Lost in optimisation of water distribution systems? A literature review of system operation

TL;DR: This paper provides a systematic review by bringing together over two hundred publications from the past three decades, which are relevant to operational optimisation of water distribution systems, particularly optimal pump operation, valve control and system operation for water quality purposes of both urban drinking and regional multiqualityWater distribution systems.

Abstract: Optimisation of the operation of water distribution systems has been an active research field for almost half a century. It has focused mainly on optimal pump operation to minimise pumping costs and optimal water quality management to ensure that standards at customer nodes are met. This paper provides a systematic review by bringing together over two hundred publications from the past three decades, which are relevant to operational optimisation of water distribution systems, particularly optimal pump operation, valve control and system operation for water quality purposes of both urban drinking and regional multiquality water distribution systems. Uniquely, it also contains substantial and thorough information for over one hundred publications in a tabular form, which lists optimisation models inclusive of objectives, constraints, decision variables, solution methodologies used and other details. Research challenges in terms of simulation models, optimisation model formulation, selection of optimisation method and postprocessing needs have also been identified. A review of operational optimisation of water distribution systems is provided.Future challenges were identified, despite the large body of existing literature.Universally agreed formulation of an operational optimisation problem is needed.Algorithm performance for a particular problem requires improved understanding.A method for selecting only one solution for a real system needs to be developed.

Summary

1 Introduction

• Water distribution systems (WDSs) represent a vast infrastructure worldwide, which is critical for contemporary human existence from all social, industrial and environmental aspects.
• A level of flexibility exists in the WDSs, which enables the supply of required water under different operational schedules, more or less economically.
• Since the 1970s, substantial research has addressed the operational optimisation of WDSs (Ormsbee and Lansey 1994) with two main areas of focus.
• Development in the use of various methods to optimise operation of WDSs is not only an interesting subject for research, but is also very complex.

2 Aim, scope and structure of the paper

• The aim of this paper is to provide a comprehensive and systematic review of publications for operational optimisation of WDSs since the end of the 1980s to nowadays to contribute to the existing review literature (Lansey 2006; Ormsbee and Lansey 1994; Walski 1985 ).
• Publications included in this review are relevant to optimal pump operation, valve control and optimal system operation for water quality purposes of both urban drinking and regional multiquality WDSs.
• The purpose of this part of the paper is to provide the current status, analysis and synthesis of the current literature, and to suggest future research directions.
• The table forms a significant part of the paper referring to over a hundred publications and is structured chronologically.

3.1 Pump operation

• Typically, electricity consumption is one of the largest marginal costs for water utilities.
• The latter two methods reduce the number of variables hence decrease the size of the search space.
• A multi-objective approach has been increasingly applied to pump optimisation problems to include considerations other than costs.
• Most recently, water quality has been traded off against pump operating costs (Arai et al.

3.1.1 Real-time control

• Time is an important factor for industrial applications.
• Evidence from the literature suggests that computational efficiency of metaheuristic algorithms in conjunction with the network simulator, such as EPANET, for large WDSs is not sufficient, however.
• Several authors have investigated how to decrease computational effort of the network simulator and/or an optimisation algorithm to provide an optimal solution in real-time.
• ANNs, which are applied most frequently, were used to determine real-time, near optimal control of WDSs by integrating with a GA incorporating demand forecasting (based on seasonal, weekly and daily periodic components) and operating continually based on SCADA data and demand forecast updates (Martinez et al.
• An open question is how to control the error of the surrogate model to ensure that the solution found is still optimal when the full network simulator is employed to validate it.

3.2.1 Urban drinking water distribution systems

• There does not seem to be a unique optimisation model for the operation of drinking WDSs.
• The third optimisation model minimises disinfectant concentration deviations at customer demand nodes from desired values (Goldman et al.
• The explanation provided was that the objective function implemented in the third model (i.e. concentration deviations) does not force the algorithm to reduce pump operating time/costs further after all of the constraints are satisfied.
• Ostfeld and Salomons (2006) discovered that pumping costs are significantly reduced if water quality is absent from the optimisation model and conversely, that the best water quality outcome corresponds to the highest pump operating costs.

