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A stimulus–response-based allocation method for the circle packing problem with equilibrium constraints

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  • Wang, Yingcong
  • Wang, Yanfeng
  • Sun, Junwei
  • Huang, Chun
  • Zhang, Xuncai

Abstract

Based on the industrial background of packing objects inside the satellites, this paper addresses the circle packing problem with equilibrium constraints. From a new view of any solid material occupying certain space, a solution of the problem can be seen as different circular objects occupy different space in the container. Hence, the circle packing problem can be treated as a space allocation problem of allocating the container space reasonably to circular objects. Through the mapping between the task allocation in swarm intelligence labor division and the space allocation in circle packing problems, we propose a stimulus–response-based allocation (SRA) method. In this paper, we design four actions, viz., fix, shift, jump and swap, for circular objects to occupy the container space. The SRA method adopts the stimulus–response mechanism of labor division to regulate the actions performed on circular objects. With the characteristic of flexibility inherent in the stimulus–response mechanism, SRA could achieve an effective space allocation under dynamically changed packing environments. Three sets of 35 benchmark instances are used to test the performance of SRA, and SRA improves the best-known results on 28 instances, matches 4 and misses 3.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:522:y:2019:i:c:p:232-247
    DOI: 10.1016/j.physa.2019.02.007
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    References listed on IDEAS

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    1. 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.
    2. Fu, Zhanghua & Huang, Wenqi & Lü, Zhipeng, 2013. "Iterated tabu search for the circular open dimension problem," European Journal of Operational Research, Elsevier, vol. 225(2), pages 236-243.
    3. Zeng, Zhizhong & Yu, Xinguo & He, Kun & Huang, Wenqi & Fu, Zhanghua, 2016. "Iterated Tabu Search and Variable Neighborhood Descent for packing unequal circles into a circular container," European Journal of Operational Research, Elsevier, vol. 250(2), pages 615-627.
    4. Yingcong Wang & Renbin Xiao & Huimin Wang, 2017. "A flexible labour division approach to the polygon packing problem based on space allocation," International Journal of Production Research, Taylor & Francis Journals, vol. 55(11), pages 3025-3045, June.
    5. Wang, Huaiqing & Huang, Wenqi & Zhang, Quan & Xu, Dongming, 2002. "An improved algorithm for the packing of unequal circles within a larger containing circle," European Journal of Operational Research, Elsevier, vol. 141(2), pages 440-453, September.
    6. López, C.O. & Beasley, J.E., 2016. "A formulation space search heuristic for packing unequal circles in a fixed size circular container," European Journal of Operational Research, Elsevier, vol. 251(1), pages 64-73.
    7. 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.
    8. Castillo, Ignacio & Kampas, Frank J. & Pintér, János D., 2008. "Solving circle packing problems by global optimization: Numerical results and industrial applications," European Journal of Operational Research, Elsevier, vol. 191(3), pages 786-802, December.
    9. Huang, Wenqi & Ye, Tao, 2011. "Global optimization method for finding dense packings of equal circles in a circle," European Journal of Operational Research, Elsevier, vol. 210(3), pages 474-481, May.
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