2010，
32（1）：184-194
第 32 卷 第 1 期 2010 年 1 月
Resources Science
Vol.32，
No.1 Jan.，
2010
文章编号：
1007-7588（2010）01-0184-11
Pareto Optimal Land-use Patterns with Three Conflicting
Benefits in an Area to the South of Liupan Mountain
Qin Xiangdong1，2，Min Qingwen1，Li Wenhua1，Geng Yanhui1
(1.Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China;
2. Graduate University of Chinese Academy of Sciences, Beijing 100049, China)
Abstract: Optimal spatial patterns of land use and the associated optimal benefits are one of the key topics in land
resources utilization, landscape ecology and sustainability science. However, research on this topic hasn’t made
significant progress for many years in its optimization methodology, especially in multi-objective land-use optimization
intending to systematically obtain all Pareto optimal solutions. This paper carried out an exploratory research on this
frontier topic by optimizing a land-use pattern located in the south to Liupan Mountain in Jinghe watershed, China, with
a total area of 300 km2, dominated by woodland, grassland and cultivated land. The research tried to maximize three
objective functions of conflicting benefits (the average land productive potential of six crops, the total quantity of soil
conservation, and sustainable habitat area for small woodland birds), by spatially reallocating woodland, grassland and
cultivated land. Based on the grid data, the paper presented a strict mathematical formulation of land-use patch and
pattern, simplified constraint of land suitability, land-use pattern optimization, and general conception of multi-objective
optimization of land-use pattern. Spatial pattern of land-use was defined as an unknown function, with location and
land-use type as its independent variable and dependent variable, respectively. Consequently, objective benefit
subjected to optimization was defined as a function of this unknown pattern function, i.e. benefit functional. According to
this mathematical representation, calculation approaches and calculation results of three sub-objectives for land-use
were presented, including sustainable habitat area for small woodland birds on the basis of habitat network and ESLI
(Ecologically Scaled Landscape Indices).
Solution space of this three-objective optimization is a Pareto optimal front surface, which was demonstrated
intuitively through its perspective drawing in 3-dimensional space, including some associated Pareto optimal land-use
patterns. These optimization results (solution space) of the study area were analyzed through a general mode of
“seven-section analysis”proposed, to get information about distribution and structure of the solution space relative to
function values of original pattern, including the equilibrium optimal section and an equilibrium optimal pattern (with
objective values all greater than those of original pattern) on it. The analysis conclusion of the equilibrium optimal
section and pattern revealed to agree with qualitative analysis obtained from the original pattern map, land suitability
map, and other parameter maps for calculation. This indicated that the model and the algorithm for the multi-objective
optimization of land-use pattern are relatively reasonable.
Key words: Optimization of land-use pattern; Multi-objective optimization; Land-use benefit; Pareto optimal front;
Solution space; Liupan Mountain in Jinghe watershed, China
1 Introduction
Although spatial patterns are attaching increasing
importance to sustainable utilization of land resource
and management of land-use[1], to systematically
obtain all optimal spatial patterns of land-use is still a
difficult problem[2], especially when optimality of the
solutions involves several conflicting objective
functions[3,4]. Traditional mode of “quantity
optimization plus spatial allocation” for land-use
planning can only provide several alternative
land-use patterns, so that it can not meet sustainable
utilization of land resource [5].
Very few researches on optimization for land-use
patterns with two or more objectives involved
“systematical” multi-objective optimization, except
Received：January 5，2009；
Accepted：
March 15，
2009
Foundation item: National Basic Research Program of China (973 Program) (No. 973-2002CB111506).
Author: Qin Xiangdong, male, postdoctoral of University of Science and Technology of China. His research focuses the fields of ecological
planning of landscape. E-mail: [email protected]
Corresponding author: Min Qingwen, His research focuses the fields of ecological agriculture and agricultural heritage conservation.
