基于动态约束的元胞自动机与复杂城市系统的模拟

为获得复杂城市系统更理想的模拟效果,提出时空动态约束的城市元胞自动机(CA)模型。用不同区域、不同时间新增加的城市用地总量作为CA模型的约束条件,形成时空动态约束的CA模型,并利用该模型模拟1988—2010年东莞市和深圳市城市扩张过程。结果表明,利用CA模型模拟的1993年城市用地总精度比静态CA模型提高了5.86%,而且模型中的动态约束条件可以反映城市发展的时空差异性。     

基于元胞自动机的城市用地变化研究

城市土地利用演化的实质是人为干预下城市生态景观的自组织机制作用过程；元胞自动机（CA）所独有的特征和构模方式使其在模拟复杂性系统如城市系统等方面表现出强大的模拟能力。利用ASTER影像数据，在CA模型下对福州市2010年和2020年的城市用地进行了模拟。从而为城市规划提供决策支持服务，对真正合理地利用城市土地，实现城市可持续发展具有重要意义。     

Modeling urban land-use dynamics in a fast developing city using the modified logistic cellular automaton with a patch-based simulation strategy

Cellular automata (CA) have been used to understand the complexity and dynamics of cities. The logistic cellular automaton (Logistic-CA) is a popular urban CA model for simulating urban growth based on logistic regression. However, this model usually employs a cell-based simulation strategy without considering the spatial evolution of land-use patches. This drawback largely constrains the Logistic-CA for simulating realistic urban development. We proposed a Patch-Logistic-CA to deal with this problem by incorporating a patch-based simulation strategy into the conventional cell-based Logistic-CA. The Patch-Logistic-CA differentiates new developments into spontaneous growth and organic growth, and uses a moving-window approach to simulate the evolution of urban patches. The Patch-Logistic-CA is tested through the simulation of urban growth in Guangzhou, China, during 2005–2012. The cell-based Logistic-CA was also implemented using the same set of data to make a comparison. The simulation results reflect that the Patch-Logistic-CA has slightly lower cell-level agreement than the cell-based Logistic-CA. However, visual inspection of the results reveals that the cell-based Logistic-CA fails to reflect the actual patterns of urban growth, because this model can only simulate urbanized cells around the edges of initial urban patches. Actually, the pattern-level similarities of the Patch-Logistic-CA are over 18% higher than those of the cell-based Logistic-CA. This indicates that the Patch-Logistic-CA has much better performance of simulating actual development patterns than the cell-based Logistic-CA. In addition, the Patch-Logistic-CA can correctly simulate the fractal structure of actual urban development patterns. By varying the control parameters, the Patch-Logistic-CA can also be used to assist urban planning through the exploration of different development alternatives.     

模拟退火算法用于产生城市土地空间布局方案

本文发展了一种模拟退火算法辅助产生城市土地空间布局方案。首先建立了城市土地空间配置问题的数学模型 ,目标函数是最小化土地开发费用、最大化不同功能地块间的空间协调性。由于问题存在的诸多空间约束条件使得可行的土地利用布局方案的搜寻过程变得十分缓慢 ,采用了将一些空间约束条件结合到目标函数中的方法 ,如结合了距离约束、方向约束、相同土地利用单元的邻近约束和地块形状的紧凑约束等约束条件。应用于湖南省长沙市暮云工业区用地规划的结果表明 ,模拟退火算法是一种辅助城市土地利用规划的有用的、有潜力的优化方法     

Simulating urban land-use changes at a large scale by integrating dynamic land parcel subdivision and vector-based cellular automata

