Abstract

The energy overconsumption at drinking-water pumping stations creates considerable energy losses. For this reason we have developed an NNGA tool of pumping management which optimizes the consumed energy by the pumping system with respect to the hydraulic functioning conditions in the distribution tank. This tool includes two models: a forecasting model for drinking water demand based on artificial neural networks and an optimization model using genetic algorithms. The results of the NNGA tool were compared with two pumping plans: the plan based on the pumping regulation model, and the plan used by the company of water and sewage of the city of Algiers. The analysis result was done with the help of performed indicators that we have developed and which enable the evaluation and diagnosis of the energetic function's system.

INTRODUCTION

The energy consumed by pumping systems represents around 20% of worldwide consumed energy; a considerable quantity of this energy is lost because of bad management in the operating phase. Energetic optimization enables the considerable reduction of the consumed energy beyond the direct and indirect consequences of this action upon different economical, technical and environmental plans (Wang & Barkdoll 2016). The purpose of optimization methods is to find the right pump combination to reduce the energy of pumping. However, the strong interaction between the non-linear network components and the various variables of the system makes the resolution of the problem very complex. For this reason, in the early work that was conducted at the beginning of the 1980s several simplification hypotheses were adopted to facilitate resolution. This is clear in Jowitt & Germanopoulos (1992) where an approach based on linear programming is presented. In Coulbeck & Orr (1984), the authors divided the optimization problem into two areas: static optimization for pumping parameters, and dynamic optimization to search for optimal pumping planning. This same method was used in the work presented by Lansey & Awumah (1994), and in the work presented by Nitivattananon et al. (1996) while taking into consideration the real-time operation of the system.

From the 1990s, stochastic methods (in particular genetic algorithms) were applied to solve the problem of the optimization of water supply systems (Simpson et al. 1994), while the first use of genetic algorithms (GA) in pumping optimization was by Mackle et al. (1995) where a simple genetic algorithm with binary coding was used to reduce the pumping cost. In Rao & Salomons (2007), the authors used an artificial neural network (ANN) based on a numerical simulation to predict the input data of a simple GA. In Savic & Walters (1997) and Barán et al. (2005) an improvement on the multi-objective aspect was introduced allowing the treatment of several objectives (energy and pump switches) at once. In Van Zyl et al. (2004), optimization performance was improved using a hybrid method that combines a GA with hillclimber search strategy. Subsequently, to reduce the calculation time especially for large systems, several authors have used the parallel computing technique (Wu & Zhu 2009). However, this technique requires means for its implementation. In Behandish & Wu (2014) a modified GA is employed to search for the decision space made of both discrete variables and continuous variables (tank levels). In the study presented by Zhuan et al. (2017), a decomposition method is proposed to reduce the electricity consumption cost of the pumping station of Huain in China.

In our approach, two improvements have been made to the ordinary genetic algorithms used in the optimization of pumping systems. The first improvement introduced concerns the generation of the initial population. Indeed, in ordinary algorithms, the generation of the initial population is made by a random generator, which can create a calculation divergence especially when the valid solution is difficult to find. To overcome this problem a certain percentage of the initial population composed only of valid solutions has been imposed, and the generation of these valid solutions is done using an algorithm which is based on the constraints of optimization of the problem. The second improvement that has been made is the non-use of a coding for the representation of the variables, which reduces the computation time by eliminating the coding and decoding operations in the calculation process.

The optimization calculation requires the determination of the water demand. In the case of using a normalized pattern, which is usually based on the average values of demand, it can lead to a good optimization result. But this type of method does not take into consideration the seasonal variability of demand, and also it does not take into consideration factors determining the demand, which negatively influences the optimization results.

For this reason, several optimization studies have used forecasting methods, such as the simulation methods, as in the case of the study presented by Napolitano et al. (2014) where the authors used a numerical simulation by the EPANET software of a water supply system to generate several scenarios, in order to make the optimal decisions provided by a GA. The same method was used in the work presented by Mambretti & Orsi (2016), with the peculiarity that the network does not have a tank.

The time series analysis method was used among other works, in the study presented by Kang et al. (2014), where an autoregressive integrated moving average (ARIMA) model was developed to predict water demand, as part of an optimization project for the Polonnaruwa pumping station (Sri Lanka). The regression method was used in the optimization study of a large hydraulic system to predict the water level of the system's reservoirs (Kim et al. 2007).

