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Articles

Using Zipf’s Law to Optimize Urban Spatial Layouts in an Urban Agglomeration Area

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Received 06 Mar 2022, Accepted 26 Jan 2024, Published online: 29 Apr 2024

References

  • Aerts, J., P. Abrantes, E. Eisinger, G. Heuvelink, and T. Stewart. 2003. Using linear integer programming for multi‐site land‐use allocation. Geographical Analysis 35 (2):148–69. doi: 10.1111/j.1538-4632.2003.tb01106.x.
  • Arshad, S., S. Hu, and B. N. Ashraf. 2019. Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan. Physica A: Statistical Mechanics and Its Applications 513:87–103. doi: 10.1016/j.physa.2018.08.065.
  • Arvidsson, M., N. Lovsjö, and M. Keuschnigg. 2023. Urban scaling laws arise from within-city inequalities. Nature Human Behaviour 7 (3):365–74. doi: 10.1038/s41562-022-01509-1.
  • Balling, R. J., J. T. Taber, M. R. Brown, and K. Day. 1999. Multiobjective urban planning using genetic algorithm. Journal of Urban Planning and Development 125 (2):86–99. doi: 10.1061/(ASCE)0733-9488(1999)125:2(86).
  • Berry, B. J. 1964. Cities as systems within systems of cities. Papers in Regional Science 13 (1):147–63. doi: 10.1111/j.1435-5597.1964.tb01283.x.
  • Bhatta, B. 2009. Modelling of urban growth boundary using geoinformatics. International Journal of Digital Earth 2 (4):359–81. doi: 10.1080/17538940902971383.
  • Brakman, S., H. Garretsen, C. Van Marrewijk, and M. Van Den Berg. 1999. The return of Zipf: Towards a further understanding of the rank-size distribution. Journal of Regional Science 39 (1):183–213. doi: 10.1111/1467-9787.00129.
  • Cai, B., Z. Shao, S. Fang, X. Huang, Y. Tang, M. Zheng, and H. Zhang. 2022. The evolution of urban agglomerations in China and how it deviates from Zipf’s law. Geo-Spatial Information Science 27 (1):38–48. doi: 10.1080/10095020.2022.2083527.
  • Cao, H. 2010. Urban–rural income disparity and urbanization: What is the role of spatial distribution of ethnic groups? A case study of Xinjiang Uyghur Autonomous Region in western China. Regional Studies 44 (8):965–82. doi: 10.1080/00343400903401550.
  • Cao, K., M. Batty, B. Huang, Y. Liu, L. Yu, and J. Chen. 2011. Spatial multi-objective land use optimization: Extensions to the non-dominated sorting genetic algorithm-II. International Journal of Geographical Information Science 25 (12):1949–69. doi: 10.1080/13658816.2011.570269.
  • Cao, K., B. Huang, S. Wang, and H. Lin. 2012. Sustainable land use optimization using boundary-based fast genetic algorithm. Computers, Environment and Urban Systems 36 (3):257–69. doi: 10.1016/j.compenvurbsys.2011.08.001.
  • Cao, K., W. Zhang, and T. Wang. 2019. Spatial optimization for land use planning: Opportunities and challenges. Transactions in GIS 23 (4):726–44. doi: 10.1111/tgis.12573.
  • Cao, S., X. Jin, X. Yang, R. Sun, J. Liu, B. Han, W. Xu, and Y. Zhou. 2019. Coupled MOP and GeoSOS-FLUS models research on optimization of land use structure and layout in Jintan district. Journal of Natural Resources 34 (6):1171. doi: 10.31497/zrzyxb.20190604.
  • Caparros-Midwood, D., R. Dawson, and S. Barr. 2019. Low carbon, low risk, low density: Resolving choices about sustainable development in cities. Cities 89:252–67. doi: 10.1016/j.cities.2019.02.018.
  • Charnes, A., K. E. Haynes, J. E. Hazleton, and M. J. Ryan. 2010. A hierarchical goal-programming approach to environmental land use management. Geographical Analysis 7 (2):121–30. doi: 10.1111/j.1538-4632.1975.tb01030.x.
  • Chen, G., X. Li, X. Liu, Y. Chen, X. Liang, J. Leng, X. Xu, W. Liao, Y. Qiu, Q. Wu, et al. 2020. Global projections of future urban land expansion under shared socioeconomic pathways. Nature Communications 11 (1):537. doi: 10.1038/s41467-020-14386-x.