E-mail: [email protected]
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2 Mathematical Formulation
Land-use Pattern Optimization
for
2.1 Pattern and Patch of Land-use based
on Raster Map
A M × N sized raster map G consists of grids with a
group of integer coordinates (i, j)=z:
G ={(i, j) | i = 1,2,…,N; j= 1,2,…,M}
(1)
Land-use pattern P is taken as a function on G.
P(z)=λ means land-use type of grid z∈G:
P:G→L={cl(cultivated land), wd(woodland), gr
(grassland), cn(construction land)}
(2)
Let Ω(G) be power set of the set G. H∈Ω(G) is a
subset of G. For representation of land-use patch,
definition of maximal connectivity about the subset H
is given as follows:
Definition 1. H is "maximal λ-connected" on the
pattern P if and only if satisfying all three conditions
as follows:
(1) (i, j)∈H: P((i, j))= λ;
(2) (i, j)∈H: (i-1, j)∈H or (i+1, j)∈H or (i, j-1)∈
H or (i, j+1)∈H;
(3) (i, j) H and P((i, j))= λ: (i±1,j) H and (i, j±
1) H
(3)
Then all patches in a pattern P with land-use type
of λ compose a set P, a functional determined by
pattern function P and parametric variable λ:
P(P, λ)={H∈Ω(G) | H is maximal λ-connected on
P.}
(4)
A
2.2 Constraint Condition of Land Suitability
Land suitability of a grid z with area a for land-use
type λ may be expressed as a function:
(5)
Constraint condition of land suitability for pattern
P is simplified as follows:
z∈G: e(z, P(z))>0 or P(z)=P0(z)
(6)
where P0 is original land-use pattern. This
constraint means that land-use type at grid z is
transformed to another type that does not violate land
suitability, or remains unchanged as that of the
original pattern.
A
two approaches as following [6]: (1) to analyzing
several typical scenarios with more than one conflicting
objective benefit, and to providing only several
near-optimal solutions [7, 8]; (2) to integrating multiple
sub-objectives into one using mathematical approaches
such as weighted sum, goal programming [9], etc. No
research has been retrieved that optimized three or
more objective benefits intending to systematically
obtain a whole Pareto optimal front for land-use
pattern.
Most research on spatial optimization of land-use
pattern aimed at solving practical problems in real
geographic areas. On the other hand, very few
researches on abstract pattern only optimized
artificial, hypothetical small-sized pattern [10, 11]. It was
difficult to confirm typicality of the former for
optimization methodology of land-use pattern, while
also difficult to confirm effectiveness of the latter for
optimization of actual land-use pattern.
This paper carried out an exploratory research on
this frontier topic based on mathematical formulation
of land-use pattern optimization problem, by
optimizing a typical, actual land-use pattern of 300
km2 area located at the south to Liupan Mountain in
Jinghe watershed, China. The research tried to
maximize three objectives of conflicting benefits (the
average land productive potential of six crops, the
total quantity of soil conservation, and sustainable
habitat area for small woodland birds), by spatially
reallocating woodland, grassland and cultivated land.
The whole solution space of this three-objective
optimization, i.e., a Pareto optimal front surface, was
demonstrated intuitively through its perspective
drawing in 3-dimensional space, including some
associated Pareto optimal land-use patterns. These
optimization results (solution space) of the study area
were analyzed through a general mode of
“seven-section analysis”proposed, to get information
about distribution and structure of the solution space
relative to function values of the original pattern. It is
indicated that the model and the algorithm for the
multi-objective optimization of land-use pattern is
relatively reasonable. The paper tried to demonstrate
that key research on multi-objective optimization of
land-use pattern should be to systematically explore
maximal benefits space of multi-functional land-use
patterns, not to provide a few optimal solutions for
practical land-use planning.