The connectionist methods, and more specifically the technique of ANN, was first used in the study presented by Cubero (1991) to predict the daily water demand of a water supply system. In Guhl & Brémond (2000) a simplification was made to the NNA by removing climate data from the input data of the model. The model was multi-output including 12 neurons for predicting the water demand over a 12-hour horizon. In the work of Rao & Salomons (2007), the authors conducted the learning and the forecasting of the model through a numerical simulation. Then, multi-ANN meta-modeling was improved and generalized by Behandish & Wu (2014), improving the robustness and precision of the model.

The NNA approach has shown great efficiency in predicting water demand, because of these many advantages, especially for its ability to deal with the non-linearity of water demand, which allows it to solve very complex problems. The other advantage of the NNA approach is its flexibility over the parameterization data, where it does not require a continuous and long database, against the other methods. In this context, several comparative studies have shown their superiority in forecasting compared to other methods (Jain et al. 2001; Adamowski 2008).

Most previous studies that have used the NNA approach have used either a multi-output NNA or multi-NNA meta-modeling. In our study, the NNA used is of the looped type distinguished by the single output, the normalization of input data and the non-use of bias. These characteristics were chosen after a selection study for different model structures.

Our optimization model is based solely on the energy consumed. On the other hand, several optimization models take into consideration the cost of energy. In order to compare the two approaches, the energy cost was integrated into a second variant.

MATERIALS AND METHODS

The management tool developed (NNAG) contains two models: an optimization model and a forecasting model. The forecasting model is based on the ANN which enables it to foresee the hourly water request upon a horizon of 24 hours. The optimization model is based on the genetic algorithm (GA) approach. It uses the foreseen water demand to define an optimal pumping plan on the optimization horizon. The tool has been validated at the Rassauta pumping station.

To enrich our study, we studied and compared the results obtained by the NNGA tool with two pumping scenarios. Indeed, in addition to the pumping schedule used by the company of water and sewage of the city of Algiers (CWSA), we have studied a scenario generated by a pumping regulation model that we have developed and which is based on the volume of water in the tank. The energy evaluation of the different pumping schedules is carried out using the performance indicators that we have developed.

PRESENTATION OF THE STUDY AREA

The pumping station studied is located in the Rassauta region on the eastern outskirts of the Algerian capital. This pumping station has three centrifugal pumps (two operational and one back-up) supplying a distribution tank of 1,500 m3. The tank supplies the eastern part of the city of Bordj El Kiffan and also the El Hamiz tank (Figure 1).

Figure 1

Schema of the pumping system of Rassauta.

Figure 1

Schema of the pumping system of Rassauta.

The pumps draw water from the suction tank (2 × 5,000 m3), whose volume of water is managed by altimetric valves, and the pumping unit is installed 3 metres below the suction plane (flooded suction), which reduces the problems associated with priming and cavitations.

The management of the pumping station is warranted by CWSA. The type of pumping used is based on a remote management system, accompanied by a regulation of the pumps. The regulation of the pumping is done by shedding the pumps according to the water level in the tank.

The distribution network of Bordj El Kiffan East has about 150,000 inhabitants and a total length of pipes of 82,831 m, divided into eight distribution sectors. The unfavorable point of the distribution network is in the locality ‘Bateau Cassé’. While the El Hamiz tank has a volume of 500 m3 characterized by a floor elevation of 38 m and overflow elevation of 42 m, this tank serves the southern part of El Hamiz city whose distribution network has about 18,408 m of pipelines divided into three distribution sectors. The water supply network is characterized by an average daily consumption of about 24,878 m3/d and maximum hourly consumption equal to 1,316 m3/h.

Despite the fact that the pumping system studied is simple, which does not allow the generalization of the results obtained to very complex systems, the high demand of the water supply network makes the volume of water in the tank sensitive to fluctuation. which is interesting for an optimization study.

MANAGEMENT PUMPING TOOL (NNGA)

Demand forecast model

The ANN method has shown a great capacity to resolve problems of forecasting water demand and this is thanks to its power to master the non-linear relationship between the determining factors of water demand (Adamowski 2008). This approach also has the advantage of not requiring a long and continuous database.

In our study, an NRA is used for each quarter, where each ANN forecasting model consists of three layers, based on the logistics function. Its structure was adopted after several tests. The input layer contains 35 neurons (three neurons for the month, seven neurons for the days of the week, 24 for the time of day, and one neuron for the consumption of the previous hour). The input data do not contain climatic data, where several studies have shown that forecasting can be done without climatic data. In fact, the water demand (t − 1) implicitly contains climatic data as well as other exogenous factors, in addition to the strong correlation between demand (t) and (t − 1), which makes it possible to take into account the effect of continuity of demand.

