267 © IWA Publishing 2012 Water Science & Technology | in press | 2012

A spatial multi-objective optimization model for

sustainable urban wastewater system layout planning
X. Dong, S. Zeng and J. Chen

ABSTRACT
X. Dong
Design of a sustainable city has changed the traditional centralized urban wastewater system
S. Zeng
towards a decentralized or clustering one. Note that there is considerable spatial variability of the J. Chen (corresponding author)
School of Environment,
factors that affect urban drainage performance including urban catchment characteristics. The Tsinghua University,
Beijing,
potential options are numerous for planning the layout of an urban wastewater system, which are 100084,
China
associated with different costs and local environmental impacts. There is thus a need to develop an
E-mail: jchen1@tsinghua.edu.cn
approach to find the optimal spatial layout for collecting, treating, reusing and discharging the
municipal wastewater of a city. In this study, a spatial multi-objective optimization model, called
Urban wastewateR system Layout model (URL), was developed. It is solved by a genetic algorithm
embedding Monte Carlo sampling and a series of graph algorithms. This model was illustrated by a
case study in a newly developing urban area in Beijing, China. Five optimized system layouts were
recommended to the local municipality for further detailed design.
Key words | multi-objective optimization, spatial layout planning, sustainable urban wastewater
system

INTRODUCTION

The urban wastewater system is one of the most important drainage performance including urban catchment character-
infrastructures for developing a sustainable city. For an inte- istics. The potential options are thus numerous for planning
grated consideration of sustainability related to costs, energy the layout of an urban wastewater system, which are often
and chemical requirements, nutrients recovery, security of associated with large differences in costs and local environ-
wastewater reuse, risks of infiltration and leakage and so mental impacts. Such complexity is further magnified by the
on, the traditional centralized urban wastewater system no extended integrated requirements for the sustainable per-
longer has overwhelming advantages (Fane & Fane ; formance of urban wastewater systems (Makropoulos et al.
Tjandraatmadja et al. ; Chen & Wang ). In , ). There is thus a need to develop an approach
response to urban development, population growth, and to find the optimal spatial layout for collecting, treating,
diminishing natural resources, decentralized wastewater reusing and discharging the municipal wastewater of a city.
management is becoming increasingly important now and In existing urban wastewater system design, the plan-
in the foreseeable future development of urban water man- ners decide the number of wastewater treatment plants
agement. Based on recent literature, research focuses, and (WWTPs) and their service areas by experience and simple
trends in the engineering and regulatory community, the qualitative analysis. An integrated evaluation is usually fol-
decentralized or clustering urban wastewater system is lowed to select a better system layout from a small amount
increasingly becoming the design norm, both in new urban of experience-based enumeration system design. For waste-
areas of developed countries (Burian et al. ; water reuse, there have been several studies on optimizing
U. S. Environmental Protection Agency ; Lombardo the reclaimed water allocation between the reclaimed
Associates, Inc. ; Rocky Mountain Institute ) and water users and the known WWTPs. Most of those studies
in developing countries (Parkinson & Tayler ; Jia are single-objective optimizations, for which the objective
et al. ; Massoud et al. ). Note that there is consider- functions are minimization of the cost of reuse water treat-
able spatial variability of the factors that affect urban ment and transportation (Oron ; Aramaki et al. ;

doi: 10.2166/wst.2012.113

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 268 X. Dong et al. | A spatial model for SUWS planning Water Science & Technology | in press | 2012

