We have recently created a kinetic model that reproduces the dynamics of exocytosis with high accuracy. The reconstruction necessitated a search, in a multi-dimensional parameter space, for 37 parameters that described the system, with no assurance that the parameters, which reconstructed the observations, are a unique set. In the present study, a Genetic Algorithm (GA) was used for a thorough search in the unknown parameter space, using a strategy of gradual increase of the complexity of the analyzed input data. Upon systematic incorporation of one to four measurable parameters, used as input signals for the analysis, the constraint set on the GA search imposed the convergence of the free parameters into a single narrow range. The mean values for each adjustable parameter represent a minimum for the fitness function in the multi-dimensional parameter space. The GA search demonstrates that the parameters that control the kinetics of exocytosis are the rate constants of the steps downstream to synaptotagmin binding, and that the equilibrium constant of the binding of calcium to Munc13 controls the calcium-dependent priming process. Thus, the systematic use of the GA creates a link between specific reactions in the process of exocytosis and experimental phenotypes.