  • Chen, Y., X. Li, K. Huang, M. Luo, and M. Gao. 2020. High‐resolution gridded population projections for China under the shared socioeconomic pathways. Earth’s Future 8 (6):e2020EF001491. doi: 10.1029/2020EF001491.
  • Chen, Z., Y. Wei, K. Shi, Z. Zhao, C. Wang, B. Wu, B. Qiu, and B. Yu. 2022. The potential of nighttime light remote sensing data to evaluate the development of digital economy: A case study of China at the city level. Computers, Environment and Urban Systems 92:101749. doi: 10.1016/j.compenvurbsys.2021.101749.
  • Chigudu, A., and I. Chirisa. 2020. The quest for a sustainable spatial planning framework in Zimbabwe and Zambia. Land Use Policy 92:104442. doi: 10.1016/j.landusepol.2019.104442.
  • Chuvieco, E. 1993. Integration of linear programming and GIS for land-use modelling. International Journal of Geographical Information Systems 7 (1):71–83. doi: 10.1080/02693799308901940.
  • Clarke, K. C., and L. J. Gaydos. 1998. Loose-coupling a cellular automaton model and GIS: Long-term urban growth prediction for San Francisco and Washington/Baltimore. International Journal of Geographical Information Science 12 (7):699–714. doi: 10.1080/136588198241617.
  • Ding, X., M. Zheng, and X. Zheng. 2021. The application of genetic algorithm in land use optimization research: A review. Land 10 (5):526. doi: 10.3390/land10050526.
  • Fang, C. 2014. Progress and the future direction of research into urban agglomeration in China. Acta Geographica Sinica 69 (8):1130–44.
  • Fang, L., P. Li, and S. Song. 2017. China’s development policies and city size distribution: An analysis based on Zipf’s law. Urban Studies 54 (12):2818–34. doi: 10.1177/0042098016653334.
  • Fragkias, M., and K. C. Seto. 2009. Evolving rank-size distributions of intra-metropolitan urban clusters in South China. Computers, Environment and Urban Systems 33 (3):189–99. doi: 10.1016/j.compenvurbsys.2008.08.005.
  • Halmy, M. W. A., P. E. Gessler, J. A. Hicke, and B. B. Salem. 2015. Land use/land cover change detection and prediction in the north-western coastal desert of Egypt using Markov-CA. Applied Geography 63:101–12. doi: 10.1016/j.apgeog.2015.06.015.
  • He, C., P. Shi, J. Li, Y. Pan, and J. Chen. 2004. Scenarios simulation land use change in northern China by system dynamic model. Acta Geographica Sinica 59 (4):599. doi: 10.11821/xb200404014.
  • Hoekstra, A. Y., and T. O. Wiedmann. 2014. Humanity’s unsustainable environmental footprint. Science 344 (6188):1114–17. doi: 10.1126/science.1248365.
  • Huang, J., and H. Lin. 2017. Spatial evolution analysis and multi-scenarios simulation of Beijing–Tianjin–Hebei urban agglomeration. Geographical Research 36 (3):506–17.
  • Huang, K., X. Liu, X. Li, J. Liang, and S. He. 2013. An improved artificial immune system for seeking the Pareto front of land-use allocation problem in large areas. International Journal of Geographical Information Science 27 (5):922–46. doi: 10.1080/13658816.2012.730147.
  • Jefferson, M. 1939. The law of the primate city. Geographical Review 29 (2):226–32. doi: 10.2307/209944.
  • Jiao, L., and X. Zhang. 2015. Characterizing urban expansion of main metropolises in China based on built-up densities in concentric rings. Resources and Environment in the Yangtze Basin 24 (10):1721–28.
  • Kuang, W., T. Yang, and F. Yan. 2018. Examining urban land-cover characteristics and ecological regulation during the construction of Xiong’an New District, Hebei Province, China. Journal of Geographical Sciences 28 (1):109–23. doi: 10.1007/s11442-018-1462-4.
  • Li, L., S. Ma, Y. Zheng, and X. Xiao. 2022. Integrated regional development: Comparison of urban agglomeration policies in China. Land Use Policy 114:105939. doi: 10.1016/j.landusepol.2021.105939.
  • Li, L., Q. Yang, H. Liu, and Y. Ma. 2014. Relationship between the city location and regional balanced development of Jilin Central urban agglomeration. Areal Research and Development 33 (2):25–29.
  • Li, X., and L. Parrott. 2016. An improved genetic algorithm for spatial optimization of multi-objective and multi-site land use allocation. Computers, Environment and Urban Systems 59:184–94. doi: 10.1016/j.compenvurbsys.2016.07.002.
