Medical wastes is now a major concern of the world community and more particularly that of Moroccans. Indeed, these wastes, classified as hazardous products, are the source of serious infections, contamination of groundwater and air pollution. Through this paper, we encouraged the use of ridesharing to cope with the risks and costs arising from the logistics of these medical wastes. Thus, we have proposed a mathematical model that governs the multi-objective nature of this logistics and the various constraints associated with it. Since the exact approach had difficulties in large instances, we proposed the Genetic Algorithm and Evolution Strategy as metaheuristic to solve the model. The Evolution Strategy showed its efficiency and stability and therefore we have demonstrated through this metaheuristic the possibility of a compromise between the main objectives of our model.