1. A method for exploiting a geological reservoir according to an exploitation scheme defined using a reservoir model comprising a meshing associated with at least one parameter of the reservoir, the reservoir being passed through by at least one production well and at least one injection well for the injection of at least one fluid into the reservoir, with dynamic data being acquired during exploitation, the method comprising: a) generating a first reservoir model for which a breakthrough time is estimated by the first reservoir model which is representative of the breakthrough time measured for the reservoir, the breakthrough time being a time elapsed at which the injected fluid is detected at the at least one production well; b) the first reservoir model is implemented by execution of program instructions on a computer and is constructed by modifying the first reservoir model by steps of: i) determining an objective function that measures a difference between acquired dynamic data and dynamic data simulated by the first reservoir model and a flow simulator; ii) reiterating step i) to minimize the objective function after modification of the first reservoir model; c) determining an optimal exploitation scheme for the reservoir by simulating exploitation of the reservoir by the first reservoir model and of the flow simulator; and d) exploiting the reservoir by implementing the optimal exploitation scheme; and wherein the first reservoir model is generated by: (1) determining a mathematical relationship between the breakthrough time and a flow distance according to a shortest path between the injection well and the production well; (2) randomly generating at least one initial reservoir model; (3) for the initial reservoir model, determining the flow distance according to a shortest path between the injection well and the production well by using a shortest path computation algorithm which is constrained by the parameters of the initial reservoir model; (4) estimating the breakthrough time for the initial reservoir model by using the flow distance and the mathematical relationship; (5) the estimated breakthrough time is compared to the measured breakthrough time; and (6) determining whether the initial reservoir model is representative with the comparison; and wherein the initial reservoir model is selected as the first reservoir model and, if not, steps (2) to (5) are reiterated.