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A novel method for measuring interaction among multiple
objectives in reservoir operation using niche theory
Xiao-kuan Ni
a
, Zeng-chuan Dong
b,*
, Wen-hao Jia
c
, Wen-zhuo Wang
b
, Wei Xie
d
,
Hong-yi Yao
e
, Mu-feng Chen
f
, Tian-yan Zhang
b
, Zhuo-zheng Li
b
a
Pudong New Area Emergency Management Bureau, Shanghai 200135, China
b
College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China
c
Pearl River Water Resources Research Institute, Guangzhou 510611, China
d
Department of Hydropower and Water Conservancy Engineering, POWERCHINA Huadong Engineering Co. Limited, Hangzhou 311122, China
e
Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
f
Department of Aquatic Ecosystem Analysis and Management, Helmholtz Centre for Environmental Research eUFZ, Magdeburg 39114, Germany
Received 29 September 2023; accepted 26 February 2024
Available online 5 March 2024
Abstract
Accurate capture and presentation of the interactive feedback relationships among various objectives in multi-objective reservoir operation is
essential for maximizing operational benefits. In this study, the niche theory of ecology was innovatively applied to the field of reservoir
operation, and a novel stateerelationship (SeR) measurement analysis method was developed for multi-objective reservoir operation. This
method enables the study of interaction among multiple objectives. This method was used to investigate the relationship among the objectives of
power generation, water supply, and ecological protection for cascade reservoir operation in the Wujiang River Basin in China. The results
indicated that the ecological protection objective was the most competitive in acquiring and capturing resources like flow and water level, while
the water supply objective was the weakest. Power generation competed most strongly with ecological protection and relatively weakly with
water supply. These findings facilitate decision-making throughout the reservoir operation process in the region. The SeR method based on the
niche theory is convenient, efficient, and intuitive, allowing for the quantification of feedback relationships among objectives without requiring
the solution of the Pareto frontier of a multi-objective problem in advance. This method provides a novel and feasible idea for studying multi-
objective interactions.
©2024 Hohai University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://
creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Niche; Interaction relationship; Reservoir operation; Multi-objective optimization; Wujiang river
1. Introduction
Reservoirs have the capacity to alter the spatiotemporal
distribution of water resources through water storage and
discharge (Wang et al., 2016), leading to a wide array of
benefits, such as flood control, power generation, ecological
protection, water supply, and shipping (Bai et al., 2015; Yang
et al., 2016; Liu et al., 2017; de la Cruz Courtois et al., 2021;
Wu et al., 2022a). Achieving the maximum comprehensive
benefits from scientific and rational reservoir operation is vital
for sustainable water resources development. This necessitates
comprehensive coordination of the benefits of different ob-
jectives (Ngo et al., 2007), which requires accurate identifi-
cation of competition and coordination patterns that are
challenging to quantify. Although it is widely acknowledged
that the mentioned objectives are not independent, they are
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Water Science and Engineering
journal homepage: wse.hhu.edu.cn
This work was supported by the National Key Research &Development
Project of China (Grant No. 2016YFC0402209) and the China Scholarship
Council.
*Corresponding author.
E-mail address: zcdong@hhu.edu.cn (Zeng-chuan Dong).
Peer review under responsibility of Hohai University.
https://doi.org/10.1016/j.wse.2024.03.002
1674-2370/©2024 Hohai University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://
creativecommons.org/licenses/by-nc-nd/4.0/).
Water Science and Engineering 2025, 18(1): 78e89
neither wholly opposed to nor fully coordinated (Yang et al.,
2017), indicating the presence of complex mutual relation-
ships that need to be measured. Stakeholders can develop
targeted strategies to optimize resource allocation, enhance
cooperation among objectives, and address potential conflicts
or trade-offs to achieve more balanced and effective reservoir
operations.
With the development of multi-objective evolutionary al-
gorithms, the Pareto frontier has emerged as a significant
carrier and direct embodiment of the interactive feedback re-
lations among multi-dimensional targets (Cohon, 1978). In
essence, the Pareto frontier holds a wealth of information that
illuminates the interaction between multiple objectives. By
extracting insights from the Pareto solution set, researchers
can gain a better understanding of how different objectives
interact with each other. Visual analysis and numerical fitting
are two commonly used methods to achieve this goal.
Many previous studies (Kim et al., 2006; Reed and Kollat,
2013) have demonstrated that visual analysis is a powerful tool
for graphically presenting the rich information contained in
Pareto sets and displaying the tradeoffs among objectives in a
straightforward and intuitive manner. It has been widely used
to address tradeoff issues in various fields, such as water
allocation (Fu et al., 2013), reservoir operation (Hurford et al.,
2014), and sewage treatment (Meng et al., 2016). However,
definition of the intricate relationships among related objec-
tives or objective evaluation of their competitiveness can be
challenging.
