Land use and land cover change simulation enhanced by asynchronous communicating cellular automata

Full text

Land use and land cover change simulation enhanced
by asynchronous communicating cellular automata
Qin Leia, Hong Jinb, Jia Lee∗,a, Jiang Zhonga
aCollege of Computer Science, Chongqing University, Chongqing 400044, China
bSchool of Architecture and Urban Planning, Chongqing University, Chongqing 400030,
China
Abstract
Land use and land cover change (LUCC) modeling is crucial to urban plan-
ning and policy making. A well-used and effective paradigm for LUCC is the
ANN-CA model which employs an artificial neural network (ANN) to calculate
a transition probability over each land cell from various driving factors, and
then uses a cellular automaton (CA) to evolve all cells consecutively to update
their land usage and coverage according to the estimated probability distribu-
tion. This paper focuses on the effect of delays or perturbations possibly taking
place between land cells on the LUCC modeling. To this end, a new ANN-
CA model is proposed which adopts an asynchronous communicating cellular
automaton (ACCA), rather than the conventional synchronous CA. Especially,
the ACCA allows every cell to communicate with its neighbors independently
at random times via a specific protocol, which offers a natural way to include
stochastic delays in exchanging the current land usages between cells. As a
result, every change of a cell’s land use in the ACCA may not affect its neigh-
bors immediately, but is subject to delays that might play an important role in
modeling the practical LUCC. Numerical analysis of the new model are carried
out in three regions of Chongqing city, China with different scales: Yongchuan
District, Sanjiao Town, and Huangguashan Village, and experimental results
demonstrate that the proposed ANN-ACCA model can achieve a higher accu-
racy for LUCC simulation as compared to conventional ANN-CA models.
Key words: land use change, cellular automaton, asynchronous
communication, simulation
1. Introduction
The study of land use and land cover change (LUCC) is crucial for under-
standing the allocation of land resources for various purposes, such as urban-
ization [1, 2], agricultural development [3], transportation [4], and ecological
∗Corresponding author
Email address: lijia@cqu.edu.cn (Jia Lee)
Preprint submitted to Elsevier May 24, 2024

conservation [5, 6]. In recent years, many governments and research institutions
have placed significant emphasis on the study of LUCC to discover the under-
lying mechanisms of land use changes and the impact of both natural factors
(e.g., slope, elevation) and socio-economic factors (e.g., roads, railroads) on land
use development [7, 8, 9, 10]. In addition, quantifying and simulating the future
evolution of spatial patterns of different land use types is crucial for regional
sustainable development studies.
Recently, the LUCC modeling has progressed significantly and many meth-
ods adopt an artificial neural network (ANN) [11, 12, 10, 9] to calculate the
initial transition probabilities of each land cell. Likewise, the change of land use
is associated with a conversion cost [13, 14], which is usually estimated based on
the opinions of policy planners and the experience of regional experts. In this
case, parameters in the LUCC simulation can be easily adapted to a real situa-
tion via setting rational conversion costs [15]. In addition, an inertial mechanism
of land adaptivity [12] is included to resolve complex local land use interactions
and to simultaneously participate in the calculation of transition probabilities
for different land use types. More specifically, most well-used LUCC models
incorporate both top-down and bottom-up components [11, 12, 7, 8, 9, 10]. The
top-down component takes into account the human intervention in the simu-
lation process, while the bottom-up component incorporates machine learning
methods and cellular automata (CAs) to simulate natural land evolution pro-
cesses. A general simulation process comprises the following steps: (1) dividing
the entire area into a number of land cells and assigning an initial usage (i.e.,
top-down component) to each cell ; (2) calculating the transition probability
(bottom-up component) through machine learning methods and updating the
land usage of each cell through a roulette selection method (bottom-up com-
ponent); (3) repeating step (2) until a predetermined end condition (top-down
component) is reached , when, for instance, the quantities of each land usage
reach the expected target value.
A cellular automaton is a dynamical system consisting of a huge number
of identical cells, in which each cell can only access and communicate with the
neighboring cells at any time [16]. Various CA models have been extensively
applied to simulate complex systems and structures that emerge from the inter-
action of simple cells [17, 18]. In the context of LUCC, most conventional CAs
used for LUCC simulations employ synchronous transition rules [19], such that
all cells change their states at the same time in accordance with a transition
function. However, this approach seems inadequate to capture the reality of
land evolution, where different cells may change at different rates and the inter-
action between cells may be delayed by various natural and human factors [20].
Thus, applying different CA models that can account for the unpredictable de-
lays in both the transitions of cells and communications between cells is crucial
for a more accurate and practical simulation of LUCC.
A convenient way to introduce asynchronism in LUCC simulation is using
an asynchronous cellular automaton (ACA) [20, 21]. An ACA allows each cell
to be updated at random times independent from other cells [22, 23], whereby
some cells may undergo transitions in ahead of other cells to simulate their
2

corresponding land cell, thereby realizing a difference in the rate of land use
change between cells. In this case, the change of any cell’s usage will immedi-
ately affect the successive transitions of its neighboring cells according to the
CA’s definition, whereas in usual and practical situation, the effect of a cell’s
land use change or even the information about the change may be subject to
unexpected delay before transferring to either neighbor of the cell [12, 24]. The
conventional ACAs, therefore, seem hard to capture the systematic and detailed
dynamics of delays in information transmission between land cells. Recently,
a special type of ACAs, called asynchronous communicating cellular automata
(ACCAs), was proposed [25], which enable each cell not only to do transitions at
random times, but also to be able to communicate with either neighbor via an
asynchronous protocol. This turns out to be able to separate the communication
and transitions of any cell, and thus the cell may update its state depending on
some past state of a neighbor, rather than the neighbor’s current state, which
tends to facilitate stochastic delays to be involved into the LUCC simulation.
Unlike other approaches that aim to improve the performance of ANN (e.g.,
using deep learning methods such as CNN or LSTM to improve the accuracy
of ANN) [7, 8], In this paper, we couple an ANN with the ACCA to implement
the LUCC simulation, giving rise to an ANN-ACCA model, which attempts
to enhance the accuracy of LUCC simulation by introducing asynchronism and
delay in both the transition of and mutual influence between land cells. In
contrast to conventional ACAs, an ACCA installs buffers in each land cell [25]
in one-to-one correspondence with all neighboring cells. In this case, when a
cell of an ACCA is activated, it has the opportunity to communicate with its
neighbors and store their states in its corresponding buffer. Also, the cell holds
a probability to change the state via a transition function, in which case the cell
determines its new state based on the information stored in its buffer, rather
than relying on the current state of its neighbors. Especially, the unpredictable
communication between cells in an ACCA leads to more complex and unique dy-
namics compared to a conventional ACA, provided that both CAs use identical
cell states and transition function [25]. Despite the more complex and unpre-
dictable dynamics, any synchronous CA can be transformed into an equivalent
ACCA, demonstrating the equivalence of computational power between these
two models [25]. The equivalence with conventional CA models plays a crucial
role to ensure the ACCAs can be applied to simulate and analysis of complex
phenomena emerging from local interactions among a large number of simple
elements, including the LUCC simulation.
The remainder of this paper is organized as follows: Section 2 describes the
definition of ACCA. Section 3 contains the definition of the ANN-ACCA model
and the way to use it in LUCC. Section 4 describes the land data of three regions
for experiments. Section 5 provides the experimental results, which demonstrate
the effectiveness of ANN-ACCA. This paper enclosed with the conclusion in
Section 6.
3

