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Urban Drainage Network Structure Optimization Using Emperor 

Penguin Optimization Algorithm 

 

J. Suganthi1*, I. Paulraj Jayasimman2 

1*Research scholar, Academy of Maritime Education and Training (AMET),  Deemed to be University, India.  

Email: sugisuresh27@yahoo.in 

2Associate Professor, Department of Mathematics, Academy of Maritime Education and Training (AMET), Deemed to 

be University, India. 2ipjayasimman@ametuniv.ac.in

1*Corresponding Author 

 

Article History: 

Received: 08-07-2024 

Revised: 21-08-2024 

Accepted: 04-09-2024 

Abstract:  

Urban drainage systems are an essential component of urban infrastructure that plays a 

critical role in managing stormwater and preventing flooding in urban areas. With the 

changing climate and urbanization, the challenges faced by urban drainage systems are 

becoming increasingly complex. Additionally, aging infrastructure further exacerbates the 

problem, creating anurban sewage line that must be made more resilient. Redundancy is 

just a fundamental characteristic of such a robust urban drainage network. Redundancy in 

urban drainage systems can help to ensure that the system continues to function during 

extreme weather events or emergencies, reducing the likelihood of flooding and damage. 

However, the exact locations where redundancy should be increased and its contribution to 

resilience are not well understood. In recent years, several studies have focused on 

developing frameworks for optimising urban drainage structures which account pipeline 

redundancy.One similar research presented a paradigm for constructing the ideal network 

layout for urban drainage infrastructure, which considers pipeline redundancy under 

consideration. The original architecture and structure of the urban drainage network was 

developed using emperor penguin optimizer algorithms and graph theory in the research. 

Complicated system modelling was done to find extra water pathways or redundancy which 

might well be implemented to boost resistance. The suggested approach has been utilised to 

the test region in Dongying City, Shandong Province, China, and its findings revealed even 

under rainfall above the design specification, the entire overflow capacity of such urban 

drainage network including pipeline redundancy significantly decreased about 20-30%, 

compared to the network without pipeline redundancies. The interest in creating 

optimization algorithms had also increased recently that can be used to design and manage 

urban infrastructure systems. One such algorithm is the Emperor Penguin Optimization 

(EPO) algorithm. EPO was a recently developed swarm-based optimization An algorithm 

which simulates Emperor penguins behaviour in their search for food in Antarctica.  

The algorithm has shown promising results in solving complex optimization problems in 

different fields, including engineering, computer science, and management. The EPO 

algorithm's key features include an emperor search strategy, local search, and 

randomization, enabling that to efficiently and successfully examine the search process. The 

algorithm's emperor penguin search strategy enables it to dynamically adjust the search 

parameters based on the problem's characteristics and progress. The local search feature 

allows it to escape local optima and explore the search space further. Finally, the 

randomization feature adds stochasticity to the search process, helping to ensure that the 

algorithm can avoid getting stuck in a sub-optimal solution. In this article, we aim to 

explore the potential of EPO as a tool for optimizing Urban drainage solutions which take 

mailto:sugisuresh27@yahoo.in
mailto:2ipjayasimman@ametuniv.ac.in


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into account pipeline redundancy. We will start by reviewing the existing Literature upon 

that optimization in urban drainage facilities, particularly the application of particle swarm 

optimization, genetic algorithms, and ant colony enhancement. The EPO algorithm will 

next be described in full including its working principle, key features, and the steps 

involved in applying it to an optimization problem. Finally, we will present a case study 

that applies the EPO technique was developed to optimise the network model of such an 

urban drainage infrastructure taking into account pipeline redundancies, and compare the 

results with other optimization algorithms. Through this, we aim to demonstrate the 

potential of EPO as a powerful tool for designing and managing urban infrastructure 

systems, particularly for enhancing the resilience of urban drainage systems. The study will 

provide valuable insights into the optimal design of urban drainage technologies which take 

into account pipeline redundancy, helping policymakers and urban planners make informed 

decisions about improvingthe adaptability of urban drainage networks. The findings can 

contribute to the development of sustainable and resilient urban infrastructure systems, 

which are essential for ensuring the well-being and prosperity of urban residents. 

