Abstract
The circular packing problem with equilibrium constraints is an optimization problem about simplified satellite module layout design. A heuristic algorithm based on tabu search is put forward for solving this problem. The algorithm begins from a random initial configuration and applies the gradient method with an adaptive step length to search for the minimum energy configuration. To jump out of the local minima and avoid the search doing repeated work, the algorithm adopts the strategy of tabu search. In the process of tabu search, we improve the traditional neighboring solutions, tabu objects and the acceptance criteria of the current solution effectively. We test two sets of benchmarks consisting of 11 representative instances from the current literature. The numerical results show that the proposed algorithm breaks the records in seven out of 11 instances, and obtains the optimal solutions for the other four instances.
Similar content being viewed by others
References
Lodi A, Martello S, Monaci M. Two-dimensional packing problems: a survey. Eur J Oper Res, 2002, 141: 241–252
Birgin E G, Martinez J M, Ronconi D P. Optimizing the packing of cylinders into a rectangular container: a nonlinear approach. Eur J Oper Res, 2005, 160: 19–33
Wang Y S, Teng H F. Knowledge fusion design method: satellite module layout. Chin J Aeronaut, 2009, 22: 32–42
Leung J, Tam T, Wong C S, et al. Packing square into square. J Parallel Distr Com, 1990, 10: 271–275
Huang W Q, Liu J F. A deterministic heuristic algorithm based on Euclidian distance for solving the rectangles packing problem. Chin J Comput, 2006, 29: 734–739
Huang W Q, He K. A caving degree approach for the single container loading problem. Eur J Oper Res, 2009, 196: 93–101
Wei L J, Zhang D F, Chen Q S. A least wasted first heuristic algorithm for the rectangular packing problem. Comput Oper Res, 2009, 36: 1608–1614
Chen D B, Liu J F, Fu Y, et al. An efficient heuristic algorithm for arbitrary shaped rectilinear block packing problem. Comput Oper Res, 2010, 37: 1068–1074
Liu J F, Xue S J, Liu Z X, et al. An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle. Comput Ind Eng, 2009, 57: 1144–1149
Teng H F, Sun S L, Ge W H, et al. Layout optimization for the dishes installed on a rotating table-the packing problem with equilibrium behavioral constraints. Sci China Ser A-Math, 1994, 37: 1272–1280
Tang F, Teng H F. A modified genetic algorithm and its application to layout optimization. J Softw, 1999, 10: 1096–1102
Qian Z Q, Teng H F, Sun Z G. Human-computer interactive genetic algorithm and its application to constrained layout optimization. Chin J Comput, 2001, 24: 553–559
Yu Y, Cha J Z, Tang X J. Learning based GA and application in packing. Chin J Comput, 2001, 24: 1242–1249
Li N, Liu F, Sun D B. A study on the particle swarm optimization with mutation operator constrained layout optimization. Chin J Comput, 2004, 27: 897–903
Zhou C, Gao L, Gao H B. Particle swarm optimization based algorithm for constrained layout optimization. Control Decision, 2005, 20: 36–40
Lei K Y, Qiu Y H. A study of constrained layout optimization using adaptive particle swarm optimizer. J Comput Res Develop, 2006, 43: 1724–1731
Huang W Q, Chen M. Note on: An improved algorithm for the packing of unequal circles within a larger containing circle. Comput Ind Eng, 2006, 50: 338–344
Wang H Q, Huang W Q, Zhang Q A, et al. An improved algorithm for the packing of unequal circles within a larger containing circle. Eur J Oper Res, 2002, 141: 440–453
Wang Y S, Shi Y J, Teng H F. An improved scatter search for circles packing problem with the equilibrium constraint. Chin J Comput, 2009, 32: 1214–1221
Blum C, Roli A. Meta-heuristic in combinatorial optimization: overview and conceptual comparison. ACM Comput Survey, 2003, 35: 268–308
Liu J F, Li G. Basin filling algorithm for the circular packing problem with equilibrium behavioral constraints. Sci China Inf Sci, 2010, 53: 885–895
Hansmann U H E, Wille L T. Global optimization by energy landscape paving. Phys Rev Lett, 2002, 88: 068105
Glover F. Tabu search: Part I. ORSA J Comput, 1989, 1: 190–206
Glover F. Tabu search: Part II. ORSA J Comput, 1990, 2: 4–32
Glover F, Laguna M. Tabu Search. Boston: Kluwer Academic Publishers, 1997
Huang W Q, Kang Y. A short note on a simple search heuristic for the disk packing problem. Ann Oper Res, 2004, 131: 101–108
Lü Z P, Huang W Q. PERM for solving circle packing problem. Comput Oper Res, 2008, 35: 1742–1755
Zhang D F, Deng A S. An effective hybrid algorithm for the problem of packing circles into a larger containing circle. Comput Oper Res, 2005, 32: 1941–1951
Huang W Q, Xu R C. Two personnification strategies for solving circles packing problem. Sci China Ser E-Tech Sci, 1999, 42: 595–602
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, J., Li, G. & Geng, H. A new heuristic algorithm for the circular packing problem with equilibrium constraints. Sci. China Inf. Sci. 54, 1572–1584 (2011). https://doi.org/10.1007/s11432-011-4351-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-011-4351-3