During the atmospheric reentry of a space vehicle the heat flux at the body surface is so large that one has to solve a very complex heat protection problem for the space vehicle surface. One of the possible passive ways to reduce the heat flux at the body surface is to optimize the reentry trajectory parameters to minimize of the heat flux integral. The purpose of this report is to solve the optimization problem of the reentry trajectory into the Earth atmosphere with respect to the heat flux integral at the stagnation point of 3D blunt body. This problem is solved by means of the floating-point Genetic Algorithms (GA) via calculation of the heat flux evolution along the reentry trajectory in the framework of the non-equili- brium multicomponent thin viscous shock layer model (TVSL). The solution of this problem by Genetic Algorithms is interesting from both practical applicative and methodological points of view, because it is a very good example to demonstrate the GA efficiency for the solution of an optimization problem with a number of complex non-linear constraints. The influence of the GA parameters as well as the body geometry, the body surface catalytic activity and certain physical constraints on the optimum solution and on the algorithm arithmetical cost efficiency is investigated
