Optimization of packing polyhedra in spherical and cylindrical containers

Authors

  • Александр Викторович Панкратов A. N. Podgorny Institute for Mechanical Engineering Problems NAS of Ukraine Dm. Pozharsky 2/10, Kharkiv, 61046, Ukraine https://orcid.org/0000-0002-2958-8923
  • Татьяна Евгеньевна Романова A. N. Podgorny Institute for Mechanical Engineering Problems NAS of Ukraine 2/10 Dm. Pozharsky str., Kharkiv, Ukraine, 61046, Ukraine https://orcid.org/0000-0002-8618-4917
  • Андрей Михайлович Чугай Podgorny Institute for Mechanical engineering problems NAS of Ukraine 2/10 Pozharsky str., Kharkiv, Ukraine, 61046, Ukraine https://orcid.org/0000-0002-4079-5632
  • Юрий Евгеньевич Стоян Podgorny Institute for Mechanical engineering problems NAS of Ukraine 2/10 Pozharsky str., Kharkiv, Ukraine, 61046, Ukraine https://orcid.org/0000-0001-5234-3986

DOI:

https://doi.org/10.15587/1729-4061.2016.60847

Keywords:

packaging, polyhedra, continuous turns, quasi-phi-function, mathematical model, nonlinear optimization

Abstract

The study focuses on the problem of packing a given set of arbitrary polyhedra allowing continuous rotation in a container of a minimum size (a sphere with a minimum radius or a cylinder with a minimum coefficient of homothety). Non-overlapping and containment constraints are described by means of radical-free quasi-phi-functions. This allows building a mathematical model as a nonlinear programming problem with a domain of feasible solutions that is described as a system of inequalities with smooth functions. The proposed solution strategy includes a fast algorithm for generating valid starting points and the COMPOLY-S optimization procedure that reduces the nonlinear programming problem with a large number of variables and a large number of inequalities to a sequence of smaller tasks and fewer non-linear inequalities. The COMPOLY-S procedure significantly reduces the computational cost (time and memory) and allows an efficient use of modern local and global NLP-solvers, such as IPOPT, Baron, LindoGlobal and GloMIQO, for solving nonlinear programming problems.

Author Biographies

Александр Викторович Панкратов, A. N. Podgorny Institute for Mechanical Engineering Problems NAS of Ukraine Dm. Pozharsky 2/10, Kharkiv, 61046

Doctor of Technics, senior scientist

Department for Mathematical Modeling

Татьяна Евгеньевна Романова, A. N. Podgorny Institute for Mechanical Engineering Problems NAS of Ukraine 2/10 Dm. Pozharsky str., Kharkiv, Ukraine, 61046

Doctor of Technics, professor, senior scientist

Department for Mathematical Modeling

Андрей Михайлович Чугай, Podgorny Institute for Mechanical engineering problems NAS of Ukraine 2/10 Pozharsky str., Kharkiv, Ukraine, 61046

PhD, senior science

Department of mathematical modeling and computational methods 

Юрий Евгеньевич Стоян, Podgorny Institute for Mechanical engineering problems NAS of Ukraine 2/10 Pozharsky str., Kharkiv, Ukraine, 61046

Postgraduate student

Department of mathematical modeling and computational methods 

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Published

2016-02-27

How to Cite

Панкратов, А. В., Романова, Т. Е., Чугай, А. М., & Стоян, Ю. Е. (2016). Optimization of packing polyhedra in spherical and cylindrical containers. Eastern-European Journal of Enterprise Technologies, 1(4(79), 39–47. https://doi.org/10.15587/1729-4061.2016.60847

Issue

Vol. 1 No. 4(79) (2016): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2016 Александр Викторович Панкратов, Татьяна Евгеньевна Романова, Андрей Михайлович Чугай, Юрий Евгеньевич Стоян

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