Hybridization of NSGA-II and MILP for optimization of the location of electric-scooters sharing-stations

Abstract

A crucial aspect of the proper functioning of bikes and electric scooters’ sharing systems is the correct location and dimensioning of the sharing stations. The resolution of the previous problem is carried out based on the maximization of coverage or the minimization of costs, but the two objectives are not usually treated at the same time. In this work, we propose a method based on the hybridization of the popular Elitist Non-Dominated Sorting Genetic Algorithm(NSGA- II) with a Mixed-Integer Linear Programming (MILP)model to approximate the Pareto Frontier of the problem. This allows the decision-maker a greater understanding of the range of possible options. The NSGA-II plays the role of an outer block that deals with the selection and sizing of each of sharing stations. The MILP model is an inner block that calculates the associated coverage of that solution. The schema was compared with an adaptative-weighting algorithm, reaching the hybridization of NSGA-II and MILP a better coverage of the Pareto Frontier.