3.2.2 Regional multiquality water distribution systems

• Multiquality WDSs are "systems in which waters of different qualities are taken from sources, possibly treated, conveyed and supplied to the consumers" (Ostfeld and Salomons 2004) .
• These costs were combined into one objective, with water quality requirements at customer demand nodes included as constraints.
• Optimisation problems in the above papers were solved as single-objective.
• Interestingly, when two water quality objectives (each representing a separate water quality parameter) are incorporated together with a pumping cost optimisation into a model, the relationship between water quality and pumping costs is not necessarily conflicting (Mala-Jetmarova et al. 2015) .

3.3 Valve control

• Valve controls were used in conjunction with both optimal pump operation and optimal system operation for water quality purposes.
• Additionally, percentages/degrees of valve closures (Kang and Lansey 2009; Kang and Lansey 2010) or openings (Ostfeld and Salomons 2006) were used to optimise chlorine levels across a network.
• In general, the pumping flow is often the main decision variable used in operational optimisation of WDSs.

4.1 Application area

• As described in Section 3, there are three application areas: pump operation (Section 3.1), water quality management (Section 3.2) and valve control (Section 3.3).
• The largest portion of papers (41%) is concerned with optimisation of pump operation only.
• Optimisation of water quality exclusive of any other operational controls (i.e. pumps and/or valves) is addressed in 15% of papers. .
• The introduction of water quality criteria, with or without valve control for pressure management (e.g. for leakage control) or water quality manipulation, appeared much later in the literature.
• Lately, more emphasis was put on holistic assessment of WDS operation, and thanks to more sophisticated simulation and optimisation methods having been introduced.

4.2 Optimisation model

• Regarding optimisation models, each is mathematically defined by three types of components: objectives, constraints and decision variables.
• Therefore, their assessment is limited to their interpretation of the provided information in the publications, where explicit formulation was partially presented or missing altogether.
• The number of types of a decision (i.e. control) variable included in optimisation models ranges from one to seven.
• A majority of optimisation models, 41% and 33%, uses one or two types of a decision variable, respectively.
• Use of more than two types of a decision variable is less frequent and the number of such models tends to decrease with the increasing number of decision variables used.

4.3 Solution methodology

• Optimisation methods have developed significantly since the 1970s.
• Further efforts to improve the computational efficiency of various optimisers led to the development and integration of surrogate models within optimisation algorithms.

4.4 Test network

• A large variety of test networks has been used in operational optimisation of WDSs.
• Large networks are being simplified for the purpose of optimisation (Cembrano et al.
• There are two test networks, which have been used 10 or more times.

5 Future research

• In contrast, it is important to develop understanding of the impact of assumptions while using simplified simulation models or surrogate models (for example in real-time control) and to control the error of the surrogate model to ensure that the solution found is still optimal.
• Concerning the methods for search space reduction, an open question is how to perform it without compromising the fidelity of the optimisation problem and undue simplification of the real system.
• While using metaheuristic algorithms, methodologies for algorithm parameter selection such as in Gibbs et al. (2010b) and Zheng et al. (2015) need to be developed.
• In multi-objective optimisation approach, methods need to be developed for selecting the best solution(s) from the Pareto set, which is representative and sufficiently small to be tractable.

6 Summary and conclusion

• This paper presented a literature review of optimisation of WDS operation since the end of 1980s to nowadays.
• The papers reviewed are relevant to optimal pump operation inclusive of real-time control, valve control and optimisation for water quality purposes for urban drinking as well as regional multiquality WDSs.
• The value of the paper is that it brings together the majority of journal publications for operational optimisation of WDSs, over two hundred in total, which have been published over the past three decades.
• Uniquely, it also contains extensive information for over one hundred publications in a tabular form, listing optimisation models inclusive of objectives, constraints, decision variables, solution methodologies used and other details.
• The lack of understanding and accepted means for incorporating uncertainties in demand forecasting and network behaviour prediction models (both quantity and quality) are, among others, the factors limiting wider implementation of those models.

Figures

Figure 1: Papers (from the appendix table) by year and optimisation approach

Figure 2: Papers (from the appendix table) by application areas

Figure 4: Optimisation methods (of papers from the appendix table) by year

Table 1: Components of a general optimisation model

Figure 6: Future research challenges

Figure 3: Optimisation models (of papers from the appendix table) by: (a) number of objectives, (b) number

Figure 5: Test networks (of papers from the appendix table) by network size

Full text

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FedUni ResearchOnline
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© 2017. This manuscript version is made available under the CC-BY-NC-
ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Mala-Jetmarova, H., Sultanova, N., Savic, D. (2017) Lost in optimization of water
distribution systems? A literature review of system operation. Environmental
Modelling and Software, 93, pp.209-254.
Which has been published in final form at:
http://doi.org/10.1016/j.envsoft.2017.02.009

1
Lost in Optimisation of Water Distribution Systems? A Literature Review of System Operation
Helena Mala-Jetmarova
a
(corresponding author); Nargiz Sultanova
b
; Dragan Savic
c
a
Honorary Research Fellow, College of Engineering, Mathematics and Physical Sciences, University of
Exeter, Streatham Campus, North Park Road, Exeter, Devon EX4 4QF, United Kingdom. E-mail:
h.malajetmarova@exeter.ac.uk
b
Lecturer Mathematics, Faculty of Science and Technology, Federation University Australia, Mt Helen
Campus, University Drive, Ballarat, Victoria 3350, Australia. E-mail: n.sultanova@federation.edu.au
c
Professor of Hydroinformatics, College of Engineering, Mathematics and Physical Sciences, University of
Exeter, Streatham Campus, North Park Road, Exeter, Devon EX4 4QF, United Kingdom. E-mail:
d.savic@exeter.ac.uk
Abstract
Optimisation of the operation of water distribution systems has been an active research field for almost half a
century. It has focused mainly on optimal pump operation to minimise pumping costs and optimal water
quality management to ensure that standards at customer nodes are met. This paper provides a systematic
review by bringing together over two hundred publications from the past three decades, which are relevant to
operational optimisation of water distribution systems, particularly optimal pump operation, valve control
and system operation for water quality purposes of both urban drinking and regional multiquality water
distribution systems. Uniquely, it also contains substantial and thorough information for over one hundred
publications in a tabular form, which lists optimisation models inclusive of objectives, constraints, decision
variables, solution methodologies used and other details. Research challenges in terms of simulation models,
optimisation model formulation, selection of optimisation method and postprocessing needs have also been
identified.
Keywords: Water distribution systems; optimisation; literature review; pump operation; water quality; valve
control
1 Introduction
Water distribution systems (WDSs) represent a vast infrastructure worldwide, which is critical for
contemporary human existence from all social, industrial and environmental aspects. As a consequence,
there is pressure on water organisations to provide customers with a continual water supply of the required
quantity and quality, at a required time, subject to a number of delivery requirements and operational
constraints. A level of flexibility exists in the WDSs, which enables the supply of required water under

2
different operational schedules, more or less economically. This flexibility gives opportunity for optimisation
of WDS operation.
Since the 1970s, substantial research has addressed the operational optimisation of WDSs (Ormsbee and
Lansey 1994) with two main areas of focus. The first area includes pump operation, as pump operating costs
constitute the largest expenditure for water organisations worldwide (Van Zyl et al. 2004). Optimal operation
of pumps is often formulated as a cost optimisation problem (Savic et al. 1997). The second area includes
optimisation of water quality across the water distribution network. This research area emerged in the 1990s
following the U.S. Environmental Protection Agency (EPA) promulgating “rules requiring that water quality
standards must be satisfied at consumer taps rather than at treatment plants” (Ostfeld 2005).
Development in the use of various methods to optimise operation of WDSs is not only an interesting subject
for research, but is also very complex. Initially, these techniques included deterministic methods, such as
dynamic programming (DP) (Dreizin 1970; Sterling and Coulbeck 1975a; Zessler and Shamir 1989),
hierarchical control methods (Coulbeck et al. 1988a; Coulbeck et al. 1988b; Fallside and Perry 1975; Sterling
and Coulbeck 1975b), linear programming (LP) (Alperovits and Shamir 1977; Schwarz et al. 1985) and
nonlinear programming (NLP) (Chase and Ormsbee 1989). Since the 1990s, metaheuristic algorithms, such
as genetic algorithms (GAs), simulated annealing (SA), to name a few, have been applied to the optimal
operation of WDSs with increased popularity. Their attractiveness for this type of optimisation is due to their
potential to solve nonlinear, nonconvex, discrete problems for which deterministic methods incur difficulty
(Maier et al. 2014; Nicklow et al. 2010). In recent years however, deterministic methods have started to
reappear, because they are more computationally efficient, thus more suitable for real-time control, as well as
other applications (Creaco and Pezzinga 2015). An example of the former is Derceto Aquadapt, a
commercial software used for real-time optimisation of valve and pump schedules (Derceto 2016), which
uses LP as the base algorithm.
2 Aim, scope and structure of the paper
The aim of this paper is to provide a comprehensive and systematic review of publications for operational
optimisation of WDSs since the end of the 1980s to nowadays to contribute to the existing review literature
(Lansey 2006; Ormsbee and Lansey 1994; Walski 1985). Publications included in this review are relevant to
optimal pump operation, valve control and optimal system operation for water quality purposes of both urban
drinking and regional multiquality WDSs.
The paper consists of two parts: (i) the main review and (ii) an appendix in a tabular form (further referred to
as the table), each having different structure and purpose. The main review is structured according to
publications’ application areas (pump, water quality and valve control) and general classification. This
classification is used because it captures all the main aspects of an operational optimisation problem
answering the questions: what is optimised (Section 4.1), how is the problem defined (Section 4.2), how is

3
the problem solved (Section 4.3) and what is the application (Section 4.4)? The purpose of this part of the
paper is to provide the current status, analysis and synthesis of the current literature, and to suggest future
research directions.
The table forms a significant part of the paper referring to over a hundred publications and is structured
chronologically. It contains a detailed classification of each paper, including optimisation models (i.e.
objective functions, constraints, decision variables), water quality parameters, network analyses and
optimisation methods used, as well as other relevant information. The purpose of the table is to provide an
exhaustive list of publications on the topic (as much as feasible) detailing comprehensive and thorough
information, so it could be used as a single reference point to identify one’s papers of interest in a timely
manner. Therefore, it represents a unique and important contribution of this paper.
The structure of the paper is as follows:
 The main review: Application areas (Section 3), General classification of reviewed publications (Section
4), Future research (Section 5), Summary and conclusion (Section 6), List of terms (Section 7), List of
abbreviations (Section 8).
 The table: Appendix (Section 9).
3 Application areas
3.1 Pump operation
Typically, electricity consumption is one of the largest marginal costs for water utilities. The price of
electricity has been rising globally, making it a dominant cost in operating WDSs. Pump operation is
optimised in order to achieve a minimal amount of energy consumed by pumps. Pumps are controlled either
explicitly by times when pumps operate (so called pump scheduling), or implicitly by pump flows (Bene et
al. 2013; Nitivattananon et al. 1996; Pasha and Lansey 2009; Zessler and Shamir 1989), pump pressures,
tank water trigger levels (Broad et al. 2010; Van Zyl et al. 2004) or pump speeds for variable speed pumps
(for example Hashemi et al. (2014), Ulanicki and Kennedy (1994), Wegley et al. (2000)). These controls are
specified as decision variables and their formulations are reviewed in Ormsbee et al. (2009). The most
frequently used is explicit pump scheduling, which can be specified by (i) on/off pump statuses during
predefined equal time intervals (for example Baran et al. (2005), Ibarra and Arnal (2014), Mackle et al.
(1995), Salomons et al. (2007)), (ii) length of the time (in hours) of pump operation (Brion and Mays 1991;
Lopez-Ibanez et al. 2008), (iii) start/end run times of the pumps (Bagirov et al. 2013). The former, although
the most frequently used, requires a large number of decision variables for (real-world) WDSs with
numerous pump stations, which increases the size of the search space. The latter two methods reduce the
number of variables hence decrease the size of the search space. This reduced search space helps the
optimisation algorithm to quickly achieve a satisfactory pump schedule. Concerning the methods for search
space reduction, an open question is how to perform it without compromising the fidelity of the optimisation
model and undue simplification of the real system.

4
Pump operating costs comprise of costs for energy consumption due to pump operation and costs due to the
maintenance of pumps. Energy consumption normally incurs energy consumption charge and demand
charge. Consumption charge is based on the kilowatt-hours of electric energy consumed by pumps during the
billing period (Ormsbee et al. 2009) and is often the only component of operating costs used in the pump
optimisation problem (for example Jamieson et al. (2007), Kim et al. (2007), Ulanicki et al. (1993)). Demand
charge is usually based on the peak energy consumption during a specific time period (Ormsbee et al. 2009),
and often determined over a time scale much longer (weeks-months) than the time period considered for
optimisation (hours-days). As it is not easily incorporated in the optimisation model (McCormick and Powell
2003), it has been included as a constraint (Gibbs et al. 2010a; Selek et al. 2012) or as an additional objective
besides pump operating costs (Baran et al. 2005; Kougias and Theodossiou 2013; Sotelo and Baran 2001).
Whether demand charges are included as a constraint or an objective depends largely on the optimisation
technique selected for solving the pump operation problem. The shape of the resulting solution space (i.e. the
solution neighbourhood structure) or the ease with which an additional constraint is incorporated determines
the best optimisation method to use. The approach for including maximum demand charges into overall
costs, which takes into account the uncertainty in the future water demand, makes an already difficult
problem of pump operation planning an even greater challenge.
Similar to demand charges, pump maintenance costs are also difficult to quantify. They are usually included
using a surrogate measure such as the number of pump switches (Lopez-Ibanez et al. 2008). It is assumed
that a reduction in the number of pump switches results in the reduction of the pump maintenance costs
(Lansey and Awumah 1994). The number of pump switches has been considered as a constraint (Boulos et
al. 2001; Lansey and Awumah 1994; Lopez-Ibanez et al. 2008; Selek et al. 2012; Van Zyl et al. 2004),
alternatively, pump energy costs and pump maintenance costs have been considered as a two-objective
optimisation problem (Bene et al. 2013; Kelner and Leonard 2003; Lopez-Ibanez et al. 2005; Savic et al.
1997). The advantage of considering pump switches as an objective over incorporating them as a constraint
is in the ability to investigate a complete tradeoff between maintenance and other costs when the former is
selected. However, an open research question with regard to pump maintenance costs within an operational
optimisation problem relates to whether there are more appropriate expressions for characterising this type of
wear and tear costs.
A multi-objective approach has been increasingly applied (Figure 1) to pump optimisation problems to
include considerations other than costs. Other objectives considered, apart from demand charge and pump
maintenance costs mentioned above, were the difference between initial and final water levels in storage
tanks (Baran et al. 2005; Sotelo and Baran 2001), the quantity of pumped water (Kougias and Theodossiou
2013), greenhouse gas (GHG) emissions associated with pump operations (Stokes et al. 2015a,b) and
operational reliability (Odan et al. 2015). Most recently, water quality has been traded off against pump
operating costs (Arai et al. 2013; Kurek and Ostfeld 2013; Kurek and Ostfeld 2014; Mala-Jetmarova et al.
2014) with the finding that those objectives are conflicting. Similarly, water losses due to leakage and pump

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Lost in optimisation of water distribution systems? a literature review of system operation" ?

This paper provides a systematic review by bringing together over two hundred publications from the past three decades, which are relevant to operational optimisation of water distribution systems, particularly optimal pump operation, valve control and system operation for water quality purposes of both urban drinking and regional multiquality water distribution systems. 

Q2. What are the future works mentioned in the paper "Lost in optimisation of water distribution systems? a literature review of system operation" ?

Future research challenges for operational optimisation of WDSs are listed in Figure 6 and grouped according to steps involved in optimisation: ( i ) simulation model, ( ii ) optimisation model, ( iii ) optimisation method, and ( iv ) solution postprocessing. Regarding optimisation problems with water quality aspects, future research may consider the development of an optimisation model with an inbuilt flexibility for a general WDS, which could be customised for a specific WDS. A further research challenge is to analyse relationships between pumping costs and water quality using a set of realistic case studies to ascertain whether they are conflicting objectives or they can be somehow integrated, leading to reduced optimisation problem complexity. A methodology for an objective comparison of optimisation methods should be developed, so the best optimisation method for a particular case can be selected. 

Q3. Why have deterministic methods started to appear in recent years?

In recent years however, deterministic methods have started toreappear, because they are more computationally efficient, thus more suitable for real-time control, as well asother applications (Creaco and Pezzinga 2015). 

Q4. What are the constraints included in the optimisation models?

Please note that hydraulic constraints (such as conservation of mass of flow, conservation of energy, andconservation of mass of constituent) were not included in these statistics as they are normally included asimplicit constraints and forced to be satisfied by WDS modelling tool, such as EPANET. 

Q5. What is the common type of surrogate model?

which are by far the most commonly used surrogate models, are based upon real neurologicalstructures and can be represented as directed graphs. 

Q6. What is the proportion of objectives included in optimisation models?

The number of objectives included in optimisation models ranges from one to four, with a vast majorityof models (84%) being single-objective. 

Q7. What is the importance of water distribution systems?

Water distribution systems (WDSs) represent a vast infrastructure worldwide, which is critical forcontemporary human existence from all social, industrial and environmental aspects. 

Q8. What is the popular example of a hypothetical WDS?

Regarding optimisation problems with water quality aspects,future research may consider the development of an optimisation model with an inbuilt flexibility for ageneral WDS, which could be customised for a specific WDS. 

Q9. What are the main types of surrogate models used to replace and approximate network simulations?

Surrogate models are efficienttools used to replace and approximate network simulations which can be very computationally expensiveand/or may become an obstacle in real-time implementations. 

Q10. What is the level of flexibility in the WDSs?

A level of flexibility exists in the WDSs, which enables the supply of required water underdifferent operational schedules, more or less economically. 

Q11. What are the main criteria for the classification of water quality optimisation for WDSs?

Based on the selected literature analysis, the following are the four main criteria for the classification ofoperational optimisation for WDSs: (i) application area, (ii) optimisation model, (iii) solution methodologyand (iv) test network. 

Q12. What are the main application areas for optimisation of water quality?

As described in Section 3, there are three application areas: pump operation (Section 3.1), water qualitymanagement (Section 3.2) and valve control (Section 3.3). 

Q13. What were the first optimisation models for multiquality WDSs?

The first optimisation models formultiquality WDSs considered pump operating costs only (Mehrez et al. 1992; Percia et al. 1997). 

Q14. What is the common type of optimisation of water quality?

Optimisation of water quality exclusive of any other operational controls (i.e. pumps and/or valves) isaddressed in 15% of papers. 

Q15. What is the promising way for selecting the solution from the Pareto set?

This mismatch leads to the research question of what is the most promising way for selecting the bestsolution from the Pareto set, which may involve providing the decision makers with a globally representativesubset of the non-dominated set that is sufficiently small to be tractable.