Journal of Global Optimization

, Volume 56, Issue 3, pp 1187–1215

Packing non-identical circles within a rectangle with open length


DOI: 10.1007/s10898-012-9948-6

Cite this article as:
He, Y. & Wu, Y. J Glob Optim (2013) 56: 1187. doi:10.1007/s10898-012-9948-6


Packing non-identical circles inside a rectangle witnesses a wide range of industrial applications. However, the non-convex constraints in this problem make it intractable using exact analytical approaches. Even via heuristic methods, the solution time for industrial-scale instances sometimes is too long to be acceptable. This article aims to challenge the existing methods for the benchmark instances. The most significant contributions of this work are: firstly, we proposed three types of packing positions for selection and used human intelligence to convert an arbitrary circle sequence into a feasible compact layout; secondly, diverse position selection criteria have been tested, and it is found that the criterion commonly used in the literature is not the best; thirdly, the traditional genetic algorithm is adapted with lower crossover rate but higher mutation rate particularly, and a minor-adjustment operator with the purpose of exploring the neighborhood of the current best solutions is introduced.


Cutting and packingCombinatorial optimizationHeuristicGenetic algorithmDecomposition

Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.Department of Industrial and Systems Engineering/Office of the ProvostNational University of SingaporeSingaporeSingapore
  2. 2.Department of International Business and Asian StudiesGriffith UniversityGold CoastAustralia