Comparison of Solution Methods the Maximal Covering Location Problem of Public Spaces for Teenagers in the Urban Environment

The article considers methods of solving the problem of optimal planning of public spaces, based on the approach of network modeling of the urban environment. The problematic of the work, is relevant for many modern cities, and lies in the fact that the urban environment is poorly adapted to provide quality leisure for young people. This leads to various behavioral and social deviations. At the same time, the task of planning the placement of public spaces and their profiling for the needs of young people is not trivial and is complicated by the diversity of possible functions and types of such spaces, as well as the variability of their scale. In addition, the task of choosing locations for leisure public spaces is complicated by the presence of competition, which reduces the overall effectiveness of the system of leisure for teenagers, and modern development imposes significant restrictions on their layout and functional content. The work compares the greedy algorithm and linear programming and draws conclusions about the applicability of the methods to solve the problem of optimal placement of public spaces. It allowed to optimally solve the problem of placement of public spaces under imposed internal and external constraints. The article presents the experimental research of the method and its implementation for St. Petersburg, Russia.