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 proble...

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Vydáno v:Annals of operations research Ročník 284; číslo 2; s. 527 - 555
Hlavní autoři: Gleixner, Ambros, Maher, Stephen J., Müller, Benjamin, Pedroso, João Pedro
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.01.2020
Springer Nature B.V
Témata:
Algorithms
Business and Management
Combinatorics
Dantzig-Wolfe decomposition
Logistics
Nonlinear programming
Operations research
Operations Research/Decision Theory
Rectangles
Recursive methods
S.I.: Decomposition Methods for Hard Optimization Problems
Theory of Computation
Global optimization
Recursive circle packing
Mixed-integer nonlinear programming
Dantzig–Wolfe decomposition
Symmetry breaking
ISSN:0254-5330, 1572-9338
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Shrnutí: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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-018-3115-5