Multiple-steps scenario optimisation for pumping plants activation in water supply systems

Economic aspects concerning the high costs related to energy requirements for managing complex water supply systems need a robust strategy, particularly considering the activation of pumping plants. Considering hydrological uncertainties, the definition of strategic rules can ensure energy savings and the well-timed activation of costly water transfers for shortage risk alleviation. The modelling approach has been developed aiming at defining strategic rules of pumps activation thresholds. It considers the need for seasonal variations of activation and the different costs of energy in diverse time slots, according to the usual cost rules adopted by the authorities. Starting with the traditional scenario analysis approach, a new algorithm has been developed considering a multiple-steps scenario optimisation implemented using GAMS interfaced with CPLEX solvers. The results should allow the water authority to establish a robust strategy for pumping activation to guarantee the fulfilment of water demands and to ensure an energy-saving policy

Optimization of water distribution networks using a deterministic approach

Water distribution networks (WDNs) are the main component of industrial and urban water distribution systems and are currently formed by pipes, nodes and loops. In this article, a deterministic mathematical programming approach is proposed, aiming to minimize the cost of looped WDNs, considering known pipe lengths and a discrete set of commercially available diameters. The optimization model constraints are mass balances in nodes, energy balances in loops and hydraulic equations, in such a way that no additional software is needed to find the appropriate pressure drops and water velocities. Generalized disjunctive programming is used to reformulate the discrete optimization problem to a mixed-integer nonlinear programming (MINLP) problem. The GAMS (General Algebraic Modeling System) environment is used to solve the problem. Four cases are studied to test the applicability of the model and the results show compatibility with the literature.This study was financially supported by the Coordination for the Improvement of Higher Education Personnel (CAPES) (Brazil) [processes 88887.217374/2018-00 and 88881.171419/2018-01] and the National Council for Scientific and Technological Development (CNPq) (Brazil) [processes 428650/2018-0 and 440047/2019-6]; and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Water Distribution Networks Optimization Considering Uncertainties in the Demand Nodes

The fluctuation in the consumption of treated water is a situation that distribution networks gradually face. In times of greater demand, this consumption tends to suffer unnecessary impacts due to the lack of water. The uncertainty that occurs in water consumption can be mathematically modeled by a finite set of scenarios generated by a normal distribution and attributed to the network design. This study presents an optimization model to minimize network installation and operation costs under uncertainties in water demands. A Mixed Integer Nonlinear Programming model is proposed, considering the water flow directions in the pipes as unknown. A deterministic approach is used to solve the problem in three steps: First, the problem is solved with a nominal value for each uncertain parameter. In the second stage, the problem is solved for all scenarios, with the independent variables of the scenario being fixed and obtained from the solution reached in the first stage, known as the deterministic solution. Finally, all scenarios are solved without fixing any variable values, in a stochastic approach. Two case studies were used to test the applicability of the model and global optimization techniques were used to solve the problem. The results show that the stochastic solution can lead to optimal solutions for robust and flexible water distribution networks, capable of working under different conditions, considering the uncertainties of node demand and variable pipe directions.The authors gratefully acknowledge the financial support from the National Council for Scientific and Technological Development (Brazil), process 309026/2022-9

Water distribution networks optimization considering unknown flow directions and pipe diameters

Water Distribution Networks (WDN) are present in a large number of industrial processes and urban centers. Reservoirs, pipes, nodes, loops, and pumps compose WDN and their design can be formulated as an optimization problem. The main objective is the minimization of the network cost, which depends on the pipe diameters and flow directions known a priori. However, in the design of new WDN in real industrial problems, flow directions are unknown. In the present paper, a disjunctive Mixed Integer NonLinear Programming (MINLP) model is proposed for the synthesis of WDN considering unknown flow directions. Two case studies are employed to test the model and global optimization techniques are used in its solution. Results show that the global optima WDN cost with the correct flow directions is obtained for the studied cases without the necessity of using additional software to calculate pressure drops and velocities in the pipes.The authors gratefully acknowledge the financial support from the National Council for Scientific and Technological Development —CNPq (Brazil), the Coordination for the Improvement of Higher Education Personnel —Process 88881.171419/2018-01 –CAPES (Brazil) and the Ministério de Economía, Industria y Competitividad CTQ2016-77968-C3-02-P (FEDER, UE)

Water Distribution Networks Optimization Using Disjunctive Generalized Programming

Water Distribution Networks (WDN) are systems of water distribution used in industrial processes and urban centers. The optimal WDN design can be very effective in saving energy, specifically in pumping service, to carry water to nodes of demand, at appropriated velocities and pressures. Indirectly, it can contribute in reducing liquid pollution and accidents caused by pressure overestimation in nodes. The design of WDN can be treated as an optimization problem with a Mixed Integer Nonlinear Programming (MINLP) formulation. The objective function, to be minimized is the WDN cost, given by the product of the pipe diameters and their lengths. The problem constraints are the mass balances in each node, the energy balances in the WDN loops and pressure and velocities limits. A set of commercial diameters is available, with proper costs and rugosity coefficients. The majority of paper published in this research field use external hydraulic simulators and meta-heuristic methods to solve the optimization problem. In the current paper a mathematical model using a deterministic Mathematical Programming approach is proposed and all variables are simultaneously optimized, avoiding the use of external software for pressure and velocities calculations. Two case studies were used to test the model applicability and coded in GAMS, using the global optimization solver BARON. Results showed that for both cases global optima was achieved, proving that it is possible to solve the problem, independently of external hydraulic simulator.The authors gratefully acknowledge the financial support from the National Council for Scientific and Technological Development - CNPq (Brazil), the Coordination for the Improvement of Higher Education Personnel - Process 88881.171419/2018-01- CAPES (Brazil) and the Spanish Ministerio de Economía, Industria y Competitividad CTQ2016-77968-C3-02-P (FEDER, UE)

An enhanced simulation-based iterated local search metaheuristic for gravity fed water distribution network design optimization

The gravity fed water distribution network design (WDND) optimization problem consists in determining the pipe diameters of a water network such that hydraulic constraints are satisfied and the total cost is minimized. Traditionally, such design decisions are made on the basis of expert experience. When networks increase in size, however, rules of thumb will rarely lead to near optimal decisions. Over the past thirty years, a large number of techniques have been developed to tackle the problem of optimally designing a water distribution network. In this paper, we tackle the NP-hard water distribution network design (WDND) optimization problem in a multi-period setting where time varying demand patterns occur. We propose a new simulation-based iterated local search metaheuristic which further explores the structure of the problem in an attempt to obtain high quality solutions. Computational experiments show that our approach is very competitive as it is able to improve over a state-of-the-art metaheuristic for most of the performed tests. Furthermore, it converges much faster to low cost solutions and demonstrates a more robust performance in that it obtains smaller deviations from the best known solutions

Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound

This paper offers a novel approach for computing globally optimal solutions to the pump scheduling problem in drinking water distribution networks. A tight integer linear relaxation of the original non-convex formulation is devised and solved by branch and bound where integer nodes are investigated through non-linear programming to check the satisfaction of the non-convex constraints and compute the actual cost. This generic method can tackle a large variety of networks , e.g. with variable-speed pumps. We also propose to specialize it for a common subclass of networks with several improving techniques, including a new primal heuristic to repair near-feasible integer relaxed solutions. Our approach is numerically assessed on various case studies of the literature and compared with recently reported results