The problem of determination of optimal initial concentrations of catalytic reaction reagents is considered. The mathematical description of the reaction is a system of ordinary differential equations. Restrictions are imposed on the values of concentrations of substances at the initial moment of time. To find a solution to the problem, a genetic algorithm with real coding has been developed, taking into account the physical and chemical meaning of the problem. The algorithm is modified at the stage of initial population filling, crossover and mutation. The developed algorithm takes into account the constraints set on the values of initial concentrations of reagents. The work of the algorithm is tested on the example of the catalytic reaction of benzyl butyl ether synthesis. As a result of numerical experiments the initial concentrations of reagents, at which the highest values of concentrations of target products of the reaction -- benzylbutyl ether and dibenzyl ether -- are provided, have been calculated. The values of concentrations of target products of reaction at other initial compositions of reaction mixture have been calculated. It is shown that the set of initial concentrations of reagents calculated with the help of the algorithm provides the highest values of concentrations of target reaction products.