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Improved genetic algorithm optimization of water distribution
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system design by incorporating domain knowledge
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Bi W., Dandy G. C. and Maier H. R.
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Bi W.: Corresponding author, PhD student, School of Civil, Environmental and Mining
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Engineering, University of Adelaide, Adelaide, South Australia, 5005, Australia.
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[email protected]. Tel: +61-8-83136139.
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Postal address: N223, Engineering North, School of Civil, Environmental and Mining
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Engineering, North Terrace Campus, University of Adelaide, Adelaide, South Australia,
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5005, Australia.
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Dandy G. C.: Professor, School of Civil, Environmental and Mining Engineering,
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University
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[email protected].
of
Adelaide,
Adelaide,
South
Australia,
5005,
Australia.
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Maier H. R.: Professor, School of Civil, Environmental and Mining Engineering,
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University
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[email protected].
of
Adelaide,
Adelaide,
South
Australia,
5005,
Australia.
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Citation: Bi W., Dandy G.C. and Maier H.R. (2015) Improved genetic algorithm optimization of water distribution system design by incorporating domain knowledge, Environmental Modelling and Software, 69, 370-381, DOI: 10.1016/j.envsoft.2014.09.010
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Abstract: Over the last two decades, evolutionary algorithms (EAs) have become a popular
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approach for solving water resources optimization problems. However, the issue of low
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computational efficiency limits their application to large, realistic problems. This paper
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uses the optimal design of water distribution systems (WDSs) as an example to illustrate
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how the efficiency of genetic algorithms (GAs) can be improved by using heuristic domain
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knowledge in the sampling of the initial population. A new heuristic procedure called the
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Prescreened Heuristic Sampling Method (PHSM) is proposed and tested on seven WDS
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cases studies of varying size. The EPANet input files for these case studies are provided as
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supplementary material. The performance of the PHSM is compared with that of another
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heuristic sampling method and two non-heuristic sampling methods. The results show that
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PHSM clearly performs best overall, both in terms of computational efficiency and the
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ability to find near-optimal solutions. In addition, the relative advantage of using the PHSM
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increases with network size.
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Keywords: Optimization; Genetic algorithms, Water distribution systems; domain
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knowledge; heuristics; computational efficiency.
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1. Introduction
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Evolutionary algorithms (EAs) have been used successfully and extensively for solving
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water resources optimization problems in a number of areas, such as engineering design,
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the development of management strategies and model calibration (Nicklow et al., 2010;
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Zecchin et al., 2012). However, a potential shortcoming of EAs is that they are
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computationally inefficient, especially when applied to problems of realistic size.
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Consequently, there is a need to improve the computational efficiency of EAs to make them
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easier to use for the optimization of realistic water resources problems (Maier et al., 2014).
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One application area where this is the case of is the design of water distribution systems
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(WDSs) (Marchi et al., 2014; Stokes et al., 2014). Over the past two decades, a variety of
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EAs have been applied to this problem, as detailed in Zheng et al. (2013a). Among these,
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genetic algorithms (GAs) have been used most extensively (Simpson et al., 1994; Dandy et
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al., 1996, Gupta et al., 1999; Vairavamoorthy et al., 2005; Krapivka and Ostfeld, 2009;
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Kang and Lansey, 2012; Zheng et al., 2013b). However, GAs have been primarily applied
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to relatively simple benchmark problems, such as the 14-pipe problem (Simpson et al.,
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1994), the New York Tunnels problem with 21 tunnels (Dandy et al., 1996), and the Hanoi
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problem with 34 pipes (Zheng et al., 2011a). In recent years, there has been a move towards
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increasing the complexity and realism of the case studies to which GAs are applied,
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including the Balerma network with 454 pipes (Reca and Martínez, 2006), the Rural
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network with 476 pipes (Marchi et al., 2012), the BWN-II network with 433 pipes (Zheng
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et al., 2013c), and the network used by Kang and Lansey (2012), which has 1274 pipes and
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will be referred to as the “KL” network for the remainder of this paper.
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Increased network size and complexity result in significant challenges in terms of
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achieving good quality near-optimal solutions given the computational budgets that are
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typically available in practice (di Pierro et al., 2009; Fu et al., 2012). This is because (i) the
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time for hydraulic simulation increases appreciably for large WDSs; and (ii) the complexity
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and size of the search space associated with a large WDS are increased significantly. As a
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result, computational efficiency has been identified as a key concern for the widespread
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uptake of GAs for the optimization of large, real-world WDSs (di Pierro et al., 2009).
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In order to address this issue, two main approaches have been adopted in the literature.
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As part of the first approach, it is argued that for large, real problems, the focus should be
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on finding the best possible solution within a realistic computational budget, rather than on
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attempting to find the global optimal solution (e.g. Tolson and Shoemaker, 2007; Gibbs et
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al., 2008; Tolson et al., 2009; Gibbs et al., 2010, 2011). This is because for such large
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problems, the global optimal solution is unlikely to be found within a reasonable
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computational timeframe.
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As part of the second approach, efforts have been made to increase the computational
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efficiency of the optimization process. This has been done in a number of ways, including
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the use of increased computational power, such as parallel and distributed computing (Wu
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and Zhu, 2009; Roshani and Filion, 2012; Wu and Behandish, 2012), the use of surrogate-
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and meta-modeling to speed up the simulation process (e.g. Broad et al,. 2005; di Pierro et
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al., 2009; Broad et al., 2010; Razavi et al., 2012), and the seeding of the initial population
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of EAs with good solutions obtained using a variety of analytical techniques (e.g. Keedwell
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and Khu, 2006; Zheng et al., 2011a; Fu et al., 2012; Zheng et al. 2014(a,b,c)). It should be
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noted that similar concepts have recently also been used in conjunction with other
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optimization techniques (e.g. Zhang et al., 2013; Housh et al., 2013) and non-optimization
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based WDS design approaches (e.g. Sitzenfrei et al, 2013).
