Currently, the conditions for admission to higher education in Russia can provide centralization of the procedure for competitive selection of applicants across the country to increase the transparency and openness of this process in relation to applicants, and to reduce the costs of universities for the organization of the admission campaign. The core of such centralization could be the federal information system for USE and admission, but at present there are no algorithms for competitive selection. The paper proposes a modification of the existing mathematical model for the organization of centralized competition for the enrollment to higher education institution in Russia, that is a multi criteria task of optimizing the criterion function of educational institutions of higher education (the higher education system as a whole), corresponding to the enrollment of applicants with the highest score according to the results of the entrance examination, ready to continue education , and the target functions of applicants, consisting in the enrollment to the most interesting (top priority) speciality or major training program. To rank applicants, a modification of the evaluation function is suggested, including a new term intended for the ordering of applicants with the same score based on the results of entrance examinations and evaluation of individual achievements. Also, a heuristic iterative algorithm for solving the formulated multicriteria optimization problem is provided based on the search for a solution for one university under condition of indicating a number of specialties and training program in the applicant’s application for admission. The speed of the algorithm is considered as logarithmic by means of a specially developed program. It is shown that the algorithm is applicable for calculating the competitive all-Russian situation in terms of execution time.