Heuristic Algorithm for the Rectangular Packing Problem with Static Non-Equilibrium Constraint
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TP301

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National Natural Science Foundation of China (61373016); Six Talent Peaks Project of Jiangsu Province (DZXX-041); National Social Science Foundation of China (16ZDA047)

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    Abstract:

    Layout design of satellite module is not only a complex coupling system design problem but also a special optimization problem. It is considered to be NP-hard. The most challenge of solving this problem is that the objective function to be optimized is characterized by a multitude of local minima separated by high-energy barriers. The Wang-Landau (WL) sampling method is an improved Monte Carlo method, which has been successfully applied to solve the protein structure prediction and other optimization problems. Taking satellite layout design as case study, this paper introduces the WL sampling method to solve the rectangular packing problem. In order to guide the WL sampling algorithm to random walk effectively in solution space, rectangular objects-oriented heuristic layout update strategies are proposed. To accelerate the search for the global optimal layout, the gradient method is executed for local search once the Monte-Carlo sweep produces a new layout. By incorporating the local search mechanism and heuristic layout update strategies into the WL sampling algorithm, a heuristic Wang-Landau sampling algorithm is constructed to solve the arbitrary rectangular packing problem with the static non-equilibrium constraint. By adding a static non-equilibrium penalty term on the basis of the extrusive elastic energy, and adopting the translation of the center of mass, the static non-equilibrium constraints of the whole system can be satisfied. Furthermore, to improve the efficiency of the algorithm significantly, an improved finite-circle method is presented to judge and calculate the overlapping depth among objects. The computational results of two sets of benchmarks consisting of ten representative instances from the literature show that the proposed packing algorithm is effective.

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刘景发,刘思妤.带静不平衡约束的矩形装填问题的启发式算法.软件学报,2018,29(2):283-298

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History
  • Received:September 01,2016
  • Revised:January 10,2017
  • Adopted:
  • Online: March 23,2017
  • Published:
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