Abstract
The nested partitions method (NPM) is a global optimization method, which can be applied to solve many large-scale discrete optimization problems. The basic procedure of this method for solving the traveling salesman problem (TSP) was introduced. Based on the analysis and determination of the strategy of the four arithmetic operators of NPM, an improved NPM was proposed. The initial most promising region was improved by weighted sampling method; The historical optimal solution of every region was recorded in a global array; the 3-opt algorithm was combined in the local search for improving the quality of solution for every subregion; the improved Lin–Kernighan algorithm was used in the search for improving the quality of solution for surrounding region. Some experimental results of TSPLIB (TSP Library) show that the proposed improved NPM can find solutions of high quality efficiently when applied to the TSP.
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Notes
- 1.
TSLIB is a library of sample instances for the traveling salesman problem (TSP) (and related problems) from various sources and of various types.
References
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman, San Francisco
Croes GA (1958) A method for solving traveling salesman problems. Oper Res 6(6):791–812
Lin S (1965) Computer solutions to the traveling salesman problem. Bell Syst J 44:2245–2269
Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling salesman problem. Oper Res 21(2):498–516
Olafsson S, Shi LY (1997) An integrated framework for deterministic and stochastic optimization. In: Proceedings of the 1997 winter stimulation conference, pp 358–365. IEEE Press, USA
Liu CJ, Su Q, W JH (2008) Application of nested partitions method in traveling salesman problem. J Syst Simul 20(24):6858–6861
Chen XY, Quan HY, Xiao W (2007) Improved adaptive hybrid ant algorithm for traveling salesman problem. Comput Eng App 43(27):84–87
Yang H, Kang LS, Chen YP (2003) A gene-based genetic algorithm for TSP. Chin J Comput 26(12):1753–1758
Chen XY, Xiao W, Quan HY (2008) Hybrid ant algorithm using LK search for traveling salesman problem. Comput Eng 34(4):228–230
Hao CW, Gao HM (2012) Modified decimal MIMIC algorithm for TSP. Comput Sci 39(8):233–236
Shen XJ, Liu YY, Huang YP (2013) Fast ant colony algorithm for solving traveling salesman problem. J Jilin Univ Eng Tech Ed 43(1):147–151
Liu Y, Ma L (2013) Fuzzy artificial bees colony algorithm for solving traveling salesman problem. Appl Res Comput 30(9):2694–2696
Sheng HP, Ma L (2012) Modified great deluge algorithm for large-scale traveling salesman problem. J Chin Comput Syst 33(2):259–262
Acknowledgments
The authors would like to thank the referees for their valuable suggestions. The work is supported by the Project of Higher Schools’ Natural Science Basic Research of Jiangsu Province of China (13KJB110006).
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Zong, D., Wang, K. (2014). Hybrid Nested Partitions Method for the Traveling Salesman Problem. In: Wen, Z., Li, T. (eds) Foundations of Intelligent Systems. Advances in Intelligent Systems and Computing, vol 277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54924-3_6
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DOI: https://doi.org/10.1007/978-3-642-54924-3_6
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