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- Title
ON TWO APPROACHES TO MODEL AND SOLVE THE PACKING PROBLEM FOR CONVEX POLYTOPES.
- Authors
Stoian, Y. E.; Chugay, A. M.; Pankratov, A. V.; Romanova, T. E.
- Abstract
We consider the packing problem for convex polytopes in a cuboid of minimum volume. To describe analytically the non-overlapping constraints for convex polytopes that allow continuous translations and rotations, we use phi-functions and quasi-phi-functions. We provide an exact mathematical model in the form of an NLP-problem and analyze its characteristics. Based on the general solution strategy, we propose two approaches that take into account peculiarities of phi-functions and quasi-phi-functions. Computational results to compare the efficiency of our approaches are given with respect to both the value of the objective function and runtime.
- Publication
Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz, 2018, Vol 54, Issue 4, p81
- ISSN
1019-5262
- Publication type
Article