaches have been proposed during the last years in the area of robust optimization. The basic idea of

robustness

is to provide a solution which is able to keep feasibility even if the input instance is disturbed, at the cost of optimality. However, the notion of robustness in every day life is much broader than that pursued in the area of robust optimization so far. In fact, robustness is not always suitable unless some

recovery strategies

are introduced. Recovery strategies are some capabilities that can be used when disturbing events occur, in order to keep the feasibility of the pre-computed solution. This suggests to study robustness and recoverability in a unified framework. Recently, a first tentative of unifying the notions of robustness and recoverability into a new integrated notion of

recoverable robustness

has been done in the context of railway optimization.

In this paper, we review the recent algorithmic results achieved within the recoverable robustness model in order to evaluate the effectiveness of this model. To this aim, we concentrate our attention on two problems arising in the area of railway optimization: the

shunting

problem and the

timetabling

problem. The former problem regards the reordering of freight train cars over hump yards while the latter one consists in finding passenger train timetables in order to minimize the overall passengers traveling time. We also report on a generalization of recoverable robustness called

multi-stage recoverable robustness

which aims to extend recoverable robustness when multiple recovery phases are required.