A balanced layout problem of cylinders in a cylindrical container of the minimal radius

Authors

  • А. В. Панкратов A. N. Podgorny Institute of Problems of Mechanical Engineering NAS, Ukraine
  • Т. Е. Романова A. N. Podgorny Institute of Problems of Mechanical Engineering NAS, Ukraine
  • А. А. Коваленко A. N. Podgorny Institute of Problems of Mechanical Engineering NAS, Ukraine

Keywords:

balanced layout, cylinders, behavior constraints, mathematical modeling, nonlinear programming

Abstract

We study a balanced layout problem of a collection of homogeneous circular cylinders onto the given bearing plates of a cylindrical container of minimal radius  taking into account behavior constraints. We consider a reduced model of a spacecraft as the mechanical system. The latter is formed by means of a cylindrical container with placed objects (technical equipment) onto the given bearing plates. Behavior constraints include dynamic equilibrium, moments of inertia, stability constraints. A mathematical model of the problem is constructed in the form of nonlinear programming problem, using phi-functions. We develop the efficient algorithm, involving the multistart method, an algorithm for constructing a set of feasible starting points and IPOPT to solve nonlinear programming problems. In order to simplify a nontrivial procedure of searching for a feasible starting point we apply a special algorithm, which is based on homothetic transformations of circles. The proposed solution method allows us: to search for local optimal solutions for the balanced layout problem of cylinders in a cylindrical container of the minimal radius, improve a convergence of the local optimization and reduce the computational time. We present a number of known benchmark instances to demonstrate the high efficiency of our approach.

Author Biographies

А. В. Панкратов, A. N. Podgorny Institute of Problems of Mechanical Engineering NAS

Doctor of Technical Sciences

Т. Е. Романова, A. N. Podgorny Institute of Problems of Mechanical Engineering NAS

Doctor of Technical Sciences

References

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Published

2015-04-01

Issue

Vol. 18 No. 1 (2015)

Section

Applied mathematics

License

Copyright (c) 2015 А. В. Панкратов, Т. Е. Романова, А. А. Коваленко

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