Modeling of territorial community formation as a graph partitioning problem

Abstract

The territorial community formation process as a graph partitioning problem is considered. The main goal of territorial community formation is to reduce the budget and save public funds. The formation process of communities where settlements, which make up the community, have an administrative building, healthcare institution, high school, kindergarten is investigated. Additional restrictions are imposed on these indicators for uniform distribution of the region's population and community incomes. The minimum distance from the community center to other settlements is taken as a function of the goal of territorial community formation. The mathematical model of this problem, which is a modified graph partitioning problem is developed. The modification lies in using specific constraints arising from the problem statement. The notion of independence of communities and adjacency of individual councils is introduced to build efficient territorial community formation algorithms. This allowed us to formalize the problem from a mathematical point of view. In turn, this made it possible to develop an algorithm for solving this problem, which is to use genetic algorithms to solve the existing problem. The developed model and algorithm of territorial community formation are tested. According to the expert group on the TC formation, the resulting solution showed satisfactory results.