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.

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  1. Gahm, Christian; Uzunoglu, Aykut; Wahl, Stefan; Ganschinietz, Chantal; Tuma, Axel: Applying machine learning for the anticipation of complex nesting solutions in hierarchical production planning (2022)
  2. Fernandes Silva, Everton; Tebaldi Oliveira, Larissa; Oliveira, José Fernando; Bragion Toledo, Franklina Maria: Exact approaches for the cutting path determination problem (2019)
  3. Sato, André Kubagawa; de Castro Martins, Thiago; Gomes, Antonio Miguel; de Sales Guerra Tsuzuki, Marcos: Raster penetration map applied to the irregular packing problem (2019)
  4. 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)
  5. Wang, Akang; Hanselman, Christopher L.; Gounaris, Chrysanthos E.: A customized branch-and-bound approach for irregular shape nesting (2018)
  6. Amaro Júnior, Bonfim; Pinheiro, Plácido Rogério; Coelho, Pedro Veras: A parallel biased random-key genetic algorithm with multiple populations applied to irregular strip packing problems (2017)
  7. Rodrigues, Marcos Okamura; Toledo, Franklina M. B.: A clique covering MIP model for the irregular strip packing problem (2017)
  8. M’Hallah, Rym; Bouziri, Ahlem: Heuristics for the combined cut order planning two-dimensional layout problem in the apparel industry (2016)
  9. Santoro, Miguel Cezar; Lemos, Felipe Kesrouani: Irregular packing: MILP model based on a polygonal enclosure (2015)
  10. Baldacci, Roberto; Boschetti, Marco A.; Ganovelli, Maurizio; Maniezzo, Vittorio: Algorithms for nesting with defects (2014)
  11. Furian, Nikolaus; Vössner, Siegfried: A hybrid algorithm for constrained order packing (2014)
  12. Elkeran, Ahmed: A new approach for sheet nesting problem using guided cuckoo search and pairwise clustering (2013)
  13. López-Camacho, Eunice; Ochoa, Gabriela; Terashima-Marín, Hugo; Burke, Edmund K.: An effective heuristic for the two-dimensional irregular bin packing problem (2013)
  14. Leung, Stephen C. H.; Lin, Yangbin; Zhang, Defu: Extended local search algorithm based on nonlinear programming for two-dimensional irregular strip packing problem (2012)
  15. Bennell, Julia A.; Song, Xiang: A beam search implementation for the irregular shape packing problem (2010)
  16. Burke, Edmund Kieran; Hellier, R. S. R.; Kendall, Graham; Whitwell, Glenn: Irregular packing using the line and arc no-fit polygon (2010)
  17. Chernov, N.; Stoyan, Yu.; Romanova, T.: Mathematical model and efficient algorithms for object packing problem (2010)
  18. Wong, W. K.; Guo, Z. X.: A hybrid approach for packing irregular patterns using evolutionary strategies and neural network (2010)
  19. Bennell, J. A.; Oliveira, J. F.: A tutorial in irregular shape packing problems (2009)
  20. Blatov, Vladislav A.; Proserpio, Davide M.: Topological relations between three-periodic nets. II: Binodal nets (2009)

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