- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Advances in Operations Research
Volume 2012 (2012), Article ID 346358, 26 pages
Phi-Functions for 2D Objects Formed by Line Segments and Circular Arcs
1Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA
2Department of Mathematical Modeling, Institute for Mechanical Engineering Problems of The National Academy of Sciences of Ukraine, Kharkov, Ukraine
Received 21 October 2011; Revised 30 January 2012; Accepted 31 January 2012
Academic Editor: Ching-Jong Liao
Copyright © 2012 N. Chernov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- E. G. Birgin, J. M. Martínez, F. H. Nishihara, and D. P. Ronconi, “Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization,” Computers & Operations Research, vol. 33, no. 12, pp. 3535–3548, 2006.
- A. M. Gomes and J. F. Oliveira, “Solving irregular strip packing problems by hybridising simulated annealing and linear programming,” European Journal of Operational Research, vol. 171, pp. 811–829, 2006.
- V. J. Milenkovic and K. Daniels, “Translational polygon containment and minimal enclosure using mathematical programming,” International Transactions in Operational Research, vol. 6, no. 5, pp. 525–554, 1999.
- J. A. Bennell and J. F. Oliveira, “The geometry of nesting problems: a tutorial,” European Journal of Operational Research, vol. 184, no. 2, pp. 397–415, 2008.
- G. Wäscher, H. Haußner, and H. Schumann, “An improved typology of cutting and packing problems,” European Journal of Operational Research, vol. 183, pp. 1109–1130, 2007.
- E. Burke, R. Hellier, G. Kendall, and G. Whitwell, “A new bottom-left-fill heuristic algorithm for the two-dimensional irregular packing problem,” Operations Research, vol. 54, no. 3, pp. 587–601, 2006.
- V. Milenkovic and E. Sacks, “Two approximate Minkowski sum algorithms,” International Journal of Computational Geometry & Applications, vol. 20, no. 4, pp. 485–509, 2010.
- V. J. Milenkovic, “Rotational polygon overlap minimization and compaction,” Computational Geometry, vol. 10, no. 4, pp. 305–318, 1998.
- V. J. Milenkovic, “Rotational polygon containment and minimum enclosure using only robust 2D constructions,” Computational Geometry, vol. 13, no. 1, pp. 3–19, 1999.
- E. Burke, R. Hellier, G. Kendall, and G. Whitwell, “Irregular packing using the line and arc no-fit polygon,” Operations Research, vol. 58, pp. 948–970, 2010.
- J. Bennell, G. Scheithauer, Y. Stoyan, and T. Romanova, “Tools of mathematical modeling of arbitrary object packing problems,” Annals of Operations Research, vol. 179, pp. 343–368, 2010.
- Y. Stoyan, G. Scheithauer, N. Gil, and T. Romanova, “Φ-functions for complex 2D-objects,” 4OR. Quarterly Journal of the Belgian, French and Italian Operations Research Societies, vol. 2, no. 1, pp. 69–84, 2004.
- Yu. Stoyan, J. Terno, G. Scheithauer, N. Gil, and T. Romanova, “Phi-functions for primary 2D-objects,” Studia Informatica Universalis, vol. 2, pp. 1–32.
- N. Chernov, Yu. Stoyan, and T. Romanova, “Mathematical model and efficient algorithms for object packing problem,” Computational Geometry, vol. 43, no. 5, pp. 535–553, 2010.
- Y. G. Stoyan and A. Chugay, “Packing cylinders and rectangular parallelepipeds with distances between them,” European Journal of Operational Research, vol. 197, pp. 446–455, 2008.
- T. Romanova, G. Scheithauer, and A. Krivulya, “Covering a polygonal region by rectangles,” Computational Optimization and Applications, vol. 48, no. 3, pp. 675–695, 2011.
- A. Wächter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Mathematical Programming, vol. 106, no. 1, pp. 25–57, 2006.
- H. Minkovski, “Dichteste gitterförmige Lagerung kongruenter Körper,” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, pp. 311–355, 1904.