Numerical fitting partially addresses this limitation by
quantifying mutual feedback relationships among objectives.
Tang et al. (2019) developed the conflict evaluation index by
projecting the Pareto frontier and measuring the distribution
range of the projection to quantify the intensity of competi-
tion. Wu et al. (2020) derived the replacement relationship
between power generation and ecological protection by fitting
the mathematical expression of the frontier. Based on the
geometric distribution of solutions on the two-dimensional
plane, Wang et al. (2022) proposed the competitiveness
index and competition efficiency index to further condense the
scale of the Pareto set of two objectives to reduce the decision-
making complexity. Wu et al. (2022b) developed the multi-
objective tradeoff index to quantify the relationships be-
tween objectives, which is defined as the slope ratio of the line
connecting every two scattered optimal solutions. In addition
to various mathematical analytical methods, Zhang et al.
(2020) used the structural equation model (SEM) to quanti-
tatively describe the relationships among objectives and per-
formed high-dimensional confirmatory factor analysis using
the values of each indicator in the non-inferior solution set as
the input.
The aforementioned studies have primarily focused on
exploring the relationships among objectives centered around
the Pareto frontier. They commonly solve the Pareto solution
set of the multi-objective problem and then analyze the mutual
feedback relationships using various techniques. However,
such analysis methods lack universality due to their low effi-
ciency and high computational complexity induced by solving
Pareto frontiers. Therefore, it is necessary to develop a more
simplified and universal technique for identifying interactions
among objectives with no need to solve the Pareto frontier.
Based on this idea, preliminary attempts have been carried out.
Meng et al. (2019) identified the most robust competition
between power generation and water demand by plotting the
process line between water demand and reservoir outflow.
Jiang et al. (2020) developed a systematic dynamics (SD)
model for multi-objective reservoir operation and analyzed the
interactions between various functions of reservoirs. However,
the modeling process is complicated and not applicable at a
large scale. Therefore, further research is needed in this area.
The concept of niche is fundamental in ecology, which
describes the relationships between organisms/biological units
and their environment in a specific ecosystem. It reflects the
relative standings formed by their interactions (Sales et al.,
2021). Since Johnson (1910) introduced the concept of
niche, many scholars have refined the concept, enriched the
connotation, and expanded the denotation. Hutchinson (1957)
proposed the idea of a spatial n-dimensional hypervolume
model including ecological factors to determine the survival
status of a species. He introduced the concept of n-dimen-
sional hypervolume niche and used the set theory and abstract
space to make the abstract niche measurable. This calculation
is simple and operable, making it widely used in many aspects,
such as habitat selection, the spatiotemporal distribution dy-
namics of species, and community evolution. The niche theory
has been developed beyond ecology and applied to many other
disciplines, such as economics (Weil et al., 2014), sociology
(Akbar et al., 2017), and management (Coles et al., 2018).
Many derivative concepts have been proposed, such as urban
niche (Cr
e et al., 2012), industrial niche (Sushandoyo and
Magnusson, 2014), building niche (Yang et al., 2015), devel-
opment niche (Bui et al., 2016), and innovation niche (Pigford
et al., 2018). The niche theory has become a robust theoretical
analysis tool for complex systems.
Inspired from ecological concepts, this study developed a
novel method for multi-objective reservoir operation. Given
that interactions among objectives in reservoir operation are
similar to the “survival of the fittest”mechanism of natural
ecosystems. This study abstracted multi-objective reservoir
operation as a virtual ecosystem, where corresponding objec-
tives are considered living organisms. In order to quantita-
tively analyze the relationships among multiple objectives, a
stateerelationship (SeR) measurement analysis framework
was developed based on the resource occupation idea of the
niche theory. The feasibility of the framework in optimal water
resources utilization was evaluated. This framework is ex-
pected to be able to help decision-makers manage main con-
tradictions in multi-objective reservoir operation.
2. Methodology
As discussed earlier, the traditional approach of calculating
the Pareto frontier to explore the relationship among multiple
objectives suffers from computational intricacy and low effi-
ciency. Additionally, the inherent randomness and dynamic
79Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
nature of multi-objective evolutionary algorithms lead to non-
fixed Pareto solutions, decreasing the method's versatility and
result stability. To overcome these limitations, this study used
bionic thinking and ecological principles of survival and
competition to construct a reservoir operation ecosystem
(ROES), in which specific objectives are metaphorically
treated as living organisms.
