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This paper examines a special class of continuous maximum coverage problems. The covering objects are ellipses, with circles considered as a particular case. The objective function is defined as the total area of the covering objects extending beyond the coverage region. Additionally, a bicriteria optimization problem is considered, where the second criterion accounts for the total area of intersections between ellipses and circles. The problem is formulated as a nonlinear optimization task. The properties of the objective function are analyzed, and its evaluation is implemented using the Shapely library in Python. For local optimization, a barrier-modified version of the BFGS method is applied. The effectiveness of the proposed approach is demonstrated through test problems, and potential practical applications of the developed model are discussed.

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Modeling and Optimization of Region Coverage with Variable-Parameter Ellipses

  • 章节

  • 发表日期：

    2026年

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  • Sergiy Yakovlev,
  • Sergiy Shekhovtsov,
  • Lyudmyla Kirichenko,
  • Olha Matsyi,
  • Oksana Pichugina,
  • Dmytro Podzeha

摘要

This paper examines a special class of continuous maximum coverage problems. The covering objects are ellipses, with circles considered as a particular case. The objective function is defined as the total area of the covering objects extending beyond the coverage region. Additionally, a bicriteria optimization problem is considered, where the second criterion accounts for the total area of intersections between ellipses and circles. The problem is formulated as a nonlinear optimization task. The properties of the objective function are analyzed, and its evaluation is implemented using the Shapely library in Python. For local optimization, a barrier-modified version of the BFGS method is applied. The effectiveness of the proposed approach is demonstrated through test problems, and potential practical applications of the developed model are discussed.