Differential Evolution for Urban Transit Routing Problem

Abstract

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.

Hybrid Differential Evolution‐Particle Swarm Optimization Algorithm for Multiobjective Urban Transit Network Design Problem with Homogeneous Buses

“…e process is repeated with the target and noisy random vector exchanged to yield the second trial vector (see Figure 4). Note that for each pair of vectors, it is required to generate a new crossover mask [40]. It is advisable to ensure that the trial vectors are feasible; otherwise, attempt to repair the infeasible trial vectors with iSRR.…”

Differential evolution with improved sub-route reversal repair mechanism for multiobjective urban transit routing problem

“…The DE algorithm proposed in this paper is based on the algorithm proposed in [7]. The algorithm is extended to solve the multiobjective UTRP with the aim of minimizing the average travel time of the passengers and the total route set length of the operator.…”

“…The algorithm is extended to solve the multiobjective UTRP with the aim of minimizing the average travel time of the passengers and the total route set length of the operator. In addition, we also provide an improvement made on the sub-route reversal repair mechanism, first introduced in [7], as a stand-alone operator in handling the infeasible route sets during the execution of the proposed DE algorithm. The proposed DE algorithm evaluates the trade-off levels between the passengers and the operator costs whereby approximated Pareto optimal sets are produced for consideration by the decision maker.…”

“…Most recently, [7] proposed a DE to solve the single objective UTRP with the aim of minimizing the average travel time of all served passengers. It is the first application of DE in the domain of UTNDP.…”

“…On the other hand, infeasible route sets are characterized with at least one missing node, or some of the route(s) is/are not connected with the rest of the framework. The repair mechanisms currently available in the literature are the Make-Small-Change (MSC) by [14], the Terminal Repair (TR) by [27], and the Sub-Route Reversal (SRR) by [7]. However, all these repair mechanisms are still far from being efficient.…”