Computation of Optimal Spacing and Density of Bus Rapid Transit Stations Using Evolutionary Algorithms

In this research, a feasible mechanism is developed to determine the optimum number of bus rapid transit (BRT) stations as well as their respective locations along the service corridor. To accomplish this, a mathematical model is developed and optimized by using three different evolutionary algorithms, namely particle swarm optimization (PSO), genetic algorithm (GA), and differential evolution (DE), and the results are compared. The total cost function is composed of two main costs namely the operator’s cost, i.e., related to costs on service provider’s end, and the user’s cost, i.e., related to costs on commuters’ end. A functional numerical example with the commuters’ demand is worked out by minimizing the cost function, which demonstrates the applicability of the framework. In our case study, PSO outclassed GA and DE on the basis of convergence rate. Since our work has proved the robustness of PSO as compared to GA and DE, we conducted our sensitivity analysis keeping PSO as our benchmark algorithm to study the influence of various parameters on the optimal cost. The computational experiments reveal that the optimal cost is substantially affected by the variations in the commuters’ demand, commuters’ walking speed, and value of the users’ access and in-vehicle time. On the contrary, the acceleration/deceleration delays at a bus station, bus operating cost, and headway have an inconsiderable impact on the optimal cost.