Hybrid Bioinspired Algorithm of 1.5 Dimensional Bin-Packing

  • Boris K. Lebedev
  • Oleg B. LebedevEmail author
  • Ekaterina O. Lebedeva
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 874)


The paper deals with the problem of 1.5 dimensional bin packing. As a data structure carrying information about packaging, a sequence of numbers of rectangles is used, representing the order of their packing. An essential role in obtaining the solution is played by a decoder, which performs the laying of rectangles according to the rules laid down in it. New methods for solving the packing problem are proposed, using mathematical methods in which the principles of natural decision-making mechanisms are laid. Unlike the canonical paradigm ant algorithm to find solutions to the graph G = (X, U) is constructed with a partition on the route of the formation and on the tops within each part, subgraphs whose edges are delayed pheromone. The structure of the solution search graph, the procedure for finding solutions on the graph, the methods of deposition and evaporation of pheromone are described. The time complexity of the algorithm, experimentally obtained, practically coincides with the theoretical studies and for the considered test problems is O(n2). In comparison with existing algorithms, the improvement of results is achieved by 2–3%.


Swarm intelligence Ant colony Adaptive behavior 1.5 dimensional bin packing Optimization 



This research is supported by grants of the Russian Foundation for Basic Research of the Russian Federation, the project № 17-07-00997.


  1. 1.
    Lodi, A., Martello, S., Monaci, M.: Two-dimensional packing problems: a survey. Eur. J. Oper. Res. 141, 241–252 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Leung, S.C.H., Zhang, D., Sim, K.M.: A two-stage intelligent search algorithm for the two-dimensional strip packing problem. Eur. J. Oper. Res. 215, 57–69 (2011)CrossRefGoogle Scholar
  3. 3.
    Martello, S., Monaci, M., Vigo, D.: An exact approach to the strip-packing problem. INFORMS J. Comput. 15, 310–319 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Duanbing, C., Wenqi, H.: Greedy algorithm for rectangle-packing problem. Comput. Eng. 33, 160–162 (2007)zbMATHGoogle Scholar
  5. 5.
    Timofeeva, O.P., Sokolova, E.S., Milov, K.V.: Genetic algorithm in optimization of container packaging. In: Proceedings of NSTU, Informatics and Management Systems, vol. 4, no. 101, pp. 167–172 (2013)Google Scholar
  6. 6.
    Hifi, M., M’Hallah, R.: A hybrid algorithm for the two-dimensional layout problem: the cases of regular and irregular shapes. Int. Trans. Oper. Res. 10, 195–216 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    De Zhang, F., ShuiHua, H., WeiGuo, Y.: A bricklaying heuristic algorithm for the orthogonal rectangular packing problem. Chin. J. Comput. 33, 509–515 (2008)Google Scholar
  8. 8.
    Leung, C.H., Zhang, D., Zhou, C., et al.: A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack packing problem. Comput. Oper. Res. 39, 64–73 (2012)CrossRefGoogle Scholar
  9. 9.
    Shi, W.: Solving rectangle packing problem based on heuristic dynamic decomposition algorithm. In: 2nd International Conference on Electrical and Electronics: Techniques and Applications, pp. 187–196 (2017)Google Scholar
  10. 10.
    Lebedev, O.B., Zorin, V.Yu.: Packaging on the basis of the method of the ant colony. Izvestiya Southern Federal University. Publishing House of TTI SFedU, no. 12, pp. 25–30 (2010)Google Scholar
  11. 11.
    Lebedev, V.B., Lebedev, O.B.: Swarm Intelligence on the basis of integration of models of adaptive behavior of ants and bee colony. Izvestiya Southern Federal University. Publishing House of TTI SFedU, no. 7, pp. 41–47 (2013)Google Scholar
  12. 12.
    Lebedev, B.K., Lebedev, V.B.: Optimization by the method of crystallization of placers of alternatives. Izvestiya Southern Federal University. Publishing House of TTI SfedU, no. 7, pp. 11–17 (2013)Google Scholar
  13. 13.
    Lebedev, B.K., Lebedev, O.B.: Modeling of the adaptive behavior of an ant colony in the search for solutions interpreted by trees. Izvestiya Southern Federal University. Publishing House of TTI SfedU, no. 7, pp. 27–35 (2012)Google Scholar
  14. 14.
    Dorigo, M., Stützle, T.: Ant Colony Optimization, p. 244. MIT Press, Cambridge (2004)zbMATHGoogle Scholar
  15. 15.
    Lebedev, O.B.: Models of adaptive behavior of ant colony in the task of designing. Southern Federal University. Publishing House of SfedU, p. 199 (2013)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Boris K. Lebedev
    • 1
  • Oleg B. Lebedev
    • 1
    Email author
  • Ekaterina O. Lebedeva
    • 1
  1. 1.Southern Federal UniversityRostov-on-DonRussia

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