2. Asynchronous Communicating Cellular Automata
2.1. Cellular automata
Let Zbe the set of all integers. A Cellular Automaton (CA) is defined
by a 5-tuple (Zd,N, Q, f, q0), where Zdrepresents d-dimensional array of cells
(d > 0). N ⊂ Zdis a finite set called neighborhood index.Qis a finite set of
states (Q=∅). f:Q|N | →Qis a local transition function. In addition, q0(∈Q)
is a special state, called quiescent state, that satisfies f(q0, ..., q0) = q0. Here a
configuration xtat time step t≥0 is a mapping xt:Zd→Qwhich assigns a
certain state in Qto every cell in the cell space.
Assume N={n0, n1, ..., nk}with k=|N | − 1. Synchronous CAs require
all cells to undergo state transitions simultaneously at each discrete time steps
in accordance with a global transition function F, such that for any t≥0,
xt+1 =F(xt) and
∀c∈Zd:xt+1(c) = F(xt)(c) = f(xt(c+n0), xt(c+n1),· · · , xt(c+nk)).
In contrast to synchronous CA, asynchronous CA allows its cells to update
their states independently and at different random times. There are two com-
mon types of asynchronous updating schemes for ACA, which are described as
follows [26, 27].
•fully asynchronous updating: At each time step, a single cell is selected at
random from the set of cells and the local rule is applied to it.
•α-asynchronous updating: At each time step, each cell has a given proba-
bility αto apply the rule and a probability 1−αto stay in the same state.
The parameter αis referred to as the synchrony rate.
The α-asynchronous updating scheme provides a probability to control the
updating rates of each cell at any time. For α-asynchronous updating scheme,
it turns into synchronous updating when α= 1. The α-asynchronous updating
scheme iterate the evolutions of CA though the global transition function F∆as
follows,
xt+1(c) = F∆(xt(c)) = f(xt(c+n0), xt(c+n1), ..., xt(c+nk)) if c∈∆(t)
xt(c) otherwise
(1)
where ∀t∈N,∀c∈Q, N={n0, n1, ..., nk}and ∆(t) : N→ P(Q) is a selection
function [26] which gives for time tthe subset of cells to be updated, where each
cell has a probability αto be selected.
2.2. Definitions of ACCA
Whether it is a synchronous or an asynchronous CA, each cell gets the latest
state of its neighbors when it updates its state[22]. An asynchronous communi-
cating cellular automaton is a special type of ACA defined as (ZZd, N , Q, f, q0),
4

in which cells may be updated randomly and independently from each other.
Unlike a conventional ACA, each cell in an ACCA carries not only a state
from the set Q, but also |N| − 1 buffers corresponding to each of its neighbors
excluding itself. These buffers are used to store the states received from commu-
nication with each neighboring cell. The introduction of buffers helps to control
the communication and transition of cells under asynchronous protocols [25].
In an ACCA, the configuration at each time step is a mapping xt:ZZd→
Q|N|× {B, L, U }, assigning each cell an |N|-tuple of states from Qand an
action mode from the set {B, L, U }. This is different from a conventional
ACA, where each cell is assigned a single state. There are three action modes:
B(broadcasting), L(listening) and U(updating), among which the Band L
modes are used for a cell to communicate with the neighboring cells, with U
mode for updating the cell’s state using the local transition function f.
Without loss of generality, assume that the global transition function of
an ACCA is xt+1 =F∆(xt). Then for each cell c∈xt∧∆(t), the cell is
activated for transition in configuration xtat time t. Its action mode can be
expressed as ψ(xt(c)) ∈ {B, L, U }.χ(xt(c)) ∈Qdenotes the current state of
cell cin configuration xt. Each θj(xt(c)) ∈Qrepresents a buffer to memorize
the (current or past) state of the adjacent cell c+nj(1 ≤j≤ |N|). The three
action modes {B, L, U }are defined in detail at transition as follows.
•B(broadcasting mode):
(1) χ(xt+1(c)) = χ(xt(c)).
(2) ∀j∈ {1,· · · ,|N| − 1}:θj(xt+1(c)) = θj(xt(c)).
(3) ψ(xt+1(c)) = rand({B , L, U}).
The mode Bprohibits a cell from altering its state or any buffer during a
transition, yet allows it to randomly switch to another mode.
•L(listening mode):
(1) χ(xt+1(c)) = χ(xt(c)).
(2) For each i∈ {1,· · · ,|N|−1}, if ψ(xt(c+ni)) = Bthen θi(xt+1 (c)) =
χ(xt(c+ni)); otherwise θi(xt+1(c)) = θi(xt(c)).
(3) ψ(xt+1(c)) = rand({B , L, U}).
The mode Lallows a cell to receive the current states from its neighbors
that are in broadcasting mode, and then updates its buffers accordingly.
If any of its neighbors are not in mode B, the corresponding buffers in the
cell will not change. Additionally, the mode of the cell may switch to a
different mode.
•U(updating mode):
(1) χ(xt+1(c)) = f(χ(xt(c)), θ1(xt(c)),· · · , θ|N|−1(xt(c))).
(2) ∀j∈ {1,· · · ,|N| − 1}:θj(xt+1(c)) = θj(xt(c)).
5