Keywords: Urban Drainage Network, Emperor Penguin Optimization Algorithm, 

Hydraulic Layout, Storm Water Management Model 

 

1. Introduction  

The recommended experimental framework, primarily depicted in Figure 1, consists of three major 

components. The initial stage is to use a graph theory technique for determine the basic structure of 

both the urban drainage network. In its second step, an emperor penguin algorithm is employed to 

obtain the optimal hydraulic design. The third step involves using complex network examination to 

identify crucial nodes that can increase loop and redundancy, and analyzing the system's resiliency 

effectiveness. The analysis primarily concentrates upon the above structure’s effectiveness inside the 

event of a functional breakdown, employing two specified metrics: mean flood duration (MFD) 

and total overflow volume (TOV) [14,15]. Whenever the outflow discharge surpasses the capacity 

of drainage, the amount of rainwater which runs through the drainage system has been referred to as 

TOV, while MFD refers to the average duration of the flood. 

 

Fig.1.An elevated summary of such proposed research paradigm.  

Termination requirements (1): include all subsequence’s; termination condition (2): confirm that all 

patterns in have been hydraulically constructed. SWMM stands for storm water management system 

[28]; TOV refers for total overflowing flow, and MFD refers for median flood timeframe. 



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A. METHODOLOGY AND DATASETS 

 The portion explains the approaches utilized before implementing those towards a research 

location in “Dongying, Shandong Province, China”, like pattern choosing, hydraulic layout, and 

complicated network evaluation. 

B. METHODOLOGY 

The infrastructure of urban drainage systems primarily based upon a framework of design choosing 

and hydraulic planning, using complex network evaluation used further to enhance the network 

model. 

C. SELECTION OF LAYOUT  

Choosing a structure comprises deciding the spot as well as amount of water pipes, selecting suitable 

pipelines, and determining the pattern of flow of water. Graph theory techniques [17,25]. Aare 

commonly used to assist with layout selection. A network was made up of connections and vertices, 

where vertices also edges represent manholes and pipes, respectively. The starting graph contains 

every possible pipeline, as well as the loop-by-loop chopping approach is used to gradually remove 

edges from the undirected base graph to build a workable tree architecture [6,28].  Figure 2 depicts 

the process utilised in this study for layout selection, which involves the following steps: (1) creating 

the base graph G (V, E) and recognising every loops inside the main graph; (2) selecting a loop and 

eliminating a border from the loop while maintaining connectivity of the remaining edges; (3) 

checking for any remaining loops in the graph and repeating step (2); (4) obtaining every subgraphs 

which won’t comprise any loops (Fig. 2). 

 

Fig 2.Selection of Layout  

D. HYDRAULIC DESIGNING 

 The hydraulic layout was generally utilized to determine the size and slopes in order to 

reduce the requirement of filling stations and pressurised pipelines. 

1. OBJECTIVE FUNCTION 

Difficulty on optimising the urban drainage network might be described like follows: 

1

( , )
N

i i i i

i

Minimize F C D H L
=

=      (1) 



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wherein F indicates the optimization technique, N signifies the overall numbers of pipelines𝑖: 
iD

represent the diameter, 
iH is the submerged depths, and

iL is the pipeline lengths. 

2. DESIGN CONSTRAINTS 

The hydraulic layout of such urban drainage infrastructure should comply towards the appropriate 

flow velocity, pipe diameter, and buried depths restrictions: 

min maxD D D       (2) 

down upD D       (3) 

1 2 3{ }, , , ,s ZD D D D D D =     (4) 

min maxv v v       (5) 

min maxdh H dh       (6) 

In which minD
represents the minimal pipeline diameter, maxD

defines the maximal pipeline diameter, D 

represents the flowing pipeline diameter, downD
denotes the downstream pipeline diameter, and upD

represents the upstream pipeline diameter 𝑣 denotes the flow rates, minv
seems to be the minimum 

flow speed, maxv
seems to be the maximum flowing velocity, mindh

seems to be the buried depths, 𝐻 

denotes the depth buried, also maxdh
represents its greatest depth buried. 