2.1. Reservoir operation ecosystem
Similar to natural ecosystems, an objective involved in
reservoir operation can be likened to a unique living organism,
and related factors can be perceived as the environment. The
combination of the two forms an organic whole, which can be
regarded as a unique ecosystem: the reservoir operation
ecosystem (ROES). ROES is a highly artificial and
naturalesocial binary composite system with a complex
structure and diverse functions. It exhibits the characteristics of
artificial regulation of nature and highlights human intervention
in the ecosystem.
As reservoir operation is a link in energy and matter flows
on the Earth, ROES is an open system that is highly depen-
dent on and reacts to the surrounding environment. The
effectiveness of the system depends on its ability to self-
organize, coordinate, and maintain orderliness. As shown in
Fig. 1, if the system is uncompetitive in these aspects, its
overall effectiveness will be disappointing. Conversely, a
better performance promotes the coordination of nature and
human society, facilitating sustainable development.
Furthermore, ROES has a hierarchical structure comparable
to natural ecosystems. A single operation objective (e.g.,
power generation, water supply, and flood control) constitutes
one basic unit of ROES. Two or more objectives of the same
type (e.g., profit-raising and disaster-reduction) form a cate-
gory (population). Two or more categories compose an
objective collection (community), and the sum of all
objective collections and the surrounding environment
compose a complete ROES. The hierarchy of this system and
its correspondence with the natural ecosystem are shown in
Fig. 2.
2.2. Construction of reservoir operation niche
2.2.1. Ecological factor of reservoir operation
The various environmental elements in ROES that directly
or indirectly affect the operation objectives are defined as the
ecological factors of reservoir operation (ROEFs). ROEFs play
a crucial role in the function of reservoir operation and its
impact on the external environment. The different
combinations of ROEFs create diverse ecological environ-
ments and provide various ecological spaces for operation
objectives.
2.2.2. Reservoir operation niche
According to the concept of niche in ecology, the reservoir
operation niche (RON) comprises the resources required to
achieve reservoir operation objectives and functional re-
lationships within a specific time and space. RON can describe
the standing of a specific operation objective in ROES. RON
has three characteristics. It has broadness, as it consists of the
sum of all ROEFs that maintain the benefits of operation ob-
jectives. It has a threshold, as each ROEF has a certain range
of values. It has functionality, reflecting the role of reservoirs
in meeting human needs.
2.2.3. Dimension of RON
With Hutchinson'sn-dimensional hypervolume niche
(Hutchinson, 1957), ROEFs with different directions in space
can be represented by dimensions and divided into sub-
dimensions. However, ROEFs that affect the realization of
operation objectives in various aspects are complex and
challenging to fully capture and elucidate. Moreover, an in-
crease in dimensions significantly amplifies the complexity of
the model, as each ROEF corresponds to a specific niche
dimension. Consequently, this complexity adversely affects
measurement accuracy. Thus, it is necessary to select critical
and practical dimensions to measure RON according to the
needs.
In practical applications, reservoir operation is typically
regulated by controlling the discharge flow, while the opera-
tion status is determined by monitoring changes in water level.
Therefore, the factors of flow and water level are selected as
the two main types of ROEFs in ROES. Correspondingly,
RON contains two key dimensions, each with its corre-
sponding threshold values that can be refined into different
specific resources or sub-dimensions. On this basis, the system
of RON is constructed as shown in Table 1.
2.2.4. Resource matrix
As operation objectives differ in their ability to utilize each
ROEF, a resource matrix is established to represent these
differences. To study the niche with noperation objectives in a
particular dimension, ROEF corresponding to this dimension
can be divided into mresource states (sub-dimensions). Then,
the quantity of the j-th resource state of ROEF occupied by the
i-th objective can be denoted as N
ij
. Based on these quantities,
a resource matrix with nobjectives and mresource states (M
r
)
can be established as follows:
Fig. 1. Influence of orderliness of ROES on system benefits.
80 Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
Mr¼2
4
N11 /N1m
««
Nn1/Nnm 3
5ð1Þ
The measurement of RON is closely linked to the resource
matrix. According to Eq. (1), the sum of the quantity of the j-
th resource state of ROEF occupied by all the objectives (X
j
),
the sum of the quantity of all resource states of ROEF occu-
pied by the i-th objective (Y
i
), and the sum of the quantity of
all resource states occupied by all the objectives (Z) are
expressed as follows:
Xj¼X
n
i¼1
Nij ð2Þ
Yi¼X
m
j¼1
Nij ð3Þ
Z¼X
n
i¼1X
m
j¼1
Nij ð4Þ
2.3. Measurement of RON
A mathematical abstraction of the hypervolume of RON is
described in this section. The niche status and the relationships
between niches were measured with three models: niche
breadth, niche coupling, and niche overlap. In addition, an
SeR framework was established to evaluate the interactions
among reservoir operation objectives. With these models and
the framework, this study aimed to gain a deeper under-
standing of the characteristics of RON and the interaction
between different operation objectives. This can help to make
more informed decisions and effectively optimize reservoir
operations.