A
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2.3 Objective Benefit Functional
Objective function J of land-use benefit is taken as a
function of an unknown function P, i.e. a land-use
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pattern, so that J is a benefit functional:
J: {P | z∈G: e(z, P(z)) >0 or P(z) =P0(z)} → R +
(positive real number set)
(7)
Now problem of land-use pattern optimization may
be formulated as follows: to seek an unknown
land-use pattern function P so as to maximize the
objective benefit functional J(P).
So the main works for multi-objective optimization
of land-use pattern is to find as many Pareto optimal
patterns as possible, and to give their objective values
in the form of Pareto optimal front.
2.4 General Conception for Multi-objective
Optimization of Land-use Pattern
In our study case, land productive potential, quantity
of soil conservation, and sustainable habitat area were
selected as three conflicting objective benefits subject
to optimization, calculation approach of which are
presented as follows. According to the above
formulation, in the following algebraic expressions,
parameters or variables with spatial variability are
expressed as known functions with grid z as their
independent variable or parametric variable.
However, if the spatial variability is relevant to those
of land-use type, these parameters or variables should
be expressed as functional of unknown pattern
A
The above mathematical formulation may be
extended directly to K-objective optimization of
land-use pattern only if formula (7) is replaced by
following one:
Jk: {P | z∈G: e (z, P(z))>0 or P(z)=P0(z)}→R + , k =
1, 2, …, K
(8)
Nevertheless, for this multi-objective optimization,
every sub-objective benefit functional Jk may conflict
each other so that no global optimum but Pareto
optimum [12] could be reached. Here we give some
definition for solution of multi-objective optimization
of land-use pattern, using Pareto optimality based on
general conceptions of multi-objective optimization
problem [13].
Definition 2. Land-use pattern“P is superior to
P' ”if and only if both satisfy:
k=1, 2, …, K: Jk(P)≥Jk(P')
k=1, 2, …, K: Jk(P) > Jk(P')
(9)
And P is“Pareto optimal pattern”if and only if no
other pattern is superior to P.
Definition 3. Objective values of all Pareto optimal
patterns compose “Pareto optimal solution set”,
graphical representation of which is called“Pareto
optimal front surface”, or“Pareto optimal front”for
short.
Definition 4. Pareto optimal pattern P is called an
“equilibrium optimal pattern relative to the original
pattern P0”
, or “equilibrium optimal pattern” for
short, if and only if:
k=1, 2, …, K: Jk(P)>Jk(P0)
(10)
Definition 5. Objective values of all equilibrium
optimal pattern compose “equilibrium optimal
solution set”, graphical representation of which (a
part of Pareto optimal front) is called“equilibrium
section of Pareto optimal front”, or “equilibrium
optimal section”for short.
Pareto optimal solution set consists of reasonable
solutions for a multi-objective optimization problem.
A
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3 Calculations of Three Objective
Functions for Land-use Benefits
function P.
3.1 Land Productive Potential
Using agro-ecological area method (AEZ),
light-temperature potential productivity is calculated
as follows. Parameters or variables include: average
short-wave solar radiation above upper boundary of
atmosphere, Ra (mm/d); average percentage of
sunshine, n/N; maximal effective shortwave-radiation
on clear day, Rse (cal/(cm2·d)); total productivity of
dry matter on full cloudy day and cloudless day, b0
and bc (kg/(hm2·d)); daily mean temperature in whole
growth period, T; leaf growth correction index, CL;
harvest index, CH; length of growth period, Ng(d).