3. EMPEROR PENGUIN OPTIMIZER  

 The emperor penguin optimizer (EPO) method was indeed the unique meta-heuristic 

technique invented by Dhiman around 2018 that is motivated from emperor penguin huddling habits. 

Emperor penguins snuggle together just to stay warm during the hard Antarctic winters, when 

temperatures might drop below dangerously lower degrees. The huddling activity of emperor 

penguins was distinctive and also is affected by a variety of elements such like distance, temperature, 

and efficient movements inside the cuddle. The EPO methodology was founded on above and other 

parameters, with the observer and update equations emulating temperature and distance, respectively. 

This algorithm has been tested on several optimization problems and has shown to be effective. The 

basic goal of emperor penguin huddling is just to optimise the environmental temperatures inside the 

cuddle and preserve energy. The temperature T was proportional towards the huddle polygon R 

circle, which means that as the radius of the huddle increases, the temperature also increases. 

𝑇 = {
0.  𝑖𝑓 𝑅 > 1
1.  𝑖𝑓 𝑅 < 1

 ,     (7) 

T0is a temperature profile It's in charge of the drilling and extraction procedures. It really is 

calculated as specified: 

0 ,
MI

T T
CI MI

= −
−

     (8) 



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where 
0T represents the temperature distributions surrounding the cluster, MI represents the maximal 

quantity of repetitions, and represents the current iteration CI . 

The separation among the best-determined optimum approach and the emperor penguin Whenever 

the huddle boundary was formed, D gets calculated. 

    ,( ) ( ) ). (.epD S A P x C P x= −      (9) 

Where, 

( )S A denotes emperor penguin social forces. 

( )P x signifies the emperor penguin's current position vector. 

𝐴, 𝐶denotes neighbour anti-collision factors. 

( )epP x signifies the vector of most optimum solutions discovered. 

A and C are in charge of fine-tuning the distance D, and they may be computed using the following 

equations: 

1,C rand=     

(10) 

0 2 0)( ,( )gA M T P ac rand T=  +  −    (11) 

) ,( ( ) ( )g epP ac P x P x= −     (12) 

Where,𝑀 is the mobility parameter that maintains a collision distance between search 

agents’ avoidance. The polygon grid accuracy is defined as ( )gP ac by comparing the difference 

between emperor and penguins. 

The calculation of S(A), which directs the optimal search agent towards the best direction, can be 

determined using Equation (13). On the other hand, Equation (14) is used to update the position of 

the search agent. 

( )
2

/ ,( ) . x l xS A f e e− −= −    (13) 

,( ( )1) epP x P x A D+ = −      (14) 

where f and l are parameters that influence exploration and exploitation. P(x+1) indicates the 

emperor penguin's next updated position. 

Table 1 shows the proposed values for the parameters utilised in the EPO algorithm, according to [1]. 

Figure 3 depicts the “flow chart of the EPO algorithm”, whereas following are the major processes in 

executing EPO: 

 

 



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Table 1: Parameter settings for the emperor penguin optimizer (EPO) algorithm [1]. 

Parameter M Rand 1 Rand 2 f l 

Minimum value  

Set to 2 

0 0 2 1.5 

Maximum value 1 1 3 2 

Step 1:Set the starting variables for rand1, rand2, R, T, T0, A, C, S(A), M, f, and l. 

Step 2:produce initial values for important parameters P(x) and compute their fitness values 

(objective function). 

Step 3:determine the best initial optimum solution based on the computed fitness. 

Step 4:Begin the first iteration by computing the new T0, S(A), Pg(ac), and A values. 

Step 5:Determine the amount of D and apply it to the best option. Pep(x) is used to compute the new 

and updated solutionsP(x+1). 

Step 6:choose the greatest new ideal solution and save it in Pep (x). Moreover, save the appropriate 

best fitness. 