2.3.1. Niche breadth model
The breadth of RON refers to the set of all the eco-
environmental elements that operation objectives can uti-
lize. With the niche breadth model, the extent of resource
occupation for each operation objective is measured, and the
niche status can be evaluated. In essence, this model evalu-
ates the degree to which each objective utilizes available
resources. Specifically, the breadth dimension of a niche is
determined by factors, such as the demand for resources,
adaptability, and the survivability of objectives within that
dimension.
The measurement of niche breadth can be obtained with the
ShannoneWiener information index formula (Shannon and
Weaver, 1963; Levins, 1968):
Bi¼X
m
j¼1Pij ln Piji¼1;2;/;nð5Þ
Pij ¼Nij
Xjð6Þ
where B
i
is the niche breadth of the i-th operation objective;
and P
ij
is the state of the i-th operation objective utilizing the j-
th resource in a resource set, i.e., the ratio of the amount of the
j-th resource utilized by the i-th objective to the total amount
utilized by all objectives.
For a cascade reservoir group in a basin, achieving overall
operation objectives is generally subject to the joint regulation
of multiple reservoirs. As the regulation capacity of each
reservoir varies, it is necessary to measure the integrated
breadth of RON across entire cascade reservoirs. This mea-
surement considers the interplay and interdependence of the
regulation capacity of each reservoir and their cumulative ef-
fect on achieving the overall operation objectives:
B0
i¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
R
r¼1½urBiðrÞ2
v
u
u
tð7Þ
where B0
iis the integrated niche breadth of the i-th operation
objective, u
r
is the weight of the r-th reservoir, B
i
(r) is the
niche breadth of the i-th operation objective for the r-th
reservoir, and Ris the number of reservoirs in the cascade.
2.3.2. Niche coupling model
The concept of coupling originates in physics, describing
the phenomenon wherein multiple systems influence one
another through various interactions. Extended to ROES, the
coupling degree can be used to measure the level of interde-
pendence among different objectives within a system. It serves
as a foundation for analyzing relationships among objectives.
The converted formula is as follows:
Table 1
System of RON.
Target layer Dimension
layer (ROEF)
Sub-dimension
layer (resource)
Unit
RON Flow Maximum flow m
3
/s
Minimum flow m
3
/s
Water level Highest water level m
Lowest water level m
Fig. 2. Hierarchical structure of ROES and comparison with natural
ecosystem.
81Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
C¼n"Y
n
i¼1
Bi, X
n
i¼1
Bi!n#1=n
ð8Þ
where Cis the coupling degree of RON, with a value range of
(0, 1]. When C¼1, the coupling degree is the largest, man-
ifesting that the objectives are entirely interdependent. When
Cis close to 0, the coupling degree is minimal, meaning that
the objectives are barely dependent on each other.
2.3.3. Niche overlap model
As shown in the Wayne diagram (Fig. 3), the relationships
between different niches can be categorized into three distinct
forms: overlap, separation, and inclusion. This suggests
different degrees of competition or cooperation among the
objectives, as they may compete for the same resources or find
ways to complement the resource utilization strategies for
each other. The overlap of RON measures the similarity in the
utilization ability of two or more objectives for the same
ROEF. This measurement reflects the convergence and
disparity in the use of resources by each objective, thereby
enabling the analysis of interactions between the objectives.
The Pianka formula of the symmetric alpha model (Pianka,
1974) is often used to measure the niche overlap:
Oik ¼X
m
j¼1PijPkj ,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
m
j¼1
P2
ij X
m
j¼1
P2
kj
sð9Þ
where O
ik
is the niche overlap degree between the i-th and k-th
objectives (i¼1, 2, ⸱⸱⸱,nand k¼1, 2, ⸱⸱⸱,n), with a value range
of [0, 1]; and P
ij
and P
kj
are the utilization statuses of the j-th
resource by the i-th and k-th objectives, respectively. A greater
overlap degree between two objectives leads to a higher
ecological similarity between them. O
ik
¼0 indicates that the
niches of the i-th and k-th objectives for the j-th resource are
entirely separated, and O
ik
¼1 means that they are completely
overlapped.
For a cascade reservoir group, as the reservoirs are hy-
draulically connected and not independent of each other, the
sum-amethod was used to measure the overlap degree of
RON across the entire cascade:
O0
ik ¼X
R
r¼1½urOikðrÞ ð10Þ
where O0
ik is the niche overlap degree between the i-th and k-th
objectives for the whole cascade, and O
ik
(r) is the niche
overlap degree between the i-th and k-th objectives for the r-th
reservoir.
