The aim of this paper is to propose a framework in order to solve the real-world waste collection problem in a city of southern Spain modeled as an Asymmetric Vehicle Routing Problem (AVRP) with side constraints and several variations. In this problem, not only are vehicle capacity and temporal constraints considered but multiple trips are also allowed. Furthermore, two objectives will be considered: the minimization of the total distance and the balance of the working day. Finally, in order to select a single solution among all efficient (or nondominated) solutions, an interactive method is designed using reference points.