(3) ψ(xt+1(c)) = rand({B , L, U}).
The mode Uallows a cell to update its state using the transition function
f, which operates based on the cell’s current state and the states stored
in its buffers, rather than the real-time states of its neighboring cells.
During this process, the cell’s buffers remain unchanged, while its action
mode may change.
Although the function rand mentioned above can represent any random func-
tion, in the implementation of this paper, it is a uniform random selection. A
cell in broadcast mode will keep transmitting its current state to all cells in its
neighborhood until the mode is shifted due to a transition in the cell. Com-
munication between neighboring cells is only possible if one cell is in mode B
and the other is in mode L. In this scenario, the cell in mode Lwill change
its buffer to reflect the current state of its neighbor in mode Bupon transition.
When a cell in mode Uundergoes a transition, it can only access the states in
the buffers but cannot delete them. More detailed mathematical properties can
be found in [25].
Although the definition of ACCA assumes the local transition function is
deterministic in general, it can be extended to the framework of probabilistic
cellular automata (PCAs) [?], for the sake of simulating the land use and
land change process via CAs [12]. Like a common CA, a PCA is defined by
(ZZd, N , Q, f, q0) except that the local function is defined as f:Q|N|→ M(Q)
where M(Q) is the set of probability measures over Q. Thus, at every time step,
each cell of the PCA may possibly be updated to any state in Qwith a certain
probability, rather than a single state as a conventional CA, and the probability
measure is decided by the current states of all cells in the neighborhood [?]. The
extension of an ACCA with a stochastic transition function is straightforward,
in which case each cell, when in mode U, will use the recorded states in its
buffers to decide a probability measure, rather than the presents states of all
neighbors.
2.3. Estimation of communication delay in ACCA
Assume that cis a land cell in the ACCA, t≥0 and M∈ {B, L, U }. To
estimate the communication delay, let P(c, t, M) denote the probability that
cell cchanges or remains in action Mat time t. Then Psatisfies the following
recursive function,
P(c, t, M ) = 




1, t = 0 ∧M=B
0, t = 0 ∧M=B
1
3α+ (1 −α)P(c, t −1, M ), t > 0
(2)
In Equation.2 when t > 0, the first term α/3 indicates that each cell has
αprobability of being selected for transition, i.e, c∈∆(t) and change the
mode to M. The second term indicates the probability that c /∈∆ (t) while
the cell cmaintains the action mode Mat time t−1. Since the selection
6

function ∆ for the all cells always works independently and synchronously, and
all cells are identical and uniformly distributed, it is known that the probability
P(c, t −1, M ) is spatially invariant for all cells and eventually converges and
stabilizes at 1/3 as the number of iterations increases. So P(c, t −1, M ) can
be abbreviated to P(M) regardless of the value of αtaken, and assuming that
P(L) = P(B) = P(U)=1/3.
In ACCA, communication between land cells is conditional on the direct
neighbours of the land cell in mode Lbeing in mode B. Assuming that the
number of neighbours of a land cell is N, the probability that any land cell
communicates with at least one neighbour, P(S), can be expressed by the fol-
lowing equation.
P(S) = αP (L)1−(1 −P(B))N(3)
The expectation of communication delay E(S) is the inverse of the probability
P(S), and the average communication delay of a cell in ACCA can be expressed
by the following equation.
E(S) = 1
P(S)=3N+1
α(3N−2N)(4)
As a result, the ACCA may yield a stochastic delay in the communica-
tions between cells of which the expectation value is inverse proportion to the
updating rate αand tends to decrease as the size of neighborhood increases.
The communication delay will enhance the LUCC simulation as compared to
conventional CAs, as we will show in the following section.
3. A Novel ANN-ACCA model for LUCC Simulation
The proposed ANN-ACCA model’s framework is depicted in Fig.1 and con-
sists of two parts: an ANN part and an ACCA part. The ANN part focuses
on the training and inference processes of the neural network. The ACCA
part outlines the iterative process of ACCA, including the behavior of the land
cells in the three different modes {B, L, U }and the calculation of the variables
affecting the transition probability of the land cells. These variables include
probability-of-occurrence, land inertia coefficient, conversation cost, and neigh-
borhood effects.
3.1. Probability-of-occurrence
Land use and land cover change is a result of the interaction between peo-
ple, nature, and the surrounding environment, leading to the development of
economies and increased social welfare. Therefore, LUCC is often modeled as a
function of social structure, economy, and physical environment, with the inde-
pendent variables known as the ”driving factors” of LUCC [28]. These driving
factors can be broadly categorized into three groups: socio-economic, natural
environment, and location factors [29]. While natural environment factors do
not directly drive LUCC, they can indirectly impact it by altering the surface,
7

X: driving factors in 2012
y: land use in 2012
Random sampling for training
Trained
ANN
Inference
�
: probability-of-
occurrence in future
ANN
Initialize land cells
and action modes
Random shift
action modes
mode =B ?
No
mode =L ?Update buffers
Yes
No
Combined
probabilities
mode = U
Probability-
of-occurrence
Self-adaptive
land inertia
Converting
cost
Neighborhood
influence
Roulette selection
Reach the
demands?
Land use in future
End
Yes
No
ACCA
Yes Broadcast
information
Figure 1: The schematic framework of the proposed ANN-ACCA.
8

