**1. Introduction**

Installing an efficient monitoring and control sensor system gives the possibility to carry out main tasks on Water Distribution Network (WDN) management and protection. Securing these critical infrastructures is a crucial task for ensuring society's welfare and prosperity. In fact, WDNs are strongly vulnerable to malicious and intentional actions [1] since they are made up of thousands of exposed elements. From a practical and economic point of view, securing all the apparatuses is not feasible. Thus, the design of an effective and cost-effective quality monitoring system represents a crucial management strategy for ensuring the delivery of good quality water to users. Optimal sensor placement becomes a necessary step for satisfactory water quality monitoring systems, also

allowing identification of the source contamination [2]. These systems should provide a fast and accurate detection, distinguishing between normal variations and contamination events; furthermore, they should be economical, easy to integrate into network, and reliable [3]. This problem has been extensively studied for the past 20 years and several approaches have been proposed to identify optimal locations of sensors (Byoung et al. (1992) [4] defined the concept of maximum coverage to locate sensors formulating the problem as integer programming problem; using the same objective as the maximum coverage, Kumar et al. (1997) [5] employed a mixed-integer programming method; Watson et al.(2004) [6] used a mixed-integer linear programming model, showing that the problem of sensor placement must simultaneously consider multiple design objectives; Berry et al. (2005) [7] pointed out the difficulty of solving sensor placement by means of integer programming optimization; Ostfeld and Salomons (2004) [8] studied the problem in unsteady conditions using a genetic algorithm framework integrated with EPANET; Uber et al. (2004) [9] used a greedy heuristic solution methodology providing a heuristic (non-optimal) solution procedure scalable to large networks, taking into account uncertainty in threat scenario). The problem received lots of attention especially after the events of 11 September 2001. However, although many research works have been carried out in this field, the challenge of the optimal sensor placement is still open in many aspects, such as identification of optimal sensor locations and evaluation of performance and applicability to real-world scenarios. Models and algorithms for solving this arduous problem include deterministic and stochastic optimization techniques, optimizing one (Kessler et al. (1998) [10] defined the total volume of contaminated water consumed ahead of detection; Ostfeld and Salomons (2005) [11] enhanced previous study by taking into account the randomness of flow rate of the intruded pollutant, stochastic demands, and reaction time of the sensors; Berry et al. (2009) [12] incorporated into a mixed-integer programming formulation the probability of sensor failure) or more objectives (McKenna et al. (2007) [13] demonstrated the importance of considering sensor failure rates showing the trade-off between the sensor detection limit and the number of sensors; Dorini et al. (2008) [14] considered four objectives in the model and used a noisy cross-entropy sensor locator algorithm to find the optimal solution; Huang et al.(2008) [15] considered three objectives in their formulation solved by using a competent genetic algorithm while the contamination events were simulated by a development of Monte Carlo method; Propato and Piller (2006) [16] used a mixed-integer linear program methodology including notions of statistical and uncertainty analysis in the design process; Wu and Walski (2008) [17] combined four objectives into a single objective), such as detection likelihood, expected contaminated water volume, affected population, detection time, and the contaminated population. The interested reader can refer to Hart and Murray (2010) [18,19] for a review of this topic. The optimal sensor placement problem was also dealt with at the Battle of the Water Sensor Networks (BWSN) [20]. The main difficulty is that, given WDN complexity, efficient numerical techniques are needed to support optimal monitoring system design and the huge number of all potential contamination events in a WDN makes the problem computationally intractable (as each of these events is characterized by a different injection location, duration, mass rate, and starting time). Indeed, the optimal sensor placement in a network represents a combinatorial optimization problem that has been proven to be NP-hard [21]. For example, Krause et al. (2008) [22] showed that, using 30 parallel processors, it took 8 days to simulate random contamination events that could occur at 5 min intervals over a 24 h period from any of the 12,527 nodes in a medium-sized distribution network. In recent years, new concepts in sensor network design have been studied; Sankary and Ostfeld (2016) [23] investigated the possibility of adopting a mobile wireless sensor network to wirelessly transmit data to fixed transceivers in real time; Rathi et al. 2016 [24] proposed a novel strategy for the selection of contamination events with associated risk to be used in design of sensor network; Zheng et al. 2018 [25] investigated the characteristics of the sensor placement strategy effectiveness using several metrics, and providing guidance for selecting the most appropriate strategy for the preparedness for contamination events.

On the other hand, the "divide and conquer" concept has recently been gaining attention in the field of WDNs, showing to be one of the most efficient management strategies. The option of dividing large-scale networks into smaller and manageable subsystems, called district metered areas (DMAs), offers undisputable advantages for the monitoring and control of consumption, pressure, leakage, and water resource quality. In the scientific literature, numerous works were dedicated to the design of DMAs. Most of them are based on the application of decomposition algorithms [26,27] based on graph [28–32] and spectral theories [33,34], multi-agent method [35], social network theory [36], modularity index [37–39]. Though being significant contributions to the field, the works mentioned above are mostly focused on DMA design. Therefore, they fail to analyze the positive effects brought by the creation of DMAs to WDN management, for reducing the impacts of potential contamination events.

The global aim of this paper is to provide a general management framework for WDN monitoring, while exploring the benefits of water network partitioning (WNP) for:


While the analysis of the former aspect is presented hereinafter as a follow-up of the work of Ciaponi et al. (2018) [40], the analysis of the latter aspect is entirely novel. In this context, the possibility of installing some or all sensors at boundary pipes will be considered, resulting in a two-fold advantage: numerical, due to the reduction in the research space of possible candidate solutions for sensor installation, and managerial, due to easiness of access and to cost savings for the possibility of sharing some electronical components for data acquisition, saving, and transmission.

In the following sections, first the methodology is presented, followed by the applications to a real case study, testing different scenarios and comparing different sensor locations with four water quality-based parameters, in order to validate the results.

#### **2. Materials and Methods**

The methodology used in this work is the combination of two main procedures, used for WNP and sensor placement, respectively. These procedures, both derived from the scientific literature, are described in the following Sections 2.1 and 2.2, respectively. Section 2.3 deals with the postprocessing of the sensor placement solutions obtained in Section 2.2.
