A Literature Review on Circle and Sphere Packing Problems: Models and Methodologies
Mhand Hifi,Rym M'Hallah +1 more
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This paper reviews the most relevant literature on efficient models and methods for packing circular objects/ items into Euclidean plane regions where the objects/items and regions are either two- or three-dimensional.Abstract:
This paper reviews the most relevant literature on efficient models and methods for packing circular objects/items into Euclidean plane regions where the objects/items and regions are either two- or three-dimensional. These packing problems are NP hard optimization problems with a wide variety of applications. They have been tackled using various approaches-based algorithms ranging from computer-aided optimality
proofs, to branch-and-bound procedures, to constructive approaches, to multi-start nonconvex minimization, to billiard simulation, to multiphase heuristics, and metaheuristics.read more
Citations
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Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO
TL;DR: This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO, and shows their individual prerequisites, formulations and applicability.
Journal ArticleDOI
A heuristic for the circle packing problem with a variety of containers
Claudia O. López,John E. Beasley +1 more
TL;DR: In this article, a heuristic algorithm based on the formulation space search method was proposed to solve the circle packing problem, which is the problem of finding the maximum radius of a specified number of identical circles that can be fitted, without overlaps, into a 2D container of fixed size.
Proceedings ArticleDOI
Constellation design for color-shift keying using billiards algorithms
Robert J. Drost,Brian M. Sadler +1 more
TL;DR: This work examines the design of CSK signaling constellations for an additive white Gaussian noise channel, incorporating the common requirement that the RGB LED outputs a specific, possibly time-varying, perceived color.
Journal ArticleDOI
A general system for heuristic minimization of convex functions over non-convex sets
TL;DR: This work describes an implementation of general heuristics to approximately solve a wide variety of problems with convex objective and decision variables from a non-convex set in a package called NCVX, as an extension of CVXPY, a Python package for formulating and solving convex optimization problems.
Journal ArticleDOI
Clusters of polyhedra in spherical confinement
TL;DR: This work uses computational methods to determine dense packings of a set of polyhedra inside a sphere, for up to 60 constituent packers, and investigates the interplay between anisotropic particle shape and isotropic 3D confinement.
References
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An improved typology of cutting and packing problems
TL;DR: An improved typology of C&P problems is presented, which is partially based on Dyckhoff’s original ideas, but introduces new categorisation criteria, which define problem categories different from those of Dykhoff.
Book
Rigorous Global Search: Continuous Problems
TL;DR: This work verifies the existence of non-Differentiable Problems in Software Environments and investigates the use of Intermediate Quantities in the Expression Values to Optimize the Solution.
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Intelligent Decision Support
TL;DR: The paper presents the system LERS for rule induction, which computes lower and upper approximations of each concept and induces certain rules and possible rules that can be induced from the input data.
Journal ArticleDOI
DC programming: overview
Reiner Horst,Nguyen Van Thoai +1 more
TL;DR: The purpose of this overview is to discuss main theoretical results, some applications, and solution methods for this interesting and important class of programming problems.
Journal ArticleDOI
Random packings of spheres and spherocylinders simulated by mechanical contraction
TL;DR: A simulation technique for creating dense random packings of hard particles is introduced, particularly suited to handle particles of different shapes, and Comparisons between the equilibrium phase diagram for hard spherocylinders and the densest possible amorphous packings have interesting implications on the crystallization of sphero cylinders as a function of aspect ratio.