Zhang ; Joksimovic et al. ). Seldom is there a multi- a 0–1 integer to specify whether a given pL could be selected
objective study, for which the objectives include cost and to locate a WWTP. Note that different combinations of
energy consumption among other things ( Joksimovic ; wastewater treatment technologies, associated with different
Fu et al. ). The existing experience-based planning requirements of pL’s area, could lead to different environ-
method for urban wastewater systems cannot respond to mental and economic performances of a designed urban
the numerous potential system layouts due to the emergence wastewater system. The pL decision variable is also used to
of the decentralized system and the integrated requirements specify what kind of treatment technology is selected. (see
for the system’s sustainable performance. the Appendix, available online at http://www.iwaponline.
To tackle the challenges above, a spatial multi-objective com/wst/066/113.pdf)
optimization model, i.e. the Urban wastewateR system The pU consists of attribute, spatial and decision vari-
Layout model (URL), was developed in this study for ables. The attribute variable represents the altitude, the
urban wastewater system layout design and planning. This quantity and quality of discharged wastewater and the
model can present a comprehensive coverage of a sufficient reclaimed wastewater demand of a selected system service
number of potential urban wastewater system layouts, from area. The spatial variable illustrates the spatial topological
which optimal options could be identified, with an inte- relations between pUs by adjacent matrix. The decision vari-
grated consideration of spatial variability and performance able is again a 0–1 integer to specify which pL would match
sustainability. The outputs of the model include the to the selected pU and whether the reclaimed wastewater is
number, location, capacity and service area of the planned supplied to the pU (see http://www.iwaponline.com/wst/
treatment facilities for collecting, treating, reusing and dis- 066/113.pdf).
charging the municipal wastewater of a city. The proposed
model was applied to sustainable urban wastewater system
Model structure
planning in a newly developed urban area in Beijing,
China. The sustainable urban wastewater system layout
URL is a spatial multi-objective optimization model. Three
was recommended to the case study area. A detailed discus-
objective functions are included to represent the sustainabil-
sion of the results is presented in the paper followed by the
ity of an urban wastewater system: the economic,
conclusion.
environmental and resource recovery performances. In
addition, there are three constraints in the model to assure
the feasibility of the generated system layout options.
MODEL DESCRIPTION
The first objective function is to minimize the system’s
life-span costs (LiC) including both capital (CC) and O&M
Model variables
(OMC) costs of WWTPs (PCC and POMC), reclaimed
wastewater regulating storage tanks (RCC and ROMC), drai-
URL defines two categories of spatial units for a given plan-
nage and reclaimed wastewater pipelines and pump stations
ning area, the potential location of WWTP (pL) and
(NCC and NOMC) as shown in Equation (1):
the system service area (pU) with a topological relation.
The pL is a possible spatial block which should satisfy the
guided technical and legal requirements of a WWTP’s ð1 þ iÞL 1
min LiC ¼ CC þ × OMC
location. The pU is the smallest spatial planning unit in i × ð1 þ iÞL
URL, which may cover one land block or several adjacent ð1 þ iÞL 1
¼ ðPCC þ RCC þ NCCÞ þ
ones of the urban master planning. pU represents the user i × (1 þ i)L
of the urban wastewater system, the size of which depends × ðPOMC þ ROMC þ NOMCÞ (1)
on the trade-off between spatial data availability, compu-
tation efficiency and planning accuracy. Based upon the where PCC and POMC depend upon the selected treatment
developed URL, the task of urban wastewater system technologies as well as the scales of WWTPs; RCC and
layout planning is thus turned to quantifying and optimizing ROMC can be calculated by a network flow programming
the connections between pLs and pUs with consideration of model using seasonal variations of reclaimed wastewater
system sustainability. production and demand (Khaliquzzaman & Chander ;
The pL consists of both attribute and decision variables. Dong ); NCC and NOMC are determined by transpor-
The former includes pL’s area and altitude while the latter is tation distances as well as elevation differences between

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 269 X. Dong et al. | A spatial model for SUWS planning Water Science & Technology | in press | 2012