The water demand of the previous hour (neuron 35) is normalized, dividing it on the maximum hourly consumption. The hidden layer has two neurons, whose activation functions are calculated without using bias. The output layer has a single neuron. For the learning of the model we used a database of 3 years (from June 2013 until June 2016). This allows adjustment of the parameters (synaptic weight) of the NNA model, which gives each input data its importance for forecasting demand.

The NNA is of the loop type, where the demand predicted at the previous time is used as the input data at the next time (Figure 2).

Figure 2

Structure of the adopted artificial neural network model.

Figure 2

Structure of the adopted artificial neural network model.

Optimization model using genetic algorithms

The GA approach is one of the best techniques for solving combinatorial optimization problems on which we are working (Olszewski 2016; Marchi et al. 2017). The GA used in our study is characterized by two modifications compared with ordinary GA.

First, the GA does not use a binary coding operator of the individuals, which makes it possible to reduce the calculation time. Indeed, the solution is represented by a decision vector N (or control vector) comprising 24 components (optimization horizon is 24 hours), and each component indicates the number of pumps running at each time step, as shown in Equation (1): 
formula
(1)
np = number of pumps; mf: number of solutions (individuals).

Second, the generation of a part of the initial population is done using a specific algorithm, which allows the creation of valid solutions, that is to say, solutions that respect the constraints of optimization, because in ordinary GA the random generation of the initial population sometimes gives initial populations that do not contain any valid individual, which causes problems of calculation (divergence) and enormously increases the calculation time.

This specific algorithm consists in the beginning of generating a random initial population.

Then, an iterative calculation process is started, where at each iteration the pumping flow rate is calculated according to the number of pumps running. Then, this number of pumps running is changed depending on the volume of water in the tank (Figure 3). This process is repeated NI times, and at the end of calculation a generation of valid individuals is created. This valid population is added to the randomly generated population to form the initial population of the GA.

Figure 3

Diagram of the generator of valid solutions.

Figure 3

Diagram of the generator of valid solutions.

These individuals will be evaluated using a fitness function (Equation (2)). These individuals go through a process of genetic operations, which generates the new generation, while sanctioning the individuals who do not respect the constraints of optimization (Equation (3)). This process will be repeated until the stop criterion is checked. At the end of the calculation the best solution represents the optimal decision variables of the problem.

In the calculation of the objective function, the pumping efficiency is considered constant, whereas in reality its value deteriorates in the course of time. Also, the optimal solution represents the best solution in terms of energy consumed without taking into consideration its effect on the downstream part in terms of pressure (in case of a possible lowering of the level). 
formula
(2)
 
formula
(3)
with np: number of pumps; ρ: density of water (kg/m3), g: standard acceleration of gravity (m/s2), H(t, n): pumping head at time t with n pumps running (m), Qp: pumping flow at time t with n pumps running (m3/h), η: pumping efficiency at time t with n pumps running (%); Vmin and Vmax: minimum and maximum volume in the tank respectively (m3); V(t): volume of water in the tank at time t (m3); V(t − 1): volume in the tank at time t − 1 (m3); Qp(t − 1): pumping flow at time t − 1 (m3/h); Qc(t − 1): consumption flow at time t − 1 (m3/h); Qmax: maximum pumping flow (m3/h); Δt: time step (h).

PROGRESSIVE REGULATION MODEL

The progressive regulation model (PRM) controls the operation of the pumps according to the volume of water in the tank. Indeed, if the volume of water exceeds a certain volume Voff, the model proceeds with a progressive stop of the pumps, where at each time step one pump is stopped. However, if the volume of water is less than a certain Von, the model proceeds with a progressive start of the pumps. The relation (4) summarizes the operating principles of the model: 
formula
(4)
The expression of Voff is given by the following equation: 
formula
(5)
The Von is given by the following formula: 
formula
(6)
Voff: stopping volume (m3); V(t): volume of water at time step t (m3); n(t): number of pumps running at time step t; Von: starting volume; np: number of pumps in the pumping station; Qp(n): pumping flow with n pumps running (m3/h).

OPTIMUM OPERATING VARIABLES OF THE PUMPING SYSTEM

In order to calculate the energy performance indicators, we have defined a number of optimal values (Table 1), which constitute a benchmark for situating the performance of the variable studied.

Table 1

List of optimal pump operating system variables

VariableFormulaDescription
Optimum pumping volume Vopt=VrVi + Vmin The volume of water needed to meet demand. 
Optimum pumping flow Qopt=Vopt/Topt The flow that creates the least pressure drop. 
Optimum pumping head Hopt=Hg+rh.Qopt2 The required head in the case of optimum operation of the pumps. 
Optimum pumping efficiency ηopt=ηmax The maximum efficiency of the pumps. 
Optimum pumping energy Eopt= (ρ.g.Hf.opt.Vopt)/(ηopt.36000The energy consumed when the operating variables have optimum values. 
VariableFormulaDescription
Optimum pumping volume Vopt=VrVi + Vmin The volume of water needed to meet demand. 
Optimum pumping flow Qopt=Vopt/Topt The flow that creates the least pressure drop. 
Optimum pumping head Hopt=Hg+rh.Qopt2 The required head in the case of optimum operation of the pumps. 
Optimum pumping efficiency ηopt=ηmax The maximum efficiency of the pumps. 
Optimum pumping energy Eopt= (ρ.g.Hf.opt.Vopt)/(ηopt.36000The energy consumed when the operating variables have optimum values. 

Vopt: optimum pumping volume (m3); Vr: water volume requested (m3); Vi: initial water storage in the tank (m3); Qopt: optimum pumping flow (m3/h); Topt: optimization time (h); Hg: system geometric head (m); rh: system hydraulic resistance (h2/m5); ηmax: maximum pump efficiency (%); Hopt: optimum pumping head (m); ηopt: optimum pumping efficiency (%); Eopt: optimum pumping energy (KWh).

ENERGY PERFORMANCE INDICATORS

In recent years, several energy performance indicators have been developed (Deng et al. 2014). In our study, we have developed two types of indicators: evaluation indicators, and diagnostic indicators. The evaluation indicators enable the evaluation of the energy consumption and to estimate the energy overconsumption. The diagnostic indicators permit detection of the source of energy dysfunction by analyzing the impact of operating variables, which are the volume, the head and the pumping efficiency. Table 2 shows these indicators.

Table 2

Energy performance indicators list

TypeIndicatorFormulaObjective
Evaluation Pumping energy indicator (IE) IE=Eopt/E Evaluate energy consumption 
Energy loss rate (LR) LR= (1−IE100 Evaluate energy losses 
Diagnostic Pumping volume indicator (IV) IV=Vopt/V Evaluate pumping volume 
Pumping head indicator (IH) IH=Hopt/H Evaluate pumping head 
Pumping efficiency indicator (IR) IR=η/ηopt Evaluate the pumping efficiency 
TypeIndicatorFormulaObjective
Evaluation Pumping energy indicator (IE) IE=Eopt/E Evaluate energy consumption 
Energy loss rate (LR) LR= (1−IE100 Evaluate energy losses 
Diagnostic Pumping volume indicator (IV) IV=Vopt/V Evaluate pumping volume 
Pumping head indicator (IH) IH=Hopt/H Evaluate pumping head 
Pumping efficiency indicator (IR) IR=η/ηopt Evaluate the pumping efficiency 

IE: pumping energy indicator; E: pumping energy (KWh); IV: pumping volume indicator (%); V: pumping volume (m3); IH: pumping head indicator; H: pumping head (m); IR: pumping efficiency indicator; η: pumping efficiency (%).

RESULTS AND DISCUSSION

Demand forecast

The forecast for water demand was excellent. The results show that the real demand and the expected demand are practically identical (Figure 4). The prediction quality criteria confirm the performance of the forecasting model with a correlation coefficient R equal to 0.95 and an average absolute error MAPE equal to 4.37 for the training part and with an R = 0.98 and a MAPE = 2.39 for the forecasting part. The NNA Forecasting Model is based only on the date and time of day (without climate data), and it is similar to the use of a standardized pattern. However, its performance was better than the normalized pattern, whose correlation coefficient R = 0.95 and the MAPE criterion = 5.44. This performance can be explained by the use of water demand (t − 1) by the NNA model.

Figure 4

Predicted, normalized and actual water demand on the optimization horizon.

Figure 4

Predicted, normalized and actual water demand on the optimization horizon.

Energy consumption

The NNGA tool has reduced the energy consumed by the pumping system by 39.4%, while the PRM model has saved 27.4%. Figure 5 shows the evolution of the energy consumption of each pumping schedule.

Figure 5

Evolution of energy consumed.

Figure 5

Evolution of energy consumed.

Water storage evolution

The evolution of the water storage (Figure 6) shows that the NNGA model enables the hydraulic conditions to be respected. On the other hand, the PRM model failed to guarantee the upper limit, where it recorded ten violations.

Figure 6

Evolution of the water storage in the distribution tank.

Figure 6

Evolution of the water storage in the distribution tank.

Energy evaluation

Table 3 shows that the planning proposed by the NNGA tool presents the best energy optimization result with pumping energy indicator IE= 0.84 and energy loss rate LR= 15.89%.

Table 3

Energy performance indicators

IndicatorCWSANNGAPRM
IE 0.51 0.84 0.70 
LR [%] 49.02 15.89 29.78 
IV 0.63 0.98 0.83 
IH 0.87 0.98 0.96 
IR 0.94 0.88 0.89 
IndicatorCWSANNGAPRM
IE 0.51 0.84 0.70 
LR [%] 49.02 15.89 29.78 
IV 0.63 0.98 0.83 
IH 0.87 0.98 0.96 
IR 0.94 0.88 0.89 

In second position, we have the PRM regulation model which obtained a good pumping energy indicator IE= 0.7, with an average rate energy loss LR= 29.78%.

In the last position, we have the pumping schedule used by the CWSA with low pumping energy indicator IE= 0.51, and high operating energy losses of LR= 49.02%.

Energy diagnosis of operating variables

CWSA pumping schedule

Diagnostic indicators have shown that energy overconsumption of CWSA planning is largely caused by an enormous loss of water volume, with the indicator IV= 0.63. This malfunction may be due to:

  • presence of unaccounted consumption;

  • poorly adjusted regulation model;

  • too badly sized;

  • leakage.

PRM pumping schedule

As for the previous schedule, the pumping volume indicator of the PRM model is the least efficient of the operating variables (IV= 0.83). This shows that the pumped volume lost is the main cause of the energy overconsumption. This poor performance is explained by the fact that the capacity of the reservoir does not correspond to the water demand and pumping regime.

NNGA pumping schedule

The volume and head pumping indicators for the NNGA are excellent, with IV= 0.98 and IH = 0.98. However, the pumping efficiency indicator is less effective (IR= 0.88). This shows the wrong choice of pumps.

Consideration of energy cost

The main purpose of the majority of optimization models of previous pumping systems is the reduction of energy cost. The goal of our model is the reduction of energy only. To make a comparison between the two models, the price of the energy unit was introduced in the objective function (Equation (7)): 
formula
(7)
with C(t): price of the energy unit according to the rate of electricity consumption (£/KWh).

To analyze the optimization performance, two days were studied: a day of normal water demand (average consumption level), and a day of low water demand (exceptional). NNGAC is the model that considers the cost of energy.

For the normal water demand day: the optimization results were identical for both models, with an energy consumption of 2,912.6 KWh and an operating cost of 7,000 £. This can be explained by the fact that the high water demand limited the possibility of having several valid pumping schedules, so that the optimal solution was imposed by the optimization constraints which are the same in both models.

For the day of low water demand: the results show that the model that considers only energy (NNGA) allowed an energy consumption of 2,668.4 KWh, less by about 8.2% compared with the consumption of the second model (NNGAC) of 2,906.9 KWh.

On the other hand, for the energy cost, the results show that even though the energy consumption of the NNGAC model is higher than the energy consumption of the NNGA, the energy cost was less than 11.8% (Figure 7). This confirms that the consideration of the energy cost in the optimization models does not necessarily reduce the energy consumed, especially in the case where valid solutions are numerous.

Figure 7

Comparison of optimization results.

Figure 7

Comparison of optimization results.

CONCLUSION

The NNGA tool has efficiently reduced the energy consumed by the pumping system by around 39.4% of the consumed energy and with total respect of the conditions of hydraulic functioning. This good performance was strengthened by the good quality of the demand of water through the forecasting model.

The comparative study between the energy optimization model and the energy cost model has confirmed that models that take into consideration energy costs can generate solutions that reduce energy costs and not necessarily the pumping energy, which will always cause ecological problems: depletion of energy resources, and emissions of greenhouse-effect gas.

The PRM model has also saved a considerable part of energy, around 27.4%. Meanwhile, the model failed to guarantee the hydraulic conditions because of the tank capacity that is not suitable for the time step used by the model.