such as climate change changing the surface shape or soil quality and slope af-
fecting land use allocation. The relationship between driving factors and land
use can be expressed as the probability-of-occurrence, which shows how active
or adapted a particular land use type is in a specific location. This probability
can be used to identify patterns in historical LUCC and inform policy making.
The driving factors required for the calculation of probability-of-occurrence vary
from study area to study area and may include factors such as slope, elevation,
and proximity to roads.
The relationship between different driving factors and land use types is cru-
cial to understand. However, these relationships are complicated and often in-
volve non-linear functions. Machine learning algorithms, such as logistic regres-
sion, support vector machines (SVM), and artificial neural networks (ANN), can
be employed to model these non-linear relationships. Among these algorithms,
ANNs are commonly preferred due to their robustness to errors, resulting in im-
proved simulation outcomes compared to Logistic-CA and CLUE [12, 11, 8]. In
simulating LUCC, a simple structure for the artificial neural network (ANN) is
often enough. A 3-layer ANN is typically sufficient in providing accurate results
while keeping computational cost low, as demonstrated in previous research [11].
In the ANN part in Fig.1, the ANN is first trained and requires data {X, y}.
Where X= [x1, x2, ...xn]Tis the driving factors at time t1and y= [y1, y2, ...ym]T
is the land use at time t1(nand mis the number of driving factors and land
cells respectively and |xi|=m). The neural network can be represented by the
following equation,
net(X) = σ(W X +B) (5)
and then the probability-of-occurrence can be expressed as follows,
ˆy=o(net(X)) (6)
where Wand Bdenote weights and biases. σdenotes the activation function
of hidden layer, and the sigmoid is usually used. And odenotes the activation
function of output layer, and since it is a multi-classification task, we use the
softmax.
σ(x) = 1
1 + e−x(7)
o(xi) = exi
Pkxk
(8)
where kdenotes the number of classes.
In order to handle the large amount of data in a 500×500 size map with
250,000 land cells, it’s necessary to perform data sampling. There are two
methods for data sampling: random sampling and uniform sampling. In random
sampling, the number of samples for each land use type is proportional to its
proportion. In contrast, in uniform sampling, the number of samples for each
land use type is the same.
The optimization of the neural network model is performed using the ADAM
method [30]. Once trained, the model is used to make predictions on all land
cells and calculate the probabilities-of-occurrence for each land cell.
9

3.2. Conversion cost
The conversion cost is an important component in the LUCC simulation,
reflecting the ease or difficulty of transitioning from one land use type to another.
This cost can be influenced by factors such as the current land use, the desired
new use, and existing infrastructure and regulations. The conversion cost can
also play a key role in shaping the overall outcome of the simulation, as it allows
for top-down control of the process. The effectiveness of using conversion costs
has been proven in several large scale LUCC models [13, 14, 31, 32].
The conversion cost matrix is usually predefined to ensure that the simula-
tion process follows a specific direction, and it mainly takes into account the
artificially set task objectives, ignoring other factors. The conversion cost, de-
fined as 0 ≤Costi→j≤1, represents the difficulty of converting land cells from
type ito type j. The higher the value, the more challenging the conversion, and
the conversion cost remains constant throughout the simulation process.
3.3. Inertia coefficient
The iterative process of ACCA involves competition and interaction between
different land cells, so an adaptive inertia coefficient can be employed to reflect
the persistence of the previous land use types. This provides a form of top-down
control and allows the land inertia coefficient to dynamically adjust the land use
types based on the difference between the macro demand and the amount of land
already allocated. If the development trend of a particular land use type runs
counter to the macro demand, the inertia coefficient will attempt to rectify this
discrepancy in the next iteration. For instance, if the macro demand calls for
more urban land and the previous urban land allocation has decreased, the
inertia coefficient will be increased to encourage the transition of other lands to
urban land.
The inertia coefficient can be expressed by the following equation,
Inertiat
m=




Inertiat−1
m; if 
Dt−1
m
≤
Dt−2
m

Inertiat−1
m×Dt−2
m
Dt−1
m; if Dt−1
m< Dt−2
m<0
Inertiat−1
m×Dt−1
m
Dt−2
m; if 0 < Dt−2
m< Dt−1
m
(9)
where Inertiat
mdenotes the inertia coefficient corresponding to land use type m
at moment t(tth iteration). Dt
mdenotes the difference between the amount of
macro demand for land use type m(the amount of target land) and the amount
currently allocated lands to mat moment t.
If the difference between macro demand and currently allocated lands is
decreasing, it is consistent with macro demand and keeps the inertia coefficient
constant. If macro demand is smaller than currently allocated lands and the
gap between macro demand and allocated lands is increasing, it will decrease
the inertia coefficient. If macro demand is larger than currently allocated and
the gap between macro demand and allocated lands is increasing, it will increase
the inertia coefficient. During the iterative process of the ACCA, the inertia
coefficient is continuously adjusted so that different land use types can compete
with each other, so that the final land allocation can meet the macro demand.
10

Figure 2: Moore Neighborhood.
3.4. Neighborhood effects
The autocorrelation of LUCC patterns is due to two main factors. Firstly,
the distribution of landscape features and environmental gradients play a sig-
nificant role in determining LUCC patterns. Secondly, the spatial interaction
between different types of land, such as the tendency for urban sprawl to occur
near existing urban areas, also contributes to the autocorrelation in the patterns
of LUCC.
In ACCA, the calculation of neighborhood effects differs from the conven-
tional CA[12]. Since asynchronous communication is considered, the transmis-
sion of information between neighbors in ACCA will become asynchronous, i.e.,
communication with neighbors will occur only when the land cell is in mode L,
and the latest state of neighbors in mode Bwill be updated to the correspond-
ing buffers. When implementing the above scheme, the neighborhood effects
are calculated by using the state in the buffers instead of the current latest
state of the neighbor. The calculation of the neighborhood effects in ACCA is
represented by the following equation,
Ωt
c,m =PN
r=1(θr(xt−1(c)) = m)
N×αm(10)
where θr(xt−1(c)) denotes the land use type of the rth buffer of the current
land cell cat time t.Nindicates the number of neighbors, for example, Fig.2
indicates Moore neighborhood with a window of 3 and the number of neighbors
N= 32−1 = 8. In ACCA, we choose the Moore Neighborhood computing
neighborhood effects. PN
r=1 (θr(xt(c)) = m) denotes the number of land use
type min the buffers of cell cat time t−1.; αmindicates the influence weight of
land use type mon the surrounding, and this parameter is part of the top-down
control and is pre-defined by human.
3.5. Combination probability and roulette selection
In traditional LUCC models, the land use type with the highest transition
probability is selected as the target type [11]. However, this method only con-
siders the dominant land use type, ignoring the competition with other types,
thus limiting the allocation of non-dominant land use types. Previous studies
used roulette selection to determine the next land use type for a given cell based
11