In addition, a stateerelationship (SeR) measurement
analysis framework was designed and used to comprehen-
sively analyze mutual feedback relationships among objectives
(Fig. 4). The framework can derive the resource acquisition
capacity of different objectives at the state (S) level and obtain
the degree of occupancy for similar resources concerning
specific objectives at the relationship (R) level. With the
analysis results of the SeR framework, decision-makers can
gain a clearer understanding of the degree of competition or
interdependence among objectives compared to the Pareto
frontier. This enables to easily comprehend the primary and
secondary degrees of benefit guarantee and helps to determine
appropriate operating principles.
3. Case study
To validate the proposed SeR framework, the cascade
reservoir group situated on the mainstream of the Wujiang
River in China was selected as a case example. The extensive
hydropower development and reservoir projects in the
Wujiang River Basin play a vital role in local energy gener-
ation and water resources management. This study aimed to
gain insights into the interactions and complexities involved in
simultaneously pursuing power generation (PG), water supply
(WS), and ecological protection (EP) objectives through the
investigation of the cascade reservoir group in the basin.
3.1. Study area
The Wujiang River Basin, located at 104180E to 109220E
and 26070Nto30
220N, covers a total area of 87 920 km
2
and
stretches 1 037 km along its mainstream. As the largest trib-
utary on the southern bank of the upper Yangtze River, it is
Fig. 3. Schematic diagram of relationship between niches in one-dimensional and two-dimensional cases.
82 Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
renowned for its abundant hydropower resources. With a
substantial natural drop of 2 124 m and a channel gradient of
0.21%, the Wujiang River Basin has significant hydropower
potential. Since the 1970s, China has launched large-scale
hydropower development projects in the basin, including the
construction of 12 reservoirs along the mainstream. Presently,
all planned hydraulic engineering projects, except the Baima
navigation and hydropower project located at the downstream
end, have been successfully executed and completed. Fig. 5
shows the geographical location of the Wujiang River Basin
and the water system.
Of the 12 reservoirs situated on the mainstream of the
Wujiang River, five of them possess above-seasonal capacity
for runoff regulation, while the others have daily regulation
capacity. The reservoirs with above-seasonal capacity are
particularly significant for investigating runoff regulation.
Table 2 provides basic information of these five reservoirs
with their locations shown in Fig. 5.
Fig. 6 shows the simplified operation rules of the Wujiang
cascade reservoir system. The upstream inflow first passes
through the Hongjiadu Reservoir for regulation. Afterwards,
the discharge of the upper reservoir is added to the runoff from
the tributary at the same time as the inflow of the next reser-
voir for regulation. The regulation process is repeated for five
dams one after another. This study considered the five reser-
voirs as a whole for the calculation and analysis for the overall
cascade reservoirs.
3.2. RON system in Wujiang River
As described in Section 2.2.3, RON comprises two primary
dimensions (ROEFs): flow and water level. Each of them in-
cludes two sub-dimensions (resources): upper boundary and
lower boundary. These sub-dimensions represent specific re-
sources associated with the respective dimensions. For the
three objectives (PG, WS, and EP) of the cascade reservoir
group in the Wujiang River Basin, their individual resource
status values were determined according to the following
rules.
In the flow dimension, the upper boundary resource for
the PG objective is the maximum generation flow of the
turbine unit, and the lower boundary is the minimum
discharge flow of the reservoir. According to the Water
Distribution Plan of Wujiang River Basin issued by the
Ministry of Water Resources of China, the water supply re-
quirements of the Wujiang River Basin were defined as the
flow resource status of the WS objective in this study. For the
EP objective, Ni et al. (2022b) introduced the Tennant flow
duration curve (T-FDC) method to calculate the multi-level
environmental flow for each reservoir in the Wujiang River
Basin, and the obtained results were adopted as the resource
status values.
In the water level dimension, the PG, WS, and EP objec-
tives are all profit-raising objectives and share a unified
approach for determining their resource status values. The
upper and lower boundaries of their resource statuses were
defined as the normal and dead water levels of the corre-
sponding reservoirs, which is in accordance with the conven-
tional profit-raising operation mode.
The regulation capacity of each reservoir determines its
weight in the system. Specifically, the two over-year regula-
tion reservoirs, Hongjiadu (HJD) and Goupitan (GPT), were
assigned a weight of 0.3; the annual regulation reservoir,
Pengshui (PS), was assigned a weight of 0.2; and the two
seasonal regulation reservoirs, Dongfeng (DF) and Wujiangdu
(WJD), were set a weight of 0.1. Consequently, a system of
RON for the cascade reservoirs was constructed (Table 3).
