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The urban transit routing problem (UTRP) involves the construction of route sets on existing road networks to cater for the transit demand efficiently. This is an NP-hard problem, where the generation of candidate route sets can lead to a number of potential routes being discarded on the grounds of infeasibility. This paper presents a new repair mechanism to complement the existing terminal repair and the makesmall-change operators in dealing with the infeasibility of the candidate route set. When solving the UTRP, the general aim is to determine a set of transit route networks that achieves a minimum total cost for both the passenger and the operator. With this in mind, we propose a differential evolution (DE) algorithm for solving the UTRP with a specific objective of minimizing the average travel time of all served passengers. Computational experiments are performed on the basis of benchmark Mandl's Swiss network. Computational results from the proposed repair mechanism are comparable with the existing repair mechanisms. Furthermore, the combined repair mechanisms of all three operators produced very promising results. In addition, the proposed DE algorithm outperformed most of the published results in the literature.

This paper considers an urban transit network design problem (UTNDP) that deals with construction of an efficient set of transit routes and associated service frequencies on an existing road network. The UTNDP is an NP-hard problem, characterized by a huge search space, multiobjective nature, and multiple constraints in which the evaluation of candidate route sets can be both time consuming and challenging. This paper proposes a hybrid differential evolution with particle swarm optimization (DE-PSO) algorithm to solve the UTNDP, aiming to simultaneously optimize route configuration and service frequency with specific objectives in minimizing both the passengers’ and operators’ costs. Computational experiments are conducted based on the well-known benchmark data of Mandl’s Swiss network and a large dataset of the public transport system of Rivera City, Northern Uruguay. The computational results of the proposed hybrid algorithm improve over the benchmark obtained in most of the previous studies. From the perspective of multiobjective optimization, the proposed hybrid algorithm is able to produce a diverse set of nondominated solutions, given the passengers’ and operators’ costs are conflicting objectives.

In this paper, the urban transit routing problem is addressed by using a real-world urban transit network. Given the road network infrastructure and the demand, the problem consists in designing routes such that the service level as well as the operator cost are optimized. The optimality of the service level is measured in terms of average journey time and the route set length. A differential evolution approach is proposed to solve the problem. An improved sub-route reversal repair mechanism is introduced to deal with the infeasibility of route sets. Computational results on a real network produce solutions that are close to the lower bound values of the passenger and the operator costs. In addition, the proposed algorithm produces approximate Pareto fronts that enable the transit operator to evaluate the trade-off between the passenger and passenger costs.

The urban transit routing problem (UTRP) deals with public transport systems in determining a set of efficient transit routes on existing road networks to meet transit demands. The UTRP is a complex combinatorial optimization problem characterized with a large search space, multi-constraint, and multiobjective nature where the likelihood of generating infeasible route sets is high. In this paper, an improved sub-route reversal repair mechanism is proposed to deal with the infeasibility. A population-based metaheuristic, namely, Differential Evolution (DE) algorithm is then proposed to handle the multiobjective UTRP with the aim of devising an efficient transit route network that optimizes both passengers' and operators' costs. Computational experiments are performed on well-known benchmark instances to evaluate the effectiveness of the proposed repair mechanism and the DE algorithm. The computational results are reported to have better parameter values in most cases when compared to other approaches in the literature.