Competent genetic-evolutionary optimization of water distribution systems

A genetic algorithm has been applied to the optimal design and rehabilitation of a water distribution system. Many of the previous applications have been limited to small water distribution systems, where the computer time used for solving the problem has been relatively small. In order to apply genetic and evolutionary optimization technique to a large-scale water distribution system, this paper employs one of competent genetic-evolutionary algorithms - a messy genetic algorithm to enhance the efficiency of an optimization procedure. A maximum flexibility is ensured by the formulation of a string and solution representation scheme, a fitness definition, and the integration of a well-developed hydraulic network solver that facilitate the application of a genetic algorithm to the optimization of a water distribution system. Two benchmark problems of water pipeline design and a real water distribution system are presented to demonstrate the application of the improved technique. The results obtained show that the number of the design trials required by the messy genetic algorithm is consistently fewer than the other genetic algorithms

Optimal design of water distribution systems based on entropy and topology

A new multi-objective evolutionary optimization approach for joint topology and pipe size design of water distribution systems is presented. The algorithm proposed considers simultaneously the adequacy of flow and pressure at the demand nodes; the initial construction cost; the network topology; and a measure of hydraulic capacity reliability. The optimization procedure is based on a general measure of hydraulic performance that combines statistical entropy, network connectivity and hydraulic feasibility. The topological properties of the solutions are accounted for and arbitrary assumptions regarding the quality of infeasible solutions are not applied. In other words, both feasible and infeasible solutions participate in the evolutionary processes; solutions survive and reproduce or perish strictly according to their Pareto-optimality. Removing artificial barriers in this way frees the algorithm to evolve optimal solutions quickly. Furthermore, any redundant binary codes that result from crossover or mutation are eliminated gradually in a seamless and generic way that avoids the arbitrary loss of potentially useful genetic material and preserves the quality of the information that is transmitted from one generation to the next. The approach proposed is entirely generic: we have not introduced any additional parameters that require calibration on a case-by-case basis. Detailed and extensive results for two test problems are included that suggest the approach is highly effective. In general, the frontier-optimal solutions achieved include topologies that are fully branched, partially- and fully-looped and, for networks with multiple sources, completely separate sub-networks

Multiobjective evolutionary optimization of water distribution systems : exploiting diversity with infeasible solutions

This article investigates the computational efficiency of constraint handling in multi-objective evolutionary optimization algorithms for water distribution systems. The methodology investigated here encourages the co-existence and simultaneous development including crossbreeding of subpopulations of cost-effective feasible and infeasible solutions based on Pareto dominance. This yields a boundary search approach that also promotes diversity in the gene pool throughout the progress of the optimization by exploiting the full spectrum of non-dominated infeasible solutions. The relative effectiveness of small and moderate population sizes with respect to the number of decision variables is investigated also. The results reveal the optimization algorithm to be efficient, stable and robust. It found optimal and near-optimal solutions reliably and efficiently. The real-world system based optimisation problem involved multiple variable head supply nodes, 29 fire-fighting flows, extended period simulation and multiple demand categories including water loss. The least cost solutions found satisfied the flow and pressure requirements consistently. The cheapest feasible solutions achieved represent savings of 48.1% and 48.2%, for populations of 200 and 1000, respectively, and the population of 1000 achieved slightly better results overall

Penalty-free feasibility boundary convergent multi-objective evolutionary algorithm for the optimization of water distribution systems

This paper presents a new penalty-free multi-objective evolutionary approach (PFMOEA) for the optimization of water distribution systems (WDSs). The proposed approach utilizes pressure dependent analysis (PDA) to develop a multi-objective evolutionary search. PDA is able to simulate both normal and pressure deficient networks and provides the means to accurately and rapidly identify the feasible region of the solution space, effectively locating global or near global optimal solutions along its active constraint boundary. The significant advantage of this method over previous methods is that it eliminates the need for ad-hoc penalty functions, additional “boundary search” parameters, or special constraint handling procedures. Conceptually, the approach is downright straightforward and probably the simplest hitherto. The PFMOEA has been applied to several WDS benchmarks and its performance examined. It is demonstrated that the approach is highly robust and efficient in locating optimal solutions. Superior results in terms of the initial network construction cost and number of hydraulic simulations required were obtained. The improvements are demonstrated through comparisons with previously published solutions from the literature

