An improved solution methodology for the urban transit routing problem

Abstract

An improved solution methodology is proposed in this paper for the urban transit routing problem (UTRP). This methodology includes a procedure for the generation of improved initial solutions as well as improved metaheuristic search approaches, involving the use of hyperheuristics to manage search operators in both trajectory-based and population-based metaheuristics. The UTRP variant considered in this paper is that of deciding upon efficient bus transit routes. The design criteria embedded in our UTRP model are the simultaneous minimisation of the expected average passenger travel time and minimisation of the system operator’s cost (measuring the latter as the sum total of all route lengths in the system). The model takes as input an origin–destination demand matrix for a pre-specified set of bus stops, along with an underlying road network structure, and returns as output a set of bus route trade-off solutions. The decision maker can then select one of these route sets subjectively, based on the desired degree of trade-off between the aforementioned transit system design criteria. This bi-objective minimisation problem is solved approximately in three distinct stages — a solution initialisation stage, an intermediate analysis stage, and an iterative metaheuristic search stage during which high-quality trade-off solutions are sought. A novel procedure is introduced for the solution initialisation stage, aimed at effectively generating high-quality initial feasible solutions. Two metaheuristics are implemented to solve instances of the problem, namely a dominance-based multi-objective simulated annealing algorithm and an improved non-dominated sorting genetic algorithm, each equipped with a hyperheuristic capable of managing the perturbation operators employed. Various novel operators are proposed for these metaheuristics, of which the most noteworthy take into account the demand of passengers.