Balance Layout Problem for 3D-Objects: Mathematical Model and Solution Methods
- 56 Downloads
The paper introduces a general mathematical model of the optimal layout of 3D-objects (full-spheres, right circular cylinders, right regular prisms, and right rectangular parallelepipeds) in a container (straight circular cylinder, paraboloid of revolution, truncated circular cone) with circular racks. The model takes into account the minimum and maximum admissible distances between objects as well as the behavior constraints of the mechanical system (equilibrium, moments of inertia, and stability constraints). We propose solution methods based on Shor’s r-algorithm, multistart algorithm, and accelerated search of terminal vertices of the decision tree.
Keywordsbalance layout problem phi-function quasi phi-function admissible distances behavior constraints nonlinear programming Shor’s r-algorithm
Unable to display preview. Download preview PDF.
- 1.G. Fasano and J. D. Pintér (eds.), Modeling and Optimization in Space Engineering, Springer Optimization and its Applications, 73 (2013).Google Scholar
- 2.C. Che, Y. Wang, and H. Teng, “Test problems for quasi-satellite packing: Cylinders packing with behavior constraints and all the optimal solutions known,” in: Optimization Online (2008), http://www.optimization-online.org/DB_HTML/2008/09/2093.html.
- 3.K. Lei, “Constrained layout optimization based on adaptive particle swarm optimizer,” C. Zhihua, L. Zhenhua, K. Zhuo, and L. Yong (eds.), Advances in Computation and Intelligence, No. 1, 434–442 (2009).Google Scholar
- 6.N. Z. Shor, Nondifferentiable Optimization and Polynomial Problems, Kluwer Acad. Publ., Boston–Dordrecht–London (1998).Google Scholar
- 9.N. Chernov, Yu. Stoyan, T. Romanova, and A. Pankratov, “Phi-functions for 2D objects formed by line segments and circular arcs,” Advances in Oper. Research, Article ID 346358, doi: 10.1155/2012/346358 (2012).
- 11.Yu. G. Stoyan, A. V. Pankratov, T. E. Romanova, and N. I. Chernov, “Quasi phi-functions for mathematical modeling of ratios of geometric objects,” Dop. NAN Ukrainy, No. 9, 53–57 (2014).Google Scholar
- 12.T. E. Romanova and A. A. Kovalenko, “Phi-functions to model constraints of inclusions in balance layout optimization problems,” Systemy Obrobky Informatsii, Issue 1, 128–133 (2014).Google Scholar
- 13.Yu. Stoyan and T. Romanova, “Mathematical models of placement optimization: Two- and three-dimensional problems and applications,” in: G. Fasano and J. D. Pint_r (eds.), Modeling and Optimization in Space Engineering, Ser. Springer Optimization and its Applications, 73, 363–388 (2013).Google Scholar
- 14.A. A. Kovalenko, A. V. Pankratov, T. E. Romanova, and P. I. Stetsyuk, “Package of circular cylinders into a cylindrical container taking into account special constraints of system behavior,” Zh. Obchysl. ta Prykl. Matem., No. 1(111), 126–134 (2013).Google Scholar