A Literature Review on Circle and Sphere Packing Problems : Models and Methodologies

Abstract EN

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.