TOPOS -- A new constructive algorithm for nesting problems. In this paper we present a new constructive algorithm for nesting problems. The layout is built by successively adding a new piece to a partial solution, i.e. to the set of pieces previously nested. Several criteria to choose the next piece to place and its orientation are proposed and tested. Different objective functions are also proposed to evaluate and compare partial solutions. A total of 126 variants of the algorithm, generated by the complete set of combinations of criteria and objective functions, are computationally tested. The computational experiments are based on data sets published in the literature or provided by other authors. In some cases this new algorithm generates better solutions than the best known (published) solutions.

References in zbMATH (referenced in 38 articles , 1 standard article )

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  1. Cherri, Luiz H.; Cherri, Adriana C.; Soler, Edilaine M.: Mixed integer quadratically-constrained programming model to solve the irregular strip packing problem with continuous rotations (2018)
  2. Wang, Akang; Hanselman, Christopher L.; Gounaris, Chrysanthos E.: A customized branch-and-bound approach for irregular shape nesting (2018)
  3. Rodrigues, Marcos Okamura; Toledo, Franklina M. B.: A clique covering MIP model for the irregular strip packing problem (2017)
  4. M’Hallah, Rym; Bouziri, Ahlem: Heuristics for the combined cut order planning two-dimensional layout problem in the apparel industry (2016)
  5. Santoro, Miguel Cezar; Lemos, Felipe Kesrouani: Irregular packing: MILP model based on a polygonal enclosure (2015)
  6. Baldacci, Roberto; Boschetti, Marco A.; Ganovelli, Maurizio; Maniezzo, Vittorio: Algorithms for nesting with defects (2014)
  7. Furian, Nikolaus; Vössner, Siegfried: A hybrid algorithm for constrained order packing (2014)
  8. López-Camacho, Eunice; Ochoa, Gabriela; Terashima-Marín, Hugo; Burke, Edmund K.: An effective heuristic for the two-dimensional irregular bin packing problem (2013)
  9. Leung, Stephen C. H.; Lin, Yangbin; Zhang, Defu: Extended local search algorithm based on nonlinear programming for two-dimensional irregular strip packing problem (2012)
  10. Bennell, Julia A.; Song, Xiang: A beam search implementation for the irregular shape packing problem (2010)
  11. Burke, Edmund Kieran; Hellier, R. S. R.; Kendall, Graham; Whitwell, Glenn: Irregular packing using the line and arc no-fit polygon (2010)
  12. Chernov, N.; Stoyan, Yu.; Romanova, T.: Mathematical model and efficient algorithms for object packing problem (2010)
  13. Wong, W. K.; Guo, Z. X.: A hybrid approach for packing irregular patterns using evolutionary strategies and neural network (2010)
  14. Bennell, J. A.; Oliveira, J. F.: A tutorial in irregular shape packing problems (2009)
  15. Blatov, Vladislav A.; Proserpio, Davide M.: Topological relations between three-periodic nets. II: Binodal nets (2009)
  16. Costa, M. Teresa; Gomes, A. Miguel; Oliveira, José F.: Heuristic approaches to large-scale periodic packing of irregular shapes on a rectangular sheet (2009)
  17. Imamichi, Takashi; Yagiura, Mutsunori; Nagamochi, Hiroshi: An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem (2009)
  18. Umetani, Shunji; Yagiura, Mutsunori; Imahori, Shinji; Imamichi, Takashi; Nonobe, Koji; Ibaraki, Toshihide: Solving the irregular strip packing problem via guided local search for overlap minimization (2009)
  19. Fasano, Giorgio: MIP-based heuristic for non-standard 3D-packing problems (2008)
  20. Ibaraki, Toshihide; Imahori, Shinji; Yagiura, Mutsunori: Hybrid metaheuristics for packing problems (2008) ioport

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