Software development for solving the dynamic problem of optimal set partitioning with determination of the coordinates of their centers

This paper addresses the software implementation of an algorithm for solving the dynamic problem of optimal set partitioning with determination of subset center coordinates. The problem involves finding a partition structure that minimizes a given objective functional while accounting for dynamic changes in input parameters and adaptive updating of center coordinates. The proposed model integrates optimal set partitioning theory and methods for solving systems of differential equations to track parameter changes over time. Developed software provides numerical simulation of the process, interactive visualization, and analysis of results. Numerical experiments demonstrate the effectiveness of the approach and improvements in the objective functional compared to classical problems with fixed centers. The proposed approach has practical significance for spatial resource allocation, logistics, planning, and other fields