In this paper, we consider the problem of estimating the vector of exponential regression parameters using the least squares method. When solving the resulting extreme problem, we have to deal with a large number of local extremes, and the search for a global extreme becomes more complicated. To find the global extremum a genetic algorithm is chosen. This method have an iterative structure, where each iteration deal with a generation of individuals. A multidimensional normal distribution is used for modeling, and during random search, the covariance matrix evolves from iteration to iteration. The presented problem is relevant and in practice is quite common, for example, when describing the decay process in nuclear physics, and in mathematics, the solution of linear differential equations has the form of a linear combination of exponents, which leads to an exponential model. This article provides numerical example that confirm the effectiveness of the method used. The results are presented in figures and tabl