Cloudiness fraction of a day:
F(z)=(Rse-0.5 (0.25+0.5n/N(z))Ra·59)/0.8Rse (11)
Proportional factor of maintenance respiration:
Ct(z)= C30 (0.044+ 0.0019T(z) + 0.001T2(z)) (12)
Light-temperature potential productivity (kg/hm2):
Ym(z) =0.36 ·[F（z）·b0 + (1-F（z）) ·bc] ·CL·CH·
Ng/(1+0.25Ng·Ct(z))
(13)
The soil productive potentiality is calculated as
follows, including Penman-Montieth recommended
by FAO. Parameters or variables include: water
demand coefficient kcj (the j-th phase); reference crop
water demand ET0j; net radiation, Rn(MJ/(m2·d)); soil
heat flux, G(MJ/(m2·d)); saturation vapour and actual
water vapor pressure, es and ea (kPa); curve slope of
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saturation vapor pressure - temperature, Δ (kPa/° C);
psychrometer constant, γ (kPa/° C); crop coefficient,
Kc; runoff coefficient, r; actual-rainfall, R(mm); soil
moisture storage rate in fallow period, α;
supplemental irrigation amount growth period, I
(mm); yield coefficient, ky; and soil effective
coefficient, g.
Reference crop evapotranspiration (mm/d):
(14)
Total evapotranspiration of a crop:
capacity larger than KP (Key Population) requires, i.
e., its area is more than a threshold AKP = KP ·IAR.
Additionally, total area of the habitat network is more
than MVMPKP (Minimum Viable Meta-population
with KP) requires, i.e. a threshold AMVMP+KP = MVMPKP·
IAR.
Category III: total area of the habitat network is
more than MVMP (Minimum Viable Meta-population without KP) requires, i.e. a threshold AMVMP =
MVMP·IAR.
Then the second objective function J2, sustainable
habitat area of a land-use P, is the total area of SHNs:
(19)
(15)
Effective precipitation in fallow period and growth
period, R'1 and R'2(mm):
R'(z)=(1- r(z))·R(z)
(16)
Soil productive potentiality (kg/hm2):
(17)
The first objective function J1, total land productive
potential of cultivated land of a land-use pattern P, is
calculated as average value of that of several crops:
(18)
3.2 Sustainable Habitat Area
According to the conception of“key patch”[14] based
on meta-population theory, Opdam et al (2003) [15]
proposed “Ecologically Scaled Landscape Indices
(ESLI)”as an evaluation index for sustainability of
habitat. We calculated sustainable habitat area for
small woodland birds using ESLI as follows.
Any woodland patch H∈P(P,wd) large enough for
double IAR (individual area requirement) of a bird
was identified as a habitat patch. These habitat
patches were taken as those in identical habitat
network if and only if their distance is less than MDD
(most dispersal distance) [14, 16]. Any habitat network is
regarded as a SHN (sustainable habitat network) if
and only if it meets at least one criterion listed below
each for a certain category of sustainability.
Category I: at least one patch has carrying capacity
larger than MVP (Minimum Viable Population)
requires, i.e., its area is more than a threshold AMVP =
MVP·IAR.
Category II: at least one patch has carrying
3.3 Quantity of Soil Conservation
Using USLE (Universal Soil Loss Equation) [17],
quantity of soil conservation Ec (t/hm2/a), i.e. the
difference of potential and reality soil erosion (Ep and
Er), is calculated as follows.
Ec(z) = Ep(z) - Er(z) = R(z)·K(z)·LS(z)·[1- C(P(z))]
(20)
Parameters or variables include: rainfall erosive
index, R; soil erodibility factor, K; slope length and
gradient factor, LS; land surface vegetation cover
factor, C, which is a known function determined by
unknown pattern function P.
The third objective function J3, quantity of soil
conservation of a land-use pattern P, is the total value
of Ec(z):
(21)
4 Study Area and Its Original
Land-use Benefits
We focus on the problem of optimum land-use
patterns in a farming-forestry-pastoral area in Jinghe
(a second grade tributary of the Yellow River)
watershed, China. The study area is located at the
southeast to Liupan Mountain in the watershed, with
length of 20km and width of 15km (Fig.1). Its
original pattern of land-use is represented by a raster
map with 400 × 300 grids, grid side-length of 50m
(Fig.2, left), identical specification for land suitability
map of study area (Fig.2, right).