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Although some of the methods mentioned above utilize engineering knowledge in their
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development (e.g. Keedwell and Khu, 2006; Zheng et al., 2011a), there have been limited
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attempts to incorporate engineering knowledge and experience directly. Only Kang and
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Lansey (2012) have combined engineering experience with GAs in order to increase the
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computational efficiency of the optimization process. This was achieved by seeding half of
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the initial GA population with solutions that result in flow velocities below a threshold
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selected from within a pre-defined velocity range. However, the approach has only been
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applied to a single case study thus far and its relative performance has not yet been assessed
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in a rigorous and comprehensive manner. In addition, the approach has a number of
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potential shortcomings. Firstly, selection of an appropriate range for the velocity threshold
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is subjective, which might make the method difficult to apply and could result in
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inconsistent results from repeated, independent implementation of the method. Secondly,
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pipe sizes that result in appropriate velocities are determined using a structured trial-and4
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error process. However, in practice, pipe sizes generally reduce with distance from the
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source (Walski, 2001). Consequently, there exists an opportunity to incorporate this domain
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knowledge into the initial pipe sizing process. Finally, there is limited control over
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population diversity, as this is achieved by seeding the initial population with 50% of
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randomly generated solutions and 50% of the solutions obtained based on engineering
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experience.
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In order to address these shortcomings, the objectives of this paper are (i) to introduce a
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new heuristic sampling method for determining the initial population of GAs for the least-
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cost design of WDSs that is based on engineering experience / domain knowledge and that
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overcomes the potential shortcomings of the method of Kang and Lansey (2012); and (ii) to
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provide a rigorous assessment of the performance of this method compared with that of
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Kang and Lansey’s sampling method (KLSM) and two sampling methods that do not
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consider any domain knowledge (i.e. random sampling (RS) and Latin hypercube sampling
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(LHS)) on seven WDS design case studies of varying size and complexity.
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The remainder of this paper is organized as follows. The proposed heuristic, domain
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knowledge based sampling method for determining the initial population of GAs for the
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least-cost design of WDSs is introduced in next section, followed by the methodology for
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assessing the performance of this method against that of the KLSM and the two non-
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heuristic sampling methods. Next, the results are presented and discussed, followed by a
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summary and conclusions.
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2. Proposed prescreened heuristic sampling method for WDS design
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The proposed heuristic sampling method for initializing the population of GAs for the
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least-cost design of WDSs based on domain knowledge is called the Prescreened Heuristic
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Sampling Method (PHSM). It uses a three-step procedure that (i) selects pipe sizes based
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on knowledge that pipe diameters generally get smaller the further they are from the source;
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(ii) dynamically adjusts the velocity threshold to account for the fact that appropriate
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velocity thresholds are likely to be network dependent; and (iii) enables the diversity of the
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initial population to be controlled by sampling from distributions centred on the solutions
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determined using the heuristic procedures in (i) and (ii). The PHSM has some similarities to
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the KLSM in that it aims to find initial pipe sizes that restrict flow velocities to lie within 5
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certain ranges. However, it overcomes the potential limitations of the KLSM outlined in the
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Introduction. Details of the three steps of the PHSM are given below.
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Step 1: Assign pipe diameters based on distances between demand nodes and supply
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sources
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As mentioned above, the first step of the PHSM is motivated by the knowledge that, in
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real WDSs, the diameters of upstream pipes are generally larger than those further
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downstream (Walski, 2001). However, for WDSs, each demand node usually has a number
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of different paths that connect it to the supply source (reservoir). This indicates that the
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spatial distance between each demand node and the reservoir may vary according to the
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paths selected to deliver the required demands. In the proposed method, the shortest
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delivery path to each demand node is selected and used to represent the spatial distance
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between that node and the source node. The rationale behind this is that it has been
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demonstrated that the majority of the demand at a node is supplied by the path with the
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shortest distance for an optimal design of WDSs (Zheng et al., 2011a). The detailed process
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of step 1 of the PHSM is as follows:
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i: Find the shortest distance to a reservoir in the water network, li for each node i
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(i=1,2…..,n, where n is the total number of demand nodes in the network) using
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the Dijkstra algorithm (Deo 1974). When dealing with a water network with
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multiple reservoirs, an augmented source node is created to connect all the
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reservoirs to enable the determination of li following Deuerlein (2008) and
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Zheng et al. (2011a).
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ii: Obtain the largest value of the shortest distance L by L=max(li).
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iii: Divide the network into P specific areas with the shortest distance to the source
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node interval of L/P, where P is the number of available pipe diameters for the
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design.
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iv: Assign pipes in each area a different diameter, with the largest diameter
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assigned to the pipes in the area nearest to the source and the smallest diameter
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to the pipes in the area furthest from the source (reservoir). All pipes in a single
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area are assigned the same diameter.
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For example, for the WDS introduced by Zheng et al. (2011a), which has 164 pipes
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(Figure 1), the largest shortest distance of all nodes (L) is obtained after steps i and ii. If
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there are five diameter options for this network (i.e. P=5), the network will be divided into
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five areas in step iii. In order to do this (i) all nodes that have a shortest-distance that is not
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greater than L/P (i.e. 0
