Packing circles within ellipses

Author(s)

Birgin, Ernesto G. ^[1] ; Bustamante, Luis Henrique ^[1] ; Callisaya, Hector Flores ^[2] ; Martinez, Jose Mario ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Comp Sci, Inst Math & Stat, Sao Paulo - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Inst Math Stat & Sci Comp, Campinas, SP - Brazil

• Document type: Journal article
• Source: International Transactions in Operational Research; v. 20, n. 3, p. 365-389, MAY 2013.
• Web of Science Citations: 7

Abstract

The problem of packing circles within ellipses is considered in the present paper. A new ellipse-based system of coordinates is introduced by means of which a closed formula to compute the distance of an arbitrary point to the boundary of an ellipse exists. Nonlinear programming models for some variants of 2D and 3D packing problems involving circular items and elliptical objects are given. The resulting models are medium-sized highly challenging nonlinear programming problems for which a global solution is sought. For this purpose, multistart strategies are carefully and thoroughly explored. Numerical experiments are exhibited. (AU)

• FAPESP's process: 10/10133-0 - Cutting, packing, lot-sizing and scheduling problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 06/53768-0 - Computational methods of optimization
• Grantee: José Mário Martinez Perez
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 09/10241-0 - Theory and software in computational methods for optimization
• Grantee: Ernesto Julián Goldberg Birgin
• Support Opportunities: Regular Research Grants