  • Li, X., and A. G. Yeh. 2002. Neural-network-based cellular automata for simulating multiple land use changes using GIS. International Journal of Geographical Information Science 16 (4):323–43. doi: 10.1080/13658810210137004.
  • Liang, X., Q. Guan, K. Clarke, S. Liu, B. Wang, and Y. Yao. 2021. Understanding the drivers of sustainable land expansion using a patch-generating land use simulation (PLUS) model: A case study in Wuhan, China. Computers Environment and Urban Systems 85:101569. doi: 10.1016/j.compenvurbsys.2020.101569.
  • Lin, J., and X. Li. 2019. Large-scale ecological red line planning in urban agglomerations using a semi-automatic intelligent zoning method. Sustainable Cities and Society 46:101410. doi: 10.1016/j.scs.2018.12.038.
  • Liu, J., J. Zhan, and X. Deng. 2005. Spatio-temporal patterns and driving forces of urban land expansion in China during the economic reform era. AMBIO: A Journal of the Human Environment 34 (6):450–55. doi: 10.1579/0044-7447-34.6.450.
  • Liu, X., X. Li, X. Shi, K. Huang, and Y. Liu. 2012. A multi-type ant colony optimization (MACO) method for optimal land use allocation in large areas. International Journal of Geographical Information Science 26 (7):1325–43. doi: 10.1080/13658816.2011.635594.
  • Liu, X., L. Xun, L. Xia, X. Xu, J. Ou, Y. Chen, S. Li, S. Wang, and F. Pei. 2017. A future land use simulation model (FLUS) for simulating multiple land use scenarios by coupling human and natural effects. Landscape and Urban Planning 168:94–116. doi: 10.1016/j.landurbplan.2017.09.019.
  • Liu, Y., W. Tang, J. He, Y. Liu, T. Ai, and D. Liu. 2015. A land-use spatial optimization model based on genetic optimization and game theory. Computers, Environment and Urban Systems 49:1–14. doi: 10.1016/j.compenvurbsys.2014.09.002.
  • Liu, Y., J. Yang, and Y. Liang. 2019. The green development efficiency and equilibrium features of urban agglomerations in China. Economic Geography 39 (2):110–17.
  • Lv, J., Y. Wang, X. Liang, Y. Yao, T. Ma, and Q. Guan. 2021. Simulating urban expansion by incorporating an integrated gravitational field model into a demand-driven random forest-cellular automata model. Cities 109:103044. doi: 10.1016/j.cities.2020.103044.
  • Lv, Y. 2016. Release of the overall plan for the coordinated development of land use in Jingjinji. The Chinese Newspaper of Land and Resources, May 5. https://www.mnr.gov.cn/dt/td/201605/t20160505_2360192.html.
  • Ma, S., X. Li, and Y. Cai. 2017. Delimiting the urban growth boundaries with a modified ant colony optimization model. Computers, Environment and Urban Systems 62:146–55. doi: 10.1016/j.compenvurbsys.2016.11.004.
  • Mansour, S., M. Al-Belushi, and T. Al-Awadhi. 2020. Monitoring land use and land cover changes in the mountainous cities of Oman using GIS and CA-Markov modelling techniques. Land Use Policy 91:104414. doi: 10.1016/j.landusepol.2019.104414.
  • Pred, A. 2017. City-systems in advanced economies: Past growth, present processes and future development options. London and New York: Routledge.
  • Rezayan, H., M. R. Delavar, A. U. Frank, and A. Mansouri. 2010. Spatial rules that generate urban patterns: Emergence of the power law in the distribution of axial line length. International Journal of Applied Earth Observation and Geoinformation 12 (5):317–30. doi: 10.1016/j.jag.2010.04.003.
  • Saaty, T. L. 1988. What is the analytic hierarchy process? Paper presented at Mathematical Models for Decision Support, Berlin, Germany, January.
  • Strzelecka, E. Z. B. 2017. The creative sector in rural areas in the policy of balanced regional development. Barometr Regionalny. Analizy i Prognozy 14 (4):15–21. doi: 10.56583/br.459.
  • Sun, J., K. Zhang, H. An, C. He, and W. Pan. 2017. Conversation by writing on “establishing a more effective new mechanism for regional coordinated development.” China Industrial Economics 11:26–61.
  • Sun, Y., and S. Zhao. 2018. Spatiotemporal dynamics of urban expansion in 13 cities across the Jing-Jin-Ji urban agglomeration from 1978 to 2015. Ecological Indicators 87:302–13. doi: 10.1016/j.ecolind.2017.12.038.
