# Toward Decentralised Sanitary Sewage Collection Systems: A Multiobjective Approach for Cost-Effective and Resilient Designs

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Cost Function (${f}_{1}$)

#### 2.2. Structural Resilience Analysis (${f}_{2}$)

#### 2.3. Degree of Centralization (${f}_{3}$)

#### 2.4. Subproblem 1: Layout Generator Algorithm

#### 2.4.1. The Assigned Zone to Each Root

#### 2.4.2. Base Graph Partitioning

- The sewers of each subgraph are identified. For each sewer in the B-Matrix, the upstream and downstream nodes are identified. If the nodes are in the same group, the corresponding sewer belongs to that group; otherwise, it is a cut sewer;
- The loops of each subgraph are identified. For each loop in the B-Matrix, the corresponding sewers are placed. If there are cut sewers among the sewers of a loop, the loop is excluded; otherwise, the sewers of the loop indicate to which subgraph the loop belongs.

#### 2.4.3. Generating the Spanning Trees of Base Subgraphs

- (i)
- Vector $\mathrm{M}$, consisting of the edges (sewers) of the growing tree;
- (ii)
- Vector $\mathrm{N}$, consisting of the vertices (nodes or manholes) of the growing tree;
- (iii)
- Vector $\mathrm{AM}$, consisting of the base graph edges adjacent to the growing tree. Each of these edges may be considered a decision variable in order to construct another growing tree branch.

- The root node, root r, is identified;
- The vector N is initialized with a single member $\mathrm{N}=\left[r\right]$. No edge has yet been selected, meaning $\mathrm{M}=[]$;
- The AM vector is updated in each stage; in the beginning, only edges connected to the root are included, i.e., $\mathrm{AM}=$(the edges connected to the root node);
- An edge from vector $\mathrm{AM}$ is chosen through optimization. For this purpose, a decision variable ${x}_{i}$ ($i=1:n-1$) in the range of (0, 1) is defined and $n$ is the total number of vertices in the base graph. Let $H$ be the current number of adjacent edges; the chosen edge number $n{a}_{i}$ from variable ${x}_{i}$ is as follows, where $n{a}_{i}$ represents the sewer “a” in the network;$$n{a}_{i}=round\left(1+{x}_{i}\times \left(H-1\right)\right)$$
- The edge vector is updated, $\mathrm{N}=\mathrm{M}+\left[a\right]$;
- The selection of edge “a” adds a new vertex “b” to the growing tree; therefore, it is required to update the vertex vector, $\mathrm{N}=\mathrm{N}+\left[b\right]$;
- All edges except “a” connected to vertex “b” are denoted as $\u201c\mathrm{ab}\u201d\left(i\right)$;
- Vector $\mathrm{AM}$ is updated by excluding edge “a” and adding edges $\u201c\mathrm{ab}\u201d\left(i\right)$. $\mathrm{AM}$ then contains all choices for the next edge of the growing tree. Before going to the next step, the following query should be applied to each new member of $\mathrm{AM}$ to make it feasible: Is $\u201c\mathrm{ab}\u201d\left(i\right)$ already in $\mathrm{AM}$ or are both end nodes of $\mathrm{ab}\left(i\right)$ present in $\mathrm{N}$?If yes, then edge $\mathrm{ab}\left(i\right)$ is removed from $\mathrm{AM}$, since its selection causes a loop in the growing tree; $\mathrm{AM}=\mathrm{AM}-\mathrm{ab}\left(i\right)$; if no, vector $\mathrm{AM}$ is acceptable;
- The algorithm goes back to step 5 and the tree continues growing until vector $\mathrm{AM}$ becomes empty. After this, a branch of the growing tree is generated, including $s$ vertices of the base graph and $s-1$ edges according to variables ${x}_{1}$ to ${x}_{s-1}$;
- The vertices of the base graph that are not present in the vertex vector $\mathrm{N}$ are identified. The number of these vertices is $n-s-1$;
- A vertex absent in $\mathrm{N}$ is selected and placed in $\mathrm{N}$ and vector $\mathrm{AM}$ is updated accordingly. Then, the algorithm goes to step 5 and a new edge is identified using Equation (10);
- This process continues until all absent vertices are placed in $\mathrm{N}$. The algorithm eventually generates a root-ending spanning tree based on the decision variables ${x}_{i}\left(i=1,n-1\right)$; however, there are a number of excluded sewers—as many as the number of loops $c$ in the base graph. These sewers must be included in the final design of the sewer network. To meet this constraint, the following modification is applied;
- Let $m$ be the number of edges in the base graph. The number of edges in the grown spanning tree at the end of the previous step is $m-c$. The excluded edges are identified as $a{c}_{i}\left(i=1\dots ,c\right)$ and added to vector $\mathrm{M}$;
- Since the excluded edges are returned to the spanning tree, they should be cut to avoid loops. For this purpose, one of the ends of the edge $a{c}_{i}$ is selected to be cut. This introduces another decision variable to the problem. A binary variable ${y}_{i}(i=1,\dots c$) is used for this purpose. When ${y}_{i}=0$, the edge is cut from its upstream, otherwise it is cut from the downstream. As an $a{c}_{i}$ is cut, a new vertex appears at the truncation end, which is named $n+i$. The process continues until all $ac$ elements are cut.