Step 7:If the iterations have not ended, return to Step 4 and repeat until the maximum number of 

iterations has been achieved. 

Step 8:Examine the fitness array to discover the best fitness and present the answer. 



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Figure 3. Flow chart of EPO 

A. EVALUATION OF COMPLEX NETWORK  

Acomplex two-layer networking evaluation was created, comprising a global networking 

examination conducted to every nodes as well as a local system evaluation performed to every node 

independently (Fig. 4). 



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Fig. 4The connection among global networking evaluation and local networks evaluation 

B. GLOBAL NETWORK ANALYSIS 

 The application of global network evaluation can be useful in identifying crucial nodes in 

urban drainage systems. closeness centrality, like as betweenness centrality and Centrality measures 

[2,5] are commonly used to evaluate the role of specific nodes in the network and their impact on the 

overall system. For large water distribution systems, the demand can be estimated using betweenness 

centrality [22]. In sewage systems, the edge betweenness centrality [8] can be adjusted to indicate 

what regularly an edge appears inside the quickest route among the supply vertices as well as the 

output. The research makes specific changes towards the centrality measurements. Betweenness 

centrality was characterised by the frequency that a particular node emerges upon that network's 

smallest route. Closeness centrality, on the opposite hand, was determined as such average distances 

from a nodes towards the exit. These modifications can help to further analyze and identify the 

“critical nodes inside the urban drainage system. 

( )
( ) st

B

s t v V st

v
C v



  

=      (15) 

𝐶𝑐(𝑣) =
1

∑ 𝑑𝐺(𝑣,𝑡)𝑡∈𝐺
                           (16) 

𝐼 = 𝑤1 × 𝐶𝐵(𝑣) + 𝑤2 × 𝐶𝑐(𝑣)              (17) 

where ( )BC v is the centrality betweenness; s, v, t are nodes; V denotes the node set; ( )st v denotes 

the number of shortest pathways from s to t through v; 
st denotes the number of shortest paths from 

s to t; 𝐶𝑐(𝑣) is the centrality of proximity; G is the graph; 𝑑𝐺(𝑣, 𝑡) is the shortest path linking nodes 

v and t in G; I is node value; and 𝑤1and 𝑤2are weights calculated by the Analytic Hierarchy Process. 

𝑤1is 0.2 and w𝑤2 is 0.8 in this investigation”. Analytic Hierarchy Process analysis was performed 

Zhang [30]. 

4. EVALUATION OF LOCAL NETWORK  

Local network evaluation, that comprises degree (d), indegree (
ind ), out-degree (

outd ), as well as the 

maximum degree (
md ), was a concentrated Evaluation of nodes having greater scores resulting on 

global system evaluation. The degree indicates how numerous edges were connected toward a node. 



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In-degree represents how all those sides approach the cluster; out-degree represents how often edges 

leave the cluster; and maximal degree represents the maximal amount of edgesthat may connect to 

the node: 

in outd d d= +     (18) 

If d = dm, redundancies may be raised; otherwise, redundancy can indeed be enhancedif d <dm,. 

Consider node c in Fig. 4, which has a greatest severity of 3; the present in-degree is 1; the existing 

out-degree was 1; there seems to be opportunity for enhance redundancies. Node b has no space for 

redundancy since it's able to have a greatest value of 4, whereas the in-degree and out-degrees 

currently are 3 and 1, correspondingly. 

C. DATASETS AND THE STUDY AREA  

The study location was 8.916 km2 in size and also is positioned inside the eastern portion of 

Dongying City Centre, Shandong Province, China (Fig. 5). [20]. 

 

Fig. 5 Location of the study area in Dongying City, Shandong Province, China. (a) China; 

(b)Dongying City; (c) Study Area Basic Graph 

For hydraulic analysis, [21]; the Storm Water Management Model (SWMM) were utilized. 

Employing a digital method of the elevation information and the current condition, the characteristics 

of the sub catchment as well as the basic stormwater technology were obtained [3,11]. The 

experimental area has a strong elevation inside the south as well as a lower elevation with in north. 



