## 8A Systems modelling

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## Stefano Alvisi

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## Extended flow control in large pressure dependent demand models

Jochen W. Deuerlein

Presenter:

Authors:

Jochen W. Deuerlein, Olivier Piller, Elhay Sylvan and Angus R. Simpson

Flow control is an important tool for providing an adequate volume of water to all the consumers, especially in the case when natural resources are limited. Using such flow control devices, it is possible to limit the flow through the pipe to a justifiable threshold. Thus, flow control can be used for providing at least a limited water supply to the entire population, especially in regions that suffer from water scarcity where the demand is higher than the available resources. In combination with proper rehabilitation of leaking pipes, flow control could replace the current wide-spread occurrence of intermittent water supply, which poses a high risk for human health (contaminant intrusion due to regular emptying of pipes) as well as the physical state of the system (transients, water hammer). Hydraulic simulation models are invaluable tools for proper planning of distribution network design. The difficulties that result from the presence of control devices in hydraulic simulation models are well reported in the literature. One prominent problem arises from the fact that mathematically flow control devices add inequality constraints to the hydraulic system equations. For example, the hydraulic steady-state can be formulated as the minimum of the convex Content function. Considering flow control devices, the unconstrained nonlinear optimization problem is replaced by a constrained nonlinear optimization problem where the flow control is represented by box constraints for the link flow. In the first part of this paper, the methods for implementing extensive flow control in pressure dependent hydraulic simulation models is discussed from a theoretical point of view. In the second part of the paper its applicability to large networks is presented. In this context, difficulties arising from degenerate solutions where the Lagrangian multipliers of the active constraints and the constraints themselves are zero are highlighted.

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## How should multiobjective algorithms be guided to reach the Pareto front?

Maria Cunha

Presenter:

Authors:

Maria Cunha and Joao Marques

Various algorithms have been proposed to solve single and multiobjective water distribution networks (WDNs) optimization problems and they usually take objectives related to cost, reliability and the environment into account. One of the most widely used methods is multiobjective evolutionary algorithms (MOEAs). The literature refers the main advantage of MOEAs: they provide a diverse set of non-dominated solutions across the front of the problem; and the main drawback: the low convergence velocities. However recent papers set out the difficulties encountered with some well-known MOEAs when it comes to handling a two objective problem for the design of WDNs. They did not manage to reach the whole Pareto front; the distribution of solutions was non-uniform with high sparsity in large regions of the front in some well-known benchmark problems. In this paper we follow a new avenue to find solutions that can cover the whole range of Pareto solutions, spending the same amount for the number of function evaluations as those authors spent. A multiobjective simulated annealing algorithm is presented and its main features are described. In general terms, single objective simulated annealing algorithms are trajectory algorithms, where, iteration by iteration, a candidate solution in the neighbourhood of current solution (the last accepted solution) is generated. The iterative process to be used in multiobjective optimization problems needs the trajectory concept to be extended. This means that the way candidate solutions are generated, with non-dominated solutions being found in different parts of the solution space, is essential for the success of the Pareto front to be sketched. Thus, the authors propose a novel way to give the algorithm special characteristics of diversification and intensification. This work confirms the importance of guiding multiobjective algorithms by using different types of generation processes to find a well distributed and near optimal set of non-dominated solutions.

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## Flow constraints for designing Water Distribution Systems

Olivier Piller

Presenter:

Authors:

Olivier Piller, Jochen Deuerlein, Sylvan Elhay and Angus Simpson

Water distribution systems (WDSs) have become large, complex interconnected infrastructure elements that need computer tools for their management decision-making and design. An important need that usually arises in long-term planning is where an optimal reinforcement or design of the network is sought. The designer needs to decide which hydraulic device to add, what their settings should be and what should be the characteristics of the pipes. A number of formulations have been proposed in the literature to solve this problem. The most popular developments use meta-heuristic techniques to solve a nonlinear, mixed integer problem that minimizes the total cost with respect to hydraulic integrity and performance constraints. Global sensitivity methods can be used to screen out insensitive decision variables to reduce the computational demand associated with an optimal Pareto front construction. In this research, we explore a novel way to test the influence of the decision variables by introducing, in the pressure-driven, steady-state model, flow constraints qmin<q<qmax on the link flows q. Indeed, it will be shown that: 1) Choosing qmax, which is smaller than the link's unconstrained flow, models the action of a flow control valve; 2) Choosing qmin, which is larger than the link's unconstrained flow, models the action of a pump; 3) Constraining the flow rate signs models check valves; 4) Fixing the flow to zero models a closed valve; 5) And choosing the capacities of the links amounts to determining link flow characteristics. A pressure-driven framework is used. Signed Lagrange multipliers are introduced for inequality constraints, and unsigned Lagrange multipliers for equality constraints. They can be interpreted as local head losses or gains. A Newton method is used to solve the saddle-point problem that generalises the GGA algorithm and the method is illustrated on a small case study.

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## Upgrade of the GISRed application for the free analysis of WDN under GIS environment

Fernando Martinez Alzamora

Presenter:

Authors:

Fernando Martinez Alzamora, Nestor Lerma Elvira, Hugo Bartolin Ayala and Oscar T. Vegas Niño

Since version 1.0 of the GISRed application, developed by our research group as an extension of ArcView 3.2, was launched in 2004, there has not been any similar public product integrating EPANET with a GIS offering so many features and analysis capabilities. Unfortunately ArcView 3.2 was soon discontinued as a separate product, and therefore, the Avenue language in which the GISRed application was developed through more than 600 scripts and many dialogs. From that time onwards GIS tools have advanced significantly, some of them developed in the public domain such as QGIS or gvSIG. Also the EPANET simulator has experienced many improvements, particularly its Toolkit through the repository. The purpose of this communication is to show the new version of GISRed adapted to the changes that have taken place since then. The core has been developed in C# under Visual Studio and can be linked to work in other environments, being the integration in QGIS the matter of this paper. The new application keeps all features of the previous one, such as the project manager, import data from other sources, dialogs to edit all the scenario data, error checker, elevation interpolation, demand allocation facilities, topological analysis, etc. Besides exporting the INP file, it allows to run directly the model using the EPANET’s Toolkit and recover the results to show them on the same environment under different formats. The new version has been extended to manage many auxiliary network components, such as manual valves, house connections, hydrants, meters, etc. which may optionally be incorporated into the model or simply taken them into account to build the model. The new version has built-in powerful spatial analysis tools, which prevent the user from having to relate the elements each other, so that the arc-node or valve-pipe topology is automatically rebuild whenever needed.

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## A Diameter Probability Distribution Genetic Algorithm for Least-cost Water Distribution Network Design

Matthew Johns

Presenter:

Authors:

Matthew Johns, Herman Mahmoud, Edward Keedwell and Dragan Savic

Evolutionary Algorithms (EAs) have been applied to the least-cost Water Distribution Network (WDN) design problem for decades. However, the application of EAs to complex real-world networks has been limited in the literature due to the significant compute time required to evaluate solutions. To address this issue, some researchers have investigated reducing the solution space in which the algorithm searches, effectively limiting the algorithm’s search to areas where the optimal solution is thought to reside. In this paper we propose a method which uses search data from previous EA runs to generate Diameter Probability Distributions (DPDs) for use in an EA’s mutation operator. The resultant Diameter Probability Distribution Genetic Algorithm (DPD-GA) is designed to reduce the search space, improving algorithm performance whilst maintaining solution optimality. A standard GA is used on three small/medium WDN problems to generate the DPDs for use in the DPD-GA’s mutation operator. DPD-GA was tested on a large WDN problem that was unseen by the DPD-GA approach prior to testing. The new algorithm exhibits faster convergence than that of a standard GA, ultimately achieving a better solution. This paper demonstrates the potential for an EA to utilise data from previous optimisation runs on different WDN problems to reduce a problems’ search space. Specifically, the DPD derived from short automated runs of a GA on small problems have learned the relationship between pipe influence and a useful diameter range. The developments presented in this paper point to EAs that could effectively learn how to solve WDN problems more efficiently each time they are tasked with a different WDN problem. Furthermore, it suggests that an algorithm trained on small benchmark problems could be used to effectively solve much larger industrial WDNs with minimal parameter tuning.