A route set construction algorithm for the transit network design problem

The transit network design problem (TNDP) aims to determine a set of bus routes for a public transportation system, which must be convenient from the viewpoints of both users (people who use public transportation) and operators (companies who own the resources to give the service). This article presents a constructive algorithm for the TNDP. It is specially designed to produce a set of routes that fulfils demand covering constraints, while taking into account the interests of both users and operators. Its general structure is inspired in the Route Generation Algorithm (RGA) of Baaj and Mahmassani, where its original expansion of routes by inserting individual vertices is replaced by a strategy of insertion of pairs of vertices. The algorithm proposed, called Pair Insertion Algorithm (PIA) can be used to generate initial solutions for a local improvement or evolutionary algorithm, as well as to complete an unfeasible solution with respect to demand covering constraints. Numerical results comparing PIA with RGA over a real test case show that both algorithms produce solutions with similar quality from the users viewpoint (in terms of in-vehicle travel time), while the former produces better solutions from the operators viewpoint (in terms of number of routes and total route duration) and requires a higher execution time. Since the TNDP arises in a context of strategic planning, a solution that reduces the operation cost of the system is highly desirable, even though it takes more time to be computed. The experimental study of the proposed algorithm also shows its ability to produce diverse solutions in both decision and objective spaces; this is a useful property when looking at the use of PIA as a subroutine in the context of another algorithm such as metaheuristics, in particular for a multi-objective problem like TNDP.