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The degree of impermeable covering was 90.9%. Researchers utilized elevation data with such a 30 

m 30 m resolution and industrial usage information with just an accuracy of 10 m 10 m. (Fig. 6). 

 

Fig. 6An illustration of the research field. (a) Elevation of the ground; (b) Land Usage 

The entire extent of the primary drainage pipeline was 25,142 m, as well as the pipeline thickness 

was 2.82 km/km2. The tunnel's dia ranges after 300 through up to a 2000 mm.The researching 

location features ponding point monitoring equipment also a neighbouring rain gauge station. Rain-

gauge station noted rainfall data from August 18 to August 20, 2018, and the flooding depth data 

from the three waterlogging stations were utilised to fine-tune the settings(Fig. 7a).  

 

Figure 7 depicts the rainfall data utilised in the research. (a) A rainfall event was utilised to calibrate 

the system; 

Because all errors are within 10%, the model is acceptable as given in the Table 2.  

Table 2The three waterlogging locations' flooding depths 

point of Waterlogging 

 

value Observed 

(m) 

value Simulated 

(m) 
00%

|
1

|sim obs
e

obs

V V
R

V

−
=   

1 0.255 0.261 2.4% 

2 0.238 0.217 8.8% 

3 0.200 0.219 9.5% 

 

Where the Table 3 displays SWMM's final calibration parameter values. 



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Table 3Characteristics for the storm water management framework that have been calibrated  

Parameters Explanation rateof Calibration 

N-imperv Manning's n for the overland flowing across the 

sub catchment's impervious part 

0.015 

N-perv Manning's n governing overland flowing across 

the preceding sub-catchment 

0.28 

Dstore-imperv 

(mm) 

Depth for depressed storing upon that sub 

catchment's impermeable section 

1 

Dstore-perv 

(mm) 

Depression storage depth upon this previous 

segment of sub catch 

6 

Maxrate (mm h-

1) 

Highest Horton curve infiltrating speed 51 

Minrate (mm h-

1) 

Horton curve minimum infiltration capacity 3.3 

 

The verification findings demonstrate that its coefficient Rewas larger as 0.9, suggesting that its 

model's reliability and correctness meet requirements (Table 1). The measured readings of its 

SWMM characteristics are shown in Table 2. Street systems as well as urban water systems have a 

substantial correlation—around 80% of total sewage networks connect with 50% of roadway 

networks [13,29]. The arrangement of buildings and roadways in the research area is used to divide 

sub catchments. To determine the flow direction, Analyses of space are conducted upon that digital 

concept of elevation. Drainage pipes in high-traffic locations have a design return period of 3-5 

years. Around Dongying City, where the research location was situated northern residential sector, 

which is a heavily populated residential neighbourhood. For safety reasons, the 5-year returning 

period regarding designing pipelines was established. 

The hydraulic evaluation [7,18] in its urban draining infrastructure utilizes rainfall between 10- and 

20-year returning intervals (see Fig. 7b). The Rainfall volumes are 80.7 mm and 92.3 mm for 10- and 

20-yearsreturning intervals, correspondingly. The rainfall structure were depicted in to Fig. 7b using 

Dongying City's rainstorm intensity calculation [4]. 

 
Fig. 7The research made utilization of rainfall data. (b) Create a storm with varied return times (5, 

10, and 20 years): 2-h hyetograph layout 



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5. RESULTS 

 Initially, the methodology and datasets presented in Section 4.2 are employed to acquire the 

configuration of the nearby drainage system. Next, its hydraulic effectiveness relating to the drainage 

network is evaluated both prior to and following optimization. Finally, the performance of the system 

is scrutinized with and without redundancy. 

