Network Voronoi Diagram Heuristic-based Particle Swarm Continuous Spatial Optimization Modeling

  • Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Nanjing University, Department of Geographic Information Science, School of Geographic and Oceanographic Sciences, Nanjing University, Nanjing 210046, China

Received date: 2013-11-20

  Revised date: 2013-12-06

  Online published: 2013-12-25

Supported by



Spatial optimization modeling for multi facilities in urbanized area is a practical and key technique, and it can provide balance configuration optimization and spatial decision support for urban public resource. A method of particle swarm spatial optimization modeling for multi facilities location based on network Voronoi diagram heuristic is proposed in this paper, in which we presented respectively some p-median location models and maximal covering location models by using ordinary Voronoi diagram heuristic and network Voronoi diagram heuristic. Those models can quantitatively extract the demands coved by the function and service of facilities through the Voronoi diagrams, and inspire spatial optimization to maximize the coverage for distributed demands by minimizing overlapped coverage. The proposed p-median location model considers the factor of demand attenuation with path distance, and the proposed maximal covering model takes it into account that facility's service provides full coverage for the demands within maximal coverage radius and partial attenuation coverage for the demands without maximal coverage radius. The genetic evolution mechanism and the dynamic neighborhood structure of particles simulated by ordinary Voronoi diagram are integrated in the particle swarm spatial optimization to improve global search and optimization performance of the algorithm. Through the research of spatial optimization configuration experiments for multi facilities in experimental city, the proposed method has been verified to be the effective and practical, it can be applied for the spatial location optimization decision in urbanized area.

Cite this article

XIE Shun-Beng, FENG Hua-Zhi, DOU Jin-Kang . Network Voronoi Diagram Heuristic-based Particle Swarm Continuous Spatial Optimization Modeling[J]. Journal of Geo-information Science, 2013 , 15(6) : 846 -853 . DOI: 10.3724/SP.J.1047.2013.00846


[1] 黎夏, 刘小平, 李少英. 智能式GIS与空间优化[M].北京:科学出版社, 2010.

[2] Okabe A, Satoh T, Furuta T, et al. Generalized network Voronoi diagrams: Concepts, computational methods and applications[J]. International Journal of Geographical Information Science, 2008, 22(9):965-994.

[3] Okabe A, Okunuki K.A computational method for estimating the demand of retail stores on a street network and its implementation in GIS[J]. Transactions in GIS, 2001, 5(3):209-220.

[4] Kennedy J, Eberhart R C. Particle Swarm Optimization[C]. Proc of IEEE International Conference on Neural Networks. Perth, Australia, l995, 1942-1948.

[5] Eberhart R C, Shi Y. Particle swarm optimization: Developments, applications and resources[C]. In: Proc. Congress on Evolutionary Computation. IEEE Service Center. Piscataway, NJ, USA, 2001, 81-86.

[6] 谢顺平, 冯学智, 鲁伟. 基于道路网络分析的Voronoi面域图构建算法[J]. 测绘学报, 2010, 39(1):88-94.

[7] Okabe A, Suzuki A. Locational optimization problems solving through Voronoi diagrams[J]. Europe Journal Operation Research, 1997(98):445-456.

[8] 陈军, 赵仁亮, 乔朝飞. 基于Voronoi图的GIS空间分析研究[J]. 武汉大学学报×信息科学版, 2003, 28 (特刊):32-37.

[9] 王新生, 余瑞林, 姜友华. 基于道路网络的商业网点市场域分析[J]. 地理研究, 2008, 27(1):85-92.

[10] 谢顺平, 冯学智, 王结臣, 等. 基于网络加权Voronoi图分析的南京市商业中心辐射域研究[J]. 地理学报, 2009, 64(12):1467-1476.

[11] 杜国明, 陈晓翔, 黎夏. 基于粒子群优化算法的空间优化决策[J].地理学报, 2006, 61(12): 1290-1298.

[12] 黎海波, 黎夏, 刘小平, 等. 多目标粒子群算法与选址中的形状优化[J]. 遥感学报, 2008, 12(5):724-733.

[13] 谢顺平, 冯学智, 都金康. 基于网络Voronoi图启发式和群智能的最大覆盖空间优化[J]. 测绘学报, 2011, 40(6):778-784.

[14] Mladenovi? N, Brimberg J, Hansen P, Moreno-Pérez J A. The p-median problem: A survey of metaheuristic approaches[J]. European Journal of Operational Research, 2007 (179):927-939.

[15] Sáez-Aguado J, Trandafir P C. Some heuristic methods for solving p-median problems with a coverage constraint[J]. European Journal of Operational Research, 2012(220):320-327.

[16] Yaghini M, Karimi M, Rahbar M. A hybrid metaheuristic approach for the capacitated p-median problem[J]. Applied Soft Computing, 2013(13):3922-3930.

[17] Church R.L., Revelle, C.S., The maximal covering location problem[C]. Papers of the Regional Science Association, 1974(32):101-118.

[18] Alexandris G, Giannikos I. A new model for maximal coverage exploiting GIS capabilities[J]. European Journal of Operational Research, 2010(202): 328-338.

[19] Karasakal O, Karasakal E K. A maximal covering location model in the presence of partial coverage[J]. Computers & Operations Research, 2004(31):1515-1526.

[20] Murawski L, Church R L. Improving accessibility to rural health services: The maximal covering network improvement problem[J]. Socio-Economic Planning Sciences, 2008(43):102-110.

[21] 马云峰, 杨超, 张敏, 等. 基于时间满意的最大覆盖选址问题[J]. 中国管理科学, 2006, 14(2): 45-51.

[22] Berman O.The p maximal cover-partial center problem on networks[J].European Journal of Operation Research, 1994(72):432-442.

[23] Berman O, Drezner Z, Krass D, et al. The variable radius covering problem[J]. European Journal of Operational Research. 2009(196):516–525.

[24] 曾建潮, 介婧, 崔志华. 粒子群算法[M]. 北京: 科学出版社, 2004.

[25] Eberhart R C, Shi Y. Particle swarm optimization: Developments, applications and resources. In: Proc. Congress on Evolutionary Computation. IEEE Service Center. Piscataway, NJ, USA, 2001: 81-86.

[26] 倪庆剑, 邢汉承, 张志政, 等. 粒子群优化算法研究进展[J]. 模式识别与人工智能, 2007, 20(3):349-357.

[27] 李宁, 刘飞, 孙德宝. 基于带变异算子粒子群优化算法的约束布局优化研究[J]. 计算机学报, 2004, 27(7):897-903.

[28] 陶新民, 刘福荣, 刘玉, 等. 一种多尺度协同变异的粒子群优化算法[J]. 软件学报, 2012, 23(7):1805-1815.