Land productive potential of six crops of study
area is shown in Fig.3, left. According to section 3.1,
the average land productive potential is (Fig.3, right)
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J1 (P0) = 51.25×106kg.
SHNs in the original pattern identified according to
Section 3.2 are shown in Fig.4. Total area of SHNs of
the original pattern is J2 (P0) = 5473ha.
Soil erosion intensity of the study area is shown in
Fig.5. According to Section 3.3, total quantity of soil
conservation of the original pattern is J3 (P0) = 1.08×
106 t/a.
5
Results: Solution Space
Three-objective Optimization
Source: national resources and environment database in China (2000)
Fig.1 Location of the study area
By means of genetic algorithm[18, 19], for land-use
pattern optimization problem of the study area, one
thousand Pareto optimal solutions were found and
represented by points, though which a smooth surface
constructed by spline interpolation represents a
Source: national resources and environment database in China (2000)
Fig.2 Original land-use pattern (left) and land suitability (right) of study area
Source: Chen Caocao [20]
Fig.3 Land productive potential of six crops in study area (left) and their average value (right)
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Fig.4 SHNs of original pattern in study area Size of blocks equals to
area index. Radius of circle equals to MDD
Pareto optimal front shown by perspective drawing in
Fig.6. The Pareto optimal front surface is divided into
seven sections by three plane that cross point 0#
(representing land-use benefits value of the original
pattern) and parallel to three coordinate plane. Pareto
optimal patterns related to each point, and its three
land-use benefit values, are shown in Fig.7. This
Source: Geng Yanhui [21]
Fig.5 Soil erosion intensity of the study area
“seven section analysis” mode for three-objective
optimization can give specific geometrical elements
on the optimal front surface clear meaning as follows.
(Word“increased”,“decreased”
,“unchanged”and
“increment” in following text is comparative to
benefits value of the original pattern.)
Point 1#: unique optimal solution for single-objec-
Fig.6 Perspective drawing of Pareto optimal front surface according to“seven section analysis”: solution space
of three-objective optimization of land-use pattern of the study area
Every point on the surface represents three objective function values of a Pareto optimal land-use pattern shown in Fig.7, with identical label (#).
Coordinates of points are expressed as percentage relative to objective function value of original land-use pattern. So coordinates of point representing
original pattern are (100, 100, 100) (0#).
Gray point 20#, 21#, 22# are respectively on invisible section IV, V, VI of the surface, which has only one objective function value greater than those of
original pattern.
Visible section VII represents objective function values of optimal patterns that are all greater than those of original pattern.
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191
Fig.7 Pareto optimal land-use patterns of the study area
Three sub-objective function values in parentheses (land productive potential, sustainable habitat area, and quantity of soil conservation) are in turn
expressed as percentage relative to those of original pattern, position of which on Pareto optimal front surface are shown in Fig. 6, with identical label (#).
tive optimization of J3 (quantity of soil conservation);
Point 2#: maximal solution for J3 if J1 (land productive potential) remains optimal solution of its single-objective optimization, similar meaning for point
3#, 4#, 5#;
Plane curve 2-6-3, 4-5: all optimal solutions for sin-
gle-objective optimization of J1 and J2 (sustainable
habitat area), respectively; Plane curve 6-12-14-9: all
Pareto optimal solutions for two-objective optimization of J1 and J3 with constraint of unchanged J2, similar meaning for plane curve 7-13-14-10 and
8-13-12-11; Space curve 3-7-4: all Pareto optimal sohttp://www.resci.cn
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lutions for two-objective optimization of J1 and J2
without constraint of J3, similar meaning for space
curve 1-10-11-2 and 5-8-9-1;
Visible section I: all Pareto optimal solutions for
three-objective optimization with J2 and J1 both
increased at the expense of decreased J3, similar
meaning for visible section II and III; Invisible
section IV: all Pareto optimal solutions for
three-objective optimization with only J1 increased at
the expense of both J2 and J3 decreased, similar
meaning for invisible section V and VI;
Central visible section VII: equilibrium optimal
solutions set for three-objective optimization with J1,
J2 and J3 all increased. Point 25# is the position at
which section VII is at a minimum distance from
point 0#.