  • Tan, M., and C. Fan. 2004. Relationship between Zipf dimension and fractal dimension of city-size distribution. Geographical Research 2:243–48.
  • Verbavatz, V., and M. Barthelemy. 2020. The growth equation of cities. Nature 587 (7834):397–401. doi: 10.1038/s41586-020-2900-x.
  • Wang, C., B. Yu, Z. Chen, Y. Liu, W. Song, X. Li, C. Yang, C. Small, S. Shu, and J. Wu. 2022. Evolution of urban spatial clusters in China: A graph-based method using nighttime light data. Annals of the American Association of Geographers 112 (1):56–77. doi: 10.1080/24694452.2021.1914538.
  • Wang, D., and Q. Yang. 2018. Rationality diagnosis and evolution characteristics of urban agglomeration scale structure in China. China Population, Resources and Environment 28 (9):123–32.
  • Wang, S., C. Fang, L. Sun, Y. Su, X. Chen, C. Zhou, K. Feng, and K. Hubacek. 2019. Decarbonizing China’s urban agglomerations. Annals of the American Association of Geographers 109 (1):266–85. doi: 10.1080/24694452.2018.1484683.
  • Wang, W., L. Jiao, W. Zhang, Q. Jia, F. Su, G. Xu, and S. Ma. 2020. Delineating urban growth boundaries under multi-objective and constraints. Sustainable Cities and Society 61:102279. doi: 10.1016/j.scs.2020.102279.
  • Wang, Y., X. Li, X. Yao, S. Li, and Y. Liu. 2022. Intercity population migration conditioned by city industry structures. Annals of the American Association of Geographers 112 (5):1441–60. doi: 10.1080/24694452.2021.1977110.
  • Wren, C. 2012. Geographic concentration and the temporal scope of agglomeration economies: An index decomposition. Regional Science and Urban Economics 42 (4):681–90. doi: 10.1016/j.regsciurbeco.2012.03.004.
  • Wu, W., H. Zhao, and S. Jiang. 2018. A Zipf’s law-based method for mapping urban areas using NPP-VIIRS nighttime light data. Remote Sensing 10 (1):130. doi: 10.3390/rs10010130.
  • Wu, Y., M. Jiang, Z. Chang, Y. Li, and K. Shi. 2020. Does China’s urban development satisfy Zipf’s law? A multiscale perspective from the NPP-VIIRS nighttime light data. International Journal of Environmental Research and Public Health 17 (4):1460. doi: 10.3390/ijerph17041460.
  • Xia, C., A. Zhang, and A. G. O. Yeh. 2022. The varying relationships between multidimensional urban form and urban vitality in Chinese megacities: Insights from a comparative analysis. Annals of the American Association of Geographers 112 (1):141–66. doi: 10.1080/24694452.2021.1919502.
  • Xinhua News Agency. 2018. Opinions of the CPC Central Committee and the State Council on establishing a more effective new mechanism for regional coordinated development. Bulletin of the State Council of the People’s Republic of China 35. https://www.gov.cn/gongbao/content/2018/content_5350042.htm.
  • Yang, X., X. Zheng, and R. Chen. 2014. A land use change model: Integrating landscape pattern indexes and Markov-CA. Ecological Modelling 283:1–7. doi: 10.1016/j.ecolmodel.2014.03.011.
  • Yang, Y., W. Bao, and Y. Liu. 2020. Scenario simulation of land system change in the Beijing–Tianjin–Hebei region. Land Use Policy 96:104677. doi: 10.1016/j.landusepol.2020.104677.
  • Zhang, C., C. Zhong, T. Jiang, and X. Li. 2020. Spatio-temporal differentiation of regional coordinated development and its influencing factors in China. Economic Geography 40 (9):15–26. doi: 10.15957/j.cnki.jjdl.2020.09.002.
  • Zhao, L., C. Li, Y. Song, and X. Li. 2020. A spatial-temporal pattern evolution analysis of urban scale development in the Guangdong–Hongkong–Macao region based on nighttime light imagery. Tropical Geography 40 (2):243–53.
  • Zhao, M., Y. Zhong, and G. Xu. 2015. Polycentric progress of the three major city regions in China, 2001–2009. Economic Geography 35 (3):52–59.
  • Zipf, G. 1949. Human behavior and principle of least effort. London: Addison-Wesley.
  • Živanović, Z., B. Tošić, T. Nikolić, and D. Gatarić. 2019. Urban system in Serbia—The factor in the planning of balanced regional development. Sustainability 11 (15):4168. doi: 10.3390/su11154168.

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