The developed performance indicators have facilitated the evaluation of energy consumption using the IE pumping energy indicator and the LR energy loss rate, which makes it possible to quantify energy overconsumption. In addition, the indicators were used to diagnose the operating variables of the pumping system, by detecting the source of the energy malfunction.

Despite the success of the model in obtaining good results, it depends on certain simplifications and compromises that should be improved in the future. Indeed, the model is based on the pumping efficiency given by the manufacturer when it actually deteriorates over time. In addition the non-consideration of the downstream pressure in the calculation of the optimal solution has to be regulated. Also the model should be adapted to handle even more complicated systems.

REFERENCES

REFERENCES
Adamowski
J. F.
2008
Peak daily demand forecast modeling using artificial neural networks
.
Journal of Water Resources Planning and Management
134
(
2
),
119
128
.
Barán
B.
,
von Lücken
C.
&
Sotelo
A.
2005
Multi-objective pump scheduling optimisation using evolutionary strategies
.
Advances in Engineering Software
36
(
1
),
39
47
.
Coulbeck
B.
&
Orr
C. H.
1984
Optimized pumping in water supply systems
.
IFAC Proceedings Volumes
17
(
2
),
3175
3180
.
Cubero
R. G.
1991
Neural networks for water demand time series forecasting
. In:
International Workshop on Artificial Neural Networks
(A. Prieto, ed.),
Springer
,
Berlin, Germany
, pp.
453
460
.
Guhl
F.
&
Brémond
B.
2000
Optimisation du fonctionnement des réseaux d'eau potable. Prise en compte de l'aspect stochastique de la demande (Optimization of the functioning of drinking water networks. Taking into account the stochastic aspect of the demand)
.
Ingénieries EAT
23
,
15
23
.
Jain
A.
,
Varshney
A. K.
&
Joshi
U. C.
2001
Short-term water demand forecast modelling at IIT Kanpur using artificial neural networks
.
Water Resources Management
15
(
5
),
299
321
.
Jowitt
P. W.
&
Germanopoulos
G.
1992
Optimal pump scheduling in water-supply networks
.
Journal of Water Resources Planning and Management
118
(
4
),
406
422
.
Kim
S. G.
,
Koo
J. Y.
,
Kim
H. Y.
&
Choi
Y. J.
2007
Optimization of pumping schedule based on forecasting the hourly water demand in Seoul
.
Water Science and Technology: Water Supply
7
(
5–6
),
85
93
.
Lansey
K. E.
&
Awumah
K.
1994
Optimal pump operations considering pump switches
.
Journal of Water Resources Planning and Management
120
(
1
),
17
35
.
Mackle
G.
,
Savic
G. A.
&
Walters
G. A.
1995
Application of genetic algorithms to pump scheduling for water supply
. In:
Genetic Algorithms in Engineering Systems: Innovations and Applications, 1995
, Conference Publication No. 414,
IET
,
UK
, pp.
400
405
.
Mambretti
S.
&
Orsi
E.
2016
Optimizing pump operations in water supply networks through genetic algorithms
.
Journal of American Water Works Association
108
(
2
),
119
125
.
Marchi
A.
,
Simpson
A. R.
&
Lambert
M. F.
2017
Pump operation optimization using rule-based controls
.
Procedia Engineering
186
,
210
217
.
Nitivattananon
V.
,
Sadowski
E. C.
&
Quimpo
R. G.
1996
Optimization of water supply system operation
.
Journal of Water Resources Planning and Management
122
(
5
),
374
384
.
Savic
D. A.
&
Walters
G. A.
1997
Genetic algorithms for least-cost design of water distribution networks
.
Journal of Water Resources Planning and Management
123
(
2
),
67
77
.
Simpson
A. R.
,
Dandy
G. C.
&
Murphy
L. J.
1994
Genetic algorithms compared to other techniques for pipe optimization
.
Journal of Water Resources Planning and Management
120
(
4
),
423
443
.
Van Zyl
J. E.
,
Savic
D. A.
&
Walters
G. A.
2004
Operational optimization of water distribution systems using a hybrid genetic algorithm
.
Journal of Water Resources Planning and Management
130
(
2
),
160
170
.
Wu
Z. Y.
&
Zhu
Q.
2009
Scalable parallel computing framework for pump scheduling optimization
. In:
World Environmental and Water Resources Congress 2009: Great Rivers
(S. Starrett, ed.),
ASCE, Reston, VA
,
USA
.