6 Discussion: Equilibrium Optimal
Section and Pattern
Compared with the whole Pareto optimal front,
equilibrium optimal section VII is quite small in
Fig.6, so that equilibrium optimal solutions are much
fewer than other Pareto optimal solutions, which
indicate comparatively few equilibrium optimal
patterns, thus low optimization degree of freedom for
all three land-use benefits increased. Distance
between point 0# to 25# is only 8.1(% ), which
indicates comparatively little increment of benefits
value of equilibrium optimal patterns, thus small
optimization range for all three benefits increased.
Point 25# is much farther from 12# and 13# than
from 14#, and far from the geometric center of
section VII (point 26#), which indicates relatively
few patterns with relatively large increment of J3
among all equilibrium optimal patterns.
An equilibrium optimal pattern, 26#, is analyzed as
shown in Fig.8. Referred to original land-use pattern
Fig.8 An equilibrium optimal land-use pattern of study area
(The pattern 26# in Fig.6 and Fig.7)
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第 32 卷 第 1 期
(Fig.2, left), land suitability map (Fig.2, right), land
productive potential and soil erosion map of original
land-use pattern (Fig.3 and Fig.5), characteristics of
the pattern 26# are listed below.
1) Land suitable for pasture (or for both pasture
and forestry) with high potential erosion modulus
were allocated whole large pieces of grassland;
2) Land suitable for farming (or for both farming
and pasture) with high land potential productive were
allocated whole large pieces of cultivated land;
3) Woodland were relatively connected and
concentrated. Narrow woodland patches connecting
whole large woodland and small pieces of woodland
let all sustainable habitats become SHN of category I.
4) Though land-use type was transformed in many
locations, area of woodland and grassland increased
only a little, and area of cultivated land decreased
only a little.
These characteristics justified this equilibrium
optimal pattern as follows. The pattern made full use
of spatial variability of soil productive potentiality
and potential erosion, so as to increase J1 in spite of
slightly decreased cultivated land, and to increase J2
and J3 in spite of almost unchanged area of woodland
and grassland. The pattern also increased J2 by
connecting and concentrating small woodland
patches to large one. J1, J2 and J3 of the pattern
increased by 6%, 5% and 4%, respectively.
7 Conclusion
Representative study cases of systematical
optimization of spatial pattern for land-use are rare to
find, especially multi-objective optimization for
land-use of real geographic area (except those which
integrate multiple objectives into one). This paper
carried out an exploratory research on this topic by a
three-objective optimization of an actual land-use
pattern at large scale.
The research is in favor of such a hypothesis that
key research on multi-objective optimization of
land-use pattern should be to systematically explore
maximal benefits space of multi-functional land-use
pattern, not to provide one or several optimal
solutions for practical land-use planning. For this
purpose, strict mathematical formulation for land-use
pattern optimization, intuitive and informative
expression of solution space, and meaningful analysis
mode of the solution space were introduced through
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六盘山南麓具有三个冲突效益的 Pareto 最优土地利用格局
pattern function and its object benefit functional,
Pareto optimal front surface, and an analysis mode of
“seven-section analysis”
, respectively.
The analysis conclusion of equilibrium optimal
section and pattern was revealed to agree with
qualitative analysis obtained from original pattern
map, land suitability map, and other parameter map
for calculation. This indicated that the model and the
algorithm for the multi-objective optimization of
land-use pattern are primarily reasonable.
Although genetic algorithm was utilized to solve
this optimization problem, even a single computation
of this problem is too expensive due to super-large
scale of the solution space, so that only one result
was obtained from a certain set of parameters in the
present research. The model and algorithm at the
experimental stage is still an initial development of
methodology for optimization procedures of land-use
pattern, and has a long way to go for decision-making
in practical land-use planning.