A. THE DESIGN OF THE URBAN DRAINAGE NETWORK 

The fundamental diagram comprises a completely interconnected looped structure containing all 

potential conduits. Subsequently, utilizing the graph theory algorithm (refer to Section 4.2.2.1) and 

the emperor penguin optimizer (refer to Section 4.2.2.2), the preliminary optimized design is 

obtained, which is demonstrated in Figure 8b. The optimized network's overall length measures 

23,527 meters, with a solitary drainage outlet. The system's pipeline seems to have a maximal dia of 

about 2000 mm as well as a minimal dia of about 300 mm. The pits are sunk to a depth of at least of 

1.0 m and then a maximal depth of about 6.0 m. The layout of any urban draining infrastructure prior 

to improvement can be observed inside Figure 8a. 

 

Fig. 8 Dongying Town's urban draining system. 

(a) Pre optimization of the urban drainage 

system 

 

Fig. 8 Urban drainage system of Dongying City 

centre. (b) early optimization of the urban 

drainage system 

B. EVALUATION OF HYDRAULIC PERFORMANCE  

Under the 10- and 20-year rainfall conditions, an examination of such hydraulic efficiency of both 

the upgraded urban drainage structure vs the main drainage channels within the experimental region 

demonstrates that perhaps the optimised network decreases overall overflowing volumes 

through 65.7% and 59.6%, correspondingly. The enhanced drainage system outperforms the old 

system in terms of mean flood duration (MFD) in the Table 4. 

Table 4The actual urban drainage systems and proposed network's effectiveness 

Index PeriodofReturn  

(year) 

Main Drainage 

system 

Optimized 

Drainage 

system 

Total overflow volume (1000 m3) 10 53.82 18.44 

20 64.90 26.20 

Mean flood duration/maximum flood 

duration (hours) 

10 0.80/5.78 0.64/4.17 

20 0.93/6.35 0.74/5.14 



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The surcharge ratio on the pipelines considerably higher inside the 20-year rainfall situation 

compared to the 10-year rainy situation (Fig. 9). 

 
Fig. 9 Surcharged pipeline transmission. The percentage of a distance of a surcharged pipeline 

towards the overall length of the pipe is known as the pipeline surcharge rate. 

The majority of its two systems surcharged pipes have been delivered down flowing water. That 

really was due to the concept that pipelines get surcharged whenever the flow of water is focused 

downstream [12,24]. and discharge throughout pipeline rises. In order to enhance redundancy 

[16,27], 

also the lower the draining capacity upon that pipelines downstream, it's therefore reasonable to think 

about adding more pipelines downstream[19]. 

C. OPTIMIZATION AND REDUNDANCY 

Gephi is indeed a tool used to show information and to carry out sophisticated networking analyses 

upon that urban drainage structure [2]. Gephi is really a network simulation and graphics tool that 

was open-sourced and free to use1 The shading of colour on the nodes symbolises its centrality 

betweenness, whereas the width of its nodes specifies the centrality and proximity(Figure 10). 

 
Fig. 10Results of complex network evaluation (node attribute value visualization) 



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By performing a “global network analysis’, nodes with higher index values are identified. In order to 

make comparisons more manageable, these values are normalized, and the resulting index values for 

each node are displayed in Table 5.  

Table 5 Findings of complex network analysis (index values of nodes) 

