Optimized Object Packings Using Quasi-Phi-Functions

DOI10.1007/978-3-319-18899-7_13zbMath1390.90483OpenAlexW2242228400MaRDI QIDQ4634983

Tatiana E. Romanova, Alexandr Pankratov, A. M. Chugay, Yu. G. Stoyan

Publication date: 13 April 2018

Published in: Optimized Packings with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-18899-7_13

zbMATH Keywords

nonlinear optimizationquasi-phi-functionscontinuous rotationsmathematical model developmentpacking 2D- and 3D-objects

Mathematics Subject Classification ID

Mixed integer programming (90C11) Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Approximation methods and heuristics in mathematical programming (90C59) Combinatorial optimization (90C27) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items

Two approaches to modeling and solving the packing problem for convex polytopes ⋮ A nonlinear programming model with implicit variables for packing ellipsoids ⋮ Parallel computing technologies for solving optimization problems of geometric design ⋮ Packing ellipsoids in an optimized cylinder ⋮ Mixed-Integer programming models for irregular strip packing based on vertical slices and feasibility cuts ⋮ The concept of modeling packing and covering problems using modern computational geometry software ⋮ Decomposition Algorithm for Irregular Placement Problems ⋮ Packing Convex 3D Objects with Special Geometric and Balancing Conditions ⋮ Configuration space of geometric objects ⋮ Packing ellipses in an optimized convex polygon ⋮ Sparsest balanced packing of irregular 3D objects in a cylindrical container ⋮ Formalizing spatial configuration optimization problems with the use of a special function class ⋮ 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 ⋮ Optimized ellipse packings in regular polygons ⋮ Packing Problems in Space Solved by CPLEX: An Experimental Analysis

Cites Work

• Quasi-phi-functions and optimal packing of ellipses
• Phi-functions for 2D objects formed by line segments and circular arcs
• A literature review on circle and sphere packing problems: models and methodologies
• Tools of mathematical modeling of arbitrary object packing problems
• Maximum packing densities of basic 3D objects
• Solving irregular strip packing problems by hybridising simulated annealing and linear program\-ming
• Heuristic approaches to large-scale periodic packing of irregular shapes on a rectangular sheet
• Translational packing of arbitrary polytopes
• MIP-based heuristic for non-standard 3D-packing problems
• Cutting circles and polygons from area-minimizing rectangles
• The complexity of cutting complexes
• Optimizing the packing of cylinders into a rectangular container: A nonlinear approach
• A global optimization point of view to handle non-standard object packing problems
• Optimal clustering of a pair of irregular objects
• Cutting ellipses from area-minimizing rectangles
• Packing different cuboids with rotations and spheres into a cuboid
• Mathematical modeling of the interaction of non-oriented convex polytopes
• Mathematical model and efficient algorithms for object packing problem
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization
• An improved typology of cutting and packing problems
• Fast neighborhood search for two- and three-dimensional nesting problems
• Irregular Packing Using the Line and Arc No-Fit Polygon
• Mathematical Models of Placement Optimisation: Two- and Three-Dimensional Problems and Applications