system service areas and WWTPs; L and i are the system same treatment facility must be connected based on the rule
life span and discount rate, respectively (see http://www. of spatial continuity, i.e. the topological relations. As shown
iwaponline.com/wst/066/113.pdf). in Figure 1, each pU will be served by the pL which has the
The second objective function is to minimize the sys- same colour as this pU. On the left-hand side of Figure 1,
tem’s total pollutant discharge loads (Load), which are both service areas of pLs have integrity, because the pUs
weighted by equivalent coefficients of different pollutants served by the same pL keep the spatial continuity. But on
(see Equation (2)). In this study, the pollutants concerned the right-hand side of Figure 1, the pUs in one service area
include chemical oxygen demand (COD), total nitrogen cannot be connected and their topological relation is broken:
(TN), total phosphorus (TP) and faecal coliform (FC) for
their importance in maintaining the quality of the receiving ∀k ¼ 1 ∼ NpL, i ¼ 1 ∼ nk , j ¼ 1 ∼ nk , ð pk Þij ≠ 0 (4)
water body in the case study area:
where NpL is the number of pLs; nk is the number of pUs ser-
min Load ¼ αCOD × LoadCOD þ αTN × LoadTN viced by the WWTP, which is located in the kth pL (pLk);
(2)
þ αTP × LoadTP þ αFC × LoadFC (pk)ij is the entry of Pk in the ith row and jth column; Pk ¼
Sk þ S2k þ⋯þ Snk k ; Sk is the adjacent matrix for describing
where αCOD, αTN, αTP and αFC are the equivalent coefficients the spatial relationship of pUs serviced by the WWTP posi-
of COD, TN, TP and FC; this selection refers to the pollution tioned in pLk (see the Appendix, available online at http://
charge system. LoadCOD, LoadTN, LoadTP and LoadFC are www.iwaponline.com/wst/066/113.pdf).
the annual emission loads of COD, TN, TP and FC dis- The second constraint is that spatially there should be a
charged from a given designed wastewater system, which match between reclaimed wastewater demand and its
can be determined by the pollutant generated by the supply in both quantity and quality, i.e.:
system service area and the pollutant removal capacity of
WWTPs (see the Appendix, available online at http:// ∀k ¼ 1 ∼ NpL, QD,k ≥ QR,k , Ck,m ≤ CpU min ,k,m (5)
www.iwaponline.com/wst/066/113.pdf).
Maximization of resource recycle capacity (Res) is the where QD,k is the reclaimed wastewater capacity of the
third objective function in URL, and in this study it is limited WWTP in pLk; QR,k is the reclaimed water demand of all
only to the matching ratio between reused wastewater pUs serviced by the WWTP in pLk; Ck,m is the concentration
supply (reuseactual) and its potential demand (reusepotential ) of pollutant m in the effluent of WWTP in pLk. CpUmin,k,m is
in a planned system service area as shown below the concentration limitation of pollutant m that is accepta-
(Equation (3)). This object function can also be expanded ble to all reclaimed wastewater users serviced by the
for the nutrient or energy recovery in urban wastewater sys- WWTP built in pLk (see http://www.iwaponline.com/wst/
tems similar to reused wastewater (see http://www. 066/113.pdf).
iwaponline.com/wst/066/113.pdf) The last constraint is that the land area of any treatment
facility cannot be larger than the available land as specified
reuseactual in the urban master plan, i.e.:
max Res ¼ (3)
reusepotential
∀k ¼ 1 ∼ NpL, Areak ≤ ApLk (6)
The first constraint is to assure the spatial integrity of the
system service area for each positioned treatment facility, as where Areak is the required land area of WWTP positioned
given in Equation (4). It suggests that all areas serviced by the in pLk, which depends on the capacity of the WWTP as well
as the selected technologies; ApLk is the land area available
for treatment facilities in pLk (see http://www.iwaponline.
com/wst/066/113.pdf).

Numerical solving strategy

URL is a typical spatial multi-objective optimization model

with multi-constraints and massive 0–1 variables. To
Figure 1 | Schematic diagram for spatial integrity of system service area. numerically solve it, a solving strategy was developed

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 270 X. Dong et al. | A spatial model for SUWS planning Water Science & Technology | in press | 2012

Figure 2 | Numerical solving strategy for calculating URL.

through the integration of Monte Carlo sampling, the non- in Deb () and Coello Coello et al. (). In URL,
dominated sorting genetic algorithm-II (NSGA-II) and NSGA-II was used to optimize the system layout, i.e. the
graph algorithms (see Figure 2). By this solving strategy, connection relationships between pUs and pLs in terms of
URL could select the non-dominated system layouts conti- the three given objective functions.
nually until Pareto optimal (Deb ) layouts are found, To generate eligible initial layouts subject to the spatial
which were then the most desired sustainable system layouts constraint in NSGA-II, a random graph connected partition
in terms of the given objective functions. algorithm (Dong ) was specially developed in this study,
Theoretically, Monte Carlo sampling could provide which is based upon the spanning tree random generation
sufficient random combinations of WWTP numbers and and Depth-First Search (DFS) (Cormen et al. ) (see
locations across the entire planned area, and could assure Figure 2). In addition, to rank the individual fitness in terms
a full spatial coverage and homogeneity of computation. It of objective functions in NSGA-II, Dijkstra’s algorithm was
reduces the complexity of URL by dramatically reducing used to lay out the pipe network (Cormen et al. ). When
the number of 0–1 variables in a single calculation loop. operating the crossover and mutation operator in NSGA-II,
In addition, this sampling method also provided the possi- the Breadth-first search (BFS) algorithm was embedded to
bility of parallel computing for improving computational account for spatial constraints (Cormen et al. ).
efficiency.
NSGA-II is an effective genetic algorithm for multi-
objective optimization developed by Deb et al. (). It THE CASE STUDY AREA
used an efficient non-domination sorting to reduce the com-
putational complexity and applied the elitist selection to The case study area is a newly developing urban area in
speed up the capture of Pareto surface. Detailed discussions southeast Beijing, China. It covers 32.2 km2 with a popu-
of Pareto optimization and genetic algorithms can be found lation of 272,000 and a semi-arid climate. Currently, only

