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Heuristic-based energy landscape paving for the circular packing problem with performance constraints of equilibrium

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  • Liu, Jingfa
  • Jiang, Yucong
  • Li, Gang
  • Xue, Yu
  • Liu, Zhaoxia
  • Zhang, Zhen

Abstract

The optimal layout problem of circle group in a circular container with performance constraints of equilibrium belongs to a class of NP-hard problem. The key obstacle of solving this problem is the lack of an effective global optimization method. We convert the circular packing problem with performance constraints of equilibrium into the unconstrained optimization problem by using quasi-physical strategy and penalty function method. By putting forward a new updating mechanism of the histogram function in energy landscape paving (ELP) method and incorporating heuristic conformation update strategies into the ELP method, we obtain an improved ELP (IELP) method. Subsequently, by combining the IELP method and the local search (LS) procedure, we put forward a hybrid algorithm, denoted by IELP-LS, for the circular packing problem with performance constraints of equilibrium. We test three sets of benchmarks consisting of 21 representative instances from the current literature. The proposed algorithm breaks the records of all 10 instances in the first set, and achieves the same or even better results than other methods in literature for 10 out of 11 instances in the second and third sets. The computational results show that the proposed algorithm is an effective method for solving the circular packing problem with performance constraints of equilibrium.

Suggested Citation

  • Liu, Jingfa & Jiang, Yucong & Li, Gang & Xue, Yu & Liu, Zhaoxia & Zhang, Zhen, 2015. "Heuristic-based energy landscape paving for the circular packing problem with performance constraints of equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 166-174.
    • Handle: RePEc:eee:phsmap:v:431:y:2015:i:c:p:166-174
    DOI: 10.1016/j.physa.2015.02.092
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    References listed on IDEAS

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    1. Galiev, Shamil I. & Lisafina, Maria S., 2013. "Linear models for the approximate solution of the problem of packing equal circles into a given domain," European Journal of Operational Research, Elsevier, vol. 230(3), pages 505-514.
    2. López, C.O. & Beasley, J.E., 2011. "A heuristic for the circle packing problem with a variety of containers," European Journal of Operational Research, Elsevier, vol. 214(3), pages 512-525, November.
    3. Costa, M. Teresa & Gomes, A. Miguel & Oliveira, José F., 2009. "Heuristic approaches to large-scale periodic packing of irregular shapes on a rectangular sheet," European Journal of Operational Research, Elsevier, vol. 192(1), pages 29-40, January.
    4. Silva, Elsa & Oliveira, José F. & Wäscher, Gerhard, 2014. "2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 237(3), pages 846-856.
    5. A. Grosso & A. Jamali & M. Locatelli & F. Schoen, 2010. "Solving the problem of packing equal and unequal circles in a circular container," Journal of Global Optimization, Springer, vol. 47(1), pages 63-81, May.
    6. Hamacher, Kay, 2007. "Energy landscape paving as a perfect optimization approach under detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 307-314.
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    Cited by:

    1. Wang, Yingcong & Wang, Yanfeng & Sun, Junwei & Huang, Chun & Zhang, Xuncai, 2019. "A stimulus–response-based allocation method for the circle packing problem with equilibrium constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 232-247.

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