URBAN EXPANSION MODELING APPROACH BASED ON MULTI-AGENT SYSTEM AND CELLULAR AUTOMATA

Urban expansion is a land-use change process that transforms non-urban land into urban land. This process results in the loss of natural vegetation and increase in impervious surfaces. Urban expansion also alters the hydrologic cycling, atmospheric circulation, and nutrient cycling processes and generates enormous environmental and social impacts. Urban expansion monitoring and modeling are crucial to understanding urban expansion process, mechanism, and its environmental impacts, and predicting urban expansion in future scenarios. Therefore, it is important to study urban expansion monitoring and modeling approaches. We proposed to simulate urban expansion by combining CA and MAS model. The proposed urban expansion model based on MSA and CA was applied to a case study area of Changsha-Zhuzhou-Xiangtan urban agglomeration, China. The results show that this model can capture urban expansion with good adaptability. The Kappa coefficient of the simulation results is 0.75, which indicated that the combination of MAS and CA offered the better simulation result. * Corresponding author


INTRODUCTION
Urban expansion is a land-use change process that transforms non-urban land into urban land (Bai et al., 2012;He et al., 2016). This process results in the loss of natural vegetation and increase in impervious surfaces. Urban expansion alters the hydrologic cycling, atmospheric circulation, and nutrient cycling processes and generated enormous environ-mental and social impacts (Wade et al., 2009;Wu et al., 2014). Therefore, urban expansion modeling is important to understand urban expansion process and mechanism, and predict the urban expansion.
Cellular Automata (CA) model has been increasingly used to simulate urban growth and land use dynamics (Li et al., 2002;He et al., 2006;Ahmed et al. 2018;Li et al. 2017;Maher et al. 2016;Süha et al. 2016). However, there are some limitations because they cannot explicitly consider the influences of social and human factors in urban expansion simulation. Multi-agent systems (MAS) can be defined as a set of agents interacting in a common environment, make land use decisions within the system. Therefore, Multi-agent systems (MAS) model is now used to simulate land use changes Cé lia et al. 2013;An 2012;Liu et al. 2014). However, this model does not take into account the effect of neighborhood land use on urban expansion. Therefore, coupling CA and MAS model to simulate urban expansion is expected to solve above issues (Ahmed et al. 2017;Tian et al. 2017 Using GIS spatial analysis model, we calculated and obtained thematic layers such as, distance to the river, distance to village road, distance to county road, distance to road, distance to highway, distance to bridge, life service, facilitate of work, leisure and entertainment layers.

Model framework
Based on multi-agents system theory and land use  (1) U i is the utility of the land use i; X j is the decision factor of department and public agents (j=1, 2, 3... k); a j is the decision weight; μ ij is the random disturbance term.

Government agent and its land use decisions
The government agents use competition function to resolve land use conflicts. The competition function is as follows: C t (i, j) is the competition of land use class t in unit (i, j); U d (i, j, t) and U p(i, j, t) are utility functions of land use class t in unit (i, j) for department and public agents, respectively; α is the public agent participation (0≤α≤1) ; P t is priority of department agent to land use class t(p t ≥0).
In order to consider the land requirements of department agent and public agent, the government needs to coordinate land use through competition adjustment as follows: C' t (i, j) is the adjusted competition for land use class t in unit (i, j); n d and n P are number of application of department and public agents to the government for the unit (i, j); δP d and δP p is the competition increase of departments and the public agent for each time.

The degree of urban land use competition
In multi-agent based interactive decision-making process, the optimal allocation of land use was implemented dynamically based on the degree of competition of all land use types, as well as the sequence of configurations of land use and the constraint condition of land use structure.

Cellular automaton model
CA model determines the space conversion of urban land use and simulates the urban expansion. CA model couples human system with the landscape system mainly through spatial competition allocations of urban land use.

Cell and its state definitions
Conventional urban cellular automaton model include urban land, non-urban land cellular states. Taking into account conversion differences of different land uses, we set up five kinds of cellular states: 1) urban-urban land; 2) non-urban land, water; 3) non-urban, arable land; 4) non-urban, forest land; 5) non-urban, unused land. The cellular space is defined in the grid space of 30 x 30m resolution.

Conversion rules and their probability
Firstly, the conversion rules are determined for each cellular.  In the formula, P v (i, j) is probability of non-urban cellular (i,j) converting to urban land; C' (i,j) is conversion degree of competition of cellular (i,j) to urban land; P w(i,j) is land conversion intensity of different land use to urban land; P n (i,j) is the influence of neighborhood cellular to center cellular.

Conversion intensity
The different land uses (non-urban land) possess different intensity of conversion from non-urban land to urban land due to their characteristics, location and difficulty of conversion to urban land. In this study, the transfer intensity of different of non-urban land to urban land is calculated. 1, 2, 3)

Influence of neighborhood cell
The probability that the central cell is influenced by the neighborhood cell is as follows: