Efficiency of evolutionary algorithms in water network pipe sizing

The pipe sizing of water networks via evolutionary algorithms is of great interest because it allows the selection of alternative economical solutions that meet a set of design requirements. However, available evolutionary methods are numerous, and methodologies to compare the performance of these methods beyond obtaining a minimal solution for a given problem are currently lacking. A methodology to compare algorithms based on an efficiency rate (E) is presented here and applied to the pipe-sizing problem of four medium-sized benchmark networks (Hanoi, New York Tunnel, GoYang and R-9 Joao Pessoa). E numerically determines the performance of a given algorithm while also considering the quality of the obtained solution and the required computational effort. From the wide range of available evolutionary algorithms, four algorithms were selected to implement the methodology: a PseudoGenetic Algorithm (PGA), Particle Swarm Optimization (PSO), a Harmony Search and a modified Shuffled Frog Leaping Algorithm (SFLA). After more than 500,000 simulations, a statistical analysis was performed based on the specific parameters each algorithm requires to operate, and finally, E was analyzed for each network and algorithm. The efficiency measure indicated that PGA is the most efficient algorithm for problems of greater complexity and that HS is the most efficient algorithm for less complex problems. However, the main contribution of this work is that the proposed efficiency ratio provides a neutral strategy to compare optimization algorithms and may be useful in the future to select the most appropriate algorithm for different types of optimization problems

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

Informational entropy : a failure tolerance and reliability surrogate for water distribution networks

Evolutionary algorithms are used widely in optimization studies on water distribution networks. The optimization algorithms use simulation models that analyse the networks under various operating conditions. The solution process typically involves cost minimization along with reliability constraints that ensure reasonably satisfactory performance under abnormal operating conditions also. Flow entropy has been employed previously as a surrogate reliability measure. While a body of work exists for a single operating condition under steady state conditions, the effectiveness of flow entropy for systems with multiple operating conditions has received very little attention. This paper describes a multi-objective genetic algorithm that maximizes the flow entropy under multiple operating conditions for any given network. The new methodology proposed is consistent with the maximum entropy formalism that requires active consideration of all the relevant information. Furthermore, an alternative but equivalent flow entropy model that emphasizes the relative uniformity of the nodal demands is described. The flow entropy of water distribution networks under multiple operating conditions is discussed with reference to the joint entropy of multiple probability spaces, which provides the theoretical foundation for the optimization methodology proposed. Besides the rationale, results are included that show that the most robust or failure-tolerant solutions are achieved by maximizing the sum of the entropies

Solving the multi-period water distribution network design problem with a hybrid simulated anealling

This work presents an optimization technique based on Simulated Annealing (SA) to solve the Water Distribution Network Design problem, considering multi-period restrictions with time varying demand patterns. The design optimization of this kind of networks is an important issue in modern cities, since a safe, adequate, and accessible supply of potable water is one of the basic necessities of any human being. Given the complexity of this problem, the SA is improved with a local search procedure, yielding a hybrid SA, in order to obtain good quality networks designs. Additionally, four variants of this algorithm based on different cooling schemes are introduced and analyzed. A broad experimentation using different benchmark networks is carried out to test our proposals. Moreover, a comparison with an approach from the literature reveals the goodness to solve this network design problem.Fil: Bermudez, Carlos Alberto. Universidad Nacional de la Pampa. Facultad de Ingeniería; ArgentinaFil: Salto, Carolina. Universidad Nacional de la Pampa. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Confluencia; ArgentinaFil: Minetti, Gabriela Fabiana. Universidad Nacional de la Pampa. Facultad de Ingeniería; Argentin

Robust Design of Pumping Stations in Water Distribution Networks

International audienceRestricted to gravity-fed networks, most water network design models minimize investment costs under a static peak water demand scenario. In networks equipped with pumping stations, design models should also account for operation costs incurred by the pump energy consumption that depends on dynamic demand and tariff. Evaluating the lifetime operation costs amounts to solve a large-scale non-convex combinatorial optimization problem for each considered design. In this paper, we address the pressurized water network design problem with a joint optimization of the pump investment and operation costs through a stabilized Benders' decomposition. To reduce the complexity of the operational subproblem, we decompose the scheduling horizon in representative days, and relax the discrete and non-convex components of the hydraulic model. We also evaluate the design robustness on stress-day scenarios and derive feasibility cuts using a dominance argument. Experiments on a typical rural branched water distribution network with one year of historical data show the accuracy of our approximations and the significant savings expected from the optimal pump resizing