Node Closeness 

centrality 

Betweenness 

centrality 

Value Node Closeness 

centrality 

Betweenness 

centrality 

Value 

PNII 1.00 0.44 0.88 PN15 0.33 0.07 0.28 

PN32 1.00 0.28 0.86 PN28 0.33 0.07 0.28 

PN3 1.00 0.03 0.81 PN48 0.29 0.18 0.27 

PN37 0.66 1.00 0.73 PN6 0.33 0.00 0.27 

PN12 0.66 0.74 0.68 PN23 0.22 0.42 0.26 

PN38 0.67 0.25 0.59 PN41 0.29 0.09 0.25 

PN39 0.44 0.99 0.56 PN53 0.22 0.36 0.25 

PN4 0.67 0.08 0.55 PN14 0.29 0.08 0.24 

PN2 0.67 0.03 0.54 PN51 0.29 0.08 0.24 

PN9 0.50 0.66 0.53 PN24 0.25 0.18 0.24 

PN33 0.67 0.00 0.53 PN34 0.29 0.00 0.23 

PN8 0.40 0.84 0.49 PN7 0.29 0.00 0.23 

PN44 0.35 0.87 0.46 PN31 0.29 0.00 0.23 

PN16 0.33 0.86 0.44 PN52 0.25 0.11 0.22 

PN40 0.50 0.16 0.43 PN26 0.20 0.24 0.21 

PN17 0.50 0.16 0.43 PN13 0.25 0.00 0.20 

PN5 0.50 0.08 0.42 PN55 0.25 0.00 0.20 

PN1 0.50 0.00 0.40 PN46 0.25 0.00 0.20 

PN36 0.45 0.13 0.39 PN42 0.25 0.00 0.20 

PN19 0.29 0.79 0.39 PN27 0.22 0.11 0.20 

PN45 0.29 0.64 0.36 PN54 0.20 0.13 0.18 

PN43 0.40 0.16 0.35 PN21 0.22 0.00 0.18 

PN18 0.40 0.11 0.34 PN50 0.22 0.00 0.18 

PN59 0.40 0.05 0.33 PN56 0.22 0.00 0.18 

PN60 0.40 0.00 0.32 PN25 0.18 0.13 0.17 

PN61 0.35 0.16 0.31 PN22 0.20 0.00 0.16 

PN20 0.25 0.55 0.31 PN30 0.20 0.00 0.16 

PN49 0.25 0.53 0.31 PN57 0.20 0.00 0.16 

PN35 0.35 0.08 0.30 PN58 0.18 0.00 0.14 

PN47 0.33 0.13 0.29 PN29 0.17 0.00 0.13 

The connections featuring the greatest index scores are further subjected to local network evaluation 

to determine potential pipeline redundancy improvement sites. The inclusion of pipelines having 

greater and smaller terminal values has been shown in Figures 11a and b, appropriately. 



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Fig. 11Structure has been optimised to account for pipeline redundancies. Network (a) adds pipes in 

which the node value was greater; Network (b) generates pipelines in which the node values is less. 

The pipeline node is denoted by PN, while the pipe is denoted by GQ. 

The existing drainage platform's network design was improved according to the findings of the 

complex network evaluation [6,23,10]. The place having the weakest node number was picked to 

improve redundancies and illustrate the usefulness of a complicated network evaluation technique 

[9,26]. The features of the implanted pipelines are summarised within Table 6. 

Structure Pipe Length 

(m) 

Diameter 

(mm) 

Slope 

(%) 

(a) 

Increase 

loops 

where 

the node 

value 

is higher 

GQ1 713 1000 1.4 

GQ2 682 1500 3.4 

GQ3 542 1000 1.8 

GQ4 419 1000 2.4 

GQ5 387 1200 2.1 

GQ6 502 1200 2.0 

(b) 

Increase 

loops 

where 

the node 

value 

is lower 

GQ7 596 1000 4.2 

GQ8 654 1200 3.7 

GQ9 445 1000 3.3 

GQ10 639 1000 3.8 

GQ11 555 1200 4.1 

GQ12 428 1000 5.5 

Table 6 Parameters of the introduced pipes networks as well as the optimised systems 

These values are “31.6% and 20.2% lower, respectively, then the preliminary optimized network. 

Meanwhile, the TOV of network (b) measures 16,690 m3 and 25,500 m3 under the 10-year and 20-

year rainfall scenarios, respectively, demonstrating a reduction of 9.5% and 2.7%” compared to the 

network. In comparison to the preliminary optimized network, the average and maximum flood 

duration of network (a) both decreases, with the maximum flood duration demonstrating a more 

noticeable decrease. The mean and maximum flood duration also decrease in network (b), albeit the 

reduction is less significant than in network (a). These results indicate that the network that 

incorporates pipes at higher node values exhibits greater resilience. 



