Pipe smoothing genetic algorithm for least cost water distribution network design

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.GECCO '13 Proceedings of the 15th annual conference on Genetic and evolutionary computation Amsterdam, Netherlands — July 06 - 10, 2013This paper describes the development of a Pipe Smoothing Genetic Algorithm (PSGA) and its application to the problem of least cost water distribution network design. Genetic algorithms have been used widely for the optimisation of both theoretical and real-world non-linear optimisation problems, including water system design and maintenance problems. In this work we propose a pipe smoothing based approach to the creation and mutation of chromosomes which utilises engineering expertise with the view to increasing the performance of the algorithm compared to a standard genetic algorithm. Both PSGA and the standard genetic algorithm were tested on benchmark water distribution networks from the literature. In all cases PSGA achieves higher optimality in fewer solution evaluations than the standard genetic algorithm

Multi-Objective Pipe Smoothing Genetic Algorithm For Water Distribution Network Design

This paper describes the formulation of a Multi-objective Pipe Smoothing Genetic Algorithm (MOPSGA) and its application to the least cost water distribution network design problem. Evolutionary Algorithms have been widely utilised for the optimisation of both theoretical and real-world non-linear optimisation problems, including water system design and maintenance problems. In this work we present a pipe smoothing based approach to the creation and mutation of chromosomes which utilises engineering expertise with the view to increasing the performance of the algorithm whilst promoting engineering feasibility within the population of solutions. MOPSGA is based upon the standard Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and incorporates a modified population initialiser and mutation operator which directly targets elements of a network with the aim to increase network smoothness (in terms of progression from one diameter to the next) using network element awareness and an elementary heuristic. The pipe smoothing heuristic used in this algorithm is based upon a fundamental principle employed by water system engineers when designing water distribution pipe networks where the diameter of any pipe is never greater than the sum of the diameters of the pipes directly upstream resulting in the transition from large to small diameters from source to the extremities of the network. MOPSGA is assessed on a number of water distribution network benchmarks from the literature including some real-world based, large scale systems. The performance of MOPSGA is directly compared to that of NSGA-II with regard to solution quality, engineering feasibility (network smoothness) and computational efficiency. MOPSGA is shown to promote both engineering and hydraulic feasibility whilst attaining good infrastructure costs compared to NSGA-II

Multi-objective pipe smoothing genetic algorithm for water distribution network design

Session S6-03, Special Session: Evolutionary Computing in Water Resources Planning and Management IIIThis paper describes the formulation of a Multi-objective Pipe Smoothing Genetic Algorithm (MOPSGA) and its application to the least cost water distribution network design problem. Evolutionary Algorithms have been widely utilised for the optimisation of both theoretical and real-world non-linear optimisation problems, including water system design and maintenance problems. In this work we present a pipe smoothing based approach to the creation and mutation of chromosomes which utilises engineering expertise with the view to increasing the performance of the algorithm whilst promoting engineering feasibility within the population of solutions. MOPSGA is based upon the standard Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and incorporates a modified population initialiser and mutation operator which directly targets elements of a network with the aim to increase network smoothness (in terms of progression from one diameter to the next) using network element awareness and an elementary heuristic. The pipe smoothing heuristic used in this algorithm is based upon a fundamental principle employed by water system engineers when designing water distribution pipe networks where the diameter of any pipe is never greater than the sum of the diameters of the pipes directly upstream resulting in the transition from large to small diameters from source to the extremities of the network. MOPSGA is assessed on a number of water distribution network benchmarks from the literature including some real-world based, large scale systems. The performance of MOPSGA is directly compared to that of NSGA-II with regard to solution quality, engineering feasibility (network smoothness) and computational efficiency. MOPSGA is shown to promote both engineering and hydraulic feasibility whilst attaining good infrastructure costs compared to NSGA-II

An analysis of the interface between evolutionary algorithm operators and problem features for water resources problems. A case study in water distribution network design