Cellular automata (CA) have been widely used to simulate complex urban development processes. Previous studies indicated that vector-based cellular automata (VCA) could be applied to simulate urban land-use changes at a realistic land parcel level. Because of the complexity of VCA, these studies were conducted at small scales or did not adequately consider the highly fragmented processes of urban development. This study aims to build an effective framework called dynamic land parcel subdivision (DLPS)-VCA to accurately simulate urban land-use change processes at the land parcel level. We introduce this model in urban land-use change simulations to reasonably divide land parcels and introduce a random forest algorithm (RFA) model to explore the transition rules of urban land-use changes. Finally, we simulate the land-use changes in Shenzhen between 2009 and 2014 via the proposed DLPS-VCA model. Compared to the advanced Patch-CA and RFA-VCA models, the DLPS-VCA model achieves the highest simulation accuracy (Figure-of-Merit = 0.232), which is 32.57% and 18.97% higher respectively, and is most similar to the actual land-use scenario (similarity = 94.73%) at the pattern level. These results indicate that the DLPS-VCA model can both accurately split the land during urban land-use changes and significantly simulate urban expansion and urban land-use changes at a fine scale. Furthermore, the land-use change rules that are based on DPLS-VCA mining and the simulation results of several future urban development scenarios can act as guides for future urban planning policy formulation.     

Modeling dynamic urban land-use change with geographical cellular automata and generalized pattern search-optimized rules

A novel generalized pattern search (GPS)-based cellular automata (GPS-CA) model was developed to simulate urban land-use change in a GIS environment. The model is built on a fitness function that computes the difference between the observed results produced from remote-sensing images and the simulated results produced by a general CA model. GPS optimization incorporating genetic algorithms (GAs) searches for the minimum difference, i.e. the smallest accumulated residuals, in fitting the CA transition rules. The CA coefficients captured by the GPS method have clear physical meanings that are closely associated with the dynamic mechanisms of land-use change. The GPS-CA model was applied to simulate urban land-use change in Kunshan City in the Yangtze River Delta from 2000 to 2015. The results show that the GPS method had a smaller root mean squared error (0.2821) than a logistic regression (LR) method (0.5256) in fitting the CA transition rules. The GPS-CA model thus outperformed the LR-CA model, with an overall accuracy improvement of 4.7%. As a result, the GPS-CA model should be a superior tool for modeling land-use change as well as predicting future scenarios in response to different conditions to support the sustainable urban development.     

An intelligent method to discover transition rules for cellular automata using bee colony optimisation

This paper presents a new, intelligent approach to discover transition rules for geographical cellular automata (CA) based on bee colony optimisation (BCO–CA) that can perform complex tasks through the cooperation and interaction of bees. The artificial bee colony miner algorithm is used to discover transition rules. In BCO–CA, a food source position is defined by its upper and lower thresholds for each attribute, and each bee searches the best upper and lower thresholds in each attribute as a zone. A transition rule is organised when the zone in each attribute is connected to another node by the operator ‘And’ and is linked to a cell status value. The transition rules are expressed by the logical structure statement ‘IF-Then’, which is explicit and easy to understand. Bee colony optimisation could better avoid the tendency to be vulnerable to local optimisation through local and global searching in the iterative process, and it does not require the discretisation of attribute values. Finally, The BCO–CA model is employed to simulate urban development in the Xi’an-Xian Yang urban area in China. Preliminary results suggest that this BCO approach is effective in capturing complex relationships between spatial variables and urban dynamics. Experimental results indicate that the BCO–CA model achieves a higher accuracy than the NULL and ACO–CA models, which demonstrates the feasibility and availability of the model in the simulation of complex urban dynamic change.     

Modeling different urban growth patterns based on the evolution of urban form: A case study from Huangpi,Central China

Spatial patterns of urban expansion mainly include infilling, edge expansion, and outlying growth patterns. The cellular automata (CA) model, is an important spatio-temporal dynamic model and effectively simulates infilling and edge-expansion urban expansion. but is evidently lacking in outlying scenarios. In addition, CA cannot explain the causes and processes of urban land expansion. Given these limitations, we proposed a novel urban expansion model called simulation model of different urban growth pattern (SMDUGP), which can work well in both adjacent (i.e., infilling and edge expansion) and outlying growth patterns. SMDUGP has two main components. First, we divided the non-urban region into two categories, namely, candidate region for adjacent pattern urban growth (CRFAP) and candidate region for outlying pattern urban growth (CRFOP). Second, different methods were utilized to simulate urban expansion in the different categories. In CRFAP, a CA model based on the potential of urban growth was proposed to simulate urban growth in relatively randomly selected urban growth regions based on the discrete selection model and Monte Carlo method as the expansion area was implemented in CRFOP. Huangpi, a suburban area in Wuhan, is utilized as the case study area to simulate the spatial and temporal dynamics of urban growth from 2004 to 2024. SMDUGP can effectively simulate outlying urban growth with a highly improved simulation precision compared with the traditional CA model and can explain the causes and processes of urban land expansion.     