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 271 X. Dong et al. | A spatial model for SUWS planning Water Science & Technology | in press | 2012

66% of municipal wastewater is treated by a centralized speed of each objective function in one Monte Carlo
WWTP. Its receiving rivers are facing continuous degra- sampling. It is evident that the developed numerical solving
dation with water quality worse than the Class V standard strategy is efficient in solving URL in this study.
prescribed in the Surface Water Quality Standard of China After a sufficient number of Monte Carlo samplings, a
(GB3838–2002), which is only suitable for landscape irriga- set of Pareto optimal solutions (POSet) was obtained,
tion. In the new master plan, it is expected that the including 335 Pareto optimal layouts that were calculated
population will increase to 600,000 and the urban area as the most desired sustainable system layouts in terms of
will be expanded to 65 km2 by 2020. To tackle both the cur- the three objective functions. Each system layout in the
rent water quality problem and the future growing water POSet was much more sustainable than those that did not
shortage, the master plan pre-sets that in 2020 100% of the belong to the set, but no dominance was observed between
municipal wastewater be treated and 50% of it be reclaimed. any two system layouts in the POSet in terms of sustainabil-
Thus, an integrated planning of urban wastewater treatment ity defined by the three objective functions. Figure 4
and reuse systems is required including its spatial layouts. illustrated the economic, environmental and wastewater
In the case study area, according to the master plan as reuse performances of the 355 Pareto optimal layouts in
well as the environmental, technical and legal requirements the POSet as represented by LiC, Load and Res. A large
for locating WWTPs, six potential locations of WWTPs Res indicated a higher matching ratio between reused waste-
(pLs) were identified by geographic information system water supply and its demand, a smaller Load suggested a
(GIS). Four secondary treatment technologies (activated low total pollutant discharge load and a higher LiC meant
sludge, denitrifying activated sludge, membrane bioreactor, more system life-span cost.
wetland) and three advanced treatment technologies (phos- Each point in Figure 4 represented one optional sustain-
phorus precipitation, coagulation and filtration, micro- able system layout, including the number, location, capacity
filtration) were also recommended for the urban wastewater as well as service area of the planned treatment facilities for
treatment and reuse systems design. The cost, pollutant collecting, treating, reusing and discharging municipal
removal efficiency and land demand of those technologies wastewater. According to the decision-makers’ preferences
were considered owing to their impacts on the performance on the weightings of economic, environmental and resource
and feasibility of system layouts. reuse performances, recommended sustainable system lay-
outs could then be identified from the POSet. For
instance, based upon the availability of local water
RESULTS AND DISCUSSIONS resources, we can screen and find those plan layouts, the
matching ratio between reused wastewater supply and
The URL was applied to plan the layout of the wastewater demand of which could satisfy the required amount of
treatment and reuse systems in the case study area above. reclaimed wastewater specified in the master plan. In this
For each Monte Carlo sampling, NSGA-II generated 500 area, the master plan required that a 50% ratio would be
individuals for initial population and calculated 500 evol- achieved between the actual supply of reclaimed water
ution generations. Figure 3 illustrates the convergence and its potential demand, therefore the recommended

Figure 3 | Convergence speed of each objective function in URL.

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 272 X. Dong et al. | A spatial model for SUWS planning Water Science & Technology | in press | 2012

Figure 4 | The three objective function values of POSet for the case study site.

Figure 5 | Spatial planning of one recommended system layout: (a) spatial service area distributions of different WWTPs; (b) spatial distributions of the reclaimed wastewater users.

sustainable system layouts can be selected by Res values facilities were suggested; the service area distributions of
0.5 from POSet. If more consideration were given to econ- which are given in Figure 5(a). Different colours indicate
omic factors, one option could be identified as the the service areas of different treatment facilities. Figure 5(b)
recommended system layout. In this layout, five treatment shows the spatial distribution of reclaimed wastewater

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 273 X. Dong et al. | A spatial model for SUWS planning Water Science & Technology | in press | 2012

Table 1 | Capacity and treatment technology selected for each treatment facility in the recommended system layout

No. of Wastewater treatment capacity Wastewater recycling capacity

facility (×104 t/d) (×104 t/d) Treatment technology

2.0 0.1 Denitrifying activated sludge þ phosphorus precipitation þ

coagulation and filtration
5.5 3.3 Wetland þ phosphorus precipitation þ coagulation and filtration
2.3 0.0 Denitrifying activated sludge þ coagulation and filtration
5.7 3.3 Membrane bioreactor þ coagulation and filtration
0.3 0.2 Denitrifying activated sludge þ phosphorus precipitation þ
coagulation and filtration

