6449
2018
2020
eng
527
555
2
284
article
Springer US
0
2018-12-14
--
--
Price-and-verify: a new algorithm for recursive circle packing using Dantzig–Wolfe decomposition
Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig–Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a “price-and-verify” algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature.
Annals of Operations Research
10.1007/s10479-018-3115-5
yes
urn:nbn:de:0297-zib-62039
accepted for publication 2018-12-14
Ambros Gleixner
Benjamin Müller
Stephen Maher
Benjamin Müller
João Pedro Pedroso
Mathematical Optimization
Mathematical Optimization Methods
Gleixner, Ambros
Müller, Benjamin
MIP-ZIBOPT
MODAL-SynLab
Siemens
MODAL-Gesamt