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

The study of the land use optimization of urban agglomerations is of great significance to the rational utilization of land resources and the sustainable development of urban agglomerations. Previous studies have simply regarded the urban agglomeration as a whole area or each city as an isolated individual, without considering the regional coordinated development of urban agglomerations in land use optimization objectives. This study proposed the first attempt to couple Zipf's law and a multiobjective optimization model of land use in an urban agglomeration. Zipf's law was applied to quantify the coordinated development of urban agglomeration and use it as one of the objectives of land use optimization. The genetic algorithm was adopted to establish the optimization model, and different future development scenarios were designed for comparison. The Beijing–Tianjin–Hebei (BTH) urban agglomeration was selected as the study area, and the proposed model obtained effective results within an acceptable time. The Zipf's law–based optimization objective provided a more coordinated scale structure for urban growth and led the urban structure to develop toward the optimized state. There was a conflict, however, between the coordination and the other two objectives (compactness and suitability). Different stakeholders need to consider the trade-offs among these optimization objectives in urban planning. Finally, based on the optimization patterns of local areas, we suggest the following: Some large-scale cities (e.g., Beijing and Tianjin) should strictly control their new urban expansion or transfer part of their resources and population; Langfang and Xingtai should accelerate their development or take over part of the noncapital function of Beijing; and Zhangjiakou and Chengde should optimize their urban morphology and suitability.