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资 源 科 学
第 32 卷 第 1 期
六盘山南麓具有三个冲突效益的
Pareto 最优土地利用格局
秦向东 1，2，闵庆文 1，李文华 1，耿艳辉 1
（1. 中国科学院地理科学与资源研究所，北京 100101；2. 中国科学院研究生院，
北京 100049）
摘 要: 土地利用空间最优格局及其相应的最优效益是土地资源利用、景观生态学和可持续发展科学的关键
课题之一，多年来在其优化方法论上未能取得明显进展，尤其在多目标土地利用空间格局优化中系统地获
取所有 Pareto 最优解及其解空间的分析方面。已有的土地利用空间格局优化研究大多数停留在“先数量优
化、后空间配置”的两步走模式，以及利用目标规划等数学方法将多个优化目标转化为单个目标的简化模
式。本文通过优化一个农林牧交错地域的土地利用格局，在方法论上对这一前沿课题作了探索性研究。研
究通过林地、草地、耕地的空间调整，最大化平均土地生产潜力、土壤保持总量、小型林地鸟类可持续生境面
积这 3 个相互冲突的效益目标函数。首先基于栅格数据，给出了土地利用斑块与格局、土地利用格局优化、
简化的土地适宜性约束的严格的数学表述，以及多目标土地利用格局优化的一般概念或定义，包括某种土
地利用类型的最大连通性、土地适宜性函数、两个格局的优于关系、Pareto 最优集及前端曲面、均衡最优解和
均衡最优格局。栅格图上的土地利用空间格局被定义为以空间位置为自变量、以土地利用类型为因变量的
未知函数。相应地，待优化的效益子目标被定义为这个未知格局函数的函数，即效益泛函。然后，按照这种
数学表述给出了土地利用效益的 3 个子目标的计算方法：基于 AEZ 方法（agro-ecological area method，农业生
态区划法）的平均土地生产潜力总量、基于生境网络斑块和 ESLI（Ecologically Scaled Landscape Indices，生态
标度的景观指数）的小型鸟类的可持续生境面积、基于 USLE (Universal Soil Loss Equation，通用土壤侵蚀方
程)的土壤保持总量。选取中国泾河流域六盘山南麓一个 300km2 的土地利用格局作为研究区域，给出了在
研究区土地利用现状格局之下这 3 个土地利用效益子目标函数的计算结果，包括基于 ESLI 的三类可持续生
境网络斑块的分布与面积。最后，在三维空间中用透视图直观展现了研究区三目标优化问题的解空间——
Pareto 最优前端曲面，以及相应的 Pareto 最优土地利用格局。提出通用的“七区分析”模式，来分析这些优化
结果（解空间），以获得解空间相对于现状格局目标函数值的分布情形，包括各个特定点、交线及边界线、各
个分区所表现的空间结构、总体趋势、边界特征、均衡最优解及有关的均衡最优格局。其中均衡最优格局与
根据现状格局图、土地适宜性图以及其他计算参数图所作的定性分析结果一致，初步表明此多目标土地利
用格局优化的模型与算法基本合理，即：能够充分利用与土地利用相关的自然属性的空间变异性，在不显著
改变各类土地利用面积的情况下增进三类土地利用目标效益。本文的研究方法强调严格的数学表述、完备
的解空间获取、信息丰富而直观的解空间的表达方式与分析模式，其研究结果虽然还难以直接应用在实际
的土地利用规划中，但是它有利于这样一种假设：多目标土地利用格局优化的核心研究内容，不是为具体的
土地利用规划提供有限个方案，而是要探索、了解在自然状态下，多种土地利用效益的极大化空间。
关键词：土地利用格局优化；多目标优化；
土地利用效益；Pareto 最优前端；解空间；
泾河流域六盘山
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