## 1 Introduction  
The rapid development of urbanization has led to the disorderly expansion of urban built-up areas and their encroachment on ecological spaces, which has resulted in a series of problems such as waste of land resources, a decrease in biodiversity, degradation of ecosystem services, and destruction of tropical natural resources, all of which seriously restrict the sustainable development of the economy and environment [1; 2; 3]. Sanya is a famous international tropical coastal tourist city located on the southernmost tip of Hainan Island, China. Driven by the development of tourism, Sanya has experienced rapid urban expansion and population growth in recent decades. In the process of urban development, a series of ecological and environmental problems have emerged, such as the destruction of precious tropical rain forests, fragile mountains, key ecologically fragile areas in the coastal zone (coral reefs), and rare freshwater ecosystems. A series of policies have been formulated by the government to protect the ecological security from the damage of urban expansion, which call for delineation the urban development boundary (UGB) to prevent urban sprawl and reserve space for future development [4]. Some cities have realized that it is important to delineate UGB to restrain the disorderly urban growth, and corresponding policies have been proposed, such as the basic ecological line in Shenzhen, China [5]. Thus,how to scientifically guide urban development and coordinate the relationship between urban growth and the ecological environment has become an urgent problem in current research. In this context, urban boundary management policies and tools to curb urban sprawl have emerged. The urban growth boundary (UGB) concept originated in Salem, OR, USA, in the 1970s and was used to delineate rural and urban land. Subsequently, it was effectively applied in Portland, Oregon, USA [6]. The UGB concept mainly emphasizes internal growth, and it aims to ease the tension between urban development and protection of the natural environment, optimizes the urban spatial structure, and formulates scientific and reasonable control policies. This is is of practical significance for sustainable economic and social development and, therefore, is widely used in China [7]. Previous research on UGBs includes several main types. The first type is ecologically oriented, which analyzes the constraints of urban growth based on the ecological sensitivity or ecological suitability, establishes ecological safety patterns, prioritizes the no-build zone in urban space, and draws on the concept of anti-planning to delineate the UGB [8; 9; 10]. The second type involves predicting the future development pattern of a city mainly based on the current urban land use pattern, development pattern, policy guidelines, and other conditions. For example, [PERSON] et al. used neural networks, the geographic information system (GIS), and remote sensing to delineate the UGB of Tehran [11]. [PERSON] et al. took into account the spatial development planning and legal framework in Germany and produced a UGB using building footprints and generally available topographic data as the input for three study areas (Frankfurt/Main, the Hanover region, and rural Brandenburg) [12]. [PERSON] et al. used an artificial neural network (ANN) model and a set of landscape metrics to delineate the UGB in the Siliguri Municipal Corporation [13]. In addition, geo-simulation models such as the cell automation (CA) [14; 15], the CA-Markov model [16], slope, land use, exclusion, urban extent, transportation, hillshade (SLEUTH) model [17], the conversion of land use and its effects at a small regional extent (CLUE-S) model [18], the future land use simulation (FLUS) model [19], and the agent-based model [20; 21] are also often used to predict the future development patterns of cities.