4. Results and discussion
The breadth, coupling degree, and overlap degree of RON
in the Wujiang River Basin were quantified with Eq. (1)
through (10). These measurements can comprehensively
Fig. 5. Map of Wujiang River Basin and distribution of main
reservoirs.
Table 2
Parameters of main reservoirs on mainstream of Wujiang River.
Reservoir Regulation
capacity
Water level (m) Beneficial
capacity
(10
8
m
3
)
Installed capacity
(MW)
Dead Normal
Hongjiadu Over-year 1 076 1 140 33.61 600
Dongfeng Seasonal 936 970 4.91 970
Wujiangdu Seasonal 720 760 13.60 1 250
Goupitan Over-year 590 630 29.02 3 000
Pengshui Annual 278 293 5.18 1 750
Fig. 4. SeR measurement analysis framework based on niche theory.
83Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
assess the extent of resource utilization, interdependence, and
similarity in resource use among the objectives. This analysis
can clarify the complexities of the cascade reservoir system in
the Wujiang River Basin and facilitate a deeper understanding
of the trade-offs and synergies between PG, WS, and EP
objectives.
4.1. Analysis of multi-objective state
This study calculated the niche breadths of the three
operation objectives for the five reservoirs and the entire
cascade of the Wujiang River Basin (Table 4). A radar chart
(Fig. 7(a)) and a ternary phase diagram (Fig. 7(b)) were
plotted to compare the differences in niche breadths among
different reservoirs.
The absolute values of the niche breadths presented in
Table 4 and Fig. 7(a) revealed a consistent pattern across the
five reservoirs and the entire cascade. The niche breadths of
EP were the largest, while those of WS were the smallest.
This consistent ranking of niche breadths for the three ob-
jectives suggested that EP was the most competitive objec-
tive in acquiring flow and water level resources. In contrast,
WS exhibited relatively weaker resource utilization
capabilities.
Additionally, except for the HJD reservoir, the niche
breadths of the objectives for different reservoirs exhibited
significant similarities. Specifically, the niche breadths of the
three objectives for the HJD reservoir were relatively smaller
than those for the other reservoirs, particularly concerning the
WS and PG objectives. This suggested that, despite possessing
a robust regulating capacity, the HJD reservoir (the leading
reservoir in the cascade system) had limited available re-
sources for regulation. Consequently, the effectiveness of the
HJD reservoir in exerting benefits was not as pronounced as
that of the downstream reservoirs.
Furthermore, the proportional relationships among niche
breadths (Fig. 7(b)) showed that the distribution for the HJD
reservoir deviated from the other reservoirs, further confirming
the above conclusion.
4.2. Analysis of multi-objective relationship
According to the calculated breadths of RON, the coupling
degree of RON was determined to be 0.996 1, 0.998 4, 0.998 4,
0.998 8, 0.998 1, and 0.997 9 for HJP, DF, WJD, GPT, PS, and
cascade reservoirs, respectively. This result revealed a high-
level coupling state among the PG, WS, and EP objectives.
The interactions among the three objectives were significant and
interconnected, necessitating further exploration to understand
the complexities of their relationships.
The niche overlap degrees, presented in Figs. 8 and 9,
provide a comprehensive visualization of the similarities and
Fig. 6. Generalized topological map of Wujiang cascade reservoir system.
Table 3
System of RON in Wujiang river.
Reservoir Weight Objective Flow-dimension
resource status
(m
3
/s)
Water level-
dimension
resource status
(m)
Maximum Minimum Highest Lowest
HJD 0.3 PG 496.5 14.4 1 140 1 076
WS 14.4 14.4 1 140 1 076
EP 202.8 31.8 1 140 1 076
DF 0.1 PG 632.1 77.0 970 936
WS 77.0 77.0 970 936
EP 435.3 60.1 970 936
WJD 0.1 PG 1 087.0 112.0 760 720
WS 112.0 112.0 760 720
EP 591.1 90.8 760 720
GPT 0.3 PG 1 910.0 190.0 630 590
WS 190.0 190.0 630 590
EP 804.3 133.6 630 590
PS 0.2 PG 2 885.0 280.0 293 278
WS 280.0 280.0 293 278
EP 1 771.3 226.2 293 278
Table 4
Breadth of RON in Wujiang river.
