Multi-objective optimization for improving equity and reliability in intermittent water supply systems

Intermittent water systems suffer from several drawbacks such as unfair distribution among users, low reliability and poor water quality. Given limited water and financial resources, making decisions for improving intermittent water supply (IWS) becomes a complex process. The paths to continuous supply are a priori undefined, however, the provision of efficient service is crucial. In the scientific literature, limited research addresses how to improve intermittent systems, to enhance the current service while transitioning to continuous supply. A multi-objective optimization (MOO) tool using a genetic algorithm has been developed to assist in investment decision-making. This approach uses multiple cost-effective intervention options to maximize equity and reliability while minimizing cost implications in an IWS system. The costs in such interventions include expenditure on pipe replacement, booster pump and elevated tank installation. The approach was first tested on a benchmark Hanoi synthetic network, and then applied to the water distribution network of Milagro (Ecuador). The developed tool reveals the extent to which equity and reliability can be driving objectives, and how they can be factored into decision-making. The application of the MOO tool in intermittent systems in order to improve existing distribution networks with strategic infrastructure addition can provide greater equity and reliability. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/ws.2020.066 om http://iwaponline.com/ws/article-pdf/20/5/1592/844226/ws020051592.pdf er 2021 Passwell Pepukai Nyahora (corresponding author) Mukand Singh Babel Water Engineering and Management, Asian Institute of Technology, Bangkok, 12120, Thailand E-mail: passwelln@gmail.com Passwell Pepukai Nyahora David Ferras Environmental Engineering and Water Technology, IHE Delft Institute of Water, Delft, 2611 AX, The Netherlands Andres Emen POLICONSTRUC-ALEXER Consortium, Ecuador


INTRODUCTION
Over half of the world's human population currently lives in urbanized areas, and the projections suggest that by 2050, two-thirds of the world's population will be urbanized (United Nations Department of Economic and Social Affairs Population Division ). Rapid increase in population is a major concern in developing countries since they have both financial constraints and infrastructure deficit. Sustainable development of urban infrastructure to cope with increasing demands is critical to ensure that the benefits of urbanization are equitably shared among the residents of that space. In that spirit, the Sustainable Development Goal 6 (SDG 6) of 2014, for instance, buttresses the right to water, and aims to ensure availability of water and sanitation for all. The first target of the SDG6 is achieving universal and equitable access to safe and affordable drinking water by 2030 (United Nations ). The aim is to set up 'safely' managed drinking water services, where 'safely' is defined in terms of accessibility, availability and the quality of the supply service (WHO & UNICEF ). Kaminsky & Kumpel () point out that although access to water has improved over the years, there is some indication that the average time of water supply is actually declining in many parts of the world.
Historically, the design of water distribution has been demand driven. A water distribution system is required to provide pressurized continuous supply. However, because of limited water resources and/or inadequate infrastructure, water supply systems are unable to support current urban growth in many parts of the world. As a result, the supply in some systems has become intermittent. Intermittent supply means that the water supply service is frequently systems as a solution to deal with supply-versus-demand deficit. The IWS has gradually turned to an operational norm in some cases. Moreover, infrastructure inadequacy also becomes evident as impacts of reticulation extensions due to urban expansion are rarely tested on the entire network (Galaitsi et al. ). For instance, an analysis of the conversion of continuous water supply into intermittent supply in Cyprus revealed the negative impacts on the integrity of the system's operation and maintenance with the reverse process (i.e. from intermittent to continuous) being rather complex (Charalambous & Laspidou ). Due to limited financial support in such cases, it is crucial to investigate optimal resource allocation for maximum benefit in the long run with minimal expenditure.
Multi-objective optimization (MOO) has been used to improve water supply systems while keeping consumer requirement in view (Farmani et (1): where S p is the supply-demand ratio obtained by dividing Q s which is the supplied flow and Q d which is the demand on the node. S av is the average supply ratio and n e is the total number of nodes. Zero indicates no equity and an increase to 1 indicates improvement to the best possible value. The reliability surrogate is presented in Equation (2), where the resilience index (I r ) is expressed as: where q i is the nodal demand, h ava, i is the average head at the node i, h req, i is the minimum allowable hydraulic head, Q j and H j are the discharge and head (respectively) at each reservoir, γ is the specific weight of water (1,000 kg/m 3 ) and P k is the power supplied by the pumps in the network (Todini ; Farmani et al. ). The continuous range for the equation is from 0 to 1. Zero represents a poor performance while 1 is the most ideal performance value.
Since both the objectives are crucial in a network functioning with intermittent supply, the two objectives have been combined. The Weighted Sum Method (WSM), used here, allows for the flexibility to maximize one objective over the other, depending on need, and each with a weighting factor (w 1 and w 2 ) to form a single objective function, as is shown in Equation (3): The total cost is the sum of the cost of pipe replacement, civil and equipment cost for the pump station and the cost of the elevated tank. To the cost objective, a penalty is added as a constraint (see Equation (4)) to assist the NSGA II in solving the problem. The objective function for the cost is expressed in Equation (4): where C pipes is the cost of pipe replacement, C pump is the cost of the pump and C tank is the cost of the elevated tank. The penalty function is expressed in Equation (5): where P is the penalty constraint, h i is the nodal pressure,    where C cwp is the civil works cost, and P k is the hydraulic power (kW) used. Equation (7) considers pump wattage raised to a negative power of a factor. Other equipment cost, which includes the pump, is expressed in Equation (8): where C ep is the equipment cost while P k is the same as for Equation (7). The sum of the two equations is the pump cost.
The investment cost for the elevated tank also has two components. The cost of civil works (C cwt ) is expressed as: where V is the tank volume (m 3 ), which is applicable to a range of volumes from 100 m 3 to 500 m 3 , as shown in  connections. In this study, the network was sectorized into four supply areas and the most affected area was selected for further study. The simplified network of the chosen sector is presented in Figure 2. It is composed of 63 pipes, 62 junctions, six reservoirs (water wells), two pumps, two tanks, and seven flow control valves. The flow control valves regulate the volume of water to mimic groundwater well yields. The simplification of the network is conducted using a WaterGEMS skeletonization tool.
Three intervention options were evaluated as part of the optimization process, and are as follows.

Intervention option 1: pipe replacement
The growth of water distribution systems over several decades and centuries is guided by population growth and economic development. Such developments may often result in continual untested network expansion and also limited pipe rehabilitation programmes. The pipe replacement approach aims at improving the current network in terms of equity and reliability. If head loss is reduced, the flow could be improved.

Intervention option 2: pipe replacement and inline booster pump
One of the factors causing equity and reliability challenges in a water system is the lack of adequate pressure, which results in the limited (often deficient) volume of the supplied water. Therefore, the addition of a pump can aid in increasing the available pressure in the system. The Todini Index is used to test the reliability of the additional pressure made available to the system. Pump selection is based on the expected normal flows and the required head in the network. In the current case, the head requirement in Hanoi is 30 m; therefore, the lowest pump was set at þ50 m.

Intervention option 3: pipe replacement, inline booster pump and elevated tank
In addition to the interventions outlined in options 1 and 2, an elevated tank is added in option 3. The pressure factor is considered in the second scenario and an elevated tank can provide buffer capacity and a steadier pressure head. However, a pump is still required to fill the tank. There is a

RESULTS AND DISCUSSION
The main objective of this study was to develop an MOO approach for the improvement of intermittent water supply. Equity and reliability were a combined objective and minimal cost was the second objective. A penalty function was added to the actual infrastructure cost to enhance the identification of optimal solutions. The three approaches presented in the preceding section were applied to both the Hanoi network and the selected section of Milagro.
The results for each of the approaches, considering the same optimization setup (cf. Table 1), are presented below.

Method verification: Hanoi network
A graphical representation of cost versus equity and reliability for pipe replacement at the end of the optimization process is presented in Figure 3.   The third approach includes initial pipe replacement with an additional booster pump and an elevated tank being fed by the pump as well. The results are presented in Figure 5. indicates that fewer nodes are deviating from the set threshold pressure range.
Equity and reliability were equally weighted and the impacts they have on each other are evident. Both are highly vital in an intermittent system because consumers perceive the service to be unreliable as well as unfair. The combination of equity and reliability ensures that as UC checks if the nodal demand is satisfied, the resilience index considers the availability of excess energy in case of any changes in the flow regime that cause a failure of service. Attaining equity of one is possible using the approach; however, the improvement of reliability requires an additional pressure head to be introduced into the system. Improving reliability with pressure-boosting systems can only work to a certain extent, since pipe redundancy plays an important role as well.

The Milagro network
The case study network was divided into sectors from which Las Pinas (cf. Figure 2) was selected for optimization. The hydraulic simulation yielded the objective values listed in Table 3 before intervention.
The reliability indicator in Table 3 reflects the optimum figure which can be attributed to the system having multiple sources; however, the equity component stays below 50%.  As seen in Figure 6, a marginal improvement of the There is a considerable decrease in the Equity and Reliability function with this option. This can be attributed to lower reliability, as reflected in Figure 7. The improvement in UC to over 0.8 causes a reduction in the Todini Index value to 0.17. The cost function increases with the addition of the pump, which also impacts the acceptable pipeline design.

CONCLUSIONS
The approach presented enables the optimization of intermittent water distribution systems considering equity, reliability and cost. Fair distribution of available water can be improved with pipe replacement in both the Hanoi and Las Pinas networks. However, in the benchmark network (i.e. Hanoi), additional pressure-aiding infrastructure may not be necessary due to its flat topography. In the application case (Las Pinas), on the other hand, such additional infrastructure improves the furthest nodal pressures as its topography is different.
Equity improvement impacts the overall reliability of the network; therefore, a combined analysis is critical to reveal the extent to which they affect each the other. Engineering expertise is essential to ensure the right interpretation of the optimization results, which will eventually lead to a feasible design being identified and implemented.
The results show the consistency of the method when applied to a looped network, since reliability improves when flows are rerouted. However, for weakly looped networks there is a lower level of reliability, which reveals the limitations of the application of the resilience index in the partially looped Las Pinas network. The parameters for the pipe, pump, and the elevated tank have to be carefully selected, considering a priori knowledge of the network.
The location of the pumps and tanks is complex; therefore, further analysis of the optimization mechanisms needs to be carried out to find the most suitable approach for a particular system. This process is also deeply dependent on the information provided by the water service provider.
Further research in developing solutions for locating and sizing the optimization of booster pumps, which can be included in the initialization of the seed population in a distribution system, is required. The optimized solutions from one intervention option may be used as seed population for the following options. The researcher also needs to consider an alternative reliability indicator besides excess energy. This may include other factors such as multiple sources and/or pipe uniformity, which can provide more insight into the overall improvement of the distribution network.

ACKNOWLEDGEMENTS
The work presented here is based on the Master's thesis conducted by the first author.