#### 2.5. Solving Subproblem 2: Hydraulic Design of the Network

## 3. Case Study

## 4. Results and Discussion

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Sitzenfrei, R.; Rauch, W. Investigating Transitions of Centralized Water Infrastructure to Decentralized Solutions—An Integrated Approach. Procedia Eng.
**2014**, 70, 1549–1557. [Google Scholar] [CrossRef] [Green Version] - Eggimann, S.; Truffer, B.; Maurer, M. To connect or not to connect? Modelling the optimal degree of centralisation for wastewater infrastructures. Water Res.
**2015**, 84, 218–231. [Google Scholar] [CrossRef] [Green Version] - Dhakal, K.P.; Chevalier, L.R. Urban Stormwater Governance: The Need for a Paradigm Shift. Environ. Manag.
**2016**, 57, 1112–1124. [Google Scholar] [CrossRef] [PubMed] - Goncalves, M.L.R.; Zischg, J.; Rau, S.; Sitzmann, M.; Rauch, W.; Kleidorfer, M. Modeling the Effects of Introducing Low Impact Development in a Tropical City: A Case Study from Joinville, Brazil. Sustainability
**2018**, 10, 728. [Google Scholar] [CrossRef] [Green Version] - Poustie, M.S.; Deletic, A.; Brown, R.R.; Wong, T.; de Haan, F.J.; Skinner, R. Sustainable urban water futures in developing countries: The centralised, decentralised or hybrid dilemma. Urban Water J.
**2014**, 12, 543–558. [Google Scholar] [CrossRef] - Libralato, G.; Volpi Ghirardini, A.; Avezzu, F. To centralise or to decentralise: An overview of the most recent trends in wastewater treatment management. J. Environ. Manag.
**2012**, 94, 61–68. [Google Scholar] [CrossRef] [PubMed] - Tchobanoglous, G.; Ruppe, L.; Leverenz, H.; Darby, J. Decentralized wastewater management: Challenges and opportunities for the twenty-first century. Water Sci. Technol. Water Supply Water Sci.
**2004**, 4, 95–102. [Google Scholar] [CrossRef] - Bakir, H.A. Sustainable wastewater management for small communities in the Middle East and North Africa. J. Environ. Manag.
**2001**, 61, 319–328. [Google Scholar] [CrossRef] - Bakhshipour, A.E.; Bakhshizadeh, M.; Dittmer, U.; Haghighi, A.; Nowak, W. Hanging Gardens Algorithm to Generate Decentralized Layouts for the Optimization of Urban Drainage Systems. J. Water Resour. Plann. Manag.
**2019**, 145, 04019034. [Google Scholar] [CrossRef] - Bakhshipour, A.E.; Dittmer, U.; Haghighi, A.; Nowak, W. Hybrid green-blue-gray decentralized urban drainage systems design, a simulation-optimization framework. J. Environ. Manag.
**2019**, 249, 109364. [Google Scholar] [CrossRef] - Bakhshipour, A.E.; Dittmer, U.; Haghighi, A.; Nowak, W. Towards sustainable urban drainage infrastructure planning: A combined multiobjective optimization and multicriteria decision-making platform. J. Water Resour. Plan. Manag.
**2021**, 147, 04021049. [Google Scholar] [CrossRef] - Bakhshipour, A.E.; Hespen, J.; Haghighi, A.; Dittmer, U.; Nowak, W. Integrating Structural Resilience in the Design of Urban Drainage Networks in Flat Areas Using a Simplified Multiobjective Optimization Framework. Water
**2021**, 13, 269. [Google Scholar] [CrossRef] - Massoud, M.A.; Tarhini, A.; Nasr, J.A. Decentralized approaches to wastewater treatment and management: Applicability in developing countries. J. Environ. Manag.
**2009**, 90, 652–659. [Google Scholar] [CrossRef] [PubMed] - Brown, V.; Jackson, D.W.; Khalifé, M. 2009 Melbourne metropolitan sewerage strategy: A portfolio of decentralised and on-site concept designs. Water Sci. Technol.
**2010**, 62, 510–517. [Google Scholar] [CrossRef] [PubMed] - Haghighi, A.; Bakhshipour, A.E. Optimization of Sewer Networks Using an Adaptive Genetic Algorithm. Water Resour. Manag.
**2012**, 26, 3441–3456. [Google Scholar] [CrossRef] - Haghighi, A.; Bakhshipour, A.E. Deterministic Integrated Optimization Model for Sewage Collection Networks Using Tabu Search. J. Water Resour. Plann. Manag.
**2015**, 141, 4014045. [Google Scholar] [CrossRef] - Moeini, R.; Afshar, M.H. Arc Based Ant Colony Optimization Algorithm for optimal design of gravitational sewer networks. Ain Shams Eng. J.
**2017**, 8, 207–223. [Google Scholar] [CrossRef] [Green Version] - Moeini, R.; Afshar, M.H. Layout and size optimization of sanitary sewer network using intelligent ants. Adv. Eng. Softw.
**2012**, 51, 49–62. [Google Scholar] [CrossRef] - Karovic, O.; Mays, L.W. Sewer System Design Using Simulated Annealing in Excel. Water Resour. Manag.
**2014**, 28, 4551–4565. [Google Scholar] [CrossRef] - Ahmadi, A.; Zolfagharipoor, M.A.; Nafisi, M. Development of a Hybrid Algorithm for the Optimal Design of Sewer Networks. J. Water Resour. Plann. Manag.
**2018**, 144, 4018045. [Google Scholar] [CrossRef] - Navin, P.K.; Mathur, Y.P. Layout and Component Size Optimization of Sewer Network Using Spanning Tree and Modified PSO Algorithm. Water Resour Manag
**2016**, 30, 3627–3643. [Google Scholar] [CrossRef] - Tekel, S.; Belkaya, H. Computerized layout generation for sanitary sewers. J. Environ. Eng.