on a set of combination probabilities, overcoming this limitation [12]. Roulette
selection allows for the selection of land use types with lower combination prob-
abilities, reflecting the inherent uncertainty in the LUCC process in reality.
Therefore, we chose roulette selection for the ACCA model in the specific im-
plementation process, instead of directly selecting the land use type with the
highest probability.
Specifically, the combined probability of the transition during each iteration
can be expressed as the following equation.
CP t
n(c) = ˆy(c|m→n)×Ωt
c,n ×Inertiat
n×(1 −Costm→n) if m=n
ˆy(c|m→n)×Ωt
c,n ×1×(1 −Costm→n) if m=n(11)
CP t
n(c) denotes the combinatorial probability that land cell cis transitioned
to type nfrom type mat time t, where ˆy(c|m→n) denotes the pre-estimated
probability for a single cell cto change the state to a new land type nfrom
the old land type m. When m=n, we must consider the effect of inertia
Inertiat
ngenerated by the current iteration on the next iteration, when m=n,
set Inertiat
n= 1 that can ignore inertia.
In each iteration, for land cell cat time t, the CP set is usually CP =
{CP t
1(c), C P t
2(c), ..., C P t
k(c)}, where kdenotes the number of land use types
and 0 ≤n≤k. Eventually, the land use type of land cell cat time t+ 1 will be
obtained from the CP by probability sampling (i.e., roulette selection and the
probability that each land type nis selected is C P t
n(c)/Pk
i=1 CP t
i(c)).
3.6. Overall
Now let’s summarize the above together. Algorithm 1 shows LUCC simula-
tion process with ANN-ACCA model. Lines 1-7 represent the initialization of
the entire process, including the training of the ANN and the initialization of
the land cells and their action modes. A more detailed definition can be found
in [25]. Cis the set of all land cells i.e. C=c1, c2, ..., cm, where mdenotes the
total number of land cells. The above three functions, when applied to C, mean
that all elements of Care executed.
The ACCA process is then carried out from line 8, updating the inertia
coefficients before the start of each iteration (line 9). In line 10, a percentage
of land cells are selected to participate in the subsequent process (lines 13-26)
based on the synchrony rate α. The transitions of land use types occur only in
mode U. Communication between land cells occurs in mode L. At the end of
each iteration, a new mode is randomly assigned to all land cells (line 27). I(x)
in line 18 indicates the indicator function, which is I(X) = 1 when X=T r ue,
otherwise I(X) = 0. The equations in lines 18 and 19 correspond to Equation.10
and Equation.11 respectively. In line 29, it is determined whether the current
quantity of each land use type reaches the target quantity D. If so, the iteration
is ended early without having to execute the total number of iterations.
12

Algorithm 1 LUCC simulation process with ANN-ACCA
Input: Driving factors and land use for training {X, y}.
Hyperparameters: Synchrony rate α; Maximum number of iterations T;
Window of neighbours N; Neighbourhood weights w; Conversion costs Cost;
Number of target land types D.
Output: land use in future.
1: net ← {X, y}(Training a neural network.)
2: ˆy←net(Xt) (Calculate the probability-of-occurrence.)
3: Q←set(y) (Get the collection of land use types.)
4: χ(C0)←y(Initialize land cells.)
5: offset ← {n1, n2, ..., nN2−1}(Moore Neighbourhoods.)
6: ∀nj∈offset, θj(C0)←χ(C0+nj) (Initialize buffers of land cells.)
7: ψ(C0)←B(Initialize the action mode of the land cells as B.)
8: for each t∈Tdo
9: Update(Inertia) (Equation.9)
10: ∆(t)←selection function with probability α
11: for each c∈Ctdo
12: if c∈∆(t)then
13: if ψ(ct) == Lthen
14: θj(ct)←χ(ct+nj), if ψ(ct+nj) == Bwith nj∈offset
15: end if
16: if ψ(ct) == Uthen
17: for each n∈Qdo
18: Ωt
c,n ←PN×NI(θj(ct) == n)×wk/(N2−1) (Equation.10)
19: CP t
n(c)←ˆy(c|χ(ct)→n)×Ωt
c,k ×Inertiat
n×1−Costχ(ct)→nif χ(ct) == n
ˆy(c|χ(ct)→n)×Ωt
c,k ×1×1−Costχ(ct)→nif χ(ct)=n
(Equation.11)
20: end for
21: χ(ct)←Roulette([C P t
0(c), C P t
1(c), ..., C P t
k(c)])
22: end if
23: if ψ(ct) == Bthen
24: χ(ct+1)←χ(ct)
25: end if
26: end if
27: ψ(ct+1(x)) ←rand({B , L, U}) (Shift the action modes uniformly at
random)
28: end for
29: if |χ(Ct)| ≥ Dor t > |T|then
30: Break
31: end if
32: end for
13

(a)
(b)
Figure 3: (a) Administrative division map of Chongqing; (b) Location of Yongchuan District.
4. Preparation of Land Use Data for LUCC Simulation
In this paper, we prepared data from three regions with different adminis-
trative levels in China: Yongchuan District, Sanjiao Town and Huangguashan
Village for LUCC simulations. The areas are 1576, 108 and 20.08 square kilome-
ters respectively. Yongchuan District is located in Chongqing, southwest China.
Fig.3 (a) shows the administrative division of Yongchuan District in Chongqing
and Fig.3 (b) shows the location of Yongchuan District. Both Sanjiao Town and
Huangguashan Village are located in Yongchuan District. Fig.4 (a) illustrates
the administrative division of Yongchuan District. Fig.4 (b) and (c) show the
locations of Huangguashan Village and Sanjiao Town respectively.
All land use data in this experiment were obtained from the Chongqing Nat-
ural Resources and Planning Bureau. Please refer to the tables in the subsequent
sub-sections for the source of the driving factors.
4.1. Yongchuan District
Yongchuan District is located in the southwest of Chongqing, China, with
area of 1576 square kilometres. For the practical simulation, we set the input
image size of Yongchuan District to 1238 ×1965, with each pixel representing
an area of 35 ×35 square metres.
The data on land use in Yongchuan District in 2012 and 2017 are used in
the experiment (See Fig.6). The 2012 data was used as the starting point in the
experiment to simulate the land use in 2017. Then by comparing the simulated
14

(a)
(b)
(c)
Figure 4: (a) Administrative division map of Yongchuan District; (b) Location of Huang-
guashan Village; (c) Location of Sanjiao Town.
15

