A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids

Author(s)

Birgin, E. G. ^[1] ; Lobato, R. D. ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, Dept Comp Sci, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Inst Math Stat & Sci Comp, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: European Journal of Operational Research; v. 272, n. 2, p. 447-464, JAN 16 2019.
• Web of Science Citations: 1

Abstract

The problem of packing ellipsoids in the three-dimensional space is considered in the present work. The proposed approach combines heuristic techniques with the resolution of recently introduced nonlinear programming models in order to construct solutions with a large number of ellipsoids. The introduced approach is able to pack identical and non-identical ellipsoids within a variety of containers. Moreover, it allows the inclusion of additional positioning constraints. This fact makes the proposed approach suitable for constructing large-scale solutions with specific positioning constraints in which density may not be the main issue. Numerical experiments illustrate that the introduced approach delivers good quality solutions with a computational cost that scales linearly with the number of ellipsoids; and solutions with more than a million ellipsoids are exhibited. (C) 2018 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 17/05198-4 - Advanced nondifferentiable optimization techniques for hard structured optimization problems
• Grantee: Rafael Durbano Lobato
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/05475-7 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 15/18053-9 - Study and implementation of deterministic methods for global optimization of nonlinear programming problems
• Grantee: Rafael Durbano Lobato
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science
• Grantee: Carlos Eduardo Ferreira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 12/23916-8 - Ellipsoid packing
• Grantee: Rafael Durbano Lobato
• Support Opportunities: Scholarships in Brazil - Doctorate