Figure 6 | Probability distributions of objective functions and the number of treatment facilities in the POSet.

users as well as the areas where there was no need for waste- of five treatment facilities is much more likely to lead to a
water reuse. Table 1 lists the capacity and the corresponding sustainable design for an urban wastewater system. Similar
selected treatment technology for each treatment facility discussions and analysis from the URL results could pro-
associated with the recommended system layout. vide further in-depth understanding of the effects of
Furthermore, based on a statistical analysis on the spatial variability and a wider consideration of different
POSet, different performances of all the optional system indicators of sustainability on the development of a sustain-
plans could be evaluated. As shown in Figure 6, of the able urban wastewater system.
335 layouts, at a 90% probability, the system life-span
cost would be no more than 1.32 × 108 RMB Yuan,
their annual equivalent pollution emission load would CONCLUSIONS
not be over 3.65 × 104 ton, and their reclaimed waste-
water ratios would be lower than 85%. More With the consideration of sustainability and the trend for a
importantly, Figure 6 also illustrates the accumulative decentralized layout of wastewater facilities, a spatial
probabilities of all the Pareto optimal layouts with multi-objective optimization model URL is presented in
three, four or five treatment facilities located in the case this study. A new combined algorithm, consisting of
study area. It was clear that the traditional centralized Monte Carlo sampling, NSGA-II and graph algorithms, is
system layout with one WWTP or an overly scattered developed as the model’s numerical solving approach. The
system layout with more than five WWTPs was not URL has been successfully applied to a case study for the
likely to be identified as a sustainable design. In addition, planning of a sustainable urban wastewater and reuse
it was also found that 80% of the 335 optional system lay- system in a newly developing urban area in Beijing. Through
outs would have five treatment facilities. This may intensive Monte Carlo sampling, a POSet with 335 optimal
suggest that according to Bayesian theory, the selection optional urban wastewater system layouts was identified,

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 274 X. Dong et al. | A spatial model for SUWS planning Water Science & Technology | in press | 2012

which illustrated not only the significantly increased com- Fane, A. G. & Fane, S. A.  The role of membrane technology
plexity of, but also the remarkably increased number of in sustainable decentralized wastewater systems. Water Sci.
Technol. 51 (10), 317–325.
options for, sustainable urban wastewater system design.
Fu, G., Butler, D. & Khu, S. T.  Multiple objective optimal
In other words, design for sustainability has led to a much control of integrated urban wastewater systems. Environ.
wider diversity of urban wastewater systems with almost Modell. Softw. 23 (2), 225–234.
non-discriminating performances. In this study, options of Jia, H. F., Long, Y., Cheng, S. T. & Li, J. H.  Study on urban
layouts were finally recommended for consideration for wastewater system planning in Foshan city. Water
further fine detailed design. Based on the statistical analysis Wastewater Eng. 31 (6), 3–7 (in Chinese).
Joksimovic, D.  Decision support system for planning of
of POSet, more information was also available to the local
integrated water reuse projects. Doctoral Thesis, University
planners for a better understanding of the urban wastewater of Exeter, UK.
system in the studied area. It is thus fair to say that the devel- Joksimovic, D., Savic, D. A. & Walters, G. A.  An integrated
oped URL model is an effective tool for urban infrastructure approach to least-cost planning of water reuse schemes.
planning and management of the future city. Water Sci. Technol. Water Supply 6 (5), 93–100.
Khaliquzzaman & Chander, S.  Network flow programming
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ACKNOWLEDGEMENT Lombardo Associates, Inc.  Cluster wastewater systems
planning. Research Report, National Decentralized Water
Resource Capacity Development Project (WU-HT-01–45),
We gratefully acknowledge Dr Mei Lu from Tsinghua Univer-
Massachusetts.
sity for her contribution to the graph algorithm development. Makropoulos, C., Morley, M., Memon, F. A., Butler, D., Savic, D.
This work was supported by the program ‘Integration of & Ashley, R.  A decision support framework
urban water pollution control technologies and development for sustainable urban water planning and
of supporting platforms’ (2009ZX07318–008). management in new urban area. Water Sci. Technol. 54 (6–7),
451–458.
Makropoulos, C. K., Natsis, K., Liu, S., Mittas, K. & Butler, D.
 Decision support for sustainable option selection in
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First received 03 August 2011; accepted in revised form 25 January 2012

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