(a) Slope (b) Average GDP (c) DEM (d) Population density
(e) Distance to main roads (f) Distance to central city (g) Distance to railway (h) Distance to water
Figure 5: Visualization of driving factors of Yongchuan Distrct: (a) aspect, (b) average GDP,
(c) DEM, (d) population density, (e) distance to main roads, (f) distance to central city, (g)
distance to railway, (h) distance to water.
(a) 2012 (b) 2017
Figure 6: Land use maps of Yongchuan District in (a) 2012 and (b) 2017.
16

Table 1: Number of pixels of various types of land in Yongchuan District in 2012 and 2017
Year Living land Water Ecological land Productive land Other land
2012 197840 17642 347185 633858 28794
2017 211753 17947 389458 577964 28197
Table 2: Details of each driving factor in Yongchuan District
Type Name Data source
Natural environment DEM www.gscloud.cn
Slope calculated
by DEM
Socio-economic Average GDP statistical survey
Population density
Location
Distance to central city
www.open-
streetmap.org
Distance to main roads
Distance to railway
Distance to water
results of 2017 with the real actual data, evaluation metrics are derived. There
are five types of land use in Yongchuan District: living land, water, ecological
land, productive land and other land. Number of pixels in detail are given
in Table 1. It can be seen that after five years of implementing the policy of
returning farmland to forest, part of the productive land in Yongchuan District
has been transferred to ecological land, which to a certain extent indicates the
transformation of the economy of Yongchuan District towards ecotourism.
For the simulation of LUCC at the scale of Yongchuan District, we used a
total of eight driving factors, which were divided into three main categories: nat-
ural environment, socio-economic and location factors. The natural environment
factors are: Digital Elevation Model (DEM) and slope. The socio-economic fac-
tors are: population density, Average GDP. The location factors are: distance
to central city, distance to main roads, distance to water and distance to railway.
Fig.5 shows a visual image of each driving factor and Table 2 shows the details
of each driving factor in Yongchuan District.
4.2. Sanjiao Town
Sanjiao Town is located in Yongchuan District, with a town area of 108
square kilometres. For the practical simulation, we set the image size of Yongchuan
District to 1186 ×1521, with each pixel representing an area of 10 ×10 square
metres.
To ensure the consistency of the experiment, the simulation experiment in
Sanjiao town uses the data from the same year as Yongchuan district, i.e., the
data from 2012 is used as a starting point to simulate the land use in 2017. Due
to the reduction of land area, the land use types in Sanjiao town are only divided
into 4 categories: living land, ecological land, productive land and other land.
17

(a) 2012 (b) 2017
Figure 7: Land use maps of Sanjiao Town in (a) 2012 and (b) 2017.
(a) Slope (b) Aspect (c) DEM (d) Distance to industrial centre
(e) Distance to main roads (f) Distance to town centre (g) Distance to highway (h) Distance to other roads
Figure 8: Visualization of driving factors of Sanjiao Town: (a) slope, (b) aspect, (c) DEM,
(d) distance to industrial centre , (e) distance to main roads, (f) distance to town centre, (g)
distance to highway, (h) distance to other roads.
18

Table 3: Number of pixels of various types of land in Sanjiao Town in 2012 and 2017
Year Living land Ecological land Productive land Other land
2012 112861 674531 17849 241507
2017 112396 649964 18919 265469
Table 4: Details of each driving factor in Sanjiao Town
Type Name Data source
Natural environment
DEM www.gscloud.cn
Slope Calculated by DEM
Aspect
Location
Distance to town centre
www.open-
streetmap.org
Distance to main roads
Distance to highway
Distance to other roads
Distance to industrial centre
Productive land includes industrial land and mining land. Living land includes
residential land. Ecological land includes forest land and gardens, etc. Other
land includes rivers and reservoirs, etc. Table 3 shows the number of pixels in
the image for each type of land in Sanjiao Town in 2012 and 2017. Fig.7 shows
the difference in land use distribution between 2012 and 2017 in Sanjiao Town.
For the experiments in the town of Sanjiao, a total of eight kinds of driving
factors are used for the simulations, depending on its land area and the data
available. The natural environment factors are: DEM, slope and aspect. The
location factors are: distance to highway, distance to main roads, distance to
other roads, distance to town centre and distance to industrial centre. Due to
the small size of Sanjiao Town, factors related to socio-economics are difficult
to obtain and are excluded, making the experiment more focused on natural
and location factors. The images of the driving factors are illustrated by Fig.
8, where the data source for each driving factor is shown in Table 4.
4.3. Huangguashan Village
Huangguashan Village is one of China’s national agro-ecological tourism
demonstration sites, located in the southern suburbs of Yongchuan District in
the western part of Chongqing. The village has a land area of 20.08 square
kilometres. In our experiments, we set the image size of the Huangguashan
Village to 667 ×771, with each pixel representing an area of 10 ×10 square
metres.
In recent years, the rapid economic development of Huangguashan Village
has triggered excessive expansion of construction land, leading to obvious con-
flicts between various types of land in the village [33]. In the experiment, we
use data from the two years 2012 and 2017 for the simulation (see Fig.9), taking
19

(a) 2012 (b) 2017
Figure 9: Land use maps of Huangguashan Village in (a) 2012 and (b) 2017.
(a) Slope (b) Aspect (c) DEM
(d) Distance to attractions (e) Distance to main roads (f) Distance to water
Figure 10: Visualization of driving factors of Huangguashan Village: (a) slope, (b) aspect, (c)
DEM, (d) distance to attractions , (e) distance to main roads, (f) distance to water.
20