Open Access articleEvolutionary Algorithms (EAs) have been widely employed to solve water resources problems for nearly two decades with much success. However, recent research in hyperheuristics has raised the possibility of developing optimisers that adapt to the characteristics of the problem being solved. In order to select appropriate operators for such optimisers it is necessary to first understand the interaction between operator and problem. This paper explores the concept of EA operator behaviour in real world applications through the empirical study of performance using water distribution networks (WDN) as a case study. Artificial networks are created to embody specific WDN features which are then used to evaluate the impact of network features on operator performance. The method extracts key attributes of the problem which are encapsulated in the natural features of a WDN, such as topologies and assets, on which different EA operators can be tested. The method is demonstrated using small exemplar networks designed specifically so that they isolate individual features. A set of operators are tested on these artificial networks and their behaviour characterised. This process provides a systematic and quantitative approach to establishing detailed information about an algorithm's suitability to optimise certain types of problem. The experiment is then repeated on real-world inspired networks and the results are shown to fit with the expected results.Engineering and Physical Sciences Research Council (EPSRC

Automated construction of evolutionary algorithm operators for the bi-objective water distribution network design problem using a genetic programming based hyper-heuristic approach

The water distribution network (WDN) design problem is primarily concerned with finding the optimal pipe sizes that provide the best service for minimal cost; a problem of continuing importance both in the UK and internationally. Consequently, many methods for solving this problem have been proposed in the literature, often using tailored, hand-crafted approaches to more effectively optimise this difficult problem. In this paper we investigate a novel hyper-heuristic approach that uses genetic programming (GP) to evolve mutation operators for evolutionary algorithms (EAs) which are specialised for a bi-objective formulation of the WDN design problem (minimising WDN cost and head deficit). Once generated, the evolved operators can then be used ad infinitum in any EA on any WDN to improve performance. A novel multi-objective method is demonstrated that evolves a set of mutation operators for one training WDN. The best operators are evaluated in detail by applying them to three test networks of varying complexity. An experiment is conducted in which 83 operators are evolved. The best 10 are examined in detail. One operator, GP1, is shown to be especially effective and incorporates interesting domain-specific learning (pipe smoothing) while GP5 demonstrates the ability of the method to find known, well-used operators like a Gaussian. © IWA Publishing 2014J.Engineering and Physical Sciences Research Council (EPSRC)Mouchel Ltd

Knowledge-based multi-objective genetic algorithms for the design of water distribution networks

This is the author accepted manuscript. The final version is available from IWA Publishing via the DOI in this recordWater system design problems are complex and difficult to optimise. It has been demonstrated that involving engineering expertise is required to tackle real-world problems. This paper presents two engineering inspired hybrid evolutionary algorithms for the multiobjective design of water distribution networks. The heuristics are developed from traditional design approaches of practicing engineers and integrated into the mutation operator of a multi-objective evolutionary algorithm. The first engineering inspired heuristic is designed to identify hydraulic bottlenecks within the network and eliminate them with a view to speeding up the algorithm’s search to the feasible solution space. The second heuristic is based on the notion that pipe diameters smoothly transition from large, at the source, to small at the extremities of the network. The performance of the engineering inspired hybrid evolutionary algorithms is compared to NSGA-II and assessed on three networks of varying complexity, two benchmarks and one real-world network. The experiments presented in this paper demonstrate that the incorporation of engineering expertise can improve evolutionary algorithm performance often producing superior solutions both in terms of mathematical optimality but also engineering feasibility.Engineering and Physical Sciences Research Council (EPSRC

Incorporating Domain Expertise into Evolutionary Algorithm Optimisation of Water Distribution Systems

