Sahelian transhumance is a type of socio-economic and environmental pastoral mobility. It involves the movement of herds from their terroir of origin (i.e., their original pastures) to one or more host terroir, followed by a return to the terroir of origin. According to certain pastoralists, the mobility of herds is planned to prevent environmental degradation, given the continuous dependence of these herds on their environment. However, these herds emit Greenhouse Gases (GHGs) in the areas they cross. Given that GHGs contribute to global warming, our long-term objective is to quantify the GHGs emitted by Sahelian herds. The determination of these herds' GHG emissions requires: (1) the artificial replication of the transhumance, and (2) precise knowledge of the space used during their transhumance. This article presents the design of an artificial replication of this transhumance through an agent-based model called MSTRANS. MSTRANS determines the space used by transhumant herds, based on the decision-making process of Sahelian transhumants. MSTRANS integrates a constrained multi-objective optimization problem and algorithms into an agent-based model. The constrained multi-objective optimization problem encapsulates the rationality and adaptability of pastoral strategies. Interactions between transhumants and their socio-economic network are modelled using algorithms and diffusion processes within the multi-objective optimization problem. The dynamics of pastoral resources are formalized at various spatio-temporal scales using equations that are integrated into the algorithms. The results of MSTRANS have been validated using GPS data collected from transhumant herds in Senegal. The MSTRANS results highlight the relevance of integrated models and constrained multi-objective optimization for modelling and monitoring the movement of transhumant herds in the Sahel. We can state that specialists in calculating greenhouse gas emissions now have a reproducible and reusable