Linear Programming Analysis of a Water Supply System with Multiple Supply Points

Gupta, Ishwar; Hassan, M. Zia; Cook, John Morse

doi:10.1080/05695557208974850

Cited by 20 publications

(15 citation statements)

References 2 publications

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“…The linear programming design procedure [16,17,19,24] is based on a special selection of the decision variables: for each link allow a set of "candidate diameters", the decision variables being the lengths of the segments of these diameters within the link. Denoting by Xi#, the length of the pipe segment of the m-th diameter in the link between nodes i and j, then…”

Section: Linear Programming Modelmentioning

confidence: 99%

“…= bp (17) (i,j)Ep ra where p designates a path in the network, and bp is the (known) head difference between its ends (all other notation is the same as in Section 5.1). Eq.…”

Section: ~_aliidi] + B~ Oiiahi + ~Cih Jmentioning

confidence: 99%

“…Having added constraints (17), the LP can be solved, and the set of optimal segments will be such that the network is hydraulically balanced be virtue of the fact that the constraints (17) have been satisfied. Denoting by Q the vector of flows in all the paths, which may be any arbitrary set of flows as long as they satisfy continuity at all nodes, then the optimal cost of the network, F, for this Q can be written as F = LP (Q) (18) where LP denotes that F is the outcome of a linear program.…”

Section: ~_aliidi] + B~ Oiiahi + ~Cih Jmentioning

confidence: 99%

“…Next, Q is modified in a way which approaches optimality. Denoting by AQp the change of flow in path p, then ~R where Wp and W, are the dual variables of constraint (17) for the paths p and r, respectively, where R are the paths which share a link (or more than one link) with path p. Using eq. (17) and the definition of J from eq.…”

Section: ~_aliidi] + B~ Oiiahi + ~Cih Jmentioning

confidence: 99%

“…Since the initial flows for each loading are quite arbitrary, there may not exist a set of segment diameters such that the head line constraints (17) are satisfied for all loadings. Therefore, two new variables are added in each of these constraints--one with a positive and the other with a negative sign, and both required to be non-negative.…”

Section: ~_aliidi] + B~ Oiiahi + ~Cih Jmentioning

confidence: 99%

See 4 more Smart Citations

Optimization in water distribution systems engineering

Shamir

1979

Mathematical Programming Studies

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The structure and operation of water distribution systems is explained briefly, and the basic mathematical tools used to analyze their physical behaviour are outlined. Methods for optimal planning, design and operation are presented and discussed. They are grouped according to the engineering problem which they address and to the method of solution. This survey is given at a level of detail which should suffice to understand each method and appreciate its potential and deficiencies. For more detail, or for actual implementation one has to refer back to the original works, which are listed at the end of the paper.

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Section: Linear Programming Modelmentioning

confidence: 99%

“…= bp (17) (i,j)Ep ra where p designates a path in the network, and bp is the (known) head difference between its ends (all other notation is the same as in Section 5.1). Eq.…”

Section: ~_aliidi] + B~ Oiiahi + ~Cih Jmentioning

confidence: 99%

Section: ~_aliidi] + B~ Oiiahi + ~Cih Jmentioning

confidence: 99%

Section: ~_aliidi] + B~ Oiiahi + ~Cih Jmentioning

confidence: 99%

Section: ~_aliidi] + B~ Oiiahi + ~Cih Jmentioning

confidence: 99%

See 3 more Smart Citations

Optimization in water distribution systems engineering

Shamir

1979

Mathematical Programming Studies

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Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches

Lenz

Becker

2021

OR Spectrum

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In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called potential-driven network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones (“looping”). The paper introduces a new mixed-integer nonlinear programming model and a new nonlinear programming model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally. On this basis, we give recommendations to practitioners about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models with respect to computational time, the number of solutions found, the number of instances solved and cost savings. Moreover, the paper extends the models for optimizing over multiple demand scenarios and is the first to include the practically relevant option that a particular pipeline may be looped several times.

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GA-ILP Method for Optimization of Water Distribution Networks

Haghighi

Samani

Samani³

2011

Water Resour Manage

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Optimization of water distribution networks has been of central importance for recent decades. Genetic Algorithms (GA) are the most famous metaheuristics widely used for this purpose with great success. However, the fact that GA basically requires a large number of computations, has led to investigate for faster solvers. In this research, a new approach is proposed in which a simple GA is linked with the Integer-Linear Programming (ILP) method resulting in a hybrid optimization scheme. Using the mathematical method of ILP, the search space is significantly reduced thereby a limited number of evaluations are required to achieve a good solution. The approach is applied to two benchmark pipe-networks in order to show its ability in terms of accuracy and speed. The results are then compared with the previous works. The obtained results indicate that the proposed model is computationally efficient, like classic methods, while is still very promising in finding the global optimum like the nature-inspired metaheuristics.

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Linear Programming Analysis of a Water Supply System with Multiple Supply Points

Cited by 20 publications

References 2 publications

Optimization in water distribution systems engineering

Optimization in water distribution systems engineering

Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches

GA-ILP Method for Optimization of Water Distribution Networks

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