Stoyan Y.G., Chugay A.M.
Multistage approach to solving the optimization packing problem for concave polyhedra

The paper considers the problem of packing nonconvex polyhedra into a container of minimum volume. An exact mathematical model of the problem of packing nonconvex polyhedra with continuous translations and rotations is constructed. Characteristics of the mathematical model are analyzed and are used as the basis to develop a multistage solution approach to obtain a nearly optimal solution, which is not the global minimum but is a proved local minimum. Numerical examples are given. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: nonconvex polyhedra, nonlinear optimization, packing, Φ-function, Geometry, Global minima, Local minimums, Minimum volumes, Multistage approach, Nonconvex, Optimal solutions, Optimization problems, Solution approach, Global optimization

Cite:
Stoyan Y.G., Chugay A.M. (2020). Multistage approach to solving the optimization packing problem for concave polyhedra. Cybernetics and Systems Analysis, 56 (2), 108–118. doi: https://doi.org/10.1007/s10559-020-00241-w http://jnas.nbuv.gov.ua/article/UJRN-0001103875 [In Ukrainian].