Table 5: Number of pixels of various types of land in Huangguashan Village in 2012 and 2017
Year Farmland Tourism land Construction land Other land
2012 62861 4244 18958 112486
2017 60730 5293 18531 113995
Table 6: Details of each driving factor in Huangguashan Village
Type Name Data source
Natural environment
DEM www.gscloud.cn
Slope Calculated by DEM
Aspect
Location
Distance to attractions www.open-
streetmap.org
Distance to main roads
Distance to water
2012 as the starting point to simulate the development in 2017, and derive eval-
uation metrics by comparing the simulation result of 2017 with the real result.
The land use types in Huangguashan Village are divided into four categories:
farmland, tourism land, construction land and other land. Table 5 shows the
number of various land use types in Huangguaoshan Village in 2012 and 2017.
A total of six kinds of driving factors are used for the simulation of the
experiment in Huangguashan Village. The natural environment factors are:
DEM, slope and aspect. The location factors are: distance to main roads,
distance to attractions and distance to water. Again, due to the relatively small
land area, factors related to socio-economics were excluded. The visualization
of the driving factors is illustrated by Fig.10 and the data source of each driving
factor is shown in Table 6.
5. Experimental results and discussions
In this section, we conducted experiments in Yongchuan district, Sanjiao
town and Huangguashan village, and made a comparison between ANN-ACCA
and normal ANN-CA [11, 12] to confirm the effectiveness of ANN-ACCA
5.1. Evaluation metrics
In this paper, two commonly used metrics for evaluating simulation results
are used: Kappa coefficient and Overall Accuracy (OA). The Kappa coefficient
is a metric that measures classification accuracy and can also be used for consis-
tency testing, and is a common metric for evaluating land use change simulation
results. It is calculated using a confusion matrix (Table 7) of predictions (P)
and actuals (A), as shown in Equation 12 and Equation 13.
OA =p0=a1+b2
n(12)
21

Table 7: Confusion matrix for calculation of evaluation metrics
P\A Land A Land B Sum
Land A a1a2sap
Land B b1b2sbp
Sum sar sbr
Table 8: The conversion cost matrix for Yongchuan District
Living
land Water Ecological
land
Productive
land
Other
land
Living land 1 0.003 1 1 0.01
Water 0.04 1 1 1 0.003
Ecological land 1 0.04 1 1 0.008
Productive land 1 0.006 1 1 1
Other land 0.1 0.001 0.1 1 1
Kappa =p0−pe
1−pe
(13)
where nis the number of land elements and pe=sar×sap+sbp ×sbr
n×n.
5.2. Experimental settings
The neural network has only 3 layers, with 12 neurons in the middle hidden
layer. The sampling method for the input data of the neural network was chosen
as uniform sampling. The sampling proportions were 50%, 60% and 80% for
Yongchuan District, Sanjiao Town and Huangguashan Village respectively. Here
the sampling proportion means how many land cells in total in the map were
used for neural network training. The experiment used the suggestions of urban
planning experts and some references [12, 33] to set other parameters, such
as conversion cost matrices, target numbers, neighborhood weights, and so on.
The overall settings aimed to guide the evolutionary process towards a specific
objective. For instance, in Huangguashan village, the parameters were designed
to increase the tourism land and decrease the farmland as much as possible.
In practice, the states of land cells outside the boundary are assigned to
NULL. Only land cells within the boundary are allowed to be computed, and
when the state of a cell involved in the computation is NULL, that cell is ignored.
5.2.1. Yongchuan District
For Yongchuan District, the maximum number of iterations was 500, and
the target numbers of living land, water, ecological land, productive land and
other land are 211753, 17947, 389458, 577964 and 28197 respectively, with cor-
responding neighbourhood weights are 0.8, 0.5, 0.7, 0.1 and 0.2. The conversion
cost matrix for Yongchuan District is shown in Table 8.
22

Table 9: The conversion cost matrix for Sanjiao Town
Living
land
Ecological
land
Productive
land
Other
land
Living land 0.64 0.04 0.21 0.12
Ecological land 0.01 0.26 0.60 0.13
Productive land 0.01 0.11 0.79 0.10
Other land 0.01 0.04 0.19 0.76
Table 10: The conversion cost matrix for Huangguashan Village
Farmland Tourism
land
Construction
land
Other
land
Farmland 1 1 1 1
Tourism land 1 1 1 1
Construction land 0 1 1 1
Other land 0 1 1 1
5.2.2. Sanjiao Town
For Sanjiao Town, the maximum number of iterations was 1000, and the
target numbers of living land, ecological land, productive land and other land
are 18919, 112396, 649964 and 265469 respectively, with corresponding neigh-
bourhood weights are 0.5, 0.3, 1.0 and 1.0. The conversion cost matrix for
Yongchuan District is shown in Table 9.
5.2.3. Huangguashan Village
For Huangguashan Village, the maximum number of iterations was 1000,
and the target numbers of farmland, tourism land, construction land and other
land are 60730, 5293, 18531 and 113995 respectively, with corresponding neigh-
bourhood weights are 0.1, 0.9, 0.6 and 0.3. The conversion cost matrix for
Yongchuan District is shown in Table 10.
5.3. Experimental results
The experiments in this section will compare ANN-ACCA with ANN-CA.
ANN-CA includes both ACA and CA, which are conditioned by the synchrony
rate α(CA when α= 1 and ACA when α < 1). Each experiment is repeated
10 times and then an average is calculated as an evaluation metric.
5.3.1. Yongchuan District
In the experiments in Yongchuan District, ANN-ACCA can improve the
Kappa coefficient by an average of 1.25% and OA by an average of 0.64%
compared to ANN-CA in five different settings (see Table 11, ∆ means im-
provement). Fig.11 shows the comparison of the experimental results for the
Yongchuan District with α= 1. The experimental results confirm the effective-
ness of ANN-ACCA at the district administrative level land scale.
23

(a) Actual map in 2017 (b) ANN-ACCA (c) ANN-CA
Figure 11: Comparison of simulation results: (a) actual map in 2017, (b) simulation results
of ANN-ACCA and (c) simulation results of ANN-CA. α= 1.
Table 11: Simulation results of CA and ACCA model (Yongchuan district)
Kappa OA
α/model CA/ACA ACCA ∆ CA/ACA ACCA ∆
1.0 0.57377 0.58283 +1.58% 0.72471 0.73056 +0.81%
0.3 0.58263 0.58847 +1.00% 0.73043 0.73420 +0.52%
0.5 0.58053 0.58742 +1.19% 0.72908 0.73353 +0.61%
0.7 0.57769 0.58542 +1.34% 0.72724 0.73224 +0.69%
0.9 0.57738 0.58396 +1.14% 0.72704 0.73130 +0.59%
24