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Fig. 12Comparison of drainage effectiveness for 10- and 20-year returning durations among the 

preliminary optimised 

Network (a) adds 3245 m of total length with a pipeline dia of up to 1500 mm. The length of system 

(b) is increased by 3317 m, and the largest pipeline dia is 1200 mm. In different rainy scenarios, 

networking (a) and (b) functionality were predicted. 

As depicted in Figure 12, the ‘total overflow volume (TOV) of network” (a) during the 10-year and 

20-year rainfall scenarios measures 12,610 m3 and 20,910 m3, respectively.  

4.5 Conclusion  

 Urbanization and climate change have made urban flooding a more frequent issue in many 

places across the world. For the purpose of managing flooding and averting disasters, urban drainage 

systems must be able to handle significant amounts of precipitation. To be effective, these systems 

must be carefully planned and designed as they are frequently complicated. A critical problem is 

optimising the network structure of urban drainage infrastructure to improve effectiveness and 

resiliency. In urban hydrology, this is a crucial scientific problem. A study crew has proposed a 

technique to optimising the network model of urban drainage structures which blends the graph 

theory technique, the complex network, and emperor penguin evolutionary algorithm modelling to 

tackle this challenge. The network topology of urban drainage systems may be optimised using this 

technology, which makes it possible to precisely identify where to enhance pipeline redundancies. 

This technique's early phase involves applying graph theory and emperor penguin algorithms to 

create the initial optimal hydraulic design and layout. Throughout this method, the network topology 

is optimised by using graph theory and mperor penguin algorithms once a completely looped 

structure with all conceivable conduits interconnected has been created. Usually, the optimised 

network that emerges is a lot more effective than the base network. The second phase involves using 

complicated network evaluation to locate the network's essential nodes and boosting structural 

redundancy where node values are greater in order to strengthen the platform's resiliency.The issue 

of where to enlarge the loop is resolved by using complex network analysis to determine the critical 

nodes in the drainage network and then pinpoint the position of additional pipes. The case study in an 



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urban setting illustrates how expanding the network's pipeline redundancies might enhance drainage 

performance. The structure that incorporates redundancies can reduce the total overflow volume 

(TOV) by 20–30% and the maximum flood duration by 2-3 hours when compared to a structure that 

does not. The results show that a network with more redundant pipelines is both more successful at 

reducing floods and has greater potential to increase resilience. 

Because of the structure and interaction of edges and nodes, pipe networks in urban drainage systems 

frequently exhibit a variety of spatial and temporal behaviours. The issue of where to enlarge the 

loop is resolved by the complicated network analysis employed in this technology, which makes it 

possible to identify the critical drainage network nodes and then pinpoint the locations of new pipes. 

The newly created network structure optimization approach presents new potential for enhancing the 

flexibility of the urban storm water structures and a means to improve pipeline redundancies. The 

suggested approach may have a number of advantages. To begin with, it makes it possible to 

precisely pinpoint where to add pipeline redundancies in order to improve the network layout of 

urban drainage systems. Secondly, it can improve drainage performance and reduce the risk of 

flooding. Thirdly, it can increase the resilience of urban storm water systems by increasing pipeline 

redundancies. Finally, it provides a new way to design and plan urban drainage systems that are 

based on complex network analysis and optimization techniques. However, there are also some 

limitations and challenges to this method. In order to improve the drainage performance of urban 

drainage networks, it is first necessary to further explore the cost-effectiveness of expanding 

redundancy. Second, it is advised that future research use resilience indicators to assess how 

redundancy affects system reliability. Thirdly, the method needs to be validated through more case 

studies and comparisons with other optimization methods. In summary, the suggested optimization 

strategy again for network layout of urban drainage channels does have the capacity to strengthen the 

resiliency of urban storm water facilities, enhance drainage effectiveness, and lower the danger of 

floods. It uses the graph theory method, the emperor methodology, and complicated networking 

evaluation to pinpoint the network's most important nodes and boost pipeline redundancy where 

node values are greater. Future studies should examine the cost-effectiveness of boosting 

redundancies and create resiliency indexes to assess how redundancy affects system reliability. 

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