**1986**, 112, 500–515. [Google Scholar] [CrossRef] - Diogo, A.F.; Graveto, V.M. Optimal Layout of Sewer Systems: A Deterministic versus a Stochastic Model. J. Hydraul. Eng.
**2006**, 132, 927–943. [Google Scholar] [CrossRef] - Diogo, A.F.; Barros, L.T.; Santos, J.; Temido, J.S. An effective and comprehensive model for optimal rehabilitation of separate sanitary sewer systems. Sci. Total Environ.
**2018**, 612, 1042–1057. [Google Scholar] [CrossRef] - Diogo, A.F.; Walters, G.A.; Ribeiro de Sousa, E.; Graveto, V.M. Three-Dimensional Optimization of Urban Drainage Systems. Comp-Aided Civ. Eng.
**2000**, 15, 409–425. [Google Scholar] [CrossRef] - Duque, N.; Duque, D.; Aguilar, A.; Saldarriaga, J. Sewer Network Layout Selection and Hydraulic Design Using a Mathematical Optimization Framework. Water
**2020**, 12, 3337. [Google Scholar] [CrossRef] - Steele, J.C.; Mahoney, K.; Karovic, O.; Mays, L.W. Heuristic Optimization Model for the Optimal Layout and Pipe Design of Sewer Systems. Water Resour. Manag.
**2016**, 30, 1605–1620. [Google Scholar] [CrossRef] - Afshar, M.H. A parameter free Continuous Ant Colony Optimization Algorithm for the optimal design of storm sewer networks: Constrained and unconstrained approach. Adv. Eng. Softw.
**2010**, 41, 188–195. [Google Scholar] [CrossRef] - Jung, Y.T.; Narayanan, N.C.; Cheng, Y.-L. Cost comparison of centralized and decentralized wastewater management systems using optimization model. J. Environ. Manag.
**2018**, 213, 90–97. [Google Scholar] [CrossRef] - Eggimann, S. The optimal degree of centralisation for wastewater infrastructures. A model-based geospatial economic analysis. Ph.D. Thesis, University of Zurich, Zurich, Switzerland, November 2016. [Google Scholar]
- Oraei Zare, S.; Saghafian, B.; Shamsai, A. Multiobjective optimization for combined quality–quantity urban runoff control. Hydrol. Earth Syst. Sci
**2012**, 16, 4531–4542. [Google Scholar] [CrossRef] [Green Version] - Eckart, K. Multiobjective Optimization of Low Impact Development Stormwater Controls Under Climate Change Conditions. Master’s Thesis, University of Windsor, Windsor, ON, Canada, July 2015. [Google Scholar]
- Damodaram, C.; Zechman, E.M. Simulation-Optimization Approach to Design Low Impact Development for Managing Peak Flow Alterations in Urbanizing Watersheds. J. Water Resour. Plann. Manag.
**2013**, 139, 290–298. [Google Scholar] [CrossRef] - Dandy, G.C.; Di Matteo, M.; Maier, H.R. Optimization of WSUD Systems. In Approaches to Water Sensitive Urban Design: Potential, Design, Ecological Health, Economics, Policies and Community Perceptions; Sharma, A.K., Gardner, T., Begbie, D., Eds.; Woodhead Publishing: Oxford, UK, 2018; pp. 303–328. ISBN 9780128128435. [Google Scholar]
- Di Matteo, M.; Dandy, G.C.; Maier, H.R. Multiobjective Optimization of Distributed Stormwater Harvesting Systems. J. Water Resour. Plann. Manag.
**2017**, 143, 4017010. [Google Scholar] [CrossRef] - Giacomoni, M.H.; Joseph, J. Multi-Objective Evolutionary Optimization and Monte Carlo Simulation for Placement of Low Impact Development in the Catchment Scale. J. Water Resour. Plann. Manag.
**2017**, 143, 4017053. [Google Scholar] [CrossRef] - Wang, M.; Sweetapple, C.; Fu, G.; Farmani, R.; Butler, D. A framework to support decision making in the selection of sustainable drainage system design alternatives. J. Environ. Manag.
**2017**, 201, 145–152. [Google Scholar] [CrossRef] - Sweetapple, C.; Fu, G.; Butler, D. Reliable, Robust, and Resilient System Design Framework with Application to Wastewater-Treatment Plant Control. J. Environ. Eng.
**2017**, 143, 4016086. [Google Scholar] [CrossRef] - Haghighi, A. Intelligent Optimization of Wastewater Collection Networks. In Intelligence Systems in Environmental Management: Theory and Applications; Kahraman, C., Ucal Sari, I., Eds.; Springer: Berlin/Heidelberg, Germany, 2016; pp. 41–65. [Google Scholar]
- Hadka, D.; Reed, P. Borg: An auto-adaptive many-objective evolutionary computing framework. Evol. Comput.
**2013**, 21, 231–259. [Google Scholar] [CrossRef] [PubMed] - Mugume, S.N.; Gomez, D.E.; Fu, G.; Farmani, R.; Butler, D. A global analysis approach for investigating structural resilience in urban drainage systems. Water Res.
**2015**, 81, 15–26. [Google Scholar] [CrossRef] [Green Version] - Haghighi, A.; Bakhshipour, A.E. Reliability-based layout design of sewage collection systems in flat areas. Urban Water J.
**2015**, 13, 790–802. [Google Scholar] [CrossRef] - Haghighi, A. Loop-by-Loop Cutting Algorithm to Generate Layouts for Urban Drainage Systems. J. Water Resour. Plann. Manag.
**2013**, 139, 693–703. [Google Scholar] [CrossRef]