(a) Actual map in 2017 (b) ANN-ACCA (c) ANN-CA
Figure 12: Comparison of simulation results: (a) actual map in 2017, (b) simulation results
of ANN-ACCA and (c) simulation results of ANN-CA. α= 1.
Table 12: Simulation results of CA and ACCA model (Sanjiao Town)
Kappa OA
α/model CA/ACA ACCA ∆ CA/ACA ACCA ∆
1.0 0.49377 0.49511 +0.27% 0.72751 0.72824 +0.10%
0.3 0.49332 0.49481 +0.30% 0.72727 0.72807 +0.11%
0.5 0.49360 0.49487 +0.26% 0.72742 0.72811 +0.09%
0.7 0.49366 0.49523 +0.32% 0.72746 0.72830 +0.12%
0.9 0.49363 0.49530 +0.34% 0.72744 0.72834 +0.12%
5.3.2. Sanjiao Town
In the experiments in Sanjiao Town, ANN-ACCA increases the kappa coef-
ficient by an average of 0.24%. and OA by an average of 0.11% compared to
ANN-CA in five different settings (see Table 12). Fig.12 shows the comparison
of the experimental results for the Sanjiao Town with α= 1.
5.3.3. Huangguashan Village
In the experiments in Huangguashan Village, ANN-ACCA improves the
Kappa coefficient by an average of 1.25% and OA by an average of 0.64%
compared to ANN-CA in five different settings (see Table 13). Fig.13 shows
the comparison of the experimental results for the Huangguashan Village with
α= 1.
5.4. Ablation study for probability-of-occurrence
The ANN-ACCA model takes into account the relationship between various
internal and external driving factors and lands, how significant would this be
for the final simulation results if the probability-of-occurrence calculated by the
ANN were removed and only the ACCA part of the model was used. This
25

(a) Actual map in 2017 (b) ANN-ACCA (c) ANN-CA
Figure 13: Comparison of simulation results: (a) actual map in 2017, (b) simulation results
of ANN-ACCA and (c) simulation results of ANN-CA. α= 1.
Table 13: Simulation results of CA and ACCA model (Huangguashan Village)
Kappa OA
α/model CA/ACA ACCA ∆ CA/ACA ACCA ∆
1.0 0.92186 0.92528 +0.37% 0.95567 0.95760 +0.20%
0.3 0.92521 0.92868 +0.38% 0.95756 0.95953 +0.21%
0.5 0.92390 0.92729 +0.37% 0.95682 0.95875 +0.20%
0.7 0.92221 0.92629 +0.44% 0.95586 0.95818 +0.24%
0.9 0.92145 0.92579 +0.47% 0.95543 0.95790 +0.26%
26

Table 14: The comparison of simulation result between different kind of probabilities
Type Kappa OA
Probability-of-occurrence 0.57377 0.72471
Probabilities with 1 0.55621 0.71628
Uniform distribution 0.56766 0.72077
Normal distribution 0.55117 0.71011
Table 15: Comparing the effects of deterministic and roulette selection methods on CA/ACCA
simulation accuracy in different regions
Region Method Kappa OA
CA/ACA ACCA ∆ CA/ACA ACCA ∆
Yongchuan district Roulette selection 0.57377 0.58283 +1.58% 0.72471 0.73056 +0.81%
Highest probability 0.56321 0.57134 +1.44% 0.71432 0.71987 +0.77%
Sanjiao Town Roulette selection 0.49377 0.49511 +0.27% 0.72751 0.72824 +0.11%
Highest probability 0.47432 0.47961 +0.53% 0.70923 0.71492 +0.57%
Huangguashan Village Roulette selection 0.92186 0.92528 +0.37% 0.95567 0.95760 +0.20%
Highest probability 0.90734 0.91567 +0.83% 0.93902 0.94842 +0.94%
section will compare the effect of the random probabilities and the output of
the neural network (probability-of-occurrence) on the simulation results.
The probability-of-occurrence in the ANN-ACCA model is derived by the
neural network by learning the relationship between various driving factors and
lands. For comparison purposes, we generate random probabilities for the study
area by other means. Here we have selected a total of three ways of randomly
generating probabilities: (1) initially all probabilities are 1; (2) random sampling
from a uniform distribution of [0,1]; and (3) random sampling from a normal
distribution of [0,1]. Because softmax is used in the probabilities output by the
neural network so that the sum of each set of probabilities is 1, the same needs
to be done for the three randomly generated probabilities.
We conducted experiments in the Yongchuan district. In Table 14, Proba-
bilities with 1 corresponds to that (1) initially all probabilities are 1. Uniform
distribution corresponds to that (2) random sampling from a uniform distribu-
tion of [0,1] and Normal distribution corresponds to that (3) random sampling
from a normal distribution of [0,1]. So Table 14 shows that the probability-of-
occurrence does improve the accuracy for simulation.
5.5. Comparison deterministic and roulette selection
This section presents comparative experiments to demonstrate the impor-
tance of land type selection strategy for roulette wheel selection in LUCC
simulation. Table 15 compares the simulation results of four combinations of
CA/ACCA and deterministic (Highest probability in Table 15)/roulette wheel
land type selection for three districts: Yongchuan District, Sanjiao Town, and
Huangguashan Village. The table displays the kappa and OA values for each
combination and district, as well as the percentage change (∆) between CA/ACCA
and deterministic/roulette selection. The results indicate that both ACCA and
roulette selection enhanced kappa and OA values relative to CA and deter-
27

ministic selection, respectively. The combination of ACCA and roulette wheel
selection yielded the highest kappa and OA values in all regions. A noteworthy
observation is that the larger the area, the greater the performance improvement
from ACCA and roulette wheel selection.
6. Conclusions
In order for insight into the effect of delay in the interactions between land
cells on the LUCC simulation, this paper proposed a novel ANN-CA model,
called ANN-ACCA, which adopts an asynchronous communicating cellular au-
tomaton to iterate the land use changes of each cell, rather than the conventional
CAs. Especially, the ACCA allows each land cell to exchange its state (land
use) with neighboring cells independently at random times, whereby the cell’s
change of land use may not affect its adjacent region immediately, resulting in
a stochastic delay in the communications between land cells. We conducted
experiments in three different areas of Chongqing, China (Yongchuan District,
Sanjiao Town and Huangguashan Village), using the data in 2012 to simulate
the land use in 2017. The results of experiments validated the effectiveness of
the ANN-ACCA model in the LUCC simulation. In particular, the ANN-ACCA
model has improved accuracy compared to the conventional ANN-CA model.
Also, the experimental results showed that the larger the area, the higher the
accuracy might be accomplished by the ANN-ACCA.
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