icccbe2010© Nottingham University PressProceedings of the International Conference on Computing in Civil and Building Engineering W Tizani (Editor)

Abstract The paper presents a genetic algorithm (GA) formulation to assist in developing the design of a water distribution network (WDN). WDNs are systems which consist of many components which are used to supply water to the point of consumption. Water distribution components include water sources, pipe lines, storage facilities, pumping stations, treatment plants and demand areas. The design of a WDN has many variable parameters such as position and size of the water sources, position and the size of the pipes and position of the treatment plants. However, the layout of the WDN is constrained by the location of existing facilities such as streets and buildings and other geographic features. The total costs of WDNs may consist of the cost of network materials such as pipes, construction works and system operation and maintenance.

Several authors have discussed the use of genetic algorithms (GAs) to optimise WDNs. Most of those authors take a subset of features of WDNs rather than the whole problem. For example, some researches considered the cost to be composed of pipe size and power required and others considered reliability of supply to the demand areas.

This paper describes a GA approach to a WDN design which adopts a broader fitness function to optimise. The paper contains a discussion of the possible GA formulation for WDN. Several breading options have been tested with the selected coding. These will be presented and the best method will be identified.

The paper concludes that the produced network depends on the parameters used in the world definition and the fitness function. The study describes future work on a framework in which GAs might be integrated with GIS to provide a practical design technique. A decision rule can be applied to how flow can be supplied from any node which is a matter of physics and management policy. The future improvements could be a decision mechanism which highlights the importance of each demand area.

Keywords: genetic algorithms, water distribution networks, optimisation, GIS, design

1 Introduction to Water Distribution Networks (WDN) Genetic algorithms have proved to be successful in solving the whole set of large and complex water distribution system optimisation problems such as network design and rehabilitation (Savic and Walters, 1997b; Simpson et al., 1994; Walters et al., 1999) and water resources planning and management (Dandy et al., 1996). The optimal network design is complicated due to nonlinear

Using genetic algorithms (GAs) to assist in the design of a water distribution network

Karwan Ghazi Fendi, Botan Ahmad AL-Hadad & Michael J Mawdesley The University of Nottingham, UK

relationship between flow and head loss and the presence of discrete variables, such as market pipe sizes (Dandy et al., 1996; Eiger et al., 1994).

GAs can be used to minimise the cost of the water transfer from a specific location (Lund and Israel, 1995; Simpson et al., 1994). In addition, GAs is also used to optimise other components of the network such as minimising the length of the pipelines (Prasad and Park, 2004) and the power required to pump the water to relatively remote areas from the water source or water treatment plants (Halhal et al., 1997; Vairavamoorthy and Ali, 2000). Furthermore, GAs can also be used in maximising the reliability of the water distribution networks by designing reliable loops with suitable pipe diameter (Prasad et al., 2003; Tolson et al., 2004).

Some GA studies included minimising the cost of construction, operation and maintenance and maximising the reliability of WDN (Halhal et al., 1997; Savic and Walters, 1997a; Dandy and Engelhardt, 2001; Dandy and Engelhardt, 2006). Other studies addressed the change from current layout to a cheaper one. The new layout may include all possible connections in the network to satisfy a predefined level of reliability (Afshar et al., 2005). Furthermore, GA models can be expanded to optimise WDN rehabilitation not only to involve new pipes but also to involve pumping and water storage tank installations (Walters et al., 1999).

None of these studies tackled the problem of minimising network pipe length, land access cost where the pipe line is passing through and the cost of water delivery to a demand area. Shorter pipe lines reduce the cost of the pipelines. Every land has an access cost to place a pipeline. For example, access cost to place a pipe across a river is more expensive than placing a pipe line in a flat area. The system must be able to deliver water to demand areas which means that a demand node must be connected to a source node. The proposed method in this work can be for other network types such as gas, sewer and road networks.

In this paper, a possible GA formulation for WDN is discussed. A possible chromosome representation and fitness function formulation are presented in this work. Section 3 demonstrates the model. Section 4 extracts conclusions and possible extensions to this work.

2 Possible GA formulation for WDN

2.1 Introduction In this paper, a water distribution network is defined as a network of pipes links any number of water sources with any number of demand areas. Other features which will be contained within a real WDN are not considered in this paper. The problem is therefore to find a network of pipes (location and size) which optimise some function.

The GA formulation consists of five parts. 1- The world: represents the physical features such as roads, rivers and buildings. 2- The grid: is a raster grid placed over the world. This can be of any scale and is used to

approximate the world. 3- The chromosome: is the representation of an individual possible solution to the problem. 4- The fitness function: is used to evaluate each individual possible solution. 5- The breeding process: this consists of the operators used to enable two individuals to combine

other solutions. These are discussed individually below.

2.2 The world The world data are the information which describes the world for which the model will be built. This information includes the boundary of the world.

The world includes terrain, rivers, roads, buildings and water sources. It also includes land use areas such residential, industrial and agriculture. The land use determines what water is required (demanded) by an area. The world is always assumed to be rectangular. The cost of crossing any particular part of the world is determined by the features in that part. World data are available from GIS databases.

2.3 Raster grid A rectangular grid is placed over the whole world. The grid size determines the minimum dimensions of features that can be modelled.

The smaller the grid size, the more details can be modelled but the larger the problem for a given size of world.

World data for each grid element can be extracted from a GIS database. A cost will be incurred for placing a water pipe across any given grid element. The cost will

depend on the world features in that element.

2.4 Chromosome representation The chromosome is the representation of a physical feature to the problem. In this case it must contain:

1- The nodes to the network which must be positioned within the world. It is therefore necessary to include their three dimensional coordinates (x,y,z) and their type. The node type determines whether nodes are a source of water, demand areas or intermediate nodes. For source and demand nodes, the amount of water available or required is necessary.

2- The connection between the nodes which represents the pipes along which the water will flow. In the initial model defined here, the properties of a connection are limited to:

a. The start and end of nodes. b. The pipe diameter. For this problem formulation, only standard pipe diameters are

allowed. Pipes are assumed to be straight lines between the terminal nodes. An example of a chromosome is shown in figure 1.

Figure 1. The Chromosome Representation

2.5 Fitness function The main objective of the design of water distribution networks is to supply water in sufficient quantities at a reasonable cost to existing and future consumers.

The adopted fitness function in this work consists of the cost of pipes and their installation and the benefit from the supply of water.

The chosen fitness function can be written as: Fitness Function = Cost of pipes & installation + Land Access Cost – Payment to the supplier (1) The cost of the pipes and their installation is a cost unit multiplied by the length of the pipe.

Different diameter sizes have different material and installation costs. Land access cost is the cost of crossing a specific area. Different land uses have different costs. For

instance, rough terrain access cost is higher than flat terrain and access cost of city centres is different from city outskirts.

The third part of the fitness function is the payment to the supplier. The payment is the amount of water delivered to demand area multiplied by the unit cost of the supplied water. The importance of demand areas are taken into consideration when the water is delivered to the demand areas. The amount of supplied water depends on capacity of the source, the required demand and the capability of the pipe system to deliver the water. In this paper, a single water source is used and assumed to be sufficient to deliver water to all demand areas.

2.6 Breeding process

2.6.1 Crossover

Several crossover types have been developed. A single point crossover is used to exchange the information between the two individuals. The one used for the demonstration in this paper is illustrated in figure 2.

Figure 2. Crossover (Crossover node is 4)

Crossover operator works when parent 1 passes the connectivity matrix and the position matrix strings to the top part of the crossover point to child 1. Similarly, parent 2 passes its code strings to the top part of the same crossover point of child 2. Then, the bottom code of the crossover point of both matrices for parent 1 goes to child 2 and parent 2 passes its code to child 1. As a result of this operator, the offspring contain code information of both parents.

2.6.2 Mutation

The mutation alters the links between nodes and changes the location of the nodes according to the mutation rate where different mutation rates are assigned to each matrix. The mutation chooses a random cell in the connectivity matrix and assigns an available pipe diameter randomly or zero where no connectivity (pipe) between nodes exists. The mutation of node position alters the position of nodes within the boundary of the world.

Crossover position 

3 Example In order to demonstrate the use of the system, consider a new town which is to be built as shown in figure 3.

Figure 3. The world model

The dimensions of world in the example world are 5 x 5 km. The selected cell size is 100m. The town includes 9 demand areas, a green area and a city centre. A rail and a river pass the city.

This is based on a real town in the UK and the dimensions and the areas might therefore thought be of as realistic.

The single source is a fixed node and placed by the river. For this example, the example is limited to 13 nodes. These parameters that are used to demonstrate the model are shown in figure 4.

Figure 4. GA parameters and other features (main model Interface)

This problem had been ‘solved’ using a GA. A typical solution is shown in figure 5a. The actual estimation obtained will vary depending on decisions which can be made by the designers. For example, figure 5b shows a solution for the same problem but with a changed location for the source node.

Evaluating such alternatives adds to the power of the process as part of a decision support system.

(a) The source is outside the city (b) The source is placed inside the city Figure 5. Different water source locations

4 Conclusions The produced network depends on the parameters used in the world definition and the fitness function. The best breeding features need to be investigated. A decision rule can be applied to how flow can be supplied from any node which is a matter of physics and management policy. The future improvements could be a decision mechanism which highlights the importance of each demand area. This mechanism controls the amount of water flow to a demand.

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