Objective HJD DF WJD GPT PS Cascade
PG 1.33 1.43 1.40 1.38 1.41 0.67
WS 1.15 1.28 1.27 1.28 1.26 0.60
EP 1.43 1.46 1.46 1.44 1.46 0.71
84 Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
differences in resource utilization among the operation ob-
jectives for each reservoir and the entire cascade system,
allowing for a deeper exploration of the interactions and in-
terdependencies among the operation objectives within the
cascade reservoir group in the Wujiang River Basin. Figs. 8
and 9(a) reveal that for each reservoir and the entire
cascade, the niche overlap degree between PG and EP was the
largest, followed by the degree between WS and EP, while that
between PG and WS was the smallest. The significant overlap
between PG and EP objectives suggested that they shared the
most similar ability to occupy flow and water level resources
simultaneously in the cascade reservoir group. In contrast, the
ability of PG and WS objectives to occupy resources at the
same time was relatively weaker.
Indeed, achieving the PG objective requires the mainte-
nance of high water levels to secure a sufficient water head
for power generation. In contrast, the WS and EP objectives
often require an increase in discharge flow, thereby reducing
reservoir impoundment and subsequently decreasing the
water head. Additionally, the WS objective necessitates the
extraction of water from the river, further affecting the
available flow for the EP objective. This inherent competi-
tion for flow and water level resources underscores the
mutually exclusive nature of these objectives, rather than
cooperative. The prioritization of one objective over another
initiates a natural competition for the limited available re-
sources. Consequently, the overlap degree of RON reflects
the intensity of competition among objectives. Accordingly,
Fig. 7. Radar chart and ternary phase diagram of breadth of RON in Wujiang River.
Fig. 8. Semi-overlapping matrices of RON in Wujiang River.
85Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
the competition between PG and EP was the most significant,
while that between PG and WS was comparatively weaker.
This consistent pattern of competition among objectives
persisted throughout the entire cascade reservoir system.
The proportional relationship illustrated by the overlap
degree of RON (Fig. 9(b)) provided additional evidence that
the distribution of the HJD reservoir significantly deviated
from that of other reservoirs, particularly in the PGeWS
dimension. This deviation corresponded to the smallest niche
breadth observed in the previous analysis for the HJD reser-
voir. Consequently, this confirmed the conclusion that the
benefit-exerting capability of the HJD reservoir was not as
effective as that of downstream reservoirs.
4.3. Comparison with multi-objective simulation
Multi-objective operation on the Wujiang cascade reservoir
group was simulated to assess whether the results of the niche
theory agreed with real-world scenarios. The intricate de-
mands for PG, WS, and EP in the basin were abstracted into a
mathematical model comprising the following objectives:
(1) PG objective ( f
1
): The maximum total PG of the
cascade reservoirs is defined as follows:
f1¼max E¼max X
I
i¼1X
T
t¼1ðNitDtÞð11Þ
Nit ¼kiqitHit ð12Þ
where Eis the total PG of the cascade reservoirs (kW$h), Iis
the total number of the cascade reservoirs, Tthe total number
of the period, N
it
is the output of the i-th reservoir during the t-
th period (kW), q
it
is the discharge of the i-th reservoir during
the t-th period (m
3
/s), H
it
is the water head of the i-th reservoir
during the t-th period (m), k
i
is the output coefficient of the i-th
reservoir, and Dtis the time interval (h).
(2) WS objective ( f
2
): The maximum water supply guar-
antee rate (WSGR) is defined as follows:
f2¼max G¼max X
M
m¼1X
T
t¼1
Gmt
MT ð13Þ
Gmt ¼8
<
:
qmt
Dmt
qmt <Dmt
1qmt Dmt
ð14Þ
where Gis the total WSGR of the cascade reservoirs, Mis the
total number of the key sections for water supply, G
mt
is the
WSGR of the m-th section during the t-th period, q
mt
is the
flow of the m-th section during the t-th period (m
3
/s), and D
mt
is the corresponding flow requirement of the m-th section
during the t-th period (m
3
/s).
(3) EP objective ( f
3
): The maximum ecological satisfaction
degree (ESD) is defined as follows:
f3¼max S¼max X
N
n¼1X
T
t¼1
Snt
NT ð15Þ
Snt ¼
8
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
:
qnt
Qlnt
qnt <Qlnt
1Qlnt qnt Qunt
2Qunt qnt
Qunt
Qunt <qnt <2Qunt
0qnt 2Qunt
ð16Þ
where Sis the total ESD of the cascade reservoirs; Nis the
total number of the key sections for ecological protection; S
nt
is the ESD of the n-th section during the t-th period; q
nt
is the
flow of the n-th section during the t-th period (m
3
/s); and Q
lnt
and Q
unt
are the lower and upper limits of the optimal envi-
ronmental flow (m
3
/s), respectively.
Fig. 9. Overlap degree of RON and ternary phase diagram in Wujiang River.
