Packing of concave polyhedra with continuous rotations using nonlinear optimisation

DOI10.1016/j.ejor.2018.01.025zbMath1403.90586OpenAlexW2788182033WikidataQ61307746 ScholiaQ61307746MaRDI QIDQ1754302

Xianqiang Yang

Publication date: 30 May 2018

Published in: European Journal of Operational Research (Search for Journal in Brave)

Full work available at URL: http://eprints.whiterose.ac.uk/139289/1/EJOR-concave%20polytopes%20final.pdf

zbMATH Keywords

packingmathematical modellingnonlinear optimisationconcave polyhedracontinuous rotations

Mathematics Subject Classification ID

Applications of mathematical programming (90C90) Computational aspects related to convexity (52B55) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Combinatorial optimization (90C27) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items (14)

Two approaches to modeling and solving the packing problem for convex polytopes ⋮ Parallel computing technologies for solving optimization problems of geometric design ⋮ Sparse balanced layout of ellipsoids ⋮ Extracting maximal objects from three-dimensional solid materials ⋮ Packing ellipsoids in an optimized cylinder ⋮ Heuristics for the two-dimensional irregular bin packing problem with limited rotations ⋮ Packing convex polygons in minimum-perimeter convex hulls ⋮ Decomposition Algorithm for Irregular Placement Problems ⋮ Packing Convex 3D Objects with Special Geometric and Balancing Conditions ⋮ Optimal Packing Problems: From Knapsack Problem to Open Dimension Problem ⋮ Sparsest balanced packing of irregular 3D objects in a cylindrical container ⋮ Irregular packing problems: a review of mathematical models ⋮ Optimized packing clusters of objects in a rectangular container ⋮ Optimized filling of a given cuboid with spherical powders for additive manufacturing

Uses Software

• Ipopt

Cites Work

• Quasi-phi-functions and optimal packing of ellipses
• Maximum packing densities of basic 3D objects
• Translational packing of arbitrary polytopes
• Cutting circles and polygons from area-minimizing rectangles
• The complexity of cutting complexes
• Polygon-based contact description for modeling arbitrary polyhedra in the discrete element method
• A global optimization point of view to handle non-standard object packing problems
• Mathematical modeling of the interaction of non-oriented convex polytopes
• Mathematical model and efficient algorithms for object packing problem
• The geometry of nesting problems: a tutorial
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• An improved typology of cutting and packing problems
• Packing of convex polytopes into a parallelepiped
• Algorithms - ESA 2003

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