Methods and algorithms for solving dynamic optimal set partitioning problems with subset center placement and integral constraints
DOI:
https://doi.org/10.34185/1562-9945-3-164-2026-16Keywords:
optimal partitioning, center placement, integral constraints, logistics problems, dynamic models, spatial zoning, resource allocation, numerical modelingAbstract
The paper presents an approach to solving solving dynamic optimal set partitioning problems with subset center placement and integral constraints. The considered class of problems arises in numerous applied contexts, including logistics, spatial resource allocation, and territorial zoning, where model parameters vary over time.
The proposed approach is based on a mathematical formalization of optimal set partitioning problems that accounts for the temporal dynamics of density and provides for the simultaneous optimization of the partition structure and the locations of subset centers. Integral constraints are interpreted as restrictions on generalized characteristics of subsets and significantly influence the properties of optimal solutions.
The primary focus is placed on the theoretical substantiation of the model, the analysis of problem properties, and the construction of a mathematical solution algorithm. The obtained results demonstrate the consistency of the proposed approach with classical optimization models and confirm its suitability for describing dynamic processes in optimal set partitioning problems.
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