An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle

The problem of packing circles into a larger containing circle is a kind of NP-hard problem. It is of high theoretical and practical value. Lacking powerful optimization method is the key obstacle to solving this problem. The energy landscape paving (ELP) method is a class of heuristic global optimization algorithm and a generation of Monte Carlo method. By incorporating new configuration update mechanism into ELP method, an improved energy landscape paving (ELP+) algorithm is put forward. The computational results, on two sets of instances taken from the literature, show the effectiveness of the proposed algorithm.

[1]  Jacek Klinowski,et al.  Taboo Search: An Approach to the Multiple Minima Problem , 1995, Science.

[2]  Mhand Hifi,et al.  A beam search algorithm for the circular packing problem , 2009, Comput. Oper. Res..

[3]  A. Schug,et al.  Energy landscape paving simulations of the trp-cage protein. , 2005, The Journal of chemical physics.

[4]  Wenqi Huang,et al.  Two personification strategies for solving circles packing problem , 1999 .

[5]  Andrea Grosso,et al.  Solving the problem of packing equal and unequal circles in a circular container , 2010, J. Glob. Optim..

[6]  José Mario Martínez,et al.  Optimizing the packing of cylinders into a rectangular container: A nonlinear approach , 2005, Eur. J. Oper. Res..

[7]  Handan Arkin,et al.  A Combination Of Replica Exchange Monte Carlo And Energy Landscape Paving Algorithms To Increase The Effectiveness Of Conformational Sampling , 2004 .

[8]  Mhand Hifi,et al.  Adaptive and restarting techniques-based algorithms for circular packing problems , 2008, Comput. Optim. Appl..

[9]  Ronald L. Graham,et al.  Curved Hexagonal Packings of Equal Disks in a Circle , 1997, Discret. Comput. Geom..

[10]  Yu Li,et al.  New heuristics for packing unequal circles into a circular container , 2006, Comput. Oper. Res..

[11]  De-fu Zhang,et al.  An effective hybrid algorithm for the problem of packing circles into a larger containing circle , 2005, Comput. Oper. Res..

[12]  Wenqi Huang,et al.  A Short Note on a Simple Search Heuristic for the Diskspacking Problem , 2004, Ann. Oper. Res..

[13]  H. Dyckhoff,et al.  Vorwort der Herausgeber zum Themenheft „Verpackungslogistik/Packaging logistics“ , 1991 .

[14]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[15]  Jingfa Liu,et al.  STUDIES OF FINDING LOW ENERGY CONFIGURATIONS IN OFF-LATTICE PROTEIN MODELS , 2006 .

[16]  O. G. Mouritsen,et al.  Efficient Monte Carlo Sampling by direct flattening of free energy barriers , 1999 .

[17]  K. Dowsland.  Optimising the palletisation of cylinders in cases , 1991 .

[18]  Nenad Mladenovic,et al.  Reformulation descent applied to circle packing problems , 2003, Comput. Oper. Res..

[19]  Huaiqing Wang,et al.  An improved algorithm for the packing of unequal circles within a larger containing circle , 2002, Eur. J. Oper. Res..

[20]  Zhipeng Lü,et al.  PERM for solving circle packing problem , 2008, Comput. Oper. Res..

[21]  Ulrich H E Hansmann,et al.  Global optimization by energy landscape paving. , 2002, Physical review letters.