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• A novel healthcare waste location-routing problem is developed with a new perspective in healthcare logistics networks. • A stochastic essence for the emission of contamination is considered. • The management of medical wastes in Coronavirus Disease 2019 is focused. • A real case study is modeled to manage the logistics of infectious and non-infectious healthcare wastes. • A Multi-Objective Water-Flow like Algorithm with novel operators is developed and compared with the others. This paper presents a novel healthcare waste location-routing problem by concentrating on a new perspective in healthcare logistics networks. In this problem, there are healthcare, treatment, and disposal centers. Locations of healthcare centers are known, however, it is required to select appropriate locations for treatment, recycling, and disposal centers. Healthcare wastes are divided into infectious and non-infectious wastes. Since a great volume of healthcare wastes are infectious, the emission of contamination can have obnoxious impacts on the environment. The proposed problem considers a stochastic essence for the emission of contamination which depends on the transferring times. In this respect, transferring times between healthcare and treatment centers have been considered as normal random variables. As transferring time increases, it is more likely for the contamination to spread. Having visited a treatment center, infectious wastes are sterilized and they will no longer be harmful to the environment. This research develops a bi-objective mixed-integer mathematical formulation to tackle this problem. The objectives of this model are minimization of total costs and emission of contamination, simultaneously. Complexity of the proposed problem led the researchers to another contribution. This study also develops a Multi-Objective Water-Flow like Algorithm (MOWFA), which is a meta -heuristic, to solve the problem. This algorithm uses a procedure based on the Analytical Hierarchy Process (AHP) to rank the non-dominated solutions in the archive set. By means of a developed mating operator, the MOWFA utilizes the best ranked solutions of the archive in order to obtain high quality offspring. Two neighborhood operators have been designed for the MOWFA as the local search methods. Extensive computational experiments have been conducted to evaluate the effectiveness of the MOWFA on several test problems compared with other meta -heuristics, namely the Multi-Objective Imperialist Competitive Algorithm (MOICA) and Multi-Objective Simulated Annealing (MOSA). These experiments also include a real healthcare waste logistic network in Iran. The computational experiments demonstrate that our proposed algorithm prevails these algorithms in terms of some well-known performance evaluation measures. [ABSTRACT FROM AUTHOR]