A bottom‐up approach to discover transition rules of cellular automata using ant intelligence

This paper presents a new method to discover transition rules of geographical cellular automata (CA) based on a bottom‐up approach, ant colony optimization (ACO). CA are capable of simulating the evolution of complex geographical phenomena. The core of a CA model is how to define transition rules so that realistic patterns can be simulated using empirical data. Transition rules are often defined by using mathematical equations, which do not provide easily understandable explicit forms. Furthermore, it is very difficult, if not impossible, to specify equation‐based transition rules for reflecting complex geographical processes. This paper presents a method of using ant intelligence to discover explicit transition rules of urban CA to overcome these limitations. This ‘bottom‐up’ ACO approach for achieving complex task through cooperation and interaction of ants is effective for capturing complex relationships between spatial variables and urban dynamics. A discretization technique is proposed to deal with continuous spatial variables for discovering transition rules hidden in large datasets. The ACO–CA model has been used to simulate rural–urban land conversions in Guangzhou, Guangdong, China. Preliminary results suggest that this ACO–CA method can have a better performance than the decision‐tree CA method.     

Exploring the performance of spatio-temporal assimilation in an urban cellular automata model

Urban cellular automata (CA) models propagate and accumulate errors during the modeling process due to the model structure or stochastic processes involved. It is feasible to assimilate real-time observations into an urban CA model to reduce model uncertainties. However, the assimilation performance is sensitive to the spatio-temporal units in the assimilation algorithm, that is, spatial block size and window length (temporal interval). In this study, we coupled an assimilation model, an ensemble Kalman filter (EnKF) and a Logistic-CA model to simulate the urban dynamic in Beijing over a period of two decades. Our results indicate that the coupled EnKF-CA model outperforms the CA-alone counterpart by about 10% in terms of the figure of merit, which reflects the agreement of modeled pixels. We also find that the assimilation performance using a finer block (1 km) is better than that using a coarser block (5 km and 10 km) because of the better depiction of spatial heterogeneity using a finer block. Moreover, the improvement of intermediate outputs using the coupled EnKF-CA model is effective for a certain period (e.g. 5 years). This implies that a high-frequency assimilation may not significantly improve the model performance. The sensitivity analyses of spatio-temporal assimilation in the EnKF-CA model provide a better understanding of the assimilation mechanism that couples with land-use change models.     

A meta-modeling approach for spatio-temporal uncertainty and sensitivity analysis: an application for a cellular automata-based Urban growth and land-use change model

The paper presents a computationally efficient meta-modeling approach to spatially explicit uncertainty and sensitivity analysis in a cellular automata (CA) urban growth and land-use simulation model. The uncertainty and sensitivity of the model parameters are approximated using a meta-modeling method called polynomial chaos expansion (PCE). The parameter uncertainty and sensitivity measures obtained with PCE are compared with traditional Monte Carlo simulation results. The meta-modeling approach was found to reduce the number of model simulations necessary to arrive at stable sensitivity estimates. The quality of the results is comparable to the full-order modeling approach, which is computationally costly. The study shows that the meta-modeling approach can significantly reduce the computational effort of carrying out spatially explicit uncertainty and sensitivity analysis in the application of spatio-temporal models.     

