Next Article in Journal
On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation
Previous Article in Journal
Memetic-Based Biogeography Optimization Model for the Optimal Design of Mechanical Systems
Previous Article in Special Issue
Hybridization and Optimization of Bio and Nature-Inspired Metaheuristic Techniques of Beacon Nodes Scheduling for Localization in Underwater IoT Networks
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Mathematics
Volume 13
Issue 3
10.3390/math13030493
mathematics-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones

by
Oksana Melashenko
1,
Tetyana Romanova
1,2,3,*,
Igor Litvinchev
4,5,*,
Carlos Gustavo Martínez Gomez
4,
Rui Yang
5 and
Bingtao Sun
5
1
A. Pidgorny Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine, Kharkiv 61046, Ukraine
2
Leeds University Business School, University of Leeds, Maurice Keyworth Building, Leeds LS2 9JT, UK
3
Faculty of Computer Science, Kharkiv National University of Radio Electronics, Kharkiv 61166, Ukraine
4
Faculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Monterrey 66455, Mexico
5
College of Mechanical and Electrical Engineering, Pingyang Institute of Intelligent Manufacturing, Wenzhou University, Wenzhou 325035, China
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(3), 493; https://doi.org/10.3390/math13030493
Submission received: 7 December 2024 / Revised: 19 January 2025 / Accepted: 29 January 2025 / Published: 31 January 2025
(This article belongs to the Special Issue Innovations in Optimization and Operations Research)
Versions Notes

Abstract

Packing soft rectangular objects in an optimized convex container is considered. Each soft rectangle can be freely translated and rotated, has a fixed area, and its dimensions can vary in certain limits. The convex container may have prohibited zones where allocation of the objects is not allowed. The soft rectangles must be arranged completely inside the container; mutual intersection and overlapping with prohibited zones is not allowed. The objective is to minimize a certain metric characteristic of the container. The corresponding nonlinear mathematical problem is formulated using the phi-function technique to present non-overlapping and containment conditions. A model-based heuristic is proposed to find reasonable solutions to the problem. Numerical results are provided for triangular, circular, and scaled polygonal containers to validate the model and demonstrate the proposed approach’s efficiency.
Keywords: packing; soft rectangular objects; container with prohibited zones; nonlinear optimization packing; soft rectangular objects; container with prohibited zones; nonlinear optimization

Share and Cite

MDPI and ACS Style

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

AMA Style

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

Chicago/Turabian Style

Melashenko, Oksana, Tetyana Romanova, Igor Litvinchev, Carlos Gustavo Martínez Gomez, Rui Yang, and Bingtao Sun. 2025. "A Model-Based Heuristic for Packing Soft Rotated Rectangles in an Optimized Convex Container with Prohibited Zones" Mathematics 13, no. 3: 493. https://doi.org/10.3390/math13030493

APA Style

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

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop