عنوان مقاله [English]
Recently, concerns have been raised about the environmental and social impacts of commercial activities. Also, most papers on the design of the supply chain network, focus on economic performance. Recently, some studies have considered environmental and social dimensions. There are still some gaps in modelling social impacts along with environmental and economic impacts. In this study, a multi-objective probabilistic model for designing a sustainable closed-loop logistics network is presented under uncertainty. The goals of this model consist of cost reduction, increasing social impact and decreasing environmental impacts. Then the model was solved not only using well-known Metaheuristic algorithms including genetic algorithm and Simulated Annealing (SA) algorithm, but also new whale optimization algorithm along with its improved combination method was used. Performance of algorithms was compared through examining different experiments and designed test problems. They compared in different situations and some important criteria. The results show the superiority of the whale optimization algorithm.