基于遗传算法自动获取CA模型的参数

本文提出了基于遗传算法来寻找CA模型最佳参数的方法。CA被越来越多地应用于城市和土地利用等复杂系统的动态模拟。CA模型中变量的参数值对模拟结果有非常重要的影响。如何获取理想的参数值是模型的关键。传统的逻辑回归模型运算简单,常常用来获取模型的参数值,要求解释变量间线性无关,所以获取的城市CA模型参数具有一定的局限性。遗传算法在参数优化组合、快速搜索参数值方面有很大的优势。本文利用遗传算法来自动获取优化的CA模型参数值,并获得了纠正后的CA模型。将该模型应用于东莞1988~2004年的城市发展的模拟中,得到了较好的效果。研究结果表明,遗传算法可以有效地自动获取CA模型的参数,其模拟的结果要比传统的逻辑回归校正的CA模型模拟精度高。     

基于随机森林的元胞自动机城市扩展模拟——以佛山市为例

本文提出一种基于随机森林的元胞自动机城市扩展(RF-CA)模型。通过在多个决策树的生成过程中分别对训练样本集和分裂节点的候选空间变量引入随机因素,提取城市扩展元胞自动机的转换规则。该模型便于并行构建,能在运算量没有显著增加的前提下提高预测的精度,对城市扩展中存在的随机因素有较强的容忍度。RF-CA模型可进行袋外误差估计,以快速获取模型参数;也可度量空间变量重要性,解释各空间变量在城市扩展中的作用。将该模型应用于佛山市1988-2012年的城市扩展模拟中,结果表明,与常用的逻辑回归模型相比,RF-CA模型进行模拟和预测分别能够提高1.7%和2.6%的精度,非常适用于复杂非线性特征的城市系统演变模型与扩展研究;通过对影响佛山市城市扩展的空间变量进行重要性度量,发现对佛山城市扩张模拟研究而言,距国道的距离与距城市中心的距离具有最重要的作用。     

地理元胞自动机模型研究进展

元胞自动机(Cellular Automata,简称CA)是一种基于微观个体的相互作用空间离散动态模型,其强大的计算功能、固有的平行计算能力、高度动态及空间概念等特征,使它在模拟空间复杂系统的时空动态演变研究具有较强的优势。文章回顾了元胞自动机的发展历程,阐述了CA在地理学中的主要应用领域和研究进展,在此基础上,以现实世界地理实体及现代城市扩张特征为视角,分析目前CA研究所面临的问题,并对其未来的研究趋势进行了初步探讨,认为以下3个方面将是未来CA研究的热点：① 利用不规则元胞及可控邻域的CA模型,对不同规则或不同邻域地理实体的模拟研究;② 采用三维元胞自动机对现代城市扩张进行立体化模拟,以克服二维CA模型的缺陷;③ 将矢量元胞自动机模型应用于地理实体的模拟研究,进一步提高模拟精度。     

多智能体与元胞自动机结合及城市用地扩张模拟

运用多智能体(Agent)和元胞自动机(CA)结合来模拟城市用地扩张的方法,将影响和决定用地类型转变的主体作为Agent引进元胞自动机模型中,Agent在CA确定的城市发展概率的基础上,通过自身及其周围环境的状况,综合各种因素的影响做出决策,决定元胞下一时刻的城市发展概率。运用Agent的决策结果,对CA模型中以随机变量体现的不确定性通过Agent决策行为给予地理意义的新解释。以城市郊区—樟木头镇为例,对1988～1993年城市用地扩张进行了模拟研究,取得了良好的模拟效果。     

城市土地利用变化中邻域相互作用的特征——日本三大都市圈的比较研究

Local spatial interaction between neighborhood land-use categories (i.e. neighborhood interaction) is an important factor which affects urban land-use change patterns. Therefore,it is a key component in cellular automata (CA)-based urban geosimulation models towards the simulation and forecast of urban land-use changes. Purpose of this paper is to interpret the similarities and differences of the characteristics of neighborhood interaction in urban land-use changes of different metropolitan areas in Japan for providing empirical materials to understand the mechanism of urban land-use changes and construct urban geosimulation models. Characteristics of neighborhood interaction in urban land-use changes of three metropolitan areas in Japan,i.e. Tokyo,Osaka,and Nagoya,were compared using such aids as the neighborhood interaction model and similarity measure function. As a result,urban land-use in the three metropolitan areas was found to have had similar structure and patterns during the study period. Characteristics of neighborhood interaction in urban land-use changes are quite different from land-use categories,meaning that the mechanism of urban land-use changes comparatively differs among land-use categories. Characteristics of neighborhood interaction reveal the effect of spatial autocorrelation in the spatial process of urban land-use changes in the three metropolitan areas,which correspond with the characteristics of agglomeration of urban land-use allocation in Japan. Neighborhood interaction amidst urban land-use changes between the three metropolitan areas generally showed similar characteristics. The regressed neighborhood interaction coefficients in the models may represent the general characteristics of neighborhood effect on urban land-use changes in the cities of Japan. The results provide very significant materials for exploring the mechanism of urban land-use changes and the construction of universal urban geosimulation models which may be applied to any city in Japan.     

分析学习智能元胞自动机及优化的城市模拟

元胞自动机被广泛应用于城市及其他地理现象的模拟,模拟过程中的最大问题是如何确定模型的结构和参数。该文提出一种基于分析学习的智能优化元胞自动机,该模型在逻辑回归模型的基础上,基于分析学习的智能方法,寻找元胞自动机模型的最佳参数。该方法允许用户控制空间变量影响权重,进而模拟出不同的城市发展模式,可为城市规划提供重要参考。     

Self-modifying CA model using dual ensemble Kalman filter for simulating urban land-use changes

There are many different methods to calibrate cellular automata (CA) models for better simulation results of urban land-use changes. However, few studies have been reported on combination of parameter update and error control using local data in CA calibration procedures. This paper presents a self-modifying CA model (SM-CA) that uses the dual ensemble Kalman filter (dual EnKF), which enables the CA model to simultaneously update model parameters and simulation results by merging observation data (local data). We applied the proposed model to simulate urban land-use changes in a 13-year period (1993–2005) in Dongguan City, a rapidly urbanizing region in south China. Simulation results indicate that this model yields better simulation results than the conventional logistic-regression CA and decision-tree CA models. For example, the validation is carried out using cross-tabulation matrix. The simulation results of SM-CA have allocation disagreement of 10.18%, 19.64%, and 30.03% in 1997, 2001, and 2005, respectively, which are 2.12%, 2.47%, and 6% lower than conventional logistic-regression CA models.     

Simulating urban growth by integrating landscape expansion index (LEI) and cellular automata

Traditional urban cellular automata (CA) model can effectively simulate infilling and edge-expansion growth patterns. However, most of these models are incapable of simulating the outlying growth. This paper proposed a novel model called LEI-CA which incorporates landscape expansion index (LEI) with CA to simulate urban growth. Urban growth type is identified by calculating the LEI index of each cell. Case-based reasoning technique is used to discover different transition rules for the adjacent growth type and the outlying growth type, respectively. We applied the LEI-CA model to the simulation of urban growth in Dongguan in southern China. The comparison between logistic-based CA and LEI-CA indicates that the latter can yield a better performance. The LEI-CA model can improve urban simulation accuracy over logistic-based CA by 13.8%, 10.8% and 6.9% in 1993, 1999 and 2005, respectively. Moreover, the outlying growth type hardly exists in the simulation by logistic-based CA, while the proposed LEI-CA model performs well in simulating different urban growth patterns. Our experiments illustrate that the LEI-CA model not only overcomes the deficiencies of traditional CA but might also better understand urban evolution process.     

基于粗集的知识发现与地理模拟——以深圳市土地利用变化为例

为了更有效地模拟地理现象的复杂演变过程,提出了用粗集理论来确定元胞自动机 (CA)不确定性转换规则的新方法。CA可以通过局部规则来有效地模拟许多地理现象的演变过程。但目前缺乏很好定义CA转换规则的方法。往往采用启发式的方法来定义CA的转换规则,这些转换规则是静态的,而且其参数值多是确定的。在反映诸如城市扩张、疾病扩散等不确定性复杂现象时,具有一定的局限性。利用粗集从GIS和遥感数据中发现知识,自动寻找CA的不确定性转换规则,基于粗集的CA在缩短建模时间的同时,能提取非确定性的转换规则,更好地反映复杂系统的特点。采用所提出的方法模拟了深圳市的城市发展过程,取得了比传统MCE方法更好的模拟效果。