Melashchenko O. Mathematical model and solution method for solving the optimization layout problem of geometric objects considering stretch and shrink transformations.

Українська версія

Thesis for the degree of Doctor of Philosophy (PhD)

State registration number

0825U001318

Thesis Registration Form

0825U001318.pdf

Applicant for

Specialization

  • 113 - Прикладна математика

Specialized Academic Board

PhD 25402

Anatolii Pidhornyi Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine

Essay

The PhD thesis is devoted to the development of mathematical models and solution methods of the optimized layout problems of geometric objects that can change their spatial shape under the pressure of external forces (soft objects), provided that the area/volume preservation of the objects, considering their continuous motions and elasticity transformations (stretching and squeezing). As a contribution of the research, the following scientific results were obtained: new tools of mathematical modeling of placement constraints for the layout problem of 2D&3D soft objects into various shaped containers were developed using the phi-function technique; a general mathematical model of the optimized layout of soft objects was introduced as a nonlinear programming problem and its scenarios were formulated depending on the problem dimensionality, the shape of objects and containers, the form of objective function and the type of elasticity transformation; a method for generating allowable placements of soft objects and a decomposition approach for searching for local extrema of the layout problem of soft objects were developed. Appropriate software has been created, and computational experiments have been conducted.

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Research papers

1. Мелащенко О., Романова Т., Шеховцов С. Компонування м’яких багатокутників в опуклому полігональному контейнері. Міжнародний науково-технічний журнал «Проблеми управління та інформатики». 2024. № 6. С. 24–32. https://doi.org/10.34229/1028-0979-2024-6-2

2. Мелащенко О., Романова Т. Компонування м’яких багатогранників у опуклому контейнері мінімального об’єму. Міжнародний науково-технічний журнал «Проблеми управління та інформатики». 2025. № 1. С. 5–21. https://doi.org/10.34229/1028-0979-2025-1-1

3. Мелащенко О. П., Романова Т. Є., Панкратов О. В., Шеховцов С. Б., Мартінес-Гомес К. Г. Пакування м’яких багатокутників у прямокутній області мінімальної висоти. Кібернетика та комп’ютерні технології. 2024. № 1. С. 5–17. https://doi.org/10.34229/2707-451X.24.1.1

4. Melashenko, O., Romanova, T., Litvinchev, I., Martínez Gomez, C. G., Yang, R., & Sun, B. (2025). A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones. Mathematics, 13(3), 493. https://doi.org/10.3390/math13030493

5. Romanova T, Stoyan Y., Pankratov A., Litvinchev I., Kravchenko O., Duryagina Z., Melashenko O., Chugai A. Optimized packing soft ellipses. Human-Assisted Intelligent Computing/ Modeling, simulations and applications, Eds. Manshahia, Mukhdeep Singh; Litvinchev, I.; Weber, Gerhard-Wilhelm; Thomas, J. Joshua; Vasant, Pandian. IOP ebooks. Bristol, UK: IOP Publishing, 2023. P. 9-1–9- 16. https://doi.org/10.1088/978-0-7503-4801-0

6. Romanova T., Stoian Y., Chuhai A., Yaskov G., Melashenko O. (2023). Fast Heuristic for Particle Packing Problem Smart Technologies in Urban Engineering Lecture Notes in Networks and Systems, P. 119–130. https://doi.org/10.1007/978-3-031-46874-2_11

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Files

Melashenko_diss.pdf

autoreferat-АНОТАЦІЯ_Мелащенко.pdf

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