Evolutionary Algorithms (EAs) have been widely used for the optimisation of both theoretical and real-world non-linear problems, although such optimisation methods have found reasonably limited utilisation in fields outside of the academic domain. While the causality of this limited uptake in non-academic fields falls outside the scope of this thesis, the core focus of this research remains strongly influenced by the notions of solution feasibility and making optimisation methods more accessible for engineers, both factors attributed to low EA adoption rates in the commercial space. This thesis focuses on the application of bespoke heuristic methods to the field of water distribution system optimisation. Water distribution systems are complex entities that are difficult to model and optimise as they consist of many interacting components each with a set of considerations to address, hence it is important for the engineer to understand and assess the behaviour of the system to enable its effective design and optimisation. The primary goal of this research is to assess the impact that incorporating water systems knowledge into an evolution algorithm has on algorithm performance when applied to water distribution network optimisation problems. This thesis describes the development of two heuristics influenced by the practices of water systems engineers when designing water distribution networks with the view to increasing an algorithm’s performance and resultant solution feasibility. By utilising heuristics based on engineering design principles and integrating them into existing EAs, it is found that both engineering feasibility and general algorithmic performance can be notably improved. Firstly the heuristics are applied to a standard single-objective EA and then to a multi-objective genetic algorithm. The algorithms are assessed on a number of water distribution network benchmarks from the literature including real-world based, large scale systems and compared to the standard variants of the algorithms. Following this, a set of extensive experiments are conducted to explore how the inclusion of water systems knowledge impacts the sensitivity of an evolutionary algorithm to parameter variance. It was found that the performance of both engineering inspired algorithms were less sensitive to parameter change than the standard genetic algorithm variant meaning that non-experts in the field of meta-heuristics will potentially be able to get much better performance out of the engineering heuristic based algorithms without the need for specialist evolutionary algorithm knowledge. In addition this research explores the notion that visualisation techniques can provide water system engineers with a greater insight into the operation and behaviour of an evolutionary algorithm. The final section of this thesis presents a novel three-dimensional representation of pipe based water systems and demonstrates a range of innovative methods to convey information to the user. The interactive visualisation system presented not only allows the engineer to visualise the various parameters of a network but also allows the user to observe the behaviour and progress of an iterative optimisation method. Examples of the combination of the interactive visualisation system and the EAs developed in this work are shown to enable the user to track and visualise the actions of the algorithm. The visualisation aggregates changes to the network over an EA run and grants significant insight into the operations of an EA as it is optimising a network. The research presented in this thesis demonstrates the effectiveness of integrating water system engineering expertise into evolutionary based optimisation methods. Not only is solution quality improved over standard methods utilising these new heuristic techniques, but the potential for greater interaction between engineer, problem and optimiser has been established

Planar Graph Generation with Application to Water Distribution Networks

The study of network representations of physical, biological, and social phenomena can help us better understand their structure and functional dynamics as well as formulate predictive models of these phenomena. However, in some applications there is a deficiency in real-world data-sets for research purposes due to such reasons as the data sensitivity and high costs for data retrieval. Research related to water distribution networks often relies on synthetic data because the real-world is data is not publicly available due to the sensitivity towards theft and misuse. An important characteristic of water distribution systems is that they can be embedded in a plane, therefore to simulate these system we need realistic networks which are also planar. Currently available synthetic network generators can generate networks that exhibit realism but the planarity is not guaranteed. On the other hand, existing water network generators do not guarantee similarity with the input network and do not scale. In this thesis, we present a flexible method to generate realistic water distribution networks with optimized network parameters such as pipe and tank diameters, tank minimum and maximum levels, and pump sizes. Our model consists of three stages. First, we generate a realistic planar graph from a known water network using the multi-scale randomized edit- ing. Next, we add physical water network characteristics such as pumps, pipes, tanks, and reservoirs to the obtained topology to generate a realistic synthetic water distribution system that can be used for simulation. Finally, we optimize the operational parameters using EPANet simulation tool and multi-objective optimization solver to generate a network with maximum resilience and minimum cost

Development of the Next Generation of Water Distribution Network Modelling Tools Using Inverse Methods

The application of optimisation to Water Distribution Network (WDN) Modelling involves the use of computer-based techniques to many different problems, such as leakage detection and localisation. The success in the application of any model-based methodology for finding leaks highly depends on the availability of a well-calibrated model. Both leak detection and localisation, as well as model calibration are procedures that constitute the field of inverse problems in WDN modelling. The procedures are interlinked and dependent as when a leak is found and the model is updated its quality improves, while when a model is calibrated its ability to detect and localise leaks also improves. This is because both inverse problems are solved with the aim to mimic the behaviour of the real system as closely as possible using field measurements. In this research, both inverse problems are formulated as constrained optimisation problems. Evolutionary Optimisation techniques, of which Genetic Algorithms are the best-known examples, are search methods that are increasingly applied in WDN modelling with the aim to improve the quality of a solution for a given problem. This, ultimately, aids practitioners in these facets of management and operation of WDNs. Evolutionary Optimisation employs processes that mimic the biological process of natural selection and “survival of the fittest” in an artificial framework. Based on this philosophy a population of individual solutions to the problem is manipulated and, over time, “evolves” towards optimal solutions. However, such algorithms are characterised by large numbers of function evaluations. This, coupled with the computational complexity associated with the hydraulic simulation of WDNs incurs significant computational burden, can limit the applicability and scalability of this technology across the Water Industry. In addition, the inverse problem is often “ill-posed”. In practice, the ill-posed condition is typically manifested by the non-uniqueness of the problem solution and it is usually a consequence of inadequate quantity and/or quality of field observations. Accordingly, this thesis presents a methodology for applying Genetic Algorithms to solve leakage related inverse problems in WDN Modelling. A number of new procedures are presented for improving the performance of such algorithms when applied to the complex inverse problems of leak detection and localisation, as well as model calibration. A novel reformulation of the inverse problem is developed as part of a decision support framework that minimizes the impact of the inherent computational complexity and dimensionality of these problems. A search space reduction technique is proposed, i.e., a reduction in the number of possible solution combinations to the inverse problem, to improve its condition considering the accuracy of the available measurements. Eventually, this corresponds to a targeted starting point for initiating the search process and therefore more robust stochastic optimisations. The ultimate purpose is to increase the reliability of the WDN hydraulic model in localising leaks in real District Metered Areas, i.e., to reduce the number false positives. In addition, to speed up the leak search process (both computationally and physically) and, improve the overall model accuracy. A calibrated model of the WDN is not always available for supporting work at distribution mains level. Consequently, two separate problem-specific methods are proposed to meet the abovementioned purpose: (a) a Leak Inspection Method used for the detection and localisation of leaks and; (b) a Calibration Method for producing an accurate average day model that is fit for the purpose of leak detection and localisation. Both methods integrate a three-step Search Space Reduction stage, which is implemented before solving the inverse problem. The aim is to minimize the number of decision variables and the range of possible values, while trying to preserve the optimum solution, i.e., reduce the inverse problem dimensionality. The search space reduction technique is established to generate a reduced set of highly sensitive decision variables. Eventually this is done to provide a viable, scalable technique for accelerating evolutionary optimisation applications in inverse problems being worthwhile on both academic and practical grounds. The novel methodologies presented here for leak detection and localisation, as well as for model calibration are verified successfully on four case studies. The case studies include two real WDN examples with artificially generated data, which investigate the limits of each method separately. The other two case studies implement both methods on real District Metered Areas in the United Kingdom, firstly to calibrate the hydraulic network model and, then, to detect and localise a single leak event that has actually happened. The research results suggest that leaks and unknown closed or open throttle valves that cause a hydraulic impact larger than the sensor data error can be detected and localised with the proposed framework which solves the inverse problem after search space reduction. Moreover, the quality of solutions can dramatically improve for given runtime of the algorithm, as 99.99% of infeasible solution combinations are removed, compared to the case where no search space reduction is performed. The outcomes of the real cases show that the presented search space reduction technique can reduce the search area for finding the leak to within 10% of the WDN (by length). The framework can also contribute to more timely detection and localisation of leakage hotspots, thus reducing economic and environmental impacts. The optimisation model for predicting leakage hotspots can be effective despite the recognized challenges of model calibration and the physical measurement limitations from the pressure and flow field tests