86 Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
To ensure the accuracy of the reservoir operation model,
special constraint conditions relevant to the characteristics and
complexities of the cascade reservoirs were defined according
to Ni et al. (2022a). The measured flow data of the Wujiang
River Basin for the past 64 years (1956e2019) were statisti-
cally analyzed with the Pearson type III distribution (Zhang
et al., 2018), with 1979 selected as a typical normal year
representing the most common hydrological situation in the
basin. The runoff of that year was substituted into the model
mentioned above, and the NSGA-III algorithm improved with
the vector-angle-based selection strategy (VA-NSGA-III) (Ni
et al., 2019) was used to yield visual non-inferior multi-
objective results in the three-dimensional space (Fig. 10).
The Pareto frontier directly highlighted the intense
competition between PG and EP in the Wujiang cascade
reservoir system. As PG was increased to maximize power
generation, the EP status, represented by ESD, gradually
decreased. The niche analysis highlighted that PG and EP
objectives tended to have a significant niche overlap, reflecting
a shared demand for flow and water level resources. The
findings of the visual analysis agreed with the results of the
niche analysis, confirming that effective coordination among
the three objectives entailed a trade-off between PG and EP.
Although the visual interpretation of the Pareto frontier
provided valuable insights into the intense competition be-
tween PG and EP objectives, it might not be effective in
identifying the complexities of competitions between PG
versus WS and WS versus EP. Their interactions might be
intricate, involving a combination of competitive and syner-
gistic relationships. These complexities might not be apparent
in a visual representation, especially when the trade-offs of
objectives are not as distinct as in the case of PG versus EP.
Relying solely on the Pareto frontier is inadequate for quali-
tative assessments of each reservoir's regulating capabilities
within the system. This limitation of visual analysis un-
derscores the value of the niche theory proposed in this study.
The niche theory allows for a more comprehensive and
quantitative understanding of interrelationships among objec-
tives by measuring niche breadths, coupling degrees, and
overlap degrees. It provides a systematic and rigorous
approach for analyzing the utilization of resources by each
objective and the degree of interaction relationships among
them.
From these interaction relationships, decision-makers can
be guided in determining operating principles. For example,
certain PG benefits may need to be compromised to prioritize
Fig. 10. Pareto frontier and its two-dimensional projection in typical normal year.
87Xiao-kuan Ni et al. / Water Science and Engineering 2025, 18(1): 78e89
WS and EP benefits in the Wujiang cascade reservoir group,
among other considerations.
5. Conclusions
This study provides reservoir managers with valuable tools
to objectively comprehend the entire reservoir operation sys-
tem. This study applied bionic thinking to reservoir operation
and introduced a new concept called reservoir operation niche
(RON), offering a novel perspective on interactions among
multiple operation objectives. Based on RON, the SeR mea-
surement analysis framework was developed, allowing for a
more profound exploration of the relationship between various
objectives in terms of their resource acquisition capacity and
the degree of occupation of similar resources between specific
pairs of objectives. The developed framework was applied to
the cascade reservoirs in the Wujiang River Basin, and the
interactions among PG, WS, and EP objectives were quanti-
fied. The main conclusions are as follows:
(1) The EP objective exhibited the most robust competition
for flow and water level resources, and the WS objective was
the weakest.
(2) A high-level coupling state existed among the three
objectives. PG competed most strongly with EP and relatively
weakly with WS. Sacrificing some PG benefits could enhance
both WS and EP benefits.
(3) As the leading reservoir, HJD exhibited a strong regu-
lating capacity. However, the resources available for its
regulation were relatively limited, resulting in less effective
benefit exertion compared to downstream reservoirs.
(4) The SeR framework, based on the niche theory, enables
a quantitative assessment of feedback intensity among objec-
tives. It is simple and intuitive, avoiding the need to solve the
Pareto frontier of multi-objective problems in advance. This
framework is not limited by the number of objectives and
contributes to enriching the theory and methods of multi-
objective interaction relationship analysis.
With this innovative methodology, reservoir managers can
gain a deeper understanding of the interdependence, compe-
tition, and potential synergies among objectives, facilitating
more informed decision-making. Ultimately, this contributes
to enhancing the efficiency, adaptability, and ecological sus-
tainability of reservoir operation.
This study only focused on two main resources, water level
and flow, in implementing the SeR analysis framework for
multi-objective reservoir operation. This represents a highly
simplified consideration of the problem. Future research can
expand to include additional resources, such as water tem-
perature, sediment, hydraulics, and water quality, to gain a
more comprehensive understanding of multi-objective inter-
action relationships.
Declaration of competing interest
The authors declare no conflicts of interest.
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