**Figure 2.**Mathematical representation of a base graph: (

**a**) example base graph; (

**b**) B-Matrix; (

**c**) A-Matrix.

**Figure 3.**Finding the assigned zone for each outlet: (

**a**) finding the assigned zone for the first root (node 4); (

**b**) finding the assigned zone for the second root (node 13); (

**c**) finding the assigned zone for the last root (node 24).

**Figure 4.**Pipe identification process: (

**a**) identifying the pipes for each subgraph; (

**b**) identifying the loops for each subgraph; (

**c**) partitioning of the base graph.

**Figure 11.**Various design scenarios: (

**a**) scenario 1, optimal fully centralized design (DC = 100%); (

**b**) scenario 2, design with 5 treatment plants (DC = 55%); (

**c**) scenario 3, the most decentralized design (DC = 27%).

Item Name | Item Value |
---|---|

Maximum velocity ${V}_{max}$ | 5 m/s |

Minimum velocity ${V}_{min}$ | 0.6 m/s |

Minimum Slope ${S}_{min}$ | 0.003 (if Q < 15 l/s) |

Maximum Slope ${S}_{max}$ | 0.5 |

Maximum proportional water depth ${\left(h/D\right)}_{max}$ | 0.75 |

Minimum cover depth ${C}_{min}$ | 1.2 m |

Variable | Type | Number | Note |
---|---|---|---|

α | Real | 8 | Input parameter of the graph partitioning algorithm (according to the number of candidate outlets) |