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

Maximum entropy based evolutionary optimization of water distribution networks under multiple operating conditions and self-adaptive search space reduction method

Previously held under moratorium from 1st December 2016 until 1st December 2021.One of the complexities in designing WDN is evaluation of network performance. The accurate network performance measures such as reliability or failure tolerance are very time consuming calculations, thus surrogate measures are used for water distribution network (WDN) design optimization. Entropy is particularly advantageous since it involves only the flow in the pipe and the demands at the nodes. This thesis developed efficient new computational methods based on the maximum entropy formalism for the optimization of water distribution systems. Thus the maximum entropy based design approach has been extended here to include multiple operation conditions. Also, the path-related properties of the flow entropy have been exploited to develop a new self-adaptive approach for solution space reduction in multiobjective evolutionary optimization of water distribution systems that resulted in a significant reduction in the number of function evaluations required to find optimal and near optimal solutions. The novelty and originality of the current research are presented next. A new penalty-free multi-objective evolutionary optimization approach for the design of WDNs has been developed. It combines genetic algorithm with least cost design and maximum entropy. The approach can handle single operating conditions (SOC) as well as multiple operating conditions (MOC) for any given network. Previously, most of the work has been done for single loading patterns and it was assumed that nodal demands are constant. In reality nodal demand vary over the time so network designed to satisfy one operating condition might not be able to satisfy other loading patterns (i.e. pressure constraints might not be meet). The model has been applied to three well known water distribution networks. The approach has also been implemented on a large real-world network in the literature. Three different methods of designing for multiple loading patterns were investigated. Extensive testing proved that MOC outperform SOC in terms of hydraulic feasibility, pipe size distribution and reliability. The approach is computationally efficient and robust. The above mentioned penalty-free approach has been extended to form a module that would improve the convergence criteria of the GA by reducing its search space. For large real-world network GA might require extremely large number of function evaluations which could lead to delayed convergence. By reducing the search space, the GA’s effectiveness and efficiency will increase as the algorithm will identify the solutions in smaller number of function evaluations. The search space reduction method presented herein is based on entropy and uses the importance of every path through network, which is an inherent property of the entropy function. The developed algorithm is dynamic, self-adaptive and does not require pre-defining the reduced sets of candidate diameters for each pipe. The method has been applied to a large network from the literature. Two cases were studied, one based on full search space and one for reduce search space (RSS) approach. Rapid stabilization was observed for the results obtained using RSS.One of the complexities in designing WDN is evaluation of network performance. The accurate network performance measures such as reliability or failure tolerance are very time consuming calculations, thus surrogate measures are used for water distribution network (WDN) design optimization. Entropy is particularly advantageous since it involves only the flow in the pipe and the demands at the nodes. This thesis developed efficient new computational methods based on the maximum entropy formalism for the optimization of water distribution systems. Thus the maximum entropy based design approach has been extended here to include multiple operation conditions. Also, the path-related properties of the flow entropy have been exploited to develop a new self-adaptive approach for solution space reduction in multiobjective evolutionary optimization of water distribution systems that resulted in a significant reduction in the number of function evaluations required to find optimal and near optimal solutions. The novelty and originality of the current research are presented next. A new penalty-free multi-objective evolutionary optimization approach for the design of WDNs has been developed. It combines genetic algorithm with least cost design and maximum entropy. The approach can handle single operating conditions (SOC) as well as multiple operating conditions (MOC) for any given network. Previously, most of the work has been done for single loading patterns and it was assumed that nodal demands are constant. In reality nodal demand vary over the time so network designed to satisfy one operating condition might not be able to satisfy other loading patterns (i.e. pressure constraints might not be meet). The model has been applied to three well known water distribution networks. The approach has also been implemented on a large real-world network in the literature. Three different methods of designing for multiple loading patterns were investigated. Extensive testing proved that MOC outperform SOC in terms of hydraulic feasibility, pipe size distribution and reliability. The approach is computationally efficient and robust. The above mentioned penalty-free approach has been extended to form a module that would improve the convergence criteria of the GA by reducing its search space. For large real-world network GA might require extremely large number of function evaluations which could lead to delayed convergence. By reducing the search space, the GA’s effectiveness and efficiency will increase as the algorithm will identify the solutions in smaller number of function evaluations. The search space reduction method presented herein is based on entropy and uses the importance of every path through network, which is an inherent property of the entropy function. The developed algorithm is dynamic, self-adaptive and does not require pre-defining the reduced sets of candidate diameters for each pipe. The method has been applied to a large network from the literature. Two cases were studied, one based on full search space and one for reduce search space (RSS) approach. Rapid stabilization was observed for the results obtained using RSS

GALAXY: A new hybrid MOEA for the Optimal Design of Water Distribution Systems

This is the final version of the article. Available from American Geophysical Union via the DOI in this record.The first author would like to appreciate the financial support given by both the University of Exeter and the China Scholarship Council (CSC) toward the PhD research. We also appreciate the three anonymous reviewers, who help improve the quality of this paper substantially. The source code of the latest versions of NSGA-II and ε-MOEA can be downloaded from the official website of Kanpur Genetic Algorithms Laboratory via http://www.iitk.ac.in/kangal/codes.shtml. The description of each benchmark problem used in this paper, including the input file of EPANET and the associated best-known Pareto front, can be accessed from the following link to the Centre for Water Systems (http://tinyurl.com/cwsbenchmarks/). GALAXY can be accessed via http://tinyurl.com/cws-galaxy

Optimising water distribution systems using a weighted penalty in a genetic algorithm

Genetic algorithms (GAs) have become the preferred water system design optimisation technique for many researchers and practitioners. The main reason for using GAs is their ability to deal with nonlinear complex optimisation problems. The optimal decision in terms of designing, expansion/extending, addition or rehabilitation of water supply systems has to review possible options and select a cost-effective and efficient solution. This paper presents a new approach in determining a penalty value depending on the degree of failure, of the set pressure criteria, and the importance of the link supplying a specific node. Further modifications are also made in the cross-over and mutation procedures to ensure an increase in algorithm convergence. EPANET, a widely used water distribution network simulation model, is used in conjunction with the proposed newly developed GA for the optimisation of water distribution systems. The developed GA procedure has been incorporated in a software package called GANEO, which can be used to design new networks, analyse existing networks and prioritise improvements on existing networks. The developed GA has been tested on several international benchmark problems and has proved to be very efficient and robust. The EPANET hydraulic modelling software as well as the developed GANEO software, which performs the optimisation of the water distribution network, is freeware. The software provides a tool for consulting engineers to optimise the design or rehabilitation of a water distribution network.Keywords: optimising, water distribution system, genetic algorith

Lost in optimisation of water distribution systems? A literature review of system design

This is the final version of the article. Available from MDPI via the DOI in this record.Optimisation of water distribution system design is a well-established research field, which has been extremely productive since the end of the 1980s. Its primary focus is to minimise the cost of a proposed pipe network infrastructure. This paper reviews in a systematic manner articles published over the past three decades, which are relevant to the design of new water distribution systems, and the strengthening, expansion and rehabilitation of existing water distribution systems, inclusive of design timing, parameter uncertainty, water quality, and operational considerations. It identifies trends and limits in the field, and provides future research directions. Exclusively, this review paper also contains comprehensive information from over one hundred and twenty publications in a tabular form, including optimisation model formulations, solution methodologies used, and other important details