A multiobjective bilevel approach based on global-best harmony search for defining optimal routes and frequencies for bus rapid transit systems

The operation of a Bus Rapid Transit System (BRTS) requires solving complex design problems, including the selection of routes and the corresponding frequency of service, among others. One challenge is the large number of potential solutions, with multiple routes having many frequency options. At least, the design should seek to minimize the total time spend by users in the system as well as the operational cost to pursue sustainability and profitability. The literature includes a wide variety of approaches to solve this Transit Network Design and Frequency Setting Problem (TNDFSP) for a BRTS. This study proposes a single framework that simultaneously considers restrictions and objectives of the users and the operator of the system. A Multi-objective Global-Best Harmony Search (MOGBHS) heuristic algorithm was implemented and tested successfully. The algorithm is based on three main components: 1) a Global-Best Harmony Search as the heuristic optimization strategy, 2) ordering of non-dominated solutions as a multi-objective optimization strategy, and 3) simulation of discrete events to evaluate solutions. A bi-level implementation of MOGBHS was adopted. At the external level, the algorithm searched the best configuration of routes, while at the internal level, the algorithm searched the best frequency for a solution for a specific route. Experiments were performed using a simulation model of an actual BRTS located in Pereira, Colombia, known as Megabus. Routes and frequencies were searched for this BRTS by minimizing waste bus capacities (operation costs) and minimizing users’ travel time (maximizing satisfaction). Results using the proposed algorithm where superior to those obtained using comparable alternatives, including NSGA-II and MOEA/D