x | Real | 145 | Input parameter of growing spanning tree algorithm (according to the number of vertices in the base graph) |

y | Binary | 64 | Input parameter of growing spanning tree algorithm (according to the number of loops in the base graph) |

d | Real | 208 | Sewer diameter |

s | Real | 208 | Sewer slope |

p | Binary | 208 | Locations of lift pump stations |

Description | Construction Cost | Operation Cost (Million Rial/Years) | ||
---|---|---|---|---|

D (mm) | Pipe (Million Rial/m) | Manhole (Million Rial) | ||

Network | 200 | $10.5\mathrm{H}-6.75$ | $59\mathrm{H}+108.82$ | 0.15 × Construction Cost |

250 | $11.5\mathrm{H}-5.5$ | $67.4\mathrm{H}+117.32$ | ||

350 | $13.14\mathrm{H}-2.3$ | $80.06\mathrm{H}+124.42$ | ||

400 | $15.71\mathrm{H}-0.60$ | $91.32\mathrm{H}+132.92$ | ||

500 | $11.2\mathrm{H}+1.15$ | $105.7\mathrm{H}+150.7$ | ||

630 | $12.2\mathrm{H}+4.71$ | $112.78\mathrm{H}+160.1$ | ||

800 | $12.93\mathrm{H}+11.58$ | $19.8\mathrm{H}+169.72$ | ||

1000 | $13.95\mathrm{H}+24.36$ | $125.5\mathrm{H}+211.12$ | ||

Pressurized pipeline (Million Rial/m) | $70{D}^{2}-3.237\mathrm{D}+1.7721$ | 0.15 × Construction Cost | ||

Pump Station | $9238.68+24.2576{Q}^{0.9484}-7719.421H{p}^{-0.3162}+0.0928{Q}^{0.0003}H{p}^{6.175}$ | $\frac{gQht}{1000\mathsf{\eta}}\Psi $ | ||

Treatment Plant | $\mathrm{14,021}{Q}^{0.95}$ | $1332{Q}^{0.5196}$ |

Scenario | Total System Annuities (Million Rials/Year) | Sewer Networks (Million Rials/Year) | Treatment Facilities (Million Rials/Year) | Average Buried Depth (m) | Average Sewer Diameters (m) | DC (%) | Structural Resilience (%) |
---|---|---|---|---|---|---|---|

1 | 3.31 × 10^{5} | 2.52 × 10^{5} | 0.795 × 10^{5} | 2.65 | 0.26 | 100 | 44 |

2 | 2.82 × 10^{5} | 1.76 × 10^{5} | 1.07 × 10^{5} | 2.49 | 0.22 | 55 | 74 |

3 | 2.76 × 10^{5} | 1.56 × 10^{5} | 1.21 × 10^{5} | 2.48 | 0.21 | 27 | 79 |

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**MDPI and ACS Style**

Zahediasl, A.; E. Bakhshipour, A.; Dittmer, U.; Haghighi, A.
Toward Decentralised Sanitary Sewage Collection Systems: A Multiobjective Approach for Cost-Effective and Resilient Designs. *Water* **2021**, *13*, 1886.
https://doi.org/10.3390/w13141886

**AMA Style**

Zahediasl A, E. Bakhshipour A, Dittmer U, Haghighi A.
Toward Decentralised Sanitary Sewage Collection Systems: A Multiobjective Approach for Cost-Effective and Resilient Designs. *Water*. 2021; 13(14):1886.
https://doi.org/10.3390/w13141886

**Chicago/Turabian Style**

Zahediasl, Arezoo, Amin E. Bakhshipour, Ulrich Dittmer, and Ali Haghighi.
2021. "Toward Decentralised Sanitary Sewage Collection Systems: A Multiobjective Approach for Cost-Effective and Resilient Designs" *Water* 